Momentum Factor Investing: What’s the Right Risk-Adjustment? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>- Erik Theissen and Can Yilanci
- A version of this paper can be found here
- Want to read our summaries of academic finance papers? Check out our Academic Research Insight category

The momentum factor represents one of our core investment beliefs: buy winners. So when research presents itself that may contradict our beliefs it provides the opportunity to dig deeper and think harder about the factors we hold so dearly. Erik Theissen and Can Yilanci begin their paper by warming us up to the idea that momentum does outperform, and when measured on a portfolio level risk-adjusted basis, they agree momentum **has delivered robust excess returns.**

But then they deliver the bad news. The “risk-adjusted” returns researchers use to assess the performance of momentum strategies might be flawed. And after adjusting for risk, momentum ** does not deliver **significant excess returns. Erik and Can present the argument that the high turnover of momentum portfolios introduce a revolving door of alternative factors in a process they describe below:

Portfolio-level risk adjustment assumes constant factor exposures of the strategy under investigation. However, it is well known that the factor exposures of momentum portfolios vary over time in a systematic way.

^{1}. Momentum portfolios are characterized by huge turnover as stocks leave and other stocks enter the portfolio every month. Which stocks enter the long and short leg of the momentum portfolio depends on previous factor realizations. Consider the market factor as an example. When the excess return on the market is positive, high beta stocks perform well and low beta stocks perform poorly. Consequently, after a period of positive market excess returns the momentum portfolio will have high beta stocks in its long leg and low-beta stocks in its short leg, resulting in a high beta of the long-short portfolio. After a period of negative market excess returns the reverse will be true, resulting in a negative market beta of the long-short portfolio. Portfolio-level risk adjustment essentially estimates an average market beta of the momentum portfolio, and the average beta may well be (and in fact is) close to zero. Stock-level risk adjustment, on the other hand, captures the time-variation in the market exposure of the strategy. A similar argument can be made for the other factors of the FF5 model.

Because momentum portfolios have dynamic factor exposures, the authors suggest that the appropriate risk estimation technique for a momentum portfolio should be done at the stock level. And this leads to their core research question:

- Does the momentum factor still outperform on a risk-adjusted basis?

The research team utilized evidence from multiple samples and global markets (20 developed markets) to conclude the following:

- No. After adjusting for the dynamic factor exposure of momentum portfolios, there are no longer risk-adjusted excess returns.

The debates surrounding the momentum factor are well-documented. “EMHers” simply cannot accept the empirical fact that the momentum factor has worked so well, historically. ^{2} Purely risk-based arguments, which we’ve explored in this blog, simply can’t explain ALL of the excess returns realized by momentum strategies. This leads researchers to explore alternative behavioral explanations. For example, momentum may represent market mispricing driven by a combination of behavioral bias and costly arbitrage.

This paper may help these two camps come together. The results suggest that momentum can actually be explained by factor models, but one needs to account for the dynamic nature of factor models. Of course, the ability of momentum strategies to successfully ‘time’ various factors needs to be discussed — is the system loading up on extra risk or exploiting mispricing? Also, what about long-only implementations versus the long/short factor implementation discussed in the paper? Long-only results still look strong.

And so the debates continue…

Risk-adjusted momentum returns are usually estimated by sorting stocks into a regularly rebalanced long-short portfolio based on their prior return and then running a full-sample regression of the portfolio returns on a set of factors (portfolio-level risk adjustment). This approach implicitly assumes constant factor exposure of the momentum portfolio. However, momentum portfolios are characterized by high turnover and time-varying factor exposure. We propose to estimate the risk exposure at the stock-level. The risk-adjusted return of the momentum portfolio in month t then is the actual return minus the weighted average of the expected returns of the component stocks (stock-level risk adjustment). Based on evidence from the universe of CRSP stocks, from momentum returns conditional on market states, from volatility-scaled momentum strategies (Barroso and Santa-Clara 2015), from sub-periods and size-based sub-samples, and from an international sample covering 20 developed countries, we conclude that the momentum effect may be much weaker than previously thought.

Notes:

Momentum Factor Investing: What’s the Right Risk-Adjustment? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>DIY Asset Allocation Weights: March 2021 was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Request a free account here if you want to access the site directly.

Exposure Highlights (**bold **implies a month over month change): ^{1}

- Full exposure to domestic equities
**.** - Full exposure to international equities.
**Full exposure to REITs.**- Full exposure to commodities.
**No exposure to long-term bonds.**

Notes:

- The information contained herein is only as current as of the date indicated and may be superseded by subsequent market events or for other reasons. Neither the author nor Alpha Architect undertakes to advise you of any changes in the views expressed herein. This information is not intended and does not relate specifically to any investment strategy or product that Alpha Architect offers. ↩

DIY Asset Allocation Weights: March 2021 was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Does Crowdsourced Investing Work? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>- Zhi Da, Xing Huang, Lawrence J. Jin
*Journal of Financial Economics,*2020- A version of this paper can be found here
- Want to read our summaries of academic finance papers? Check out our Academic Research Insight category

Historically, as Richard Thaler pointed out in his book Misbehaving, financial academics have looked at humans as “Econs.” An Econ, unlike a human, values everything down to a penny before they make a decision, knows all possible alternatives, weighs them accurately, and always optimizes. ^{1}

In recent years we’ve moved away from thinking of humans as Econs. We are now left with the age-old question: How do humans form expectations about future asset returns? The literature provides convincing evidence of return extrapolation, the notion that investors’ expectations about an asset’s future return are a positive function of the asset’s recent past returns. However, there is less direct evidence on how investors form expectations about individual stock returns, whether these expectations are rational, and how they relate to subsequent returns.

Based on the sample used in this study, one thing is clear: don’t buy crowdsourced investment ideas!

By analyzing a novel dataset from Forcerank ( a crowdsourcing platform for ranking stocks), the authors find ^{2}:

- Individuals extrapolate from a stock’s recent past returns when forming expectations about its future return. In fact, the coefficients on distant past returns are in general lower than those on recent past returns: quantitatively, returns four weeks earlier are only about 9% as important as returns in the most recent week.
- The extrapolative pattern remains almost identical after controlling for past fundamental news, news sentiment, and risk measures
- Investors put more weight on negative past returns, and this weight decays more slowly into the past for negative returns.
- An individual stock’s return relative to its peer performance also seems to affect investor beliefs.
- Compared to nonprofessionals, financial professionals display a lower degree of extrapolation suggesting that professionals rely less on past stock returns when forming expectations about returns over the next week. Additionally, professionals’ expectations rely on past returns over a longer history.
- Consensus Forcerank score significantly predicts future stock returns with a negative sign suggesting that beliefs of Forcerank users are systematically biased.
- Return predictability of the Forcerank score is stronger among stocks with lower institutional ownership and a higher degree of extrapolation.

Overall, the authors interpret the evidence as suggesting that the beliefs of these Forcerank users represent the thinking process of a broader group of behavioral investors in the market. Consistent with the beliefs of Forcerank users, extrapolators form expectations about the future returns of individual stocks by extrapolating from the recent past returns

of these stocks, and they trade stocks according to these extrapolative beliefs. Fundamental traders, on the other hand, serve as arbitrageurs who correct for mispricing. However, these traders are risk-averse and hence cannot completely undo the mispricing caused by extrapolators.

Using novel data from a crowdsourcing platform for ranking stocks, we investigate how investors form expectations about stock returns over the next week. We find that investors extrapolate from stocks’ recent past returns, with more weight on more recent returns, especially when recent returns are negative, salient, or from a dispersed cross-section. Such extrapolative beliefs are stronger among nonprofessionals and large stocks. Moreover, consensus rankings negatively predict returns over the next week, more so among stocks with low institutional ownership and a high degree of extrapolation. A trading strategy that sorts stocks on investor beliefs generates an economically significant profit.

Notes:

Does Crowdsourced Investing Work? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>The Forecasting Power of Value, Profitability, and Investment Spreads was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Yiqing Dai, Tariq Haque, and Ralf Zurbruegg contribute to the literature on factor investing with their study “Factor Return Forecasting Using Cashflow Spreads” which appears in the September 2020 issue of the International Review of Economics & Finance. They sought to improve factor forecasts by augmenting the book-to-market (BM) spread with the difference in operating profitability (the OP spread ^{2}) and the difference in investment (the INV spread ^{3}). The sample period is July 1963–June 2017.

Following is a summary of their findings:

- The OP and INV spreads have significant predictive power for the value factor (HML: High book-to-market Minus Low book-to-market), the profitability factor (RMW: Robust Minus Weak profitability), and the investment factor (CMA: Conservative Minus Aggressive investment).
- Controlling for the OP and INV spreads significantly improves the predictive power of the BM spread over HML, RMW, and CMA.
- Because of correlations, the BM, OP, and INV spreads each have much stronger predictive power when all are used simultaneously as predictors compared to when each is used alone to predict factor returns.
- For HML and RMW, the BM and OP spreads have a strong negative correlation (-0.66 and -0.81 respectively), implying that an increase in the BM spread comes with a decrease in the OP spread. Given that the BM spread and the OP spread have opposite effects in factor returns, this negative correlation indicates that using one spread alone to forecast returns could lead to large forecasting errors. For example, an increased BM spread tends to be associated with a decreased OP spread, so that while the increased BM spread implies a higher factor return this is then offset by the decreased OP spread which implies reduced factor returns. For CMA, the BM spread has a moderate negative correlation with the OP spread (-0.398), as well as a moderate positive correlation with the INV spread (0.440). The OP spread and the INV spread are moderately negatively correlated (-0.365). These moderate correlations imply that a joint control for the BM, OP, and INV spreads is needed to improve factor forecasting.
- The OP and INV spreads are not just substitutes for the traditional Fama-French factors.
- Their results hold in multiple robustness tests.

To exploit the predictive power of the BM and cashflow spreads, the authors created a dynamic composite factor that adjusts its exposure to the HML, RMW and CMA factors according to whether the BM and cashflow spreads of these factors are high compared to historical levels. Net of transaction costs, their dynamic composite factor has a Sharpe ratio that is 52% higher than that of a static factor that has constant and equal exposure to the HML, RMW and CMA factors, and has a highly significant monthly alpha of 0.224% (t-stat= 3.96) even after allowing for the five factors from Fama and French and the momentum factor.

Their findings led Dai, Haque, and Zurbruegg to conclude:

“We show that our profitability and investment spreads have significant predictive power in factor returns. Additionally, we show that controlling for these spreads increases the predictive power of the BM spread. Our results demonstrate that factor returns forecasting needs a joint control for the BM, profitability, and investment spreads, to account for the correlations among these spreads.”

They Added:

“Given the strong predictive power of these characteristic spreads, we further develop a dynamic factor that takes into account the current BM, profitability,and investment spreads for the HML, RMW and CMA factors relative to their historical levels, and which ultimately generates a significantly higher Sharpe ratio than a similar factor that has constant and equal exposure to HML, RMW,and CMA.”

The empirical findings of Dai, Haque, and Zurbruegg are logical because “ensemble” (multi-metric) strategies tend to work better than single-factor strategies as they benefit from diversification of sources of risk. Importantly, their methodology could be used for factors other than the value factor and that the “value spread”, “profitability spread” and “investment spread” can be computed for any long/short factor by looking at the cash flow characteristics of the stocks comprising the long and short legs of other factors. Of course, using this information to time the market is difficult. For example, while we know that the CAPE 10 provides information on future equity returns (higher values predict lower returns and vice versa), using it as a timing tool has not proven productive as cheap (expensive) stocks can get cheaper (more expensive).

Notes:

- The difference in the BM ratio between the long side of the value and the short side of the value factor portfolio. Imagine when the difference between the value stocks B/M vs the Expensive stocks B/M is extremely high, the return generated from the value factor would also be high. ↩
- The profitability spread asks to what extent firms in the long leg have higher expected returns than those in the short leg owing to their higher profitability ↩
- investment spread asks to what extent firms in the long leg invest have lower expected returns than those in the short leg due to more aggressive investment. ↩

The Forecasting Power of Value, Profitability, and Investment Spreads was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>RealVision: Tony/Wes Discuss Investment Philosophy & ETF Operations was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>External link to the video here.

Here is an overview of the conversation:

- 00:00:46 Professional Background
- 00:04:48 Alpha Architect Mission
- 00:10:23 Systematic Decision Making
- 00:15:58 Is Value Investing Dead?
- 00:20:10 Evidence-Based Investing
- 00:24:22 High-Conviction Value and Momentum Factor Exposures
- 00:30:10 Breaking Down the Asset Management Business
- 00:32:27 How Military Background Influences Investing Strategy
- 00:38:24 Allocating More Capital
- 00:41:19 Becoming the Shopify of ETFs
- 00:43:27 Assessing Economic Forecasting
- 00:48:34 Future of Quantitative Trading
- 00:54:15 Impact of GameStop on Market Landscape
- 00:59:18 Investor Psychology

RealVision: Tony/Wes Discuss Investment Philosophy & ETF Operations was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>The Risk and Returns to Private Debt Investments was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>- Douglas Cumming, Grant Fleming, and Zhangxin (Frank) Liu
- Financial Analysts Journal
- A version of this paper can be found here
- Want to read our summaries of academic finance papers? Check out our Academic Research Insight category

The subject of private debt and its associated performance characteristics has not been covered sufficiently in the academic literature. Relatively few research articles have attempted to characterize the returns and risk on the types of private debt strategies available to investors. This is true, in spite of the position private debt holds as the dominant source of capital for private firms in the US and across the world.

In this research, the authors constructed “by hand” data on 443 private direct loans made by specialist credit investment funds in 13 Asia-Pacific markets that occurred between 2001 and 2015. Special attention was paid to the representativeness of the sample. Countries included China, India, Australia, and Indonesia which helped to ensure diversity in legal systems, economic systems, size, and age of the associated credit market. There is, however, an important caveat with respect to the data. The authors note that the total track record is collected for each manager, however, some are unable or do not actually raise funds. Therefore, the data likely imparts a positive bias to the distribution of fund managers. In any case, the research is notable in that it does contain insights into the private debt market despite the potential bias.

- Should bond investors consider expanding their opportunity set to include the acquisition of private debt on the secondary market?
- Is the performance of private debt, whether buy-and-hold in the primary issuance market or acquired in the secondary market superior to public credit?

- YES. Returns are higher in the secondary debt market. In a primary issuance, the manager participates in setting the price, covenants, collateral, information and control rights as well as other nonprice terms of the debt. In a secondary acquisition, credit fund managers purchase a private loan in a deal typically brokered by an investment bank. A stark contrast, with no opportunity to manage the credit risk of the loan. This hypothesis was confirmed in the empirical tests of the differences between the two strategies. Secondary trading generated returns in excess of those to the primary issuance alternative. The results were statistically significant after controlling for the effects of the global financial crisis, quality and cost of the legal system, manager experience, economies of scale for the fund family, size of the fund itself, and subordinated or LBO status.
*Note the following empirical findings reported in the Chart below:*The coefficient on “secondary” is positive and significant for all models tested. This indicates secondary strategies earn higher returns than primary issuances; The coefficient on LBO (where LBO represents private equity ownership) was not significant, indicating no difference between returns for LBO and non-LBO structures; Manager experience was significant and positively related to returns; There was no relationship between returns and fund manager economies of scale, size, and cost of contract enforcement. - YES and NO. The authors construct a private credit return index from the data (including both primary and secondary issuances) and calculate an excess return index using traditional public credit (JPMorgan Asia Credit Index) and equity indexes (MSCI-EM, R3000, SP500). Although the results suggest that the private credit return index outperforms both public credit and equity indexes, these results are subject to a considerable bias associated with the use of IRRs in this context. I would consider them to be unreliable when compared to market-based returns.

The takeaway from this research comes from the demonstrated potential to add value in terms of risk and return that is available in the Asia-Pacific private credit markets. The freedom to take advantage of this potential is subject to the due diligence constraints present when investors seek out other sources of credit outside of the US. To my knowledge, this is the first article to supply an empirical rationale for lowering the bar for specific credit fund managers. If an experienced fund manager invests in primary issuance strategies only, should they be allowed to acquire debt in the secondary market in these countries? The answer is a qualified *yes*.

Private debt fund managers invest in debt positions of private companies through (1) new issuances or (2) secondary acquisition of loans. In the study reported here, we used data from more than 400 investments in private companies in 13 Asia-Pacific markets between 2001 and 2015 to

examine which strategy performs best. Conditional on market and industry factors, trading private debt delivers higher returns than buying and holding a primary issuance. So, institutional investors should permit fund managers the flexibility to trade. Furthermore, a portfolio of private debt investments delivers excess returns to public markets over time, with

excess returns affected by volatility, funding liquidity, and the global

financial crisis. An investment in Asia-Pacific private debt should improve risk-adjusted returns for a global or emerging market fixed income portfolio.

The Risk and Returns to Private Debt Investments was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>The R&D Premium: Is it Risk or Mispricing? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Since the development of the CAPM, academic research has attempted to find models that increase the explanatory power of the cross-section of stock returns. We moved from the single-factor CAPM (market beta), to the three-factor Fama-French model (adding size and value), to the Carhart four-factor model (adding momentum), to Lu Zhang’s *q*-factor model (beta, size, investment, profitability), to the Fama-French five-factor (adding value to the *q*-factor model) and six-factor models (adding back value and momentum to the *q*-factor model). There have also been versions that use different metrics for profitability and value, and Stambaugh and Yuan’s mispricing (anomaly)-based model. Regardless of the model used, stocks with high research and development (R&D) expenses have delivered a premium. Thus, the R&D premium remains an anomaly to all models. Despite a large literature confirming the anomaly, there is far less consensus on why it exists. Some studies attribute the R&D anomaly to investor mispricing. Others argue that it reflects a premium that compensates risk.

Woon Sau Leung, Khelifa Mazouz, and Kevin Evans contribute to the literature with their study “The R&D Anomaly: Risk or Mispricing?” published in the June 2020 issue of the Journal of Banking & Finance. Their data sample contained all NYSE, AMEX, and Nasdaq stocks and covered the period July 1975 to June 2013. They measured R&D intensity as the ratio of R&D expenditure to market value(MV), total assets(A), or sales(S), denoted as RD-MV, RD-A, and RD-S, respectively. For various reasons they only reported the results for RD-MV—RD-MV is associated with greater anomalous returns than RD-A and RD-S. RD-MV is analogous to price multiples and can therefore be readily applied to practical investment analysis, and it is less likely to be influenced by creative accounting. They found “a monotonic increase in average returns with RD-MV. The increase in return from 0.67 percent for Portfolio 1 to 2.23 percent for Portfolio 10 represents a statistically and economically significant return to the zero-cost spread portfolio (10-1). The R&D anomaly persists after we adjust for size, value, and momentum effects.” In addition, the zero-cost spread portfolio (Portfolio 10-1) yielded a Carhart four-factor alpha of 1.35 percent and a Fama French five-factor alpha of 1.52 percent per month, both significant at the 1 percent level—the R&D anomaly cannot be explained by existing pricing factors, including the relatively recent investment and profitability factors.

They also found that R&D-intensive companies generally are “smaller, have higher book-to-market equity ratio, better past stock performance, smaller asset growth, lower operating profitability, higher idiosyncratic volatility, lower stock liquidity, more extreme positive daily returns, greater information asymmetry, tighter capital constraints, less tangible assets, and greater firm-specific human capital.” These findings are generally consistent with a risk-based explanation.

To address this question, Leung, Mazouz and Evans began by providing a logical risk-based explanation for the R&D premium:

“There are four risks to R&D. Technical risk is the uncertainty of the success or failure of each stage of development, which is idiosyncratic. The risk of obsolescence is that competitive firms develop faster driving future cash flows to zero, which is idiosyncratic. The third risk is uncertainty about the expected cost of completion of the project. This is also idiosyncratic but evolves endogenously as managers learn about the probability of success as stages are completed. The final risk is the uncertainty surrounding the potential cash flows from the project. Cash flows upon completion are a stochastic process and include both idiosyncratic and systematic components.”

Leung, Mazouz and Evans then sought to identify the economic sources of R&D risk.

“If R&D projects convey a larger systematic risk premium that relates to future stochastic cash flows, we examine whether the R&D factor captures investors’ intertemporal hedging concerns and proxies for state variables that predict the future market and economic conditions.” They found that “the R&D premium correlates positively with innovations to the aggregate dividend yield, and negatively with shocks to the default spread and risk-free rate, demonstrating the sensitivity of R&D stocks to variables that predict future business conditions. Moreover, the loadings on these three state variable innovations are significantly priced in the cross-section of R&D stock returns and even drive outsize and book-to-market equity factors. These results demonstrate that the R&D premium represents a significant and incremental reward for bearing intertemporal risk.”

The finding of a risk-based explanation by Leung, Mazouz and Evans contrasts with the findings of Baruch Lev, Suresh Radhakrishnan and Mustafa Ciftci in their 2008 study “The Stock Market Valuation of R&D Leaders.” They found that “only a small part of the returns can be attributed to risk compensation.” They also found that “R&D is less reliable (verifiable) an asset than physical capital” and that “the association between R&D intensity and future earnings volatility of leaders is lower than that of followers. Collectively, the findings suggest that R&D leaders are mispriced by investors due to lack of information.” Note that it is possible that the publication of such research could lead to the elimination of any mispricing.

As noted above, one mispricing explanation is based on limited investor attention to R&D that is attributed to accounting conservatism: R&D costs are expensed, as financial statements do not report internally generated intangible assets under generally accepted accounting principles. Such conservative accounting treatments complicate investors’ valuation of an R&D-intensive firm, which often results in mispricing of its equity.

Leung, Mazouz, and Evans also examined other mispricing explanations, beginning with investor sentiment—the propensity of individuals to trade on noise and emotions rather than facts. It represents investors’ beliefs about future cash flows that the prevailing fundamentals cannot explain. Such activity can lead to mispricing. Examples of times when investor sentiment ran high are the 1968-69 electronics bubble, the biotech bubble of the early 1980s, and the dot.com bubble of the late 1990s. Sentiment fell sharply, however, after the 1961 crash of growth stocks, in the mid-1970s with the oil embargo, and in the crash of 2008.

Since 2006 researchers have explored investor sentiment’s impact on markets. Malcolm Baker and Jeffrey Wurgler have even constructed an investor sentiment index based on six metrics: trading volume as measured by NYSE turnover, the dividend premium (the difference between the average market-to-book ratio of dividend payers and non-payers), the closed-end fund discount, number of IPOs, first-day returns on IPOs, and the equity share in new issues. (Data is available at Wurgler’s New York University webpage.) Studies such as “The Short of It: Investor Sentiment and Anomalies” (2012), “Investor Sentiment and the Cross-Section of Stock Returns” (2006), “Investor Sentiment and the Mean-Variance Relation” (2011), and “Investor Sentiment: Predicting the Overvalued Stock Market ” (2018) have demonstrated that investor sentiment is a statistically and economically significant contrarian predictor of market returns.

The mispricing arguments related to R&D are that stocks with high levels of R&D are hard to value and more costly to arbitrage. Therefore, they are subject to larger mispricing and thus display corrections following shifts in sentiment. Contrary to this prediction, Leung, Mazouz and Evans found that sentiment has no effect on R&D portfolios—there was a monotonic increase in returns across R&D deciles following both sentiment states. They added that:

“any mispricing detected in R&D stocks is likely driven by the size effect rather than R&D intensity.”

The authors next examined whether limits to arbitrage have any effects on the R&D anomaly, and they failed to find evidence of mispricing in R&D stocks.

Their findings are consistent with those of Jangwook Lee and Jiyoon Lee, authors of the March 2020 study “Mispricing or Risk Premium? An Explanation of the R&D-to-Market Anomaly.” They examined the evidence on the R&D anomaly in Korea. Korea provides a unique opportunity because R&D expenditures are capitalized under certain (more conservative) conditions.

Lee and Lee noted:

“If the positive relationship between R&D and stock returns is attributable to limited investor attention that arises mainly from conservative accounting treatment of R&D there should not exist a positive association between the capitalized components of R&D and stock returns. The risk-based explanation, on the other hand, predicts a positive relationship between capitalized components of R&D and stock returns to the extent that the capitalized portion of R&D is risky.”

They demonstrated that both the expensed and capitalized portions of R&D are positively associated with returns. For example, they found that:

“a one-standard-deviation increase in CAP (EXP), which is defined as capitalized (expensed) components of R&D over the market value of equity, is associated with an increase in monthly stock returns of 17.9 (23.7) basis points after controlling for characteristics that are known to be associated with risks such as size, the book-to-market ratio, and momentum.”

And the returns increased monotonically with R&D intensity. They also showed that the positive R&D return relationship weakens with the extent of progress toward completion of R&D projects.

Their findings are consistent with the risk-based theoretical prediction of Jonathan Berk, Richard Green and Vasant Naik, authors of the 2004 study “Valuation and Return Dynamics of New Ventures.” They explained:

“Firms learn about the potential profitability of the project throughout its life, but that technical uncertainty about the R&D effort is only resolved through additional investment. Consequently, the risks associated with the ultimate cash flows have a systematic component even while the purely technical risks are idiosyncratic.”

Lee and Lee also found that firms whose R&D expenditures consisted only of capitalized components of R&D earned 24.9 basis points less per month than firms whose R&D expenditures consisted only of expensed components. This is exactly what we should expect if R&D is related to risk because capitalized R&D should be less risky in order to meet the six criteria established by the Korean accounting practices. They also found that the decrease in returns following progress toward R&D completion is fully explained by conventional risk factors. Their findings led them to conclude:

“The results suggest overall that the positive R&D-return relationship is attributable to compensation for bearing risk.”

Lee and Lee did offer this important observation:

“This paper also adds to the literature on the information benefits of R&D capitalization by providing evidence that R&D capitalization provides useful information regarding risk to investors, and we thereby contribute to the debate among academics and practitioners overcapitalization versus expensing of R&D expenditures.”

There is considerable evidence of a significant positive relationship between R&D and future stock returns that is not explained by existing asset pricing models. Their findings led Leung, Mazouz, and Evans to conclude that:

“The R&D anomaly is a reward for the systematic risk embedded in the real option features of R&D project—anomalous returns to high R&D stocks represent compensation for heightened systematic risk not captured in standard asset pricing models.”

Lee and Lee came to the same conclusion.

Because of the differences in accounting treatments for intangible versus tangible assets (expensing or capitalizing), and the findings of an R&D premium, this topic has received much attention from academics and practitioners alike. Some have tried to address the problem by adding back expensed R&D to the balance sheet, and others by including R&D as a priced factor.

The R&D Premium: Is it Risk or Mispricing? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Meb Faber Podcast: Doug Discusses 1042 QRP and ESOP Transactions was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>ESOP’s are a niche but incredibly attractive way for a business owner to sell their business for both themselves and the long-term viability of the company. The episode starts with a broad overview and then dives into the inner workings of an ESOP sale. Doug explains how the tax benefits of a 1042 election allow the owner to defer capital gains tax and even invest the proceeds into a portfolio of blue-chip stocks.

As the conversation winds down, Doug shares why ESOP’s may be an ideal way for middle-market private equity companies to exit investments.

External link to the video here.

Meb Faber Podcast: Doug Discusses 1042 QRP and ESOP Transactions was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>ESG Factors and Traditional Factors was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>- Ananth Madhavan, Aleksander Sobczyk and Andrew Ang
*Financial Analyst Journal,*2021- A version of this paper can be found here

Environmental, Social, and Governance (ESG) investing has become a priority for a lot of investors. We have previously written on ESG being combined with factor investing here and here. However, if one chooses to ignore our previous musings on the subject and only pursue ESG, how would that decision impact the overall factor exposure of the portfolio?

In this paper, the authors address the question:

- To what extent are factors linked to environmental, social, and governance (ESG) performance?

By analyzing (holdings based analysis) the MSCI ESG scoring system, which covers 1,312 active US equity mutual funds (representing $3.9 trillion AUM or 93% of the total AUM of US equity mutual funds) and more than 600,000 equity and fixed-income securities which the scoring system measures on three ESG categories (sustainable impact, values alignment, and risks), compared to factors (value, size, quality, momentum, and volatility) the authors find:

1. There is little relation between funds sorts on individual ESG components and active returns, however there is a significant relationship between ESG components and factor exposures. In fact,

2. Funds with significantly large ESG attributes have factor exposures that differ from the market. Specifically, funds with high environmental (E) scores tend to load up with quality and momentum factor stocks. Some 75% of “E” scores can be explained by style factors, but factors explain only 25% of “S” scores and a mere 14% of “G” scores. Funds with high E scores also overweight low volatility and larger companies.

3. Fund alphas and active returns are linked to factor ESG components, but there is no link between fund alphas and active returns to ESG components unrelated to style factors.

An important takeaway from this paper is not to conclude that the factor traits of ESG are set in stone. Factor traits of ESG investing could certainly change over time. This paper only analyzes data from June 2014 to June 2019. A period in which ESG investing has dramatically risen in popularity, which could be driving some of the factor exposures.

This research highlights the need for investors and/or their advisors to be aware that ESG portfolio construction may lead to factor tilts that differ from the market as a whole. Therefore it’s imperative for investors to be conscious of not only the ESG exposure they seek but also overall market exposures. If the overweighting of specific factors is not desired in the portfolio, investors will need to mitigate the increased factor exposure in which ESG investing favors.

Using data on 1,312 active US equity mutual funds with $3.9 trillion in assets under management, we analyzed the link between funds’ bottom-up, holdings-based environmental, social, and governance (ESG) scores and funds’ active returns, style factor loadings, and alphas. We found that funds with high ESG scores have profiles of factor loadings that are different from those of low-scoring ESG funds. In particular, funds with high environmental scores tend to have high quality and momentum factor loadings. In partitioning the ESG scores into components that are related to factors and idiosyncratic components, we found strong positive relationships between fund alphas and factor ESG scores

.

ESG Factors and Traditional Factors was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Do ETFs Adversely Affect Market Quality? Nope. was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>- Box, Davis, Evans, and Lynch
- Working paper
- A version of this paper can be found here

*Editor’s note: Seeing how the results may have shifted since the “ARK phenomenon” would be a great robustness test for this paper.*

ETFs are growing at a rapid pace and becoming a significant contributor to intraday activity (and we are only making the problem worse!). Naturally, some will begin to wonder how the ETF innovation impacts trading in the underlying securities that ETFs own. Initially, it was thought that ETF trading would improve price discovery, however, recent academic research has concluded that ETFs may have adverse effects on the market. ^{1}

The paper under discussion jumps into the debate via a minute-by-minute intraday stock database to identify if ETFs have positive or negative effects on the efficiency of the stock market.

The core research question is the following:

- Do ETFs materially impact their underlying securities in a negative way?

- No. ETF flows and demand shocks do not appear to have undue influence on the underlying constituents. But it’s complicated and we recommend you read the paper for more details.

The authors state the following:

No relationship between ETF order flow and returns on the constituent securities at 1-, 5-, and 10-minute intraday intervals, and only a weak relationship at a daily interval.

Intraday Arbitrage Between ETFs and Their Underlying Portfolios, Box, Davis, Evans, and Lynch 2019

Their conclusion from a cadre of tests is as follows:

Identifying intraday arbitrage opportunities between ETFs and the constituents, we find little evidence that arbitrage opportunities precede trading in the underlying. Instead, arbitrage opportunities are initiated by shocks to the underlying and subsequently corrected through updates in the best bid and offer quotes. Thus, while we observe quote adjustments in response to price discrepancies, we find limited evidence of arbitrage trading. Additionally, our results indicate that bid-ask spreads remain steady during arbitrage opportunities. Not only are we unable to document arbitrage in the face of mispricing, we also find no evidence that the convergence of prices removes liquidity from the market.

Intraday Arbitrage Between ETFs and Their Underlying Portfolios, Box, Davis, Evans, and Lynch 2019

ETFs represent the new kids on the block. New kids on the block, especially when they are stealing your lunch money, are bound to attract scrutiny from competitors, academic researchers, and politicians. A primary attack has been the accusation that ETF activity is distorting the market and making price discovery less transparent or adding to the lack of breadth in the market. This paper gives the ETF industry a soapbox to stand on and highlights that the product is not manipulating markets and price discovery in a material way.

Prior research suggests that ETF arbitrage affects the market quality of underlying securities. We directly test this proposition by examining minute-by-minute returns and order imbalances, but find little evidence that trading in ETFs impacts the underlying. Panel vector autoregression shows ETF returns largely follow the underlying returns. We also find that mispricing events are preceded by underlying price and order imbalance shocks, corrected by ETF quote adjustments unrelated to order imbalance, inconsistent with an arbitrage explanation. Extending our analysis to a daily frequency also reveals little to no relation between ETFs and the market quality of their constituent securities.

Notes:

- For investors that don’t work directly with ETF’s, exactly how ETF’s function and trade aren’t as straightforward as appears on the surface. Due to the somewhat complicated process of ETF activity in the secondary market, we wrote a white paper on Understanding How ETF’s Trade in the Secondary Market. That post will set a solid baseline of understanding for you to fully appreciate this paper. You can also check out our piece on how to start an ETF, which will give the reader insights into the ecosystem and moving parts associated with ETFs. ↩

Do ETFs Adversely Affect Market Quality? Nope. was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Global Factor Performance: February 2021 was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>- Standardized Performance
- Factor Performance
- Factor Exposures
- Factor Premiums
- Factor Attribution
- Factor Data Downloads

Notes:

- free access for financial professionals ↩

Global Factor Performance: February 2021 was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Will the Real Value Factor Funds Please Stand Up? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>- Martin Lettau, Sydney C. Ludvigson, Paulo Manoel
- Working paper
- A version of this paper can be found here

If you’re a value investor who has determined that you have better things to do with your time, at some point you may have decided to outsource the investment task to a fund manager. And if you read our blog (especially this post) you’re probably looking to oursource to a systematic process versus a discretionary one. The first step in your due diligence process is easy: ask your smart friends for advice and google for “Value Funds.” A plethora of options will be available, as there are thousands of funds with “value” in their description. ^{1}

But do these funds actually seek to capture the so-called “value factor?” Sadly, naming funds “value” is a lot more popular than actually investing in systematica “value.” Using a sample of 2,638 active mutual funds (574 value plus 1,130 growth funds), 955 ETFs, and 114 hedge funds, the authors focus on three basic issues.

- Do active fund managers exploit traditional value factor risk premia across the universe of US mutual funds?
- Does the average fund exhibit similar asymmetry?
- What about other traditional factors like size and momentum?

While the results obtained for ETFs and hedge funds were similar to that of mutual funds, this summary will deal with mutual funds.

- NO. Across the universe of mutual funds, the analysis in this article documents the finding that funds tend to hold securities on the low return leg of the long/short value factor portfolio. This was especially true for funds using the book-to-market ratio
^{2}to identify value stocks. ETFs and hedge funds exhibited a similar tilt towards low book-to-market ratios. There were no funds that exhibited a tilt towards high book-to-market stocks, even when the fund was explicitly marketed as a value fund. Not to be eclipsed, the same pattern was observed for earnings-to-price, dividend-to-price, and the Morningstar value/growth measure for the same mutual funds, ETFs, and hedge funds. More details are supplied in Figure 1 below. For context, note the book-to-market ratio ranges from “1” to “5”, where “1” = the extremely low quintile of book-to-market and “5” = the extremely high quintile value. Forty percent of funds fell between quintile 1 and quintile 2– extremely low value; 9% fell between Q2 and Q3–moderate value; however, only 7 of 2,657 funds in the sample had a ratio greater than Q4–high or very high value. Essentially, there were no real value funds in the US universe of all mutual funds in the sample. The takeaway here is that it is almost impossible to replicate a value portfolio, or the Fama-French value or “H” portfolio by looking to the mutual fund industry. If one focuses on explicitly labeled “value funds” the situation is not much better. Note from Figure 1 that the majority of value funds fall between Q2 and Q3.5–middle of the road. However, there was an abundance of growth-oriented funds, that were in fact, high “growth”. Amazingly, the majority of growth funds fall between Q1 and Q2. Growth is everywhere and value is nowhere to be found. The results were robust to other measures of value and characteristics of other vehicles such as ETFs and hedge funds. The reader should be aware that the sample size and therefore, the representativeness of hedge funds and ETFs to a lesser degree, is poor. - YES. On average, the average mutual fund allocates its holdings to stocks with book-to-market scores between Q1 and Q2 at 40% and allocates only 6% to stocks to Q5. Value funds tilt more toward low Q stocks, with 24% to Q1 and 13% with Q5 scores. It gets worse: only 7% of value funds held more than 25% of their portfolios in Q5 stocks. Again growth funds presented a stark contrast. Almost all (95%) of growth funds allocated over a quarter of their holdings to low book-to-market stocks. A respectable representation for the Fama-French “L” portfolio.
- The asymmetry observed with value metrics was not present with size and momentum factors, although the average mutual fund does not appear to exploit the high return risk premia associated. The average fund had scores slightly above Q3: momentum at 3.28, investment at 3.08, and profitability at 3.17, indicating little to no significant exposures in either direction to these factors. A very small percentage (4%) of funds have a high momentum tilt with a score above Q4. However, the variability of the momentum score over time was higher than for other factors, so the overall distribution is less indicative of the average funds’ momentum tilt at any one point in time. As to intention, the authors suggest that the momentum characteristic is likely a function of the contemporaneous holdings of low book-to-market stocks as opposed to an intentional bet on momentum. The results with respect to size are not new. Mutual funds do not exploit the small stock premium, even if it does exist. Only 2% of all mutual funds exhibit a score that is representative of the small stock leg of the classic long/short factor portfolio. The conventional wisdom explains it: large funds hold large-capitalization stocks because smaller stocks are more expensive to trade. Enough said.

The analysis of the factor exposures/characteristics of mutual funds suggests that the array of strategies offered by the fund industry are really quite limited. It is all but impossible to replicate value, momentum and size-based portfolios or any combination of such, by investing in mutual funds. ^{3} Further, the consistent exposure to low book-to-market stocks is frankly difficult to defend given the large body of empirical work on return drivers in the equity market. The adherence to low book-to-market strategies that promise a low return and are basically neutral to momentum for example, is more than puzzling. Many more questions arise, than are answered in this research regarding the active management offered by mutual funds. The authors propose at least four that convey why this research matters:

“1. Why is the distribution of mutual fund portfolios so strongly tilted towards low book-to-market ratios and why are there virtually no high BM funds at all even though high BM stocks are associated with higher returns than low BM stocks?

2. Why do funds that label themselves as “value” hold more low BM stocks than high BM stocks while “growth” funds hold almost exclusively low BM stocks?

3. Why are portfolios of active mutual funds not more tilted towards other factors that are associated with high returns, i.e. small and high momentum stocks?

4. Why don’t mutual funds combine multiple factor strategies (e.g., high BM – high momentum) that have been shown to be more profitable than univariate strategies.”

This paper provides a comprehensive analysis of portfolios of active mutual funds, ETFs and hedge funds through the lens of risk (anomaly) factors. We show that that these funds do not systematically tilt their portfolios towards profitable factors, such as high book-to-market (BM) ratios, high momentum, small size, high profitability and low investment growth. Strikingly, there are almost no high-BM funds in our sample while there are many low-BM “growth” funds. Portfolios of “growth” funds are concentrated in low BM-stocks but “value” funds hold stocks across the entire BM spectrum. In fact, most “value” funds hold a higher proportion of their portfolios in low-BM (“growth”) stocks than in high-BM (“value”) stocks. While there are some micro/small/mid-cap funds, the vast majority of mutual funds hold very large stocks. But the distributions of mutual fund momentum, profitability and investment growth are concentrated around market average with little variation across funds. The characteristics distributions of ETFs and hedge funds do not differ significantly from the those of mutual funds. We conclude that the characteristics of mutual fund portfolios raises a number of questions about why funds do not exploit well-known return premia and how their portfolio choices affects asset prices in equilibrium.

Notes:

- Or get access to the AA Portfolio Architect tool which is specifically designed to assess fund characteristics. ↩
- Note that the paper is utilizing Book/market where value is represented by a high ratio, unlike the more standard price/book ratio where a low ratio represents value ↩
- Although, Alpha Architect, and others, via more factor-centric indexes are trying to help solve this problem! ↩

Will the Real Value Factor Funds Please Stand Up? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Excess Returns Podcast: Jack discussing Momentum and Trend was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Commentary/Links:

- In the conversation, I mentioned a post titled “Factor Investing and Trading Costs.” Here is the link to that article which examines the arguments about the true scalability of factor investing.
- Clarification–Around the 14-minute mark, I stated that the top 50 firms sorted on “EBIT/TEV” are in the 99th percentile on FCF/TEV, E/P, S/P–this is not exactly the case (an unnecessary exaggeration on my part), but they are most likely within the top 20% to 30% on those related metrics.

External link to the video here.

Excess Returns Podcast: Jack discussing Momentum and Trend was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Do Security Analysts Follow the Academic Evidence? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>In their 2017 paper, “Analysts and Anomalies” Joseph Engelberg, David McLean, and Jeffrey Pontiff examined the recommendations of U.S. security analysts over the period 1994 through 2014 and found that analysts’ predictions go in the opposite direction of the academic evidence—they conflict with well-documented anomalies (similar findings were reported here). And the results were statistically significant. They also found that buy recommendations do not predict returns, while sell recommendations predict lower returns. Another interesting finding was that among the group of “market” anomalies (such as momentum and idiosyncratic risk), which are based only on stock return, price and volume data, analysts produce more favorable recommendations and forecast higher returns among the stocks that are stronger buys according to market anomalies. This is perhaps surprising as analysts are supposed to be experts in firms’ fundamentals. Yet, they performed best with anomalies that are not based on accounting data. Their evidence suggests that analysts even contribute to mispricing as their recommendations are systematically biased by favoring stocks that are overvalued according to an anomaly-based composite of mispricing scores.

The only good news was that Engelberg, McLean, and Pontiff found that over time, as anomaly variables have become widely known, analysts have incorporated more of this information into their recommendations and price targets—the negative correlation weakened over their sample period. However, even during the later years of their sample there was still a negative or, at best, neutral relationship.

They concluded:

“Analysts today are still overlooking a good deal of valuable, anomaly-related information.”

Vitor Azevedo and Sebastian Müller contribute to the literature with their October 2020 study, “Analyst Recommendations and Anomalies Across the Globe.” They examined the value of analyst recommendations with a dataset of 45 countries and 3.8 million firm-month observations covering the period 1994 to 2019.

In order to analyze the relation between analyst recommendations and anomalies, they created composite scores on 11 anomalies identified by Robert Stambaugh, Jianfeng Yu, and Yu Yuan, authors of the 2012 study “The Short of It: Investor Sentiment and Anomalies.” The 11 pricing anomalies reflect sorts on measures that include:

- financial distress (firms with high failure probability have lower, not higher, subsequent returns),
- net stock issuance (issuers underperform non-issuers),
- accruals (firms with high accruals earn abnormally lower returns on average than firms with low accruals),
- net operating assets (defined as the difference on a company’s balance sheet between all operating assets and all operating liabilities scaled by total assets, it is a strong negative predictor of long-run stock returns),
- momentum (high past recent returns forecast high future returns),
- the gross profitability premium (more profitable firms have higher returns than less profitable ones),
- asset growth (companies that grow their total assets more earn lower subsequent returns),
- return on assets (more profitable firms have higher expected returns than less profitable firms) and
- investment-to-assets (higher past investment predicts abnormally lower future returns).
- O-Score: This is an accounting measure of the likelihood of bankruptcy. Firms with higher O-scores have lower returns.
- Post-earnings Announcement Drift: If earnings surprises are positive (negative), future stock prices drift upward (downward)— stock prices drift in the same direction as the earnings surprise.

The most underpriced (overpriced) stock received the lowest (highest) rank. Then, they computed the arithmetic average of the anomaly ranks for each firm-month with at least five anomalies, and used the average anomaly ranks to assign these firms into quintiles for each country-month and estimate a long-short portfolio, which goes long (short) in the most underpriced (overpriced) stocks.

Following is a summary of their findings:

- Analyst recommendations lead to highly significant (at the 1% confidence level) abnormal returns in international markets, though not in the U.S. where analysts tend to recommend U.S. stocks which are overvalued based on anomalies.
- In international markets analysts do not contribute to global mispricing, tending to give more favorable recommendations to underpriced (based on anomaly ranking) stocks—analyst recommendations are positively related to composite, anomaly-based mispricing scores.
- A recommendations-based long-short strategy generates a value-weighted (equally-weighted) raw return of 0.48% (0.58%) per month with a t-statistic of 5.05 (8.51) in worldwide stock markets excluding the U.S. In contrast, the same strategy for U.S. stocks yields economically negligible and statistically insignificant value-weighted and equally-weighted raw returns of 0.08% and -0.02% per month, respectively.

- The pronounced market differences in profitability persist for a range of alternative asset pricing models, including the CAPM, the Fama and French (1993) three-factor model, the Carhart (1997) four-factor model, the Fama and French (2015) five-factor model, the behavioral factor model of Daniel et al. (2020), the mispricing factor model of Stambaugh and Yuan (2017), and the (augmented) q-factor model of Hou et al. (2015) and Hou et al. (2020).
- Recommendations are more valuable in less developed and in less individualistic markets (helping explain U.S. results) and during low-sentiment periods.

The authors did note that there is evidence that the performance of the recommendations-based strategy has declined over time (evidence of increasing market efficiency).

“For the first part of our sample period from January 1994 to December 2006, the strategy’s value-weighted four-factor alpha amounts to 0.45% per month (t-statistic: 4.07) for World-ex-US. In the second part of the sample period from January 2007 to June 2019, the strategy’s international four-factor alpha decreases to 0.25% per month (t-statistic: 2.34).”

Their findings led Azevedo and Müller to conclude:

“Our results support limits-to-arbitrage and behavioral explanations of global stock market inefficiencies…The fact that analyst recommendations are less profitable in individualistic countries and in high sentiment periods supports the view that even market professionals are subject to behavioral biases that affect market outcomes.”

While the evidence on analyst recommendations in international markets showed that they added value, that doesn’t necessarily translate into alpha for mutual funds. One reason is that recommendations don’t have expenses, while implementing them does (transactions costs and fund expense ratios). To see whether mutual funds are able to exploit analyst recommendations we turn to the results from the 2020 Mid-Year SPIVA Scorecard:

- Over the 15-year period, across all international equity categories, a large majority of active managers underperformed their respective benchmarks. For example, 81% of active global funds underperformed, 85% of international funds underperformed, 68% of international small-cap funds underperformed, and in the supposedly inefficient emerging markets, 84% of active funds underperformed.

- Over the 15-year period, on an equal-weighted (asset-weighted) basis, active global funds underperformed by 1.3% (0.4%) per annum, active international funds underperformed by 1% (0.3%) per annum, and active emerging market funds produced the worst performance, underperforming by 1.8% (0.6%) per annum. And while, on an equal-weighted basis, international small-cap funds underperformed by 0.3%, on an asset-weighted basis, they managed to outperform by 0.4%.

As you can see, mutual funds were not able to exploit analyst recommendations. The takeaway for investors, whether in the U.S. or in international markets is that the strategy most likely to allow you to achieve your goals is to use funds that invest systematically (such as index funds) and eschew individual security selection. The other takeaway is that over time, and despite the claims that the trend to passive investing would reduce market efficiency, markets are becoming more efficient. The reasons for this are the subject of Andrew Berkin and my new book, the 2020 edition of The Incredible Shrinking Alpha.

Do Security Analysts Follow the Academic Evidence? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>DIY Asset Allocation Weights: February 2021 was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Request a free account here if you want to access the site directly.

Exposure Highlights (**bold **implies a month over month change): ^{1}

- Full exposure to domestic equities
**.** - Full exposure to international equities.
- Partial exposure to REITs.
**Full exposure to commodities**.**Partial exposure to long-term bonds.**

Notes:

- The information contained herein is only as current as of the date indicated and may be superseded by subsequent market events or for other reasons. Neither the author nor Alpha Architect undertakes to advise you of any changes in the views expressed herein. This information is not intended and does not relate specifically to any investment strategy or product that Alpha Architect offers. ↩

DIY Asset Allocation Weights: February 2021 was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Hot Topic: Does “Gamma” Hedging Actually Affect Stock Prices? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>- Guido Baltussen, Zhi Da, Sten Lammers and Martin Martens
*Journal of Financial Economics,*Forthcoming- A version of this paper can be found here

More and more evidence seems to suggest that social Media impacts daily momentum and volatility. Some hedge funds that were short GME the past couple of months should have read these blog posts. In a similar vein, there is plenty of twitter chatter on the topic and anecdotal evidence that during the last week of February 2020 ( when the US market crashed more than 10%), market volatility was exacerbated by market makers with short gamma positions. Gamma measures how much the price of a derivative accelerates when the underlying security price moves. Products with gamma exposure are typically options and leveraged ETFs. When prices of underlying assets move, market makers need to conduct hedging activities. Consequently, they have to buy additional securities when prices are rising and sell when prices are falling in order to ensure their positions are delta-neutral. Trading in the direction of the market price movement will exacerbate market swings and thereby result in increased market intraday momentum.

A quick example to makes things more concrete. Let’s say you are a reddit “WSBer” trying to manipulate the market. The user mentions that fellow members should buy out of the money calls in addition to the underlying stock. Why are they suggesting this? To create a “gamma squeeze’. How would this work? Well, the option market maker who sold this out of the money option WSBer needs to hedge their short position in the option, even though that sold call may be way out of the money. And what’s crazy is that if the price of the stock moves higher, the option dealer who sold the call needs to worry about hedging their short position as an increasing rate, thus driving potential demand that may put even more gas on the fire. That’s the theory, at least.

The authors of this study researched market intraday momentum, in other words, time-series momentum at the market level at the intraday frequency. They did this with 54 different time series across equities, bonds, and commodities going back to the 1970s covering 45 years of history. They ask the following research questions:

- Is market intraday momentum everywhere?
- Is gamma hedging an important driver?

The authors define a trading day as the 24-hour-period from the market close on day t − 1 to the market close on day t. The trading day is divided into five parts: overnight (ON, from close to open); first half-an-hour (F H, the first 30 minutes after the market open); middle-of-the-day (M, from the end of F H to an hour before the market close); second-to-last-half-an-hour (SLH, the second-to-last 30 minute interval); last half-an-hour (LH, the last 30 minutes before the market close). The combination of the first two partitions is labelled as “ONFH” (ONF H = ON +F H). The combination of the first four partitions is labelled as “rest-of-the-day” (ROD = ON + F H + M + SLH). ROD is the focus of the paper.

The authors find:

1. YES-The rest-of-day return (rROD) positively and significantly predicts the last half-an-hour return (rLH) across all major asset classes and markets. This effect is robust over time across our sample period of 1974 to 2020, and distinct from cross-sectional intraday return seasonality. A simple market intraday momentum trading strategy produces consistent returns over time, translating into high and attractive (annualized) Sharpe ratios between 0.87 and 1.73 at the asset class level.

2. YES- By studying two datasets (SP500 index options and leveraged ETFs) the authors confirm that hedging demand on a particular index drives the magnitude of its market intraday momentum pattern.

3. While the authors do find evidence that large price jumps during the day predict subsequent returns, consistent with intraday hedging activities, the bulk of the hedge seems to take place towards the end of the day.

This paper contributes to the voluminous literature on return momentum ( see for example Jegadeesh and Titman, 1993 for the cross-section and Moskowitz et al., 2012 for the time series). Instead, this study focuses on market momentum within a trading day. Most interestingly, it brings evidence to a novel economic force: hedging demand coming from options and leveraged ETFs amplify price changes and affect market return dynamics over several days.

Table 7 shows that indeed intraday momentum is much more pronounced on negative NGE days. On days with positive NGE, however, there is no significant intraday momentum. This provides strong support for our hedging demand hypothesis, i.e., that intraday momentum is partially driven by option hedging demand

Hedging short gamma exposure requires trading in the direction of price movements, thereby creating price momentum. Using intraday returns on over 60 futures on equities, bonds, commodities, and currencies between 1974 and 2020, we document strong “market intraday momentum” everywhere. The return during the last 30 minutes before the market close is positively predicted by the return during the rest of the day (from the previous market close to the last 30 minutes). The predictive power is economically and statistically highly significant and reverts over the next few days. We provide novel evidence that links market intraday momentum to the gamma hedging demand from market participants such as market makers of options and leveraged ETFs.

.

Hot Topic: Does “Gamma” Hedging Actually Affect Stock Prices? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>The Quality Factor—What Exactly Is It? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Chi Cheong Allen Nga and Jianfu Shen contribute to the literature, providing out-of-sample results, with their study “Quality Investing in Asian Stock Markets,” published in the September 2020 issue of Accounting & Finance. They examined two quality investing strategies using gross profitability (GP, revenues minus costs of goods sold, scaled by total assets) or FSCORE (a measure of financial strength), respectively, over the period 2000–2016 in Hong Kong, Japan, Korea, Singapore, and Taiwan stock markets. ^{1} They noted that previous studies documented that the FSCORE can successfully screen winners from losers in value stocks and that the ratio of GP has strong predictive power on stock returns. Following is a summary of their findings:

• Both FSCORE and GP are significantly positively associated with subsequent stock returns in cross-sectional regressions.

• The FSCORE anomaly returns ranged from 0.16 percent per month in Japan to 0.38 percent per month in Taiwan. The ranged for GP anomaly returns was from 0.15 percent (Korea) to 0.86 percent (Singapore).

• The returns on quality are not driven by small firms.

• Actively managed financial institutions buy significantly more high-quality stocks than low-quality stocks in each of five Asian markets. The trading pattern is not significant in passively managed institutions.

• Quality investing, instead of simple value investing based on only the book to market ratio, is more popular in the institutional investment decisions——institutional investors tend to follow the academic literature on anomalies.

Nga and Shen did note that:

“gross profitability cannot screen winners from losers in Japan and Korea, in which the portfolio of high GP stocks gives similar return as low GP stocks.”

They added that this finding was consistent with evidence from other studies which show substantial variation of the GP effect in international markets. In other words, there are exceptions to the general tendencies.

Their findings led Nga and Shen to conclude:

“The results in our paper support the argument that institutional investors such as hedge fund and mutual fund are sophisticated, and they trade on some stock return anomalies.” Their findings provide out-of-sample supporting evidence for the pervasiveness of the quality factor.

There’s one more point we need to discuss—how investors in value funds can gain exposure to the quality factor.

While some value strategies use the single metric of P/B (price-to-book) to determine value, others include other metrics such as P/E (price-to-earnings) and P/CF (price-to-cash flow). The metrics which include earnings-related measures provide exposure to the profitability factor (and the related quality factor). For example, since 2013, in their portfolio construction design, Dimensional’s value funds use not only P/B but also a measure of profitability. Alpha Architect’s value strategies utilize EBIT/Enterprise Value and utilize several quality screens (to include the FSCORE concept mentioned above; read the details here.) AQR Capital Management’s offerings, in addition to using P/B, also use P/E, P/CF, price-to-forecasted earnings, and sales-to-enterprise value. Bridgeway’s value funds also use multiple metrics including P/E and P/CF. In other words, you can gain exposure to profitability and quality indirectly through investments in value funds that use metrics other than P/B.

As one example, using the regression tool at www.portfoliovisualizer.com, and AQR’s four-factor model (beta, size, value, and momentum) plus quality (QMJ), from September 2011 through July 2020 Bridgeway’s Omni Small -Cap Value Fund (BOSVX) had a 0.48 loading on the QMJ factor. Similarly, over the period from 2013 through July 2020, Dimensional U.S. Small Value Fund (DFSVX) had a loading on QMJ of 0.5.

We have one last important point to cover. Multifactor funds are more efficient than single factor funds. One reason is that if you use the component approach, such as buying a value fund and a quality fund, you could have one factor-based fund buying a stock, while another factor-based fund will be selling the same stock. For example, if a stock is falling in price, it might drop to a level that would cause a value fund to buy it, while a momentum fund would be selling the same security. Investors would thus be paying two management fees and also incurring trading costs twice, without having any impact on the portfolio’s overall holdings.

Summarizing, the evidence suggests that the quality (high FSCORE or GP) is an important characteristic for investors to consider, along with cheapness (value). Thus, investors should consider including exposure to quality in their portfolio design.

Notes:

- Note that Alpha Architect has developed an enhanced version of this metric, described here. ↩

The Quality Factor—What Exactly Is It? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>A Review of Ben Graham’s Famous Value Investing Strategy: “Net-Nets” was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>But our objective in reviewing this collective research was not to identify if the Graham “Net-net” strategy works from a historical perspective, instead, we seek to answer the following question, “Could the returns reported in the research have been achieved by an investor in practice?”

To meet this objective, we developed a methodology to analyze the evidence and determine its reliability. Subsequently, we found that each of the studies suffered, or may have potentially suffered, from a number of biases that adversely impacted the reliability of the results contained therein. We, therefore, concluded that, in essence, a practitioner could not have achieved the returns reported in the research. Lastly, we briefly discussed the implications of our findings for practitioners of the investment strategy, as well as for evidence-based investors at large.

In 1934, between two world wars and in the midst of the great depression came the publication of Security Analysis by Benjamin Graham and David Dodd, an investment classic.

“A classic is something that everybody wants to have read and nobody wants to read.”attributed to Mark Twain

Within the weighty tome Graham details an investment strategy that involves purchasing stocks for less than their *“current-asset value”*, *“a rough index of the liquidating value”*. ^{1} In turn, the *“current-asset value of a stock consists of the current assets alone, minus all liabilities and claims ahead of the issue. It excludes not only the intangible assets but the fixed and miscellaneous assets as well.”* ^{2} Colloquially, such firms are referred to as “net nets” because their market capitalization is “net” of the “net current asset value”. ^{3}

For context it is worth noting that the Dow Jones Industrial Average (DJIA) reached 381.17 on September 3, 1929 and bottomed at 41.22 on July 8, 1932 – an 89.2% drawdown! ^{4} One can only marvel at the intestinal fortitude demonstrated by implementing *any* stock investment strategy in the face of such capital destruction.

Furthermore, with the behaviour of the market such as it was in the lead up to the publication of Security Analysis, one wonders how Graham’s faith was maintained in the behaviour of market participants, given the ultimate reliance on market participants to achieve the desired capital appreciation.

“Successful investing is having everyone agree with you… later”Jim Grant

Graham is often considered to be the father of value investing. However, despite such reverence, his strategy of purchasing securities trading at less than their Net Current Asset Value (NCAV) has been the focus of relatively limited research. In our quest for research examining the returns achieved by purchasing such securities, we uncovered ten studies that were conducted by academics and practitioners alike.

Our analysis was focussed on answering one *primary* question:

**Could the returns reported in the research have been achieved by an investor in practice?**

At first glance it seems an almost preposterous research endeavour; why examine something that is seemingly self-evident? Well, the returns reported in the majority of the research revealed an outperformance of such magnitude that our inherent scepticism stirred us into forensic examination.

“[I]n theory there is no difference between theory and practice, while in practice there is”

Benjamin Brewster (often attributed to Yogi Berra)

In order to meet our research objective and answer the question, “Could the returns reported in the research have been achieved by an investor in practice?”, we systematically and objectively analysed each study in its own right. Accordingly, we analysed a cross section of items in each of the studies including, but not limited to, the: valuation metric, weighting method, purchase/rebalancing rules, portfolio formation methodology and holding period(s). With regard to reliability specifically, we analysed the studies for: survivorship bias, look ahead bias, sample size issues, potential for human error, publication credibility, time period bias, data source reliability, minimum market capitalization requirements, return calculation methodology and errors generally.

To enhance understanding we provide additional detail pertaining to certain items below:

In general, the longer the test period the more reliable the results, the shorter the test period the less reliable the results. That said, where individual studies are deemed reliable, but for the time period utilized, we could potentially marry them to other such studies and aggregate the results in an attempt to circumvent the time period bias.

According to commentary and research published in “What Works on Wall Street (Fourth Edition)” by James O’Shaughnessy investing the lowest (i.e. cheapest) decile of stocks sorted by price to book has produced material outperformance for periods as long as 18 years. However, over even longer periods that relationship has not held. Ideally then, we would want multi-decade examination periods to be employed. (here is a simulation study on value portfolios to add additional context)

We used the following ranges to determine the presence of time period bias:

- < 10 years; inadequate/unreliable
- 11 to 20 years; somewhat reliable
- 20 years; more reliable
- 40 years; most reliable

A reliable and reputable data source is a necessity when conducting empirical research. Seemingly, the utilization of the CRSP/Compustat data base covering US listed securities from 1926, the gold standard in stock research, would circumvent any concerns when examining US listed securities. Unfortunately, even this database has had concerns raised over its reliability in a highly recommended article titled “The Myth of 1926: How Much Do We Know About Long-Term Returns on U.S. Stocks?” by Edward F McQuarrie. ^{5} McQuarrie finds that, in essence, 1973 onwards represents the point at which data contained within the CRSP/Compustat data base is most reliable. However, in a final twist James O’Shaughnessy states in “What Works on Wall Street (Fourth Edition)” that *“[c]ompustat also added many small stocks to its dataset in the late 1970s that could have caused an upward bias to result, since many of the stocks added were added because they had been successful.”*

Consequently, if even the leading database for empirical research into stocks has question marks over its reliability, we would be wise to assume that other databases may also suffer from some form of bias or contain errors of some degree.

For an investment strategy to be effective, it must be tradable in practice. However, some studies do not mandate a minimum market capitalization requirement for the stocks contained in the investment universe under examination. Consequently, the results in such studies can be unduly influenced by stocks that are, in practice, virtually untradeable, even when attempting to deploy relatively modest amounts of capital.

To be clear, we do not refer to mere micro capitalization stocks, despite their identification as a major source of the proliferation of “anomalies” identified by academics. ^{6} In fact, we are not even concerned with stocks close to the upper bound of “nano capitalization” classification per se. ^{7} Rather, our concern lies with the very smallest stocks that trade infrequently and at a very low “dollar” volume.

We have seen empirical evidence where the smallest decile of stocks was reported to have generated a Compound Annual Growth Rate (CAGR) of 84%! ^{8} Of course, the driver of those returns were almost certainly stocks that were uninvestable in reality. We explore this issue further by referring once again to “What Works on Wall Street (Fourth Edition)” by James O’Shaughnessy. O’Shaughnessy found that between 1964 and 2009 stocks with a market capitalization less than a deflated USD 25 million (2009 dollars) generated a CAGR of 63.2%! ^{9} However, *“when you require that all stocks have share prices of greater than $1, have no missing return data, and have limited the monthly return on any security to 2,000 percent per month”* the CAGR fell to 18.2%. Furthermore, when the analysis was extended to 1926 he found that the CAGR fell to 15%. And finally, *“[w]hen you look at the results for investable microcap names, those with market capitalizations between a deflated $50 million and a deflated $250 million, you see that most of the return for tiny stocks disappears.”*

Incorporating the principle identified above, where research contains (or may contain) stocks that are (or likely to be) untradeable we may refer to it as suffering from **“uninvestable stock bias”**.

To achieve our objective of answering the question, “Could the returns reported in the research have been achieved by an investor in practice?”, the answer was reliant on the return methodology adopted to quantify the reported returns.

What follows is a list of the various terminology used to describe the returns in the studies examined: annual geometric mean return, mean returns, abnormal performance, abnormal return, average raw buy-and-hold, average market-adjusted buy-and-hold, abnormal buy-and-hold performance, average return p.a., market return, raw returns, market index returns, buy-and-hold raw return, market-adjusted return, average raw return, average return, compound annual growth rate, cumulative raw return, excess return, percentage of positive excess return, cumulative excess return, simple average, and annualized return!

While the jargon is mind boggling, in general, the returns reported in the research generally refer to two simple return calculation methodologies: the arithmetic mean and/or the geometric mean.

**In a dependant return series that exhibits volatility (like stock returns) the arithmetic mean will, as a matter of mathematical law, overstate returns relative to the geometric mean.** ^{10}

For ease of reference, where returns have been calculated using the arithmetic mean we may simply refer to the research as suffering from **“inflated return bias.”**

For clarity, it should be noted that the geometric mean, when calculated for annual periods is also often referred to as the Compound Annual Growth Rate (CAGR) or the “annualized” return. The geometric mean return represents the *actual return potentially achievable by an investor in practice*, and therefore it is the sought-after measure when quantifying investment returns.

Given the importance of the return calculation methodology a few rudimentary examples are worthwhile. Firstly, let us assume an investor starts with $100 and they incur a 60% loss after 1 year resulting in a portfolio value of $40 ($100 * (1 – 60%)). Then, in year 2 they generate a 100% gain resulting in a final portfolio value of $80 (40 * (1+100%)). The arithmetic average return in this case would be 20% ((-60% + 100%) / 2)! Clearly, the result is nonsensical to an investor in practice. In contrast, the geometric mean would reflect practitioner reality and yield a result of -10.56% (80/100^(1/2)-1).

Another theoretically extreme example is provided in the table below:

Remarkably, it is theoretically possible to achieve an arithmetic mean twice that of the market (16.00% vs 8.00%; 2x); and simultaneously attain only a fraction of that return based on the geometric mean (4.99% vs 0.95%; 0.19x).

Finally, we provide a practical and wholly independent example to illustrate the misleading nature of an arithmetic mean when dealing with investment returns. Accordingly, we reproduce below Table 1 from the “Summary Edition Credit Suisse Global Investment Returns Yearbook 2019”:

There is a material difference between the arithmetic and geometric mean achieved for all equity markets examined. For Japan, the arithmetic mean is more than double the geometric mean!

Notwithstanding that discussed above, one may still be tempted to use the arithmetic mean as a guidepost to estimate the more practically meaningful geometric mean; we would caution against such an endeavour. In addition to the mathematical pitfalls illustrated in our examples above, psychologically speaking, such thinking may be driven, in part, by confirmation bias (“net nets outperform!”) and sunk cost fallacy (i.e. having put in the time and effort to read a study one may *want* to walk away “knowing something definitive”). In addition, statistically, as the number of holdings in a portfolio falls (an issue when examining the relatively small universe of firms trading below NCAV) the volatility of that portfolio may increase thereby leading to a greater potential divergence between the geometric and arithmetic mean. How portfolio volatility changes with the number of holdings in a portfolio was examined, for example, by Elton and Gruber in “Risk Reduction and Portfolio Size: An Analytical Solution” and by Alpha Architect here and here. ^{11}

So, mathematically, psychologically and statistically attempting to estimate the geometric mean is precarious and even more speculative than it may initially appear.

“The first principle is that you must not fool yourself and you are the easiest person to fool.”Richard P. Feynman

This leads us to an obvious question, “*Why* would you use an arithmetic mean to calculate stock returns?”. Indeed, when it first dawned on us that such a methodology was used to quantify stock returns, we were left utterly dumbfounded. We asked finance academics why they utilize the arithmetic mean, and the primary reasons given were that it is:

- Required for the statistical methods applied in academic research e.g. regression analysis
- Used to calculate risk measures e.g. Sharpe ratio, standard deviation etc.
- Used to circumvent the effect of the start and end date which may unduly influence the returns

While the above serves a purpose in *academic research* it does little for an investment practitioner trying to determine how much they can earn on their capital in reality. ^{12} While on occasion academic research does contain the geometric mean return (i.e. CAGR) it is not, in our experience, a common occurrence. ^{13} Indeed, most academic finance research appears to be conducted using arithmetic mean returns. Simply including the CAGR alongside the arithmetic average within academic research would greatly enhance its utility to the practitioner community, and we hope the measure is increasingly adopted. That said, it is our understanding that the academic community rejected the notion of “maximum drawdown” as a measure of “risk”, despite it being arguably the most important risk-related metric for a practitioner. ^{14} Consequently, the adoption of seemingly “common sense” measures may not be as inevitable as one would hope. Indeed, there appears to be a significant gap between the ivory tower and practitioner land, consequently, we are probably all the poorer as a result.

While our overall methodology used to examine the various studies may seem onerous, we believe it was required as all too often we have seen the cognitively deficient assertion that “all the evidence about “x” says “y” without any thorough examination of underlying evidence, in and of itself. It goes without saying, no matter the quantum of studies showing the same or similar results they remain collectively worthless if they each contain material methodological flaws – they ought to be dismissed rather than “anchored” to in the mistaken belief that they possess some utility. ^{15}

It is often said “I’ve never seen a bad back test”. We think it prudent to amend that quote to, “I’ve never seen *bad back test results!*”.

The table below lists the research papers examined along with their key parameters and stipulated returns:

A summary analysis of each study follows. We encourage readers to refer to the corresponding detailed analysis as well as the original research paper as nuance and clarity may be lost in the pursuit of relative brevity.

“Ben Graham’s Net Current Asset Values: A Performance Update” by Henry R. Oppenheimer was published in the Financial Analysts Journal (1986). The study examined the performance of securities that were trading at no more than two-thirds of their NCAV during the 13 year period from 1970-82 period in the US.

Table IV from the study is reproduced below:

Below we have adapted the data from Table IV and looked at the performance in both absolute and relative terms to the S&P 500 Total Return (TR, i.e. *including* dividends):

**Gross returns: **CAGR of 28.5% (with rounding impacting our calculations) vs 9.3% for the S&P 500 TR; an absolute outperformance of 19.2% and a multiple of 3.1 relative to the S&P 500 TR.

We then simulated reality by adding commissions and taxes to quantify the potential “net returns”. Commissions of 5% (2.5% to buy 2.5% to sell) were incorporated and we utilised the capital gains taxes rates of the corresponding years in the study. ^{16} Where applicable, we adjusted for tax loss carry forward and assumed our hypothetical investor resided in the US and sat in the highest marginal tax bracket but held on long enough to be eligible for the long-term capital gains tax rates. In contrast, we assumed an investor in the S&P 500 bought and held, never realizing their gains (and for simplicity we did not adjust their dividends for tax).

**Net returns** (i.e. including commissions and taxes): CAGR of 18.9% vs 9.3% for the S&P 500 TR; an absolute outperformance of 9.6% and a multiple of approximately 2.0 relative to the S&P 500 TR.

Table V from the study is reproduced below:

Reconciliation work carried out in our detailed analysis led to the determination that table V reports arithmetic mean returns and therefore suffers from inflated return bias. Nonetheless, we proceed with our examination.

When it comes to dividends the spread between “Positive Earnings and Dividends” (Panel D) and Positive Earnings and No Dividends (Panel E) is stark. No economic rationale comes to mind for why a net net paying dividends would underperform one that does not pay dividends.

However, as it often is, the devil is in the details, which appear to have gone unnoticed since publication in 1986:

Note 9 (p. 47) specifies the following:

*“all comparisons with the exchange benchmarks returns without dividends are used for both the security return and the benchmark return.”*

That is to say, to our understanding, the dividends have been *excluded* in the returns displayed in Table V (among others), and therefore the returns have been artificially reduced by the amount of the dividend paid out. On that basis it is not at all unexpected that the dividend payers would *seemingly* underperform their non-dividend paying counterparts.

In light of the above, we are of the opinion that no reliable conclusion can be drawn in relation to the impact of dividends on the returns of “net nets” based on this study.

The author sees the differential between “Positive Earnings” (Panel B) and “Negative Earnings” (Panel C) as marginal. The author concludes that *“**No clear-cut pattern emerges from an examination of these panels. If anything, firms operating at a loss seem to have slightly higher returns and risk than firms with positive earnings.”*

It is possible (probable in our view) that “positive earners” had a greater propensity to pay dividends. Therefore, if those dividends were *not* included in the measurement of their returns they would be artificially reduced. Of course, it is also possible (albeit unlikely in our view) that “negative earners” paid the greater share of dividends subsequently understating their returns. Irrespective, we are of the opinion that no reliable conclusion can be drawn in relation to the impact of earnings on the return of “net-nets” based on this study.

No minimum market capitalization cut-off for the securities examined in this study was mandated. Furthermore, we note that the reported median market capitalization of securities in the portfolios examined was 4.1m. That is to say, half the firms examined had a market capitalization equal to or *below* 4.1m which is particularly small, even by today’s inflation-adjusted standards. In light of the foregoing, it is highly probable that a considerable number of firms included in the study were, in effect, uninvestable.

While compounded gross returns were provided in some instances, certain sub-strategies were measured using the arithmetic mean returns, and therefore they suffered from inflated return bias. In addition, the study utilized data that *excluded* dividends thereby compromising the reliability of a number of conclusions reached therein. ^{17} Critically, it is highly probable that the reported returns were impacted by uninvestable stock bias.

Detailed analysis: An Analysis of “Benjamin Graham’s Net Current Asset Values: A Performance Update” (also available on Alpha Architect here).

“Graham’s Net-Nets: Outdated or Outstanding?” published in “Value Investing: Tools and Techniques for Intelligent Investment” by James Montier (2009) examined the performance of securities that were trading at no more than two-thirds of their “net current assets” during the 23 year period from 1985-2007 globally and regionally (namely, in the US, Europe, and Japan).

*“An equally weighted basket of net-nets generated an average return above 35% p.a. versus a market return of 17% p.a.”*

*“Not only does a net-net strategy work at the global level, but it also works within regions (albeit to varying degrees). For instance, net-nets outperformed the market by 18%, 15%, and 6% in the USA, Japan and Europe, respectively.”*

We summarise the results in the table below (some of which were gleaned from Figure 22.2):

It should be noted that no detail pertaining to the methodology and data source used to undertake study was disclosed.

In our detailed analysis, we reconciled the returns to references made to the Oppenheimer study. We identified, *“with a strong likelihood, that the author has calculated the arithmetic mean return”*, and consequently that the reported returns were overstated.

We also stated that *“… a cursory glance at Figure 22.2 illustrates returns of 24% p.a. to the “USA Market” from 1985-2007; this also indicates an arithmetic mean has been used because, to our knowledge, the US market simply did not achieve a compound annual growth rate of 24% from 1985 to 2007!”*. No information was disclosed with regard to the index used to represent the “USA Market”. However, it should be noted that the arithmetic mean return for the S&P500 (including dividends) from 1985 to 2007 was 13.65%; *nowhere near* the 24% graphically represented! ^{18}

The returns reported in “Graham’s Net-Nets: Outdated or Outstanding?” were *not* compounded returns (i.e. geometric mean returns). Whatever the return calculation methodology adopted, it appears that even their graphical representation is erroneous. Consequently, in our opinion, no credibility whatsoever ought to be attributed to the returns reported in the study.

Detailed analysis: An Analysis of “Graham’s Net-Nets: Outdated or Outstanding?” (also available on Alpha Architect here).

The objective of the paper, “Testing Benjamin Graham’s Net Current Asset Value Strategy in London”, was to examine the performance of securities that were trading at greater than 1.5 times the Net Current Asset Value (NCAV)/Market Value (MV) (i.e. less than 2/3 of NCAV) during the 26 year period from 1980 to 2005 on the London Stock Exchange.

Table 2 from the study is reproduced below:

The study reported an average raw buy and hold return of 31.19% to the NCAV portfolios 12 months after formation! What exactly are “average raw returns” and are these returns truly reflective of a practitioner’s reality? Significantly, the “Average raw returns” are calculated as the arithmetic mean of returns; consequently, the study suffered from inflated return bias. ^{19}

Furthermore, the authors did not mandate a minimum market capitalization cut off for the securities they examined, and as a result they included even the very smallest firms in the market.

They state *“…stocks are allocated to an NCAV/MV portfolio if their ratio is higher than 1.5. The numbers shown are the percentage of the average NCAV/MV portfolio falling into each size decile.… nearly 79 percent number of companies are very small (belong to size 1 and size 2)”. *Table 6, which confirms the aforementioned is reproduced below:

The smallest decile of the market is where 63.23% of the investment candidates were identified, and it is in this decile where the greatest trading constraints are likely to be faced. From table 2 we note that “value weighting” the NCAV/MV portfolio resulted in a 4.58% (31.19% – 26.61%) reduction in the “average raw buy-and-hold” return for portfolios held for 12 months; this implies that the smallest stocks disproportionately contributed to the reported outperformance.

Therefore, not only were the reported “average raw returns” unattainable in practice, they were also highly likely to have been afflicted by uninvestable stock bias**.**

The study suffered from inflated return bias and is highly likely to have also suffered from uninvestable stock bias thereby rendering the reported returns unattainable in reality.

Detailed analysis: An Analysis of “Testing Benjamin Graham’s Net Current Asset Value Strategy in London” (also available on Alpha Architect here).

In 2010 investment practitioners Philip Vanstraceele and Luc Allaeys published a research paper titled “Studying Different Systematic Value Investing Strategies on the Eurozone Market” which examined the performance of stocks in the “Eurozone” identified by a NCAV screen during the 10 year period from 1999 to 2009.

The paper claimed, “*In our methodology the NCAV-ratio should be greater than 1,33, and we define the ratio as Net Current Assets Value / Market Value. This ratio is used to find companies that are trading below their net current assets value.”*

For clarity, it should be noted that a ratio of 1.33 of Net Current Asset Value/Market Value equals 75% of NCAV.

Upon further analysis the claim appeared to be spurious in light of the sheer number of firms they reported to have tested at various market capitalization cuts offs. And indeed, upon further investigation our strong suspicion was confirmed. ^{20}

In fact, what was *actually* tested were those firms that traded at the highest *relative *“ratio of Net Current Assets Value / Market Value” (MV), **not** what was specified in the methodology of the study. Having established that we can proceed with a review of the returns achieved. The measure of *relative* cheapness may at least provide us with an insight as to the ability of the NCAV/MV metric to sort “winners” from “losers”.

Significantly, the authors examined the returns by calculating the CAGR.

We have restated the returns as reported in the study with regard to portfolios constructed using the NCAV/MV metric below (*“MV; the minimum Market Value in Millions and C ; the number of companies in the portfolio”*):

The NCAV MV25 C20 generated a CAGR of 13.44% vs the DJ Euro Stoxx -3.13%, an outperformance of 16.57%!

We chart below the CAGR of the 20 stock portfolios (i.e. “C20”) along with that of the market:

While, it appears as though the “cheapest” firms produced market beating return from 1999 to 2009 in the Eurozone across a full spectrum of market capitalizations, when we examined returns by decile, the efficacy of the NCAV/MV metric was brought into question.

Below we restate the returns reported in the paper of decile 1 (D1) and decile 2 (D2) (minimum market capitalization 100m) alongside those of the MV100 C20 portfolio for comparative purposes: ^{21}

The MV100 C20 portfolio consists of the 20 firms that possessed the highest ratio of NCAV/MV i.e. the cheapest stocks. Therefore those 20 firms would be subsumed within D1. While the cheapest 20 firms generated a CAGR of 10.48% the cheapest decile, which contained those firms, generated a CAGR of -2.18%. Yet D2, which contained more expensive firms, generated a higher CAGR of 11.93%!

The above implies a lack of robustness to the hypothesis that cheapness, as measured by the NCAV/MV was the driver of returns, for if it was, we would expect a consistent reduction in returns as the NCAV/MV decreased (i.e. firms became more expensive), as opposed to the inconsistent sequence identified above.

Furthermore, it should be noted that the 10.48% CAGR achieved by the MV100 C20 portfolio *excluded* dividends, whereas the -2.18 CAGR of D1 *included* dividends, further confounding the results.

Initially, the CAGR achieved by portfolios across a wide spectrum of market capitalizations seemed to definitively indicate the firms with the highest NCAV/MV (i.e. the cheapest) reliably and consistently outperformed the market as measured by the DJ Euro Stoxx. However, the robustness of the results was brought into question when we analysed the returns to the decile portfolios which revealed an inconsistency which could not be explained.

Detailed analysis: Analyzing Deep Value in the Eurozone.

Celebrated value investors Tweedy, Browne Company LLC published a booklet in 2009 that contained over 50 studies titled “What Has Worked in Investing: Studies of Investment Approaches and Characteristics Associated with Exceptional Returns”. Contained therein was a study whose objective it was to examine the performance of securities that were selling at 66% or less of their NCAV from April 1970 to April 1981, thereby creating a 12 year study period.

The study included firms with market capitalizations as low as *“$1 million”*, which, even by today’s inflation adjusted standards is likely to have resulted in the manifestation of uninvestable stock bias.

Table 4 from What Has Worked in Investing is reproduced below:

The “Average Return” is almost certainly the arithmetic mean occasioning in inflated return bias. We reached this conclusion as a number of other studies published in the booklet expressly state that returns were “compounded”, whereas in this case no such specification was made. Furthermore, using historical data we found that the specified 1 Year S&P500 of 8.5% reconciles almost perfectly to the S&P500 arithmetic mean return calculated using calendar year returns. ^{22} Oddly, the 1 Year S&P500 return presented against *“Stock Selection Criteria”* *“66% of net current asset value”* is different to all other portfolios (i.e. 9.1% vs 8.5%). Presumably, this is because a different time period was used for these portfolios, but we did not note any explanation for this difference in the study.

In addition to time period bias (12 years) the study is almost certain to have also suffered from inflated returns bias and is highly likely to have been afflicted by uninvestable stock bias also.

While we did not expect well renowned practitioners to produce practically inapplicable research our analysis nonetheless provides a reminder as to why one should actively go in search of disconfirming evidence and question everything, irrespective of its source.

“The important thing is not to stop questioning.”Albert Einstein

Detailed analysis: What Has Worked in Investing (Tweedy, Browne) – Examining Net Nets

“Emerging Markets: Evaluating Graham’s Stock Selection Criteria on Portfolio Return in Saudi Arabia Stock Market” by Nadisah Zakaria and Fariza Hashim examined the performance of securities that were trading at greater than 1.5 of their Net Current Asset Value (NCAV)/Market Value (MV) (i.e. less than 2/3 of NCAV) during the 15 year period from 2000 to 2014 on Tadawul (i.e. the Saudi Arabian Stock Exchange). The Tadawul possessed a market “*capitalization of USD385.3 million” *as* “of 31 ^{st} December 2011”*.

The study encompassed a small sample size (fewer than 10 firms were eligible for investment in the years from 2007 to 2011 inclusive) and no minimum market capitalization requirement was imposed.

Table 3 summarizing the relevant returns is reproduced below:

What are “buy-and-hold abnormal returns (BHAR)”? In essence, in this instance, the BHAR represents the geometric mean return less the market return.

So, while equally weighting (“EWI”) and holding 12 months produced a 20.17% BHAR the next question that comes to mind is, “what was the equally weighted market return that was outperformed by 20.17%”? Unfortunately, this was not reported.

In addition, it is worth noting that value weighting (“VWI”) resulted in a materially lower BHAR implying that the smaller companies were driving the “abnormal returns”.

The study suffered from time period bias (15 years) and the sample size examined was particularly small. Significantly, the study is also highly likely to have suffered from uninvestable stock bias given that no minimum market capitalization requirement was imposed. Furthermore, the market addressed possessed a capitalization of less than USD 400m raising further concerns with regard to liquidity. Also noteworthy is that regulatory restrictions during the study period would have prevented foreign investors from being able to access the potential opportunities.

Detailed analysis: Examining Saudi Arabian Net Nets

“An Empirical Analysis Of Ben Graham’s Net Current Asset Value Rule” by Joseph D Vu was published in The Financial Review (1988) and it examined the performance of securities that were trading at less than their NCAV during the 8 year period from 1977 to 1984 on the New York Stock Exchange (NYSE) and American Stock Exchange (AMEX).

The study suffered from a small sample size post 1977 and presented, in all likelihood, arithmetic mean returns (i.e. “Raw Returns”) resulting in inflated return bias. In addition, no minimum market capitalization was required for the securities under examination.

From Table 1 in the study we calculate and summarise the monthly return statistics from both before (t-24 to t-1) and after (t0 to t24) a security traded below its NCAV, and therefore qualified for investment. For reference we also quantify and report the cumulative market return (which was not reported in the original study):

Observing the cumulative excess return graphically reveals much:

Post event returns turn positive almost immediately. In the first year the cumulative raw return was 37.60% versus 22.60% for the market, an excess return of 15.00% (i.e. a 66.37% outperformance). For the total two year post event period the cumulative raw return was 60.70% versus 37.00% for the market, an excess return of 23.70% (i.e. a 64.05% outperformance).

From the breakdown of the return statistics it appears that the first year post formation resulted in the bulk of return suggesting that a one year rebalancing period may prove to be return enhancing.

From April 1977 to December 1984 it appears as though firms trading below NCAV on the NYSE and AMEX demonstrated near perfect market timing capability – seemingly a magical time to be a deep value investor!

In addition to time period bias resulting from the 8 year examination period, the study is also likely to have suffered from inflated return bias and was exposed to uninvestable stock bias.

Detailed analysis: Examining “An Empirical Analysis of Ben Graham’s Net Current Asset Value Rule”

“How the small investor can beat the market” by Joel M. Greenblatt, Richard Pzena and Bruce L. Newberg was published in the Journal of Portfolio Management (1981). ^{23} The paper was their Master’s thesis while studying at Wharton business school. The objective of the paper was to largely examine the performance of positive earning securities that were trading at or below their “liquidation value” during the 6 year period from April 1972 to April 1978 in the US.

While a minimum market capitalization of “over $3 million” was required for a stock to be considered, even after adjusting for inflation stocks close to the stipulated $3 million cut off may still have been insufficiently liquid to enable trading to occur in a “reasonable manner”. In addition, one needs to bear in mind that the researchers had to manually collect the necessary data thereby increasing the risk of human error.

Table 1 summarizing the portfolio returns has been reproduced below:

If you immediately and intuitively understand the data in Table 1 we refer you to the following:

“I know you think you understand what you thought I said, but I’m not sure you realize that what you heard is not what I meant”attributed to Alan Greenspan

A few points (which are covered in greater depth in our detailed analysis) are warranted:

- “Period” returns do not reconcile to the
*“Annual Compound Return”*specified at the foot of the table. - Annual Compound Returns – we assume the Annual Compound Returns were calculated by applying the stated sell strategy/holding period whereby the authors
*“sold a stock after a 100% gain or after 2 years, whichever came first”*. - Sample Size – the average portfolio contained 15 stocks and ranged from 0 to 52.
- Dividends – the Annual Compound returns
*did not*include dividends and are therefore understated (during the test period*“Dividends averaged between 3% and 4% annually”*). - Taxes, Commissions and slippage –
*“we assumed commissions of 2.5% on purchase price plus a 2.5% bid/ask spread (the bid/ask spread was applied to the 60% of our stocks that were purchased over-the-counter), a 2.5% commission on selling price, and a 25% capital gains tax (over 90% of the stocks were held long enough to qualify for capital gains treatment).”*The commissions included are in line with the higher trading costs associated with the time period examined.^{24} - P/E floating with bond yields –
*“We required a P/E corresponding to twice the prevailing triple A yield in each period (e.g. triple A yield = 8%; required PPE equal or below the reciprocal of 16%, or 6.25).”*The Triple A bond yield during the period studied ranged from approximately 7 to 9 implying a requirement for a P/E below 5.5 to 7.^{25}This means that the P/E requirement of ≤ 5 for Portfolio 3 and 4 was less than the maximum floating P/E allowed for Portfolio 1 and 2.

Having laid out the above we are better placed to analyse the results, bearing in mind the relatively small sample size, notwithstanding that the authors *“attempted to select a statistically significant and unbiased sample of stocks”*.

The highest returning portfolio was Portfolio 4 (42.2%) which required stocks in the portfolio to possess the lowest valuation in terms of both liquidation value (≤ 0.85) and P/E ratio (≤ 5.0).

Interestingly, Portfolio 3 (32.2%) returned more than Portfolio 2 (27.1%) despite its allowance for a higher liquidation cut off (≤ 1.0 vs. ≤ 0.85 for Portfolio 2) but a lower P/E threshold (≤ 5.0 vs ≤ ~5.5 to 7 for Portfolio 2).

Portfolio 1 which allowed for the highest valuation in terms of liquidation value (≤ 1.0) and P/E (≤ ~5.5 to 7) generated the “lowest” return (20.0%).

Overall, the results imply valuation drives futures returns, however, the merit of liquidation value vs the P/E ratio to explain future returns is less clear.

In terms of relative returns all portfolios greatly outperformed the “OTC” and “Value Line” portfolios which generated an Annual Compound Return (before taxes and commissions) of 1.3% and -0.3% respectively. Significantly, the outperformance of all portfolios survived taxes, commissions and slippage. However, all returns during the period were severely impacted by the ravages of inflation which averaged approximately 7.5% per annum (geometric mean) from 1972 to 1976. ^{26}

“How the small investor can beat the market” demonstrated that the Annual Compound Returns for firms with positive earnings trading at or below liquidation value, combined with a low price to earnings ratio greatly outperformed OTC and Value Line firms during the examination period (April 1972 to April 1978), even after taking into account taxes, commissions and slippage.

That said, the examination period (6 years) was simply too short to provide *definitive* guidance as to the efficacy of investing in firms trading at or below liquidation value. Furthermore, the study may have suffered from uninvestable stocks bias and it also harbored a number of idiosyncrasies which we highlighted in our detailed analysis. In aggregate, the study represents a small, though not untainted piece in the larger puzzle of determining what we “really know” about returns of such firms from an empirical standpoint.

Detailed analysis: Examining Greenblatt’s “How the small investor can beat the market”

“Testing Benjamin Graham’s net current asset value model” by Chongsoo An, John J. Cheh , and Il-woon Kim published in Journal of Economic & Financial Studies (2015) examined the performance of securities that were trading at less than their NCAV during the 14 year period from January 2, 1999 to August 31, 2012 in the US market.

The authors presented “annualized returns” (i.e. CAGR). *“The annualized returns of three portfolios and S&P 500 during the study period are presented in Exhibit 2. Annualized returns are the returns that should have been realized every year to earn total returns during the study period. Theoretically, the stocks with a higher NCAV/MV value should be generating annualized returns higher than the stocks with a low value. The results of this study, however, are mixed. Portfolio 1 (4.15%) and Portfolio 2 (2.49%) beat the market with a big margin as shown in Exhibit 2, while Portfolio 3 (0.51%) does not do well compared to the S&P500 (0.96). It is also puzzling to see in Exhibit 2 that the returns are decreasing as the value of N is increasing from 1 to 2 and to 5. We believe that these mixed results are due to the fact that the number of firms in each portfolio is decreasing from 84, to 31 and to 10. As the sample size is getting smaller, the results of the study are getting less reliable and sometimes inconsistent.”*

It should be noted that the sample size was particularly small as disclosed in the narrative. In addition, no minimum market capitalization was specified for the securities examined thereby exposing the results to the perils of uninvestable stock bias.

Interestingly, the Portfolio returns were in the opposite sequence to that which was expected. *“It was expected that the stocks with a higher NCAV/MV value (e.g., N=5) would be generating returns higher than the stocks with a low value (e.g., N=1).”*

What is particularly interesting about these results is the low level of absolute return outperformance relative to the market when compared to the other studies examining the returns to firms trading below NCAV. For example, for Portfolio 1, the best performing portfolio, the absolute outperformance relative to the S&P 500 was just 3.19% (4.15%-0.96%). Furthermore, net of fees and commissions the absolute return outperformance would have been even lower. Indeed, the annualized return to three-month Treasury bills over the 14 year period was approximately 2.3%; a figure reasonably comparable to the net of fee and commission return likely to have been achieved. ^{27} Furthermore, net of taxes (and effort) investing in firms with an NCAV > MV (i.e. trading at a discount to NCAV) appears to have been a forlorn endeavor in the US market over the test period.

The “average” (i.e. arithmetic mean) returns were reported as follows:

Recall the annualized returns (CAGR/geometric mean) for Portfolio 1, 2 3 and the S&P 500 was 4.15%, 2.49%, 0.51% and 0.96% respectively. In contrast the *“simple averages [i.e. arithmetic mean] of all rebalancing returns realized in backtesting… with one year holding period” *for Portfolio 1, 2, 3 and the S&P 500 was 17.17%, 17.78%, 14.87% and 2.91% respectively.

Using Portfolio 1 as an example, that represents a 13.02% return differential (17.17% – 4.15%). To illustrate the magnitude of that differential, compounding $100,000 at the Portfolio 1 annualized return rate of 4.15% yields $176,696 (100,000*(1.0415)^14-1) over 14 years (the length of the study period). In contrast, wrongly assuming that one could “compound” at the (arithmetic) average rate of 17.17% per Portfolio 1 would result in the mistaken belief that a terminal value of $784,537 (100,000*(1.1717)^14-1) was achievable. That represents a $607,841 (or 77.5%) difference in potential expectation.

The authors also examined a “Hedging Strategy” which reported impressive results, however, we believe it lacked robustness. We examined it in our detailed analysis along with the reported returns achieved by utilizing different holding periods.

Despite the quantification of annualized returns, the study cannot be considered reliable due to its likely exposure to uninvestable stock bias. In addition, the particularly small sample size of securities meeting the necessary criteria is also of concern.

Conveniently, the authors also presented the arithmetic average returns which provided a timely, relevant and objective lesson into why attempting to estimate the geometric mean from the arithmetic mean is an inadvisable action.

Reliability concerns notwithstanding, the study demonstrated that even over a 14 year period investing in firms trading below NCAV may not provide immunity from a low return environment – a sobering realization.

Detailed analysis: An Analysis of “Testing Benjamin Graham’s net current asset value model”

“Ben Graham’s Net Nets: Seventy-Five Years Old and Outperforming” by Tobias Carlisle, Sunil Mohanty, and Jeffrey Oxman (2010) aimed to provide an update on the research published by Henry R. Oppenheimer in his 1986 paper, “Ben Graham’s Net Current Asset Values: A Performance Update”. ^{28} Following the methodology adopted in Oppenheimer’s research, the authors selected securities that were trading at no more than two-thirds of their NCAV. Their 25 year examination period ran from 31 December 1983 to 31 December 2008 and they focussed on US-listed securities.

While this study purported to be an update of Oppenheimer’s 1986 study unfortunately it did not contain the all corresponding tables. Specifically, the most useful table from Oppenheimer’s study was Table IV which displayed the return in each year of the study and presented the “Annual Geometric Mean Return”.

“Exhibit 2 summarizes the results for the 25-year period of the study”, which deals with the 12 month holding period:

We note that the table heading states it is a “26” year period, however the study covers 25 years.

They present “monthly” “Mean Returns” (i.e. arithmetic mean). Exhibit II does indeed replicate the data presented in Table II of Oppenheimer’s study. Furthermore, based on reconciliation work carried out in “An Analysis of Benjamin Graham’s Net Current Asset Values: A Performance Update”, it reinforces our view that the arithmetic mean returns have also been presented in this case. Therefore, the results have been afflicted by inflated return bias.

30 month holding periods are examined and presented in Exhibit III (partially reproduced below).

At first glance Exhibit III, through its measurement of the “Terminal Wealth of $10,000” appears to be the representation of the *actual dollar return* achievable by an investor in practice (i.e. geometric mean/compounded return). However, like we discovered in “An Analysis of Testing Benjamin Graham’s Net Current Asset Value Strategy in London” and “What Has Worked in Investing (Tweedy, Browne) – Examining Net Nets” researchers “compounded” the arithmetic mean in attempt to put the returns in more “meaningful terms”. Indeed, we believe this to be the case in this study also. For instance, the 1983 monthly mean return of 3.59% when compounded for the stipulated 30 months with a starting value of $10,000 yields (rounding aside) the reported ~$28,846.24 (10,000*(1.0359)^30). When 3.59% is compounded monthly it results an *annualized* (i.e. compounded) return of 55.7% ((28,846.24/10,000)^(12/30)-1). Similarly, in 1993 the reported monthly mean return was 7.97%. When $10,000 is compounded for 30 months at 7.97% it yields (rounding aside) the reported ~$99,867.78 (10,000*(1.0797)^30). When 7.97% is compounded monthly it results in an *annualized* (i.e. compounded) return of 151.1% ((99,867.78/10,000)^(12/30)-1).

The implied returns are as extraordinary as they are illusionary!

Exhibit 4 is reproduced below:

Having established that Oppenheimer’s results were compromised due to the exclusion of dividends we proceed by examining the same issue in this study.

The authors state, *“Monthly returns are presented for the NCAV portfolios against various benchmarks, and sorted by earnings record and dividend payments. Rpt and Rmt are the NCAV portfolio and benchmark returns respectively….For all benchmarks, we use returns including dividends, except for the following: S&P 500, AMEX, and Nasdaq. These items are returns without dividends.”* Why total returns (i.e. including dividends) were not used with regard to the S&P 500, AMEX, and Nasdaq is unknown. While portfolios may have been sorted by “earnings and dividend payments”, it remains unclear whether the data used to measure the returns incorporated the dividend payments themselves.

*“The results in this section indicate a rational connection between risk and return. Dividend-paying firms are viewed as less risky because the dividend signals to shareholders that managers believe the future cash flows of the firm are stable enough to accommodate an ongoing dividend.”*

To accept the above conclusion an investor must also accept that “risk” is represented by the various “Risk Adjusted” measures presented, along with their implicit association with price volatility. Indeed, the acceptance of “beta” as an appropriate measure of risk adjusted returns runs contrary to the “low-beta anomaly”. ^{29}

Also, of concern is that no hypothesis (i.e. preceding the testing) was provided (in either study) for such results. Absent a more sound economic rationale for why positive earning non-dividend paying firms, 2.42% (and negative earning firms, 3.38%) would generate higher returns than positive earning dividend-paying firms, 1.48% (and positive earning firms, 1.96%), data mining or the exclusion of dividends from the return data may provide greater explanatory power for the reported results compared to that provided within the study itself.

Exhibit 5 and the corresponding narrative is reproduced below:

*“Quintile 1 contains the fifth of the firms that have the highest discount, and Quintile 5 contains the firms trading closest to two-thirds of NCAV. With one caveat… the returns are higher for firms with higher discounts to NCAV. The caveat is as significant as it is perplexing: securities in Quintile 1– those with the lowest purchase price to NCAV – have the lowest returns. As noted earlier, we have eliminated as outliers firms with stock prices less than one percent of the NCAV per share, so we do not believe outliers are driving this result.”*

Some food for thought pertaining to the reported results: in general, value investing research shows returns that are consistent with the relative “cheapness” of the underlying portfolios examined. ^{30} Firms trading at less than 2/3 of NCAV would, almost certainly, consist of firms that in aggregate sit in the bottom decile of price to book (or by academic convention, the top decile of book to market). Perhaps then, sorting these firms again based on a discount to NCAV possess limited utility; rather, other metrics (e.g. “quality measures”) may be required to eliminate the relatively poor performers. Indeed, in “Analyzing Deep Value in the Eurozone” we also observed that the firms that traded in the cheapest decile sorted by relative price to NCAV produced lower returns than those in the second cheapest decile.

As such then, we have no definitive explanation regarding the above results and only proffer thoughts for further contemplation.

The authors attempted to explain the “excess returns” by regressing a number of factors against the NCAV returns. For interested readers we recommend reviewing the underlying paper, however, we nonetheless provide the key extract from the paper below:

*“we are confident that the market risk, small-firm effect (SMB) and liquidity factors (ILLIQ) are the only *[our emphasis]

Indeed, the results of the regression analysis may elicit a range of reactions. Some may consider the results to be “objective and instructive”, while for other the results may evoke the quote, “Lies, damned lies, and statistics”!

We leave it to readers to ascertain the utility, or otherwise, of that presented by the authors in this section. ^{31}

No minimum market capitalization requirement was specified for the securities examined and therefore the results are highly likely to have suffered from uninvestable stock bias.

The authors conclude, *“The results are as clear as they are compelling: Seventy five years on, Graham’s NCAV rule continues to identify securities that generate above-market returns.”*

When looking at the findings reported in the paper from a practitioner’s point of view, our conclusion is different. The study suffered from inflated return bias and is also highly likely to have been impacted by uninvestable stock bias. For the practitioner not afraid to be confronted with a conclusion that may be inconsistent with their prior beliefs, we offer our version of the authors conclusion based on our extensive analysis of the study:

*“The results are as clear [unclear] as they are compelling [overstated]: Seventy five years on, Graham’s NCAV rule continues to identify securities that [may] generate above-market returns, [we simply do not know based on the methodology adopted in this study].”*

Detailed analysis: Examining “Ben Graham’s Net Nets: Seventy-Five Years Old and Outperforming”

Graham’s genius and intestinal fortitude in developing the strategy of investing in firms trading below their NCAV was remarkable, especially when one considers the era in which it transpired. Despite that, the research examining the strategy has been relatively limited when compared to the volume of investment literature published on more commonly discussed valuation metrics. Due to the remarkable returns reported in many of the studies our objective was to determine if “**the returns reported in the research could have been achieved by an investor in practice”. **To answer this question and fulfil our objective we developed an extensive methodology to “analyse the evidence”.

When viewed from the perspective of a practitioner (as opposed to an academic researcher) our analysis revealed that the underlying research contained methodological shortcomings, often resulting in the inability for the reported returns to be attained in reality.

Specifically, of the ten studies examined five suffered from inflated return bias (among other issues) and we therefore disregard their results. Of the remaining five studies one did not actually examine the return to stocks trading below NCAV and we therefore disregard it also. Of the four remaining studies three were highly likely to have suffered from uninvestable stock bias, in addition to other issues previously detailed.

That leaves just one, study, “How the small investor can beat the market”, which was not beyond reproach either. The study examined a relatively small sample of firms during the six year period from 1972 to 1978 in the US. Among other concerns, clearly, a study spanning just six years and examining just one market is insufficient to determine the efficacy of any investing strategy for it demonstrates both a lack of “persistence” and “pervasiveness”. ^{32}

In essence then, an investor could have potentially, though not assuredly, achieved the returns reported in just one out of the ten studies examined.

**We therefore conclude that when viewed from the perspective of a practitioner, the empirical evidence analysed is insufficient to support the view that investing in securities trading below their NCAV provides a reliable source of material outperformance.**

**Stated simply, “Could the returns reported in the research have been achieved by an investor in practice?” Essentially, no.**

Does our research suggest investing in firms trading below NCAV is a “bad strategy”? No, the “absence of evidence is not the evidence of absence”. By this we mean the lack of robustness in, and insufficiency of, the empirical evidence pertaining to firms trading below NCAV does not prove that the strategy cannot generate market beating performance.

Indeed, great investors such as Buffett, Schloss, Cundill and, of course, Graham himself advocated for the purchase of securities trading below a conservative liquidation value. ^{33} However, our analysis of the sample of research identified demonstrates that the performance capability of such a strategy remains largely unknown from a practitioner’s standpoint.

While our analysis focussed on the evidence concerning firms trading below NCAV and found it wanting, its implications resonate much further. For “evidence-based investors” it ought to evoke the questions, “How well do I understand the evidence on which I base my capital allocation decisions?”, “Can the returns reported in that evidence actually be translated into investment reality?”.

Being an evidenced based investor sounds intelligent, understanding the evidence is being an intelligent investor.

We commenced with a quote attributed to Mark Twain and it seems only fitting that we conclude with another quote also attributed to him:

“It ain’t what you know that gets you in trouble, it’s what you know for sure that just ain’t so.”

Notes:

- Benjamin Graham and David Dodd. Security Analysis: Sixth Edition. McGraw Hill 2009, pg. 586; Graham also wrote about this strategy for Forbes in 1932, “Ben Graham Then and Now” (https://www.forbes.com/forbes/2008/1110/056.html#3f4004de21e4) ↩
- Benjamin Graham and David Dodd. Security Analysis: Sixth Edition. McGraw Hill 2009, pg. 553 ↩
- Tobias E. Carlisle. Deep Value, Wiley 2014, pg. 21 ↩
- Wall Street Crash of 1929, https://en.wikipedia.org/wiki/Wall_Street_Crash_of_1929 ↩
- More details here. ↩
- Kewei Hou, Chen Xue, Chen Xue, Lu Zhang , “Replicating Anomalies” (2017). https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2961979. ↩
- Microcap Stock: A Guide for Investors: The term “microcap stock” applies to companies with low or “micro” capitalizations, meaning the total value of the company’s stock. A typical definition would be companies with a market capitalization of less than $250 or $300 million. The smallest public companies, with market capitalization of less than $50 million, are sometimes referred to as ‘nanocap stocks.’ (https://www.sec.gov/reportspubs/investor-publications/investorpubsmicrocapstockhtm.html) ↩
- Chee Seng Cheong A Fin, Justin Steinert, “The size effect: Australian evidence”, JASSA Issue 2 Winter 2007. ↩
- Approximately equal to an inflation-adjusted USD 31m in 2020. https://www.usinflationcalculator.com/ ↩
- Inequality of arithmetic and geometric means https://en.wikipedia.org/wiki/Inequality_of_arithmetic_and_geometric_means ↩
- Elton, E. and Martin Gruber, 1977, Risk Reduction and Portfolio Size: An Analytical Solution, The Journal of Business 50, p 415-437. ↩
- One could make an argument that the arithmetic mean return combined with the standard deviation may be “sufficiently” informative. However, when dealing with extreme return events assumptions pertaining to the nature of the underlying distribution of returns (i.e. normal distribution vs e.g. “Chebyshev Bound” ) and the corresponding confidence bound make the task unnecessarily complex and fraught with the need to make unnecessary assumptions. In contrast, the compound annual growth rate would provide the necessary information simply, accurately, and succinctly. ↩
- Wesley Gray and Jack Vogel, “Analyzing Valuation Measures: A Performance Horse-Race over the Past 40 Years.” https://papers.ssrn.com/sol3/Papers.cfm?abstract_id=1970693 ↩
- Wesley R. Gray, Jack Vogel, “Using Maximum Drawdowns to Capture Tail Risk”, 2013. https://papers.ssrn.com/sol3/Papers.cfm?abstract_id=2226689 ↩
- Anchoring (cognitive bias) https://en.wikipedia.org/wiki/Anchoring_(cognitive_bias) ↩
- A Century Of Stock Market Liquidity And Trading Costs, Charles M. Jones, Graduate School of Business Columbia University, 2002 (https://papers.ssrn.com/sol3/papers.cfm?abstract_id=313681);
We assumed our investor was in the highest tax bracket

For 1978 long term capital gains tax rates were 39.875/33.85%, we adopted the lower of these rates

For 1981 long term capital gains tax rates were 28/20%, we adopted the lower of these rates (https://taxfoundation.org/federal-capital-gains-tax-collections-1954-2009/) ↩ - That said, also as a result of using data that excluded dividends, it is theoretically possible that the reported returns may have been generally understated throughout the study depending on the impact, if any, of including firms that may have been untradeable. ↩
- http://www.stern.nyu.edu/~adamodar/pc/datasets/histretSP.xls ↩
- We were able to get in contact with the author, Glen Arnold, Ph.D. and he confirmed that “Each post-portfolio formation month has a number, 1, 2, 3 etc. The returns are measured for the post-portfolio month e.g. month 35, for each of the portfolios starting in different years. They are then simply averaged arithmetically.” ↩
- Confirmed by an author. ↩
- D1 contains the firms highest NCAV/MV ratio i.e. the cheapest. ↩
- http://www.stern.nyu.edu/~adamodar/pc/datasets/histretSP.xls ↩
- MarketFox Interview with Rich Pzena in which he briefly discusses the study (https://i3-invest.com/podcasts/i3-podcast-marketfox-interview-with-rich-pzena/) ↩
- A Century Of Stock Market Liquidity And Trading Costs, Charles M. Jones, Graduate School of Business Columbia University, 2002 (https://papers.ssrn.com/sol3/papers.cfm?abstract_id=313681) ↩
- https://fred.stlouisfed.org/series/AAA ↩
- https://www.inflation.eu/inflation-rates/united-states/historic-inflation/cpi-inflation-united-states.aspx ↩
- http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histretSP.html ↩
- We contacted the corresponding author on a number of occasions to seek clarity on aspects of the study and never received a response, nor did we receive a response from the second listed author, and the first listed author did not have in his possession the underlying data which we wished to review. ↩
- For research on Low-Volatility/Low-Beta see here: https://alphaarchitect.com/category/architect-academic-insights/factor-investing/low-volatility-investing/ ↩
- For further value investing research see here: https://alphaarchitect.com/category/architect-academic-insights/factor-investing/value-investing/ ↩
- The same research team (Tobias Carlisle, Sunil Mohanty, and Jeffrey Oxman) authored the paper “Dissecting the Returns on Deep Value Investing” (2012) (https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1928694 ) in which they examined numerous factors in an attempt to “explain the returns” to firms trading below NCAV (albeit with a variation of the valuation methodology applied in this study). ↩
- Andrew L. Berkin , Larry E. Swedroe, “Your Complete Guide to Factor-Based Investing: The Way Smart Money Invests” (2016). “Persistent – It holds across long periods of time and different economic regimes”, “Pervasive – It holds across countries, regions, sectors, and even asset classes”. ↩
- Though none, to our knowledge, advocated for the indiscriminate buying of securities purely on the basis of their trading below NCAV. ↩

A Review of Ben Graham’s Famous Value Investing Strategy: “Net-Nets” was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Mutual fund investments in private firms was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>- Sungjoung Kwon, Michelle Lowry, Yiming Qian
- Journal of Financial Economics
- A version of this paper can be found here

Although one of the largest investors in public companies, mutual funds have increased investments in private firms at least since the mid 1990s. Market valuation of those investments increased from $16 million in 1995 to over $8 billion in 2015. The authors of this study focus on three factors that have potentially contributed to this trend and provide insight into the following questions:

- Do private firms seek out alternative sources of capital to avoid or postpone public listing?
- Do mutual funds seek out private companies as investments in order to obtain higher returns, to increase diversification and/or to participate in IPO offerings?
- Are mutual funds sources of “dumb money”, that is, willing to invest at high valuations?

- YES.
**From the perspective of private companies:**The hypothesis, in this case, is that the ability to stay private for longer periods of time allows private companies to develop larger economies of scale and postpone costs of public listing associated with regulatory requirements. The authors present substantial evidence in support of the “delay” motivation. Mutual funds provided 38%(average)/32%(median) of financing beyond that supplied by VCs, between 2011-2016 in this analysis. The attraction for mutual funds as a source of capital to private companies resides mainly with their reluctance to demand strong control rights and a desire to exit at targeted dates. - YES. From the perspective of mutual funds: The attraction of private companies to mutual funds is associated with gaining competitive advantages by expanding the universe of investible opportunities. As the number of public companies has declined, portfolios offered by mutual funds are less differentiated from competitors. Allocations to the private market also ensure larger share allocations when those firms IPO. The fierce competition from passive vehicles and ETFs offering lower fees further exacerbate the pressures mutual funds face. Mutual funds with private investments prior to an IPO had a higher chance of receiving an allocation 64% vs those without an allocation at 21%. Mutual funds exhibited an average return of 4.8% monthly for private investments that exited with an IPO. The authors construct an equally-weighted benchmark as a comparison and conclude mutual funds earned 1.7x to 2.6x from private investments. The correlation between the constructed index and private investments was -.04, suggestive of diversification benefits accruing to mutual funds. There was no evidence found to indicate that other sources of capital such as PE and corporate VC were less available to fill the void.
- NO.
**From the perspective of the VC:**In their discussion, the authors make an interesting statement: “VCs possibly look to mutual funds as a source of*dumb money*willing to invest at high valuations”. Hmmm. OK, we’re game. They argue for the key role that VCs play on company boards and in capital-raising. VCs would come down on the side of mutual funds as a favored source of capital if they were willing to accept higher valuations or lower ownership percentages than alternative sources. There was little support found for this hypothesis. Why would all investors included in the same round of fundraising, where all receive the same terms, be willing to invest alongside dumb money? They don’t. There was little to no evidence that fundraising rounds that included mutual funds were overpriced. Risk adjustments using the market and 3 Fama-French factors failed to indicate mutual funds received lower alphas.

The research and discussion presented in this article relates to the current debate on the costs and benefits of becoming a public firm. Apparently, the costs of going public seem to outweigh the benefits at an increasingly larger margin. The benefits of capital and liquidity normally associated with being a public company, now accrue to private companies in predictable ways. Further, this research provides evidence that the IPO market is also changing in a systematic fashion. Thanks to regulatory changes that resulted in a larger supply of capital available to private firms, the number of IPOs in the US has declined. How these developments will affect the role of regulation with respect to protecting individual investors is becoming more critical.

Historically, a key advantage of being a public firm was broader access to capital, from a disperse group of shareholders. In recent years, such capital has increasingly become available to private firms as well. We document a dramatic increase over the past twenty years in the number of mutual funds participating in private markets and in the dollar value of these private firm investments. We evaluate several factors that potentially contribute to this trend: firms seeking extra capital to postpone public listing, mutual funds seeking higher risk-adjusted returns and initial public offering (IPO) allocations, and venture capitalists (VCs) seeking new investors to substantiate higher valuations. Results indicate that the first two factors play a significant role.

Mutual fund investments in private firms was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Is the Market Getting more Efficient? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>In 1998, Charles Ellis wrote “Winning the Loser’s Game,” in which he presented evidence that while it is possible to generate alpha and win the game of active management, the odds of doing so were so poor that it’s not prudent for investors to try. At the time, roughly 20 percent of actively managed mutual funds were generating statistically significant alphas (they were able to outperform appropriate risk-adjusted benchmarks). Today, that figure is much lower—about 2 percent (even before considering the impact of taxes). In our 2015 book, “The Incredible Shrinking Alpha,” my co-author Andrew Berkin and I described several major themes behind this trend toward ever-increasing difficulty in generating alpha:

- Academic research is converting what once was alpha into beta (exposure to factors in which you can systematically invest, such as value, size, momentum, and profitability/quality). And investors can access those new betas through low-cost vehicles such as index mutual funds and ETFs.
- The pool of victims that can be exploited is persistently shrinking. Retail investors’ share (stocks held in their brokerage accounts) of investment dollars had fallen from about 90 percent in 1945 to about 20 percent by 2008. Surely, it is much lower today And their share of trading is today is only about 10 percent.
- The amount of money chasing alpha has dramatically increased. For example, 20 years ago, hedge funds managed about $300 billion; today it is about $3 trillion.
- The costs of trading have fallen dramatically, making it easier to arbitrage away anomalies.
- The absolute level of skill among fund managers has increased—the competition has gotten tougher.

These trends have contributed to the decline in the ability of active managers to generate alpha. In his wonderful book “Adaptive Markets: Financial Evolution at the Speed of Thought” Andrew Lo, while acknowledging that the markets are not perfectly efficient, described the process by which markets adapt, becoming ever more efficient as entrepreneurs exploit inefficiencies (anomalies) post-publication—the adaptive markets hypothesis.

Anthony A. Renshaw, author of the paper “The Weakening Index Effect,” published in the Summer 2020 issue of the Journal of Index Investing, provided us with another example of shrinking/disappearing anomalies, increasing the hurdles active managers face in their attempts to generate alpha. The Index Effect is the phenomenon where stocks that are added to an index experience positive excess returns in the days before being officially added, while stocks that are removed from an index experience negative excess returns. Renshaw noted that the Index Effect has been documented since S&P first started announcing index changes in advance in October 1989. Following is a summary of his findings:

- For the S&P 500 Index, prior to 2011, many of the returns had been surprisingly large: −17.0% for deletions in 1989–1992; +9.3% for additions in 1998–2000. However, for the last three-years (2016-18), the 10-day buy-and-hold returns were just +15 bps for additions and −23 bps for deletions, both of which are smaller than their standard errors.
- As you can see in the following charts, prior to 2011 there was a pronounced index effect in the S&P 500. Post 2011 it not only weakened, it virtually disappeared— there is no statistically significant difference in returns between additions and deletions.

- The weakening of the Index Effect has been particularly pronounced for indexes composed of large- and mid-cap stocks.
- The Index Effect still can be observed in many (but not all) indexes with small-cap stocks. For example, for the S&P 1500 Index, the returns to the 10-day buy-and-hold strategy over the last three years (2016-18) were still an economically significant 4.9% for additions and −4.7% for deletions. However, the 1-day buy-and-hold was not effective for additions, and less effective for deletions.
- The results for the FTSE Developed Index are similar to those of the S&P 500 in that the magnitude of the Index Effect has weakened in recent years. The Index Effect is no longer present for additions. While still present for deletions, has been close to zero as recently as 2014–2016.
- The Index Effect continues to be present for unscheduled deletions but not for unscheduled additions. The unscheduled deletions have the following common characteristics: negative returns are associated with: low weight in the index (small stocks); low medium-term momentum; low profitability; low earnings yield; high volatility; and high market sensitivity (beta).
- The weakening of the Index Effect has occurred concurrently with a substantial increase in passive investing.
- ETF market makers (e.g., authorized participants) trade on price disparities as soon as they occur, eliminating any sustained positive or negative price movements—ETF trading improves liquidity and market efficiency.
- Due to limits to arbitrage, the Index Effect can still be found in some indexes with small-cap stocks and those with notably illiquid names.

One of the claims of active fund managers is that the rise of indexing and passive investing in general would make the markets less informationally efficient. It would also create more opportunities for exploiting index funds that focus on minimizing tracking error—they are forced to trade, and, thus, likely to take a loss when rebalancing occurs. If that were the case, the rise in passive investing would have led to an increase in the Index Effect. Yet, the exact opposite has occurred. The opportunities to generate alpha continue to shrink, making active investing more and more of a loser’s game.

Is the Market Getting more Efficient? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Trend-Following Filters – Part 2/2 was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Part 1 of this analysis, which is available here, examines filters modeled on second-order processes from a digital signal processing (DSP) perspective to illustrate their properties and limitations. To briefly recap, a time series based on a second-order process consists of a mean *a* and a linear trend *b* which is contaminated with random normally distributed noise ε(t) where ε(t) ~ N(0, σ_{ε}^{2}):

- second-order process – mean
*a*and linear trend*b*: x(t) =*a*+*b**t + ε(t)

The filters analyzed in Part 1 include double moving average, double linear weighted moving average, double exponential smoothing, and alpha-beta tracking filters. Part 2 extends the analysis to filters modeled on third-order processes. A third-order process consists of a mean *a*, a linear trend *b*, and a quadratic trend *c* which is contaminated with random normally distributed noise ε(t):

- third-order process – mean
*a*, linear trend*b*, and quadratic trend*c*: x(t) =*a*+*b**t + ½**c**t^{2}+ ε(t)

The filters analyzed are triple moving average, triple linear weighted moving average, triple exponential smoothing, and alpha-beta-gamma tracking filters. Note: This article assumes familiarity with Part 1 and also with the characteristics of financial time series and the digital signal processing concepts discussed in “An Introduction to Digital Signal Processing for Trend Following”, which is available here.

Triple moving average (TMA) is a time series forecasting and process control method that uses three single moving averages to estimate time series that contain linear and quadratic trends ^{1}. The triple moving average set of equations is:

where N is the number of input data points, i.e., the moving average length N (N > 1), included in the three single moving averages used to calculate the triple moving average, and x(t) represents the price at integer time t.

The triple moving average generates five main outputs: an estimate of the mean y_{0}(t) at time step t, an estimate of the linear trend y_{1}(t) at time step t, an estimate of the quadratic trend y_{2}(t) at time step t, a mean prediction y_{0}^(t) made at time step t for the next time step t+1, and a linear trend prediction y_{1}^(t) made at time step t for the next time step t+1. The quadratic trend prediction y_{2}^(t) for the next time step t+1 is the same as the quadratic trend estimate y_{2}(t) since a triple moving average does not model cubic and higher-order trends.

The triple moving average mean filter y_{0}(t) is a type of FIR low pass filter, i.e., it passes frequencies below the cutoff frequency f_{c} and attenuates frequencies above the cutoff frequency. The value N determines the cutoff frequency, which is inversely proportional to N (the cutoff period P_{c} is proportional to N). The filter coefficients sum to 1.0.

FIR mean filter difference equation:

**Example:** Triple moving average mean filter with length N = 10

Passes frequencies below the -3 dB (half power) cutoff frequency f_{c} of approximately 0.0824, which corresponds to a cutoff period P_{c} of approximately 12 time samples. Completely suppresses frequencies of 0.1, 0.2, 0.3, 0.4, and 0.5, which correspond to periods of 10, 5, 3.3333, 2.5, and 2 time samples, respectively. (Suppression occurs because, for example, the average value of a 10 time-sample period sine wave over 10 time samples is zero, the average value of two 5 time-sample period sine waves over 10 time samples is zero, etc.) There is a magnitude peak above 1.0 (i.e., 0 dB) at a period of approximately 21 time samples.

The triple moving average linear trend filter y_{1}(t) is a type of FIR bandpass filter. The filter has a center (also called “resonant”) frequency f_{0}, corresponding to a center period P_{0}, which passes at maximum power. The value N determines the center frequency f_{0}, which is inversely proportional to N (the center period P_{0} is proportional to N). The filter coefficients sum to 0.0.

FIR linear trend filter difference equation:

**Example:** Triple moving average linear trend filter with length N = 10

The center frequency f_{0} is approximately 0.05, which corresponds to a center period P_{0} of approximately 20 time samples. The filter completely suppresses frequencies of 0.1, 0.2, 0.3, 0.4, and 0.5, which correspond to periods of 10, 5, 3.333, 2.5, and 2 time samples, respectively.

The triple moving average quadratic trend filter y_{2}(t) is a type of FIR bandpass filter. The filter has a center (also called “resonant”) frequency f_{0}, corresponding to a center period P_{0}, which passes at maximum power. The value N determines the center frequency f_{0}, which is inversely proportional to N (the center period P_{0} is proportional to N). The filter coefficients sum to 0.0.

FIR quadratic trend filter difference equation:

**Example:** Triple moving average quadratic trend filter with length N = 10

The center frequency f_{0} is approximately 0.5, which corresponds to a center period P_{0} of approximately 20 time samples. The filter completely suppresses frequencies of 0.1, 0.2, 0.3, 0.4, and 0.5, which correspond to periods of 10, 5, 3.333, 2.5, and 2 time samples, respectively.

The following price chart of the daily S&P 500 stock index closing values for 2018 and 2019, which includes 503 trading days, shows the triple moving average mean (dashed blue line), linear trend (solid blue line), and quadratic trend (solid green line) for filter length N = 10. The single moving average mean (dashed red line) for filter length N = 10 is shown for comparison.

The amplitude of the linear trend filter output is proportional to the local slope of the price, i.e., the greater the amplitude, the steeper the slope. Similarly, the amplitude of the quadratic trend filter output is proportional to the local slope of the linear trend. However, the output of both filters can be affected by the presence of cycles and higher order trends.

Trading signals using triple moving average mean, linear trend, and quadratic trend filters can potentially be generated, for example, when:

- the price crosses above (buy) or below (sell) the mean line
- the mean line reaches a local crest (sell) or trough (buy)
- the linear trend line crosses above (buy) or below (sell) the zero line
- the linear trend line reaches a local crest (sell) or trough (buy)
- the quadratic trend line crosses above (buy) or below (sell) the zero line
- the quadratic trend line reaches a local crest (sell) or trough (buy)

or by a combination of these conditions.

The graph below illustrates the concepts of amplitude, crest, and trough:

Triple linear weighted moving average (TLWMA) is a modified form of the triple moving average that uses linear weighted moving averages instead of moving averages to estimate the mean, linear trend, and quadratic trend. The triple linear weighted moving average set of equations is:

where N is the number of input data points, i.e., the linear weighted moving average length N (N > 1), included in the three single linear weighted moving averages used to calculate the triple linear weighted moving average, and x(t) represents the price at integer time t.

The triple linear weighted moving average generates five main outputs: an estimate of the mean y_{0}(t) at time step t, an estimate of the linear trend y_{1}(t) at time step t, an estimate of the quadratic trend y_{2}(t) at time step t, a mean prediction y_{0}^(t) made at time step t for the next time step t+1, and a linear trend prediction y_{1}^(t) made at time step t for the next time step t+1. The quadratic trend prediction y_{2}^(t) for the next time step t+1 is the same as the quadratic trend estimate y_{2}(t), since a triple linear weighted moving average does not model cubic and higher-order trends.

The triple linear weighted moving average mean filter y_{0}(t) is a type of FIR low pass filter. The value N determines the cutoff frequency, which is inversely proportional to N (the cutoff period P_{c} is proportional to N). The filter coefficients sum to 1.0.

FIR mean filter difference equation:

**Example:** Triple linear weighted moving average mean filter with length N = 10

Passes frequencies below the -3 dB (half power) cutoff frequency f_{c} of approximately 0.1075, which corresponds to a cutoff period P_{c} of approximately 9.3 time samples. There is a magnitude peak above 1.0 (i.e., 0 dB) at a period of approximately 17 time samples.

The triple linear weighted moving average linear trend filter y_{1}(t) is a type of FIR bandpass filter. The value N determines the center frequency f_{0}, which is inversely proportional to N (the center period P_{0} is proportional to N). The filter coefficients sum to 0.0.

FIR linear trend filter difference equation:

**Example:** Triple linear weighted moving average linear trend filter with length N = 10

The center frequency f_{0} is approximately 0.0588, which corresponds to a center period P_{0} of approximately 17 time samples.

The triple linear weighted moving average quadratic trend filter y_{2}(t) is a type of FIR bandpass filter. The value N determines the center frequency f_{0}, which is inversely proportional to N (the center period P_{0} is proportional to N). The filter coefficients sum to 0.0.

FIR quadratic trend filter difference equation:

**Example:** Triple linear weighted moving average quadratic trend filter with length N = 10

The center frequency f_{0} is approximately 0.0625, which corresponds to a center period P_{0} of approximately 16 time samples.

The following S&P 500 daily price chart shows the triple linear weighted moving average mean (dashed blue line), linear trend (solid blue line), and quadratic trend (solid green line) for filter length N = 10. The single linear weighted moving average mean (dashed red line) for filter length N = 10 is shown for comparison.

Trading signals using triple linear weighted moving average mean, linear trend, and quadratic trend filters can potentially be generated in a similar manner to those described for triple moving average mean, linear trend, and quadratic trend filters.

Triple exponential smoothing (TES) is similar to the triple moving average, except that it uses exponential smoothing instead of moving averages to estimate the mean, linear trend, and quadratic trend ^{2}. The triple exponential smoothing set of equations is:

where α is the exponential smoothing constant (0 <= α <= 1) used in the three single exponential smoothings used to calculate the triple exponential smoothing and x(t) represents the price at integer time t.

Triple exponential smoothing generates five main outputs: an estimate of the mean y_{0}(t) at time step t, an estimate of the linear trend y_{1}(t) at time step t, an estimate of the quadratic trend y_{2}(t) at time step t, a mean prediction y_{0}^(t) made at time step t for the next time step t+1, and a linear trend prediction y_{1}^(t) made at time step t for the next time step t+1. The quadratic trend prediction y_{2}^(t) for the next time step t+1 is the same as the quadratic trend estimate y_{2}(t), since triple exponential smoothing does not model cubic and higher order trends.

The triple exponential smoothing mean filter y_{0}(t) is a type of IIR low pass filter. The value of the exponential smoothing constant α determines the cutoff frequency, which is proportional to α (the cutoff period P_{c} is inversely proportional to α).

IIR mean filter difference equation (requires proper initialization):

**Example:** Triple exponential smoothing mean filter with exponential smoothing constant α = 0.1325

The filter has about the same -3 dB (half power) cutoff frequency f_{c} of approximately 0.0824 (cutoff period P_{c }of approximately 12 time samples) as a triple moving average filter with length N = 10. There is a magnitude peak above 1.0 (i.e., 0 dB) at a period of approximately 40 time samples.

The triple exponential smoothing linear trend filter y_{1}(t) is a type of IIR bandpass filter. The value of the exponential smoothing constant α determines the center frequency f_{0}, which is proportional to α (the center period P_{0} is inversely proportional to α).

IIR linear trend filter difference equation (requires proper initialization):

**Example:** Triple exponential smoothing linear trend filter with exponential smoothing constant α = 0.1325

The center frequency f_{0} is approximately 0.0303, which corresponds to a center period P_{0} of approximately 33 time samples.

The triple exponential smoothing quadratic trend filter y_{2}(t) is a type of IIR bandpass filter. The value of the exponential smoothing constant α determines the center frequency f_{0}, which is proportional to α (the center period P_{0} is inversely proportional to α).

IIR quadratic trend filter difference equation:

**Example:** Triple exponential smoothing quadratic trend filter with exponential smoothing constant α = 0.1325

The center frequency f_{0} is approximately 0.0323, which corresponds to a center period P_{0} of approximately 31 time samples.

The following S&P 500 daily price chart shows the triple exponential smoothing mean (dashed blue line), linear trend (solid blue line), and quadratic trend (solid green line) with smoothing constant α = 0.1325. The single exponential smoothing mean (dashed red line) with smoothing constant α = 0.1325 is shown for comparison.

Trading signals using triple exponential smoothing mean, linear trend, and quadratic trend filters can potentially be generated in a similar manner to those described for triple moving average mean, linear trend, and quadratic trend filters.

The alpha-beta-gamma (α−β−γ) filter is used for object tracking in track-while-scan radar systems, based on an acceleration motion model ^{3} ^{4}. The function of the tracking filter is to process noisy position measurement inputs into “smoothed” position, velocity, and acceleration estimate outputs. The alpha-beta-gamma tracking filter set of equations is:

where α is the position smoothing constant, β is the velocity smoothing constant, γ is the acceleration smoothing constant, and x(t) is the observed position of the object (or price in this case) at integer time t. Note that the alpha-beta-gamma filter position estimate is analogous to the mean estimate, the velocity estimate is analogous to the linear trend estimate, and the acceleration estimate is analogous to the quadratic trend estimate of the other filters described above. The α, β, and γ smoothing constants are subject to the following stability constraints:

The alpha-beta-gamma tracking filter generates five main outputs: an estimate of the position y_{0}(t) at time step t, an estimate of the velocity y_{1}(t) at time step t, an estimate of the acceleration y_{2}(t) at time step t, a position prediction y_{0}^(t) made at time step t for the next time step t+1, and a velocity prediction y_{1}^(t) made at time step t for the next time step t+1. The acceleration prediction y_{2}^(t) for the next time step t+1 is the same as the acceleration estimate y_{2}(t), since the alpha-beta-gamma tracking filter does not model jerk and higher order maneuvers.

Various alpha-beta-gamma filter smoothing constant relationship equations have been developed to calculate optimal values, based on an assumed underlying process model that approximates the dynamic behavior of the target or on a set of filter design objectives, such as providing good transient response and small noise and prediction error ^{5} ^{6}. They include:

Notes:

- Discounted least squares error (critically damped) smoothing constants α, β, and γ produce results equivalent to triple exponential smoothing if

where α3 is the triple exponential smoothing constant.

- The alpha-beta-gamma tracking filter is closely related to the three-state steady-state Kalman filter, where the three states are position, velocity, and acceleration
^{7}.

The alpha-beta-gamma position tracking filter y_{0}(t) is a type of IIR low pass filter. The α, β, and γ smoothing constant values determine the cutoff frequency of the filter.

IIR position tracking filter difference equation (requires proper initialization):

**Example:** Alpha-beta-gamma position tracking filter using random acceleration-based smoothing constants α = 0.3289, β = 0.0654, and γ = 0.0065

The filter has a -3 dB (half power) cutoff frequency f_{c} of approximately 0.0824 (cutoff period P_{c }of approximately 12 time samples), similar to that of a triple moving average mean filter with length N = 10. There is a magnitude peak above 1.0 (i.e., 0 dB) at a period of approximately 31 time samples.

The alpha-beta-gamma velocity tracking filter y_{1}(t) is a type of IIR bandpass filter. The α, β, and γ smoothing constant values determine the center frequency f_{0} of the filter.

IIR velocity tracking filter difference equation (requires proper initialization):

**Example:** Alpha-beta-gamma velocity tracking filter using random acceleration-based smoothing constants α = 0.3289, β = 0.0654, and γ = 0.0065

The center frequency f_{0} is approximately 0.0345, which corresponds to a center period P_{0} of approximately 29 time samples.

The alpha-beta-gamma acceleration tracking filter y_{2}(t) is a type of IIR bandpass filter. The α, β, and γ smoothing constant values determine the center frequency f_{0} of the filter.

IIR acceleration tracking filter difference equation (requires proper initialization):

**Example:** Alpha-beta-gamma acceleration tracking filter using random acceleration-based smoothing constants α = 0.3289, β = 0.0654, and γ = 0.0065

The center frequency f_{0} is approximately 0.0357, which corresponds to a center period P_{0} of approximately 28 time samples.

The following S&P 500 daily price chart shows the alpha-beta-gamma position (dashed blue line), velocity (solid blue line), and acceleration (solid green line) tracking filters using random acceleration-based smoothing constants α = 0.3289, β = 0.0654, and γ = 0.0065.

Trading signals using alpha-beta-gamma position, velocity, and acceleration tracking filters can potentially be generated in a similar manner to those described for triple moving average mean, linear trend, and quadratic trend filters.

For a time series with an underlying third-order process, assuming that the current quadratic trend (acceleration) y_{2}(t) is locally constant and using the same time step convention as is used for the one time-step predictions above, mean (position) predictions y_{0}^ at future integer time steps can be made at time step t, using the following equation:

One measure that can be used to evaluate the appropriate filter length or smoothing constant values to use with a particular time series is to calculate the root mean square error (RMSE) of the one time-step predictions of the filter over a sample of observations. The one time-step prediction error x_{e}(t) at each time step t is the difference between the input value x(t) at time step t and the prediction y_{0}^(t-1) made for time step t at the previous time step t-1:

The root mean square error over a sample of N observations is:

In general, the filter length or smoothing constant values that produce the minimum RMSE can be helpful in determining a useful setting. Unlike filters that are modeled on first order processes, filters modeled on third order processes will usually have a non-trivial minimum RMSE value when applied to financial time series. However, values that minimize RMSE may not necessarily correspond to maximum trading profitability. In addition, the value that minimizes RMSE in one sample of observations will not necessarily be the same in a different sample, due to the volatility, non-normality, and non-stationarity usually observed in financial time series.

While mean (position) filters modeled on third order processes are able to follow input time series that contain a locally constant quadratic trend (acceleration) with less lag compared to filters modeled on first or second order processes, if the input time series contains cubic or higher order trends (jerk or higher order target maneuvers), for example, third order mean (position) filter estimates will lag the input.

Filters modeled on fourth or higher order underlying processes can also be used, but filters modeled on second or third order processes are usually sufficient to capture the significant trends in most financial time series.

Third order process linear trend (velocity) and quadratic trend (acceleration) filters are bandpass filters which are “tuned” to a specific center frequency or period, based on the filter coefficients, with an associated phase response. As a result, if the input time series contains a cycle with a period that is *less* than the center period of the filter, the filter output will crest (trough) *after* the input time series cycle crest (trough). Conversely, if the input time series cycle period is *greater* than the center period, the filter output will crest (trough) *before* the input time series crest (trough). This behavior can be observed in the linear and quadratic trend and in the velocity and acceleration filter outputs in the S&P 500 daily price charts.

Since financial time series are non-stationary with means and variances that change over time, the use of filters with fixed parameters will not perform well at all times for trading purposes. As a result, filter coefficients that are “fitted” to a particular portion of a time series history will not necessarily produce good results in the future.

I would like to thank Larry Stabile for reviewing this article and providing many helpful comments and suggestions.

The derivation of the triple moving average, triple linear weighted moving average, and triple exponential smoothing sets of equations is mathematically complex and beyond the scope of this article.

For reference, the proof of the “fundamental theorem of exponential smoothing”, which includes that for double, triple, and higher-order exponential smoothing, can be found in ^{8}. The proof can be extended to double, triple, and higher-order moving averages by substituting the following for α in the equations, where N is the single moving average length:

Similarly, the proof can be extended to double, triple, and higher order linear weighted moving averages by substituting the following for α in the equations, where N is the single linear weighted moving average length:

These substitutions equate the average age of the data included in exponential smoothing to the average age of the data included in the corresponding moving average and linear weighted moving average.

Notes:

- Brown, R. G.,
*Smoothing, Forecasting, and Prediction of Discrete Time Series*, Prentice Hall, 1962. ↩ - Brown, R. G., Smoothing, Forecasting, and Prediction of Discrete Time Series, Prentice Hall, 1962. ↩
- Simpson, H. R., “Performance Measures and Optimization Condition for a Third-Order Sampled Data Tracker”,
*IEEE Transactions on Automatic Control*, AC-8 (2), 182-183, April 1963. ↩ - Neal, S. R., “Discussion on ‘Parametric Relations for the α-β-ν Filter Predictor’”,
*IEEE Transactions on Automatic Control*, AC-12 (3), 315-317, June 1967. ↩ - Navarro, A. M., “General Properties of Alpha Beta and Alpha Beta Gamma Tracking Filters”, Report PHL 1977-02, Physics Laboratory, National Defense Research Organization, Netherlands, January 1977. ↩
- Kalata, P. R., “The Tracking Index: A Generalized Parameter for α-β and α-β-γ Target Trackers”,
*IEEE Transactions on Aerospace and Electronic Systems*, AES-20 (2), 174-182, March 1984. ↩ - Bridgewater, A. W., “Analysis of Second and Third Order Steady-State Tracking Filters”,
*Proceedings of AGARD Conference, No. 252, Strategies for Automatic Track Initiation*, 9-1 – 9-10, October 1978. ↩ - Brown, R. G.,
*Smoothing, Forecasting, and Prediction of Discrete Time Series*, Prentice Hall, 1962. ↩

Trend-Following Filters – Part 2/2 was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Battle of the Sexes, Who’s Better at Fudging the Numbers? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>- V.K.Gupta, S. Mortal, B. Chakrabarty, X. Guo, D. B. Turban
*Academy of Management Journal,*2019- A version of this paper can be found here

There are estimates that although approximately 15% of public firms may engage in accounting fraud annually, but less than 1% are actually caught. It can be important to develop tools for diagnosing financial misreporting like the Financial Statement Deviation (FSD) to measure the level of irregularities in financial statements (higher the FSD Score and the greater the likelihood that numbers in the financial statement contain errors and/or were manipulated) without the need of accounting data. By using FSD, this paper investigates whether executive gender has an impact on corporate decisions and actions. Specifically, the authors ask the following questions:

- Do firms with female CFOs have a lower likelihood of financial misreporting than comparable firms with male CFOs?
- Is the relation between CFO gender and financial misreporting contingent on governance mechanisms (e.g., institutional ownership and analyst coverage) such that misreporting of firms with male CFOs will differ more from that of firms with female CFOs when governance is weak?

The sample is made up of 2,186 unique US-based firms and 18,659 firm-year observations. By intersecting six different databases (Execucomp, Compustat, Institutional Shareholder Services, CRSP, IBES, and Thomson Reuters) the authors find ^{1}:

- Female CFOs represent 8% of our sample, consistent with other findings that women remain underrepresented in the top tiers of public corporations
- The correlation between Female CFO and financial misreporting (as captured by FSD Score) is negative and significant (correlation = -.03, p < .05), implying that firms with female CFOs have a lower likelihood of financial misstatement
- Using panel regression, there is a significant negative effect (β = -0.026, t = -3.02, p < .01) of having a female CFO on the likelihood of financial misreporting (that is, FSD Score), indicating that female CFO firms have 2.6% lower FSD Score than male CFO firms. This is an economically meaningful effect in comparable literature
- Firms with female CFOs have a significantly lower likelihood of financial misreporting compared to firms with male CFOs when institutional ownership is low
- Similarly, firms with female CFOs have a significantly lower likelihood of financial misreporting compared to firms with male CFOs when analyst coverage is low

This study extends and confirms the literature on the relation between the upper echelon gender heterogeneity and corporate misconduct such as earnings quality (Krishnan & Parsons, 2008) and securities fraud (Cumming et al., 2015). Understanding whether executive gender influences firm-level outcomes is important as the ascent of women to the upper echelons of the corporate world challenges the “implicit masculine bias” in scholarly understanding of managerial decision-making (Ho, Li, Tam, & Zhang, 2015).

Additionally, this research extends ongoing scholarship on corporate governance, which generally sees governance mechanisms as agnostic to the gender of the executive. As increasing numbers of women ascend to executive positions, the issue of how governance mechanisms have differential influence depending on the gender of the executive is a worthy topic for future scholarship and of considerable interest to managers and other organizational stakeholders.

The increasing presence of women in upper echelon positions draws attention to the possible effects of executive gender on corporate decisions and actions. In this study, we formulate theory about the impact of CFO gender on financial misreporting to generate two key insights. First, we hypothesize that firms with female CFOs will have a lower likelihood of financial misreporting than comparable firms with male CFOs. Second, we argue that the relation between CFO gender and financial misreporting will be contingent on governance mechanisms (e.g., institutional ownership and analyst coverage) such that misreporting of firms with male CFOs will differ more from that of firms with female CFOs when governance is weak. Our results, based on a novel leading indicator of the likelihood of financial misreporting, provide support for our predictions. Various alternative econometric specifications, including (but not limited to) exogenous shocks, propensity score matching, and modeling treatment-effects, random effects, firm-fixed effects, and hybrid effects provide general support for our theory and hypotheses. Implications and directions for future research are discussed.

Notes:

- The authors perform a number of robustness tests that confirm results ↩

Battle of the Sexes, Who’s Better at Fudging the Numbers? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Global Factor Performance: January 2021 was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>- Standardized Performance
- Factor Performance
- Factor Exposures
- Factor Premiums
- Factor Attribution
- Factor Data Downloads

Notes:

- free access for financial professionals ↩

Global Factor Performance: January 2021 was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>The Definitive Study on Long-Term Factor Investing Returns was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>- Baltussen, Swinkels, Vliet
*Journal of Financial Economics,*forthcoming- A version of this paper can be found here

Interest in factor investing was hot several years back but seems to have died on the back of poor relative performance and a move to hotter products in thematics and ESG. But, for better or worse, we haven’t moved on. We are boring and we trust the process. We still believe that markets do a decent job at pricing risks and rewards, but they aren’t perfect. There is a bunch of noise caused by these pesky humans, which are driven by fear and greed behaviors that create systematic mispricing opportunities that are neither cheap and/or easy to exploit. Factor portfolios seem to be an efficient way of capturing the various risk/returns available in the market. And the reality is investing is not a pure science — there’s some art involved as well.

But not everyone agrees that factors are the way to go, nor should they. ^{1}

The factor debates could fill a library with journal articles (or a blog with over a 1,000 posts, like our own!). In my mind, one of the biggest frictions to understanding factors is getting everyone to agree on the baseline facts. I think this recent paper (which is being published in the JFE, a top-flight “A-pub” journal) from the team at Robeco does a great job establishing the baseline facts regarding factors over the ultra-long-term. We can still argue if past performance will predict future performance, but at least this paper helps establish a baseline on “what is the past performance?”

This paper also has me questioning the “risk vs. mispricing” debates. Prior to reading this I was in the “equal-weight” camp — premiums are likely due to some fundamental risk and a healthy dose of mispricing that is tough to exploit. But now I’m shifting more towards, “Maybe emotional humans plus arbitrage frictions are everything.”

After reading this paper a few times — and reviewing the internet appendix (authors hooked me up) — I am in awe of this paper and the work required to make this happen. What an effort. We commend the authors for sharing this incredible paper.

Here are the core research questions the authors ask:

- Do factors hold up over the full sample period?
- Do factors hold up in the ‘out of sample’ period?
- Can factors be explained via “rational” economic risks?

The authors look at factors over the 1800 to 2016 time period. ^{2} The authors focus on exploring 6 core factors that we all know and love: time-series momentum (i.e. trend-following), cross-sectional momentum (i.e., momentum or relative strength), value, carry, return seasonality, and betting against beta (i.e., low vol). Next, they examine these factors in the context of 4 asset classes : stocks, bonds, commodities, and currency. In total, the authors explore 24 factor premiums across the different factors and markets.

- YES. Factors work over the full sample. The authors examine the 24 core factor premiums across the entire time period and find that they are generally robust, which isn’t too surprising since a large part of the sample is “in-sample” and well understood.
- YES. The authors leverage newer empirical techniques that seek to mitigate the problems with data-mining (discussed here in “Take that Alpha and shove it“). On net, the out of sample exploration of factors is
*pretty consistent*with the evidence we all know and love. The few exceptions are “value” in the context of FX and the BAB effect outside of stocks (i.e., not robust in bonds, commodities or FX). - Not really. The authors explore a sample with 43 bear market years and 74 recession years, multiple wars, depressions, and so forth. Surprisingly, the authors find the following:

Across several tests we find no supporting evidence for these explanations, with global return factors bearing basically no relationship to market, downside or macroeconomic risks.

As a former Eugene Fama student that endured years of successful brainwashing in the ways of EMH (but was never completely sold!), this statement is a bit hard to digest. I’ll need to chew on it a bit more and read the paper a few more times.

This paper does a great job of outlining the baseline facts regarding the long-term evidence on factors across time and asset classes. The fact that factors ‘work’, in general, is not altogether surprising. We would already expect factors to work if our baseline hypothesis is that markets were reasonably efficient at pricing pains and gains over time. However, where this paper has me thinking is in the “why do factors work” sections. My prior is that factor portfolios capture elements of fundamental risks and mispricing that is difficult and painful to exploit. The authors suggest that maybe factors don’t proxy for fundamental risk at all. That is a surprising finding.

We examine 24 global factor premiums across equity, bond, commodity and currency markets via replication and out-of-sample evidence between 1800 and 2016. Replication yields ambiguous evidence within a unified testing framework that accounts for p-hacking. Out-of-sample tests reveal strong and robust presence of the large majority of global factor premiums, with limited out-of-sample decay of the premiums. We find global factor premiums to be generally unrelated to market, downside, or macroeconomic risks in the 217 years of data. These results reveal significant global factor premiums that present a challenge to traditional asset pricing theories.

Notes:

- The bayesian analysis makes this more clear in the context of replication studies. From the paper: “These results imply that one does not need to be very skeptical to disregard the empirical evidence.” ↩
- Is the data perfect? Of course not. We’ve played with the data sources and they can be dirty, nasty, and ugly. But that is the reality of research and the potential benefit of exploring new data is new insights. ↩

The Definitive Study on Long-Term Factor Investing Returns was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>How Does ETF Liquidity Affect ETF Returns, Volatility, and Tracking Error? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>- Kyounghun Bae, Daejin Kim
- Journal of Financial Economics
- A version of this paper can be found here

Although the ETF market has grown exponentially over the recent 20 years, ETFs that are less popular are not always liquid. A majority of the dollars flowing into ETFs are concentrated in 3 products, accounting for 46.7% of total ETF trading volume (see Figure 3 below). If the next 8 ETFs are included that percentage increases to 61.5%. If that doesn’t astound the reader, consider that the AUM$ of the top 10 represent 36% of total AUM$ for ETFs. That translates to roughly 64% of ETFs measured in terms of AUM$ are relatively “unpopular”. In terms of trading volume, those ETFs excluding the top 10 represent only 38.5%. Anyway you look at it, there is a potential liquidity challenge with a major portion of the ETF market.

**Why does this matter?** If the liquidity of the unpopular ETFs is insufficient, it may affect the proper functioning of the ETF market in those products with consequent increased transactions costs for investors.

**How might this happen?** The problem emanates from the unique structure of the ETF that results in two prices that are intricately related. For example, although ETFs are traded on exchanges, the shares included in an ETF are first created and redeemed in the primary market. If you want to understand this process better I highly encourage you read Wes’s article titled, “Understanding How ETFs Trade in the Secondary Market.” Now with a baseline understanding of how ETFs trade, we can recognize that there is a price for the ETF product on the exchange and another price or Net Asset Value (NAV) determined on the value of the underlying basket of stocks. The returns on each should be very similar. However, a number of factors can drive a wedge between them, resulting in differences in returns, and consequent differences in ETF variances and ETF tracking error. Divergence in the ETF returns and the NAV returns should be eliminated by arbitrage efforts of “authorized participants” (APs) — essentially market makers. However, under conditions of low liquidity, the APs may be incented to refrain from replicating the index (unprofitable prices) at the same time trading in the ETF basket occurs. Any delay in the timing of arbitrage activity, because APs prefer to wait for increased bid-ask spreads, for instance, will be accompanied by an increase in the tracking error of the ETF and increased transaction costs for investors. Not pretty, but it does motivate the authors to analyze the impact of illiquidity on ETF tracking error, variance, and returns in the secondary US ETF market.

The answers to the following 3 questions provide evidence on the degree of efficiency in the ETF market as well as to the magnitude of the problem. The data was comprised of all ETFs ever listed or traded on US exchanges between 1993-2012, where the country of domicile is limited to the US. All delisted ETFs that traded during the sample period were included. Daily prices for ETFs, NAVs, and underlying indexes were obtained from Bloomberg.

- Does ETF liquidity affect tracking error?
- Does ETF liquidity affect returns?
- Does liquidity affect ETF variance?

- YES. The analyses conducted substantiate a causal link between illiquidity of the ETF, illiquidity of the underlying asset, and the consequent impact on tracking error. Specifically, the presence of illiquidity in the underlying basket magnifies the impact of ETF illiquidity on tracking error. The authors present evidence that a positive relationship exists between ETF illiquidity and tracking error, using daily and annual data. ETF illiquidity was measured as the
*daily relative effective spread*= ratio of the effective half-spread to trade price; where the effective half-spread = absolute difference between quote midpoint and trade price. The structure (in-kind vs. cash) of ETFs also differed in terms of illiquidity, with in-kind exhibiting less sensitivity to ETF illiquidity than the cash method. Non-leveraged ETFs were used to examine the impact of illiquidity of the underlying basket of stocks on ETF illiquidity. Not surprisingly, stocks with less liquidity have a larger impact, even if the asset classes and markets are identical. - YES. The empirical results suggest that liquidity is a priced risk factor in the US ETF market. That is, the return on an ETF is dependent on the covariance of the ETF liquidity and return with the market liquidity and return. An ETF liquidity beta is estimated and determined to have a positive and significant risk premium of approximately 0.14% annualized. The authors discuss the application of the LCAPM to ETF returns and conclude the model is a good fit for the ETF market.
- YES. Using the Lo and MacKinlay (1990) econometric model and derive the ETF variance with respect to the NAV variance. The empirical tests provided evidence for a positive relationship between the two variances. They interpret the difference between the two as risk due to infrequent trading in the secondary market, in addition to the risk of the underlying basket of stocks.

Apparently, the illiquidity present in the ETF market increases the transaction costs for AP/market makers and ETF investors. If market makers (APs) fail to replicate the index immediately and properly in order to avoid increasing the costs of such market-making, they will undoubtedly increase tracking error of the product and fail to meet investor objectives. The illiquidity of the underlying constituents of an ETF and the tracking error that may result is something investors ought to be conscious of. One could consider investing in the underlying basket into their own hands and skipping the ETF structure altogether, however that exposes investors in active investment vehicles to high tax hurdles and increases in trading costs.

An excellent article if the reader is interested in understanding the microstructure foundations of trading in the ETF market.

We investigate the effect of exchange-traded fund (ETF) liquidity on ETF tracking errors, returns, and volatility in the US. We ﬁnd that illiquid ETFs have large tracking errors. The effect is more pronounced when underlying assets are less liquid. Returns and liquidity of illiquid ETFs are more sensitive to underlying index returns or ETF market liquidity, or both. Thus, a positive liquidity premium exists in US ETF markets. The ETF variance could be larger than its net asset value variance owing to infrequent trading. In summary, illiquid ETFs are more likely to deviate from their underlying indexes and could be riskier than underlying portfolios.

How Does ETF Liquidity Affect ETF Returns, Volatility, and Tracking Error? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Value and Momentum and Investment Anomalies was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>For example, the study “Value and Momentum Everywhere” by Clifford Asness, Tobias Moskowitz and Lasse Pedersen, published in the June 2013 issue of The Journal of Finance, examined these two factors across eight different markets and asset classes (individual stocks in the U.S., the U.K., continental Europe, and Japan, as well as country equity index futures, government bonds, currencies and commodity futures) and found:

- There are significant return premia to value and momentum in every asset class. The value premium was persistent in every stock market, with the strongest performance in Japan. The momentum premium was also positive in every market, especially in Europe, though statistically insignificant in Japan. (see here for more details on Japan)
- Value strategies are positively correlated with other value strategies across otherwise unrelated markets, and momentum strategies are positively correlated with other momentum strategies globally. This persistence assuages data mining concerns. (see here for more details)
- Value and momentum are negatively correlated with each other within and across asset classes. Their negative correlation and high positive expected returns imply that combining strategies result in improved Sharpe ratios.

Deniz Anginer, Sugata Ray, H. Nejat Seyhun and Luqi Xu contribute to the literature on value and momentum with their February 2020 study “Value and Momentum in Anomalies.” They examined the performance of value and momentum across the following capital asset pricing model (CAPM) anomalies. Specifically, they investigated whether the time variation in the predictive ability of anomalies is random or serially correlated over time.

- Net stock issues: Net stock issuance and stock returns are negatively correlated. It’s been shown that smart managers issue shares when sentiment-driven traders push prices to overvalued levels.
- Composite equity issues: Issuers underperform non-issuers, with “composite equity issuance” defined as the growth in the firm’s total market value of equity minus the stock’s rate of return. It’s computed by subtracting the 12-month cumulative stock return from the 12-month growth in equity market capitalization.
- Accruals: Firms with high accruals earn abnormally lower average returns than firms with low accruals. Investors overestimate the persistence of the accrual component of earnings when forming earnings expectations.
- Net operating assets: The difference on a firm’s balance sheet between all operating assets and all operating liabilities, scaled by total assets, is a strong negative predictor of long-run stock returns. Investors tend to focus on accounting profitability, neglecting information about cash profitability, in which case net operating assets (equivalently measured as the cumulative difference between operating income and free cash flow) capture such a bias.
- Asset growth: Companies with high growth rates in their total assets earn lower subsequent returns. Investors overreact to changes in future business prospects implied by asset expansions.
- Post-earnings announcement drift: If earnings surprises are positive (negative), future stock prices drift upward (downward)—stock prices drift in the same direction as the earnings surprise.
- Investment-to-assets: Higher past investment predicts abnormally lower future returns.
- O-score: This is an accounting measure of the likelihood of bankruptcy. Firms with higher O-scores have lower returns.
- Momentum: High (low) recent (in the past year) past returns forecast high (low) future returns over the next several months.
- Gross profitability premium: More-profitable firms have higher returns than less-profitable firms.
- Return on assets: More-profitable firms have higher expected returns than less-profitable firms.
- Size: Smaller firms have higher expected returns than larger ones.
- Value (book-to-market): High book-to-market (value) firms have higher expected returns than low book-to-market (growth) firms.

The authors began by first defining “anomaly momentum” as the future abnormal returns to anomaly-identified stocks that exhibit better (or more positive) returns than other anomalies. They then defined “anomaly value” as the future abnormal returns to anomaly-identified stocks that exhibit higher recent book-to-market ratios. Their sample includes U.S. stocks over the period January 1975 through December 2014.

Following is a summary of their findings:

- There is significant persistence in the relative rankings of anomalies with respect to their past one-month returns as well as their past year’s historical adjusted book-to-market ratio—77 (85) percent of the anomalies exhibit a relative (absolute) momentum.
- Anomalies that have performed well in the past month continue to outperform those that have performed poorly by about 60 basis points (bps) per month. The performance is stronger for absolute momentum.
- Anomalies that exhibit a value orientation outperform anomalies that exhibit a growth orientation going forward by about 30 bps per month—77 percent of the anomalies exhibit a relative value effect.
- Their strategy significantly outperforms a naive diversification strategy of equal weighting across anomalies.
- The performance of their strategy improves using absolute momentum (time series) and value rankings instead of relative rankings (cross-sectional).
- Combining momentum and value to construct the “super winner” portfolio, investing in the anomalies that are both “winning” in terms of past month’s performance and “winning” in terms of past year’s historical adjusted book-to-market ratio, results in an abnormal return of 1.08 percent per month. In contrast, the “super losing” portfolio (“losing” past performance as well as past adjusted book-to-market ratio) has an abnormal return of only 0.11 percent per month. Hence, investing in super winning portfolios generates an additional 0.97 percent per month.
- Their results are robust to a wide variety of specifications.
- The anomaly momentum/value is distinct from and cannot be explained by individual stock momentum/value or industry momentum/value.

Their findings led the authors to conclude:

“Our findings further corroborate the hypothesis that mispricing is an important source of anomaly profits.”

They added:

“We are the first to document that value works across anomalies and that anomaly-value and anomaly-momentum can be combined to create a powerful trading strategy.”

Finally, they suggested:

“that anomaly momentum can reduce tail risk when used to time investment decisions.”

Their study contributes to the body of evidence suggesting that investors can improve the efficiency of their portfolios by using investment vehicles that incorporate both value and momentum strategies.

Value and Momentum and Investment Anomalies was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>DIY Asset Allocation Weights: January 2021 was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Request a free account here if you want to access the site directly.

Exposure Highlights (**bold **implies a month over month change): ^{1}

- Full exposure to domestic equities
**.** - Full exposure to international equities.
- Partial exposure to REITs.
- Partial exposure to commodities.
- Full exposure to long-term bonds.

Notes:

- The information contained herein is only as current as of the date indicated and may be superseded by subsequent market events or for other reasons. Neither the author nor Alpha Architect undertakes to advise you of any changes in the views expressed herein. This information is not intended and does not relate specifically to any investment strategy or product that Alpha Architect offers. ↩

DIY Asset Allocation Weights: January 2021 was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>How Powerful is the Wealth Effect? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>- Marco Di Maggio, Amir Kermani and Kaveh Majlesi
*Journal of Finance,*2020- A version of this paper can be found here

Anyone who’s spent better than thirty-five minutes listening to financial news has likely heard about the “Wealth Effect.” The theory suggests that the upward trajectory in prices of assets lines the pockets of consumers itching to spend their newfound wealth. Financial news particularly loves the concept because it drives more spending and creates a flywheel effect on the stock market driving prices and ratings even higher. The authors of this paper inquire directly into analyzing if stock market trends drive household spending habits and whether this link depends on households’ overall wealth.

By analyzing granular household-level data (on the universe of households’ portfolio holdings at the security level, as well as information about their debt obligations and real estate transactions) from Sweden during the period 1999-2007, the authors find: ^{1}

- The marginal propensity to consume (MPC) of (unrealized) capital gains for households in the top 50% of the financial wealth distribution is about 5% and it does not exhibit significant variation between, for instance, households in the 50th to 70th percentile and households in the top 5% of the wealth distribution. In contrast, the MPC for households in the bottom half of the distribution is significantly higher at about 13% ( even if this segment of the population owns less than 7% of overall stockholdings.
- Consistent with the evidence in Baker, Nagel, and Wurgler (2007), we find that households are significantly more responsive to changes in dividends. In fact, the MPC out of dividends, for all of our wealth groups, is around 35%, i.e. about seven times the MPC out of capital gains for the top 50th percentile of wealth distribution.
- Among households with enough financial wealth, MPC out of capital gains is significantly larger for older households. This finding is consistent with life cycle models.

These results on MPC out of dividends and capital gains are consistent with near-rational behavior in which households separately optimize their consumption with respect to capital gains and dividend income as if they were independent of each other. In particular, dividend income changes are significantly more persistent than changes in capital gains, and, as long as households consider capital gains and dividend income as separate sources of income, this can rationalize an MPC out of dividend income that is significantly larger than MPC out of capital gains ( see also the concept of *free dividends fallacy *by Hartzmark and Solomon, 2017, covered here).

This study fills the literature with findings on the causal impact of changes in stock market wealth on households’ consumption. For the amount of press it gets, we would have expected a larger Wealth Effect. Also, if politicians sought to exploit the wealth effect the data would suggest that they encourage firms to increase their dividend distributions as much as possible.

This paper employs Swedish data on households’ stock holdings to investigate how consumption responds to changes in stock market returns. We instrument the actual capital gains and dividend payments with past portfolio weights. Unrealized capital gains lead to a marginal propensity to consume of 23% for the bottom 50% of the wealth distribution and about 3% for the top 30% of the wealth distribution. Household consumption is significantly more responsive to dividend payouts across all parts of the wealth distribution. Our findings are consistent with households treating capital gains and dividends as separate sources of income.

Notes:

- The authors perform a number of robustness tests and control for endogeneity issues. ↩

How Powerful is the Wealth Effect? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>The 2021 Annual Finance Research Geek Fest: Top 5 Most Interesting Papers was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>There is so much research available it is a bit difficult to read it all — and many of the papers have still not been made available. Nonethless, I tried to highlight some of the work that was interesting to me. We encourage everyone to explore the research library on their own since you might enjoy different topics.

Here are the top 5 papers that were interesting ^{3} to me:

- Forest through the Trees: Building Cross-Sections of Stock Returns: I’m still trying to understand what is going on in this paper, but one thing is clear — their figures/graphics are incredible!
- In Search of the Origins of Financial Fluctuations: The Inelastic Markets Hypothesis: Have you ever wondered how fund flows might affect asset prices? Check this paper out!
- What Drives the Size and Value Factors?: I was convinced that there was nothing left to be said on this topic. I was wrong. Flows matter.
- Do Women Receive Worse Financial Advice? This is a remarkable study that uses undercover agents in Hong Kong. Fascinating.
- The Great Divorce Between Investment and Profitability: More information on the dynamics and foundations for the profitability factor, which we cover often on this blog. (and use in practice)

Also, I went through the PhD poster session, which is work conducted by a current PhD student (i.e., new researchers).

- Decomposing Factor Momentum: There has been a lot of new research discussing the ability to tactically allocate across factors based on momentum.
^{4}This research goes deeper with a decomposition of the returns and finds that factor momentum probably works because it holds the factors that earn the highest premiums over the sample.

Enjoy all this academic finance research!

Notes:

- here is information on the broader conference ↩
- Of course, read this recent paper first before falling head over heels in love with the research. ↩
- note, interesting isn’t a value judgement, but merely a ‘taste’ ↩
- Here is an example and here. ↩

The 2021 Annual Finance Research Geek Fest: Top 5 Most Interesting Papers was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Trend-Following Filters: Part 1/2 was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Many traders use strategies based on trends that occur in stock, bond, currency, commodity, and other financial asset price time series in order to “buy low” and “sell high”. A trend is considered to be the overall direction of prices over a period of time. If prices have generally increased the trend has a positive slope and is called “bullish”. If prices have generally decreased, the trend has a negative slope and is called “bearish”. If there is no discernable positive or negative trend, the trend is often referred to as “sideways”. ^{1}

Trend-based trading strategies include:

- momentum – trading in the same direction as the recent trend on the expectation that the trend will continue. (see here for an example)
- mean reversion – anticipating reversals from “extreme” price levels considered to be “overbought” or “oversold”
- contrarian – trading against the prevailing trend on the expectation that the trend will soon end. (see here for an example)

Since financial time series data are digital by nature, digital filtering techniques are used by many technical analysts to transform and analyze them, e.g., to attenuate noise and identify trends. For example, moving averages and exponential smoothing are commonly used directly and are also embedded in many technical indicators, such as moving average crossover (MAC) and moving average convergence-divergence (MACD). Moving averages and exponential smoothing are examples of low pass digital filters, which are modeled on the assumption that the input follows a first-order process, i.e., one that has a locally constant mean value *a* and is contaminated with normally distributed random noise ε(t) where ε(t) ~ N(0, σ_{ε}^{2}):

- first order process – mean
*a*: x(t) =*a*+ ε(t)

Low pass filters are designed to estimate the mean value *α* of a first-order process by attenuating the random noise ε(t). However, if the input contains trends, the output of a low pass filter will lag the input because it is not designed to model trends. While the lagged response can be used as a way to “sidestep” some of the noise and short-term price fluctuations during a trend, there is a cost of delayed response once a trend begins or ends.

Note: A zero order process just consists of random noise, which is equivalent to a first order process with mean *a* = 0:

- zero order process: x(t) = ε(t)

The following graphs show examples of times series with underlying zero and first order processes:

Because financial time series typically exhibit trends, it is appropriate to use filters that are modeled on the assumption that the input follows an underlying process containing trends, for example:

- second order process – mean
*a*and linear trend*b*: x(t) =*a*+*b**t + ε(t) - third order process – mean
*a*, linear trend*b*, and quadratic trend*c*: x(t) =*a*+*b**t + ½**c**t^{2}+ ε(t)

The following graphs show examples of times series based on underlying second and third order processes:

Part 1 of this analysis examines filters modeled on second-order processes, specifically double moving average, double linear weighted moving average, double exponential smoothing, and alpha-beta tracking filters, from a digital signal processing (DSP) perspective to illustrate their properties and limitations.

Part 2 will examine filters modeled on third-order processes, specifically triple moving average, triple linear weighted moving average, triple exponential smoothing, and alpha-beta-gamma tracking filters.

These filters are sometimes called “zero lag” filters, although they reduce but do not totally eliminate lag in all circumstances.

- The characteristics of financial time series along with the underlying concepts of frequency and period measurement, time domain, and frequency domain, the four basic types of filters, finite impulse response (FIR) and infinite impulse response (IIR) filters, and filter frequency response are discussed in “An Introduction to Digital Signal Processing for Trend Following”, which is available on the Alpha Architect website blog here. This article assumes familiarity with that material.
- The unit pulse response graphs shown for each filter in this article display the time domain responses on the integer time scale t = 0, 1, 2, …. The coefficients of an FIR filter correspond to the time-reversed order of the unit pulse response.
- The frequency magnitude spectrum graphs shown for each filter display the frequency domain response over the normalized frequency range 0 <= f <= 0.5 cycles per time sample on the horizontal scale. The lower limit f = 0 can be thought of as a wave of infinite length or as a steady direct current (DC) level. The upper limit f = 0.5 is called the “Nyquist frequency”, which is the highest frequency of a signal that can be recorded per time sample for the signal to be accurately reconstructable in the time domain.
- Graphs showing the magnitude spectrum for each filter in terms of period P, i.e., the number of time samples to complete one cycle, on the horizontal scale are also included, since period is the measurement that is most commonly used by and familiar to technical analysts. These graphs have a lower limit of 2 time samples, since the Nyquist frequency f = 0.5 corresponds to a period of P = 1/f = 2 time samples per cycle.
- In the frequency phase spectrum graphs shown for each filter, phase values are constrained to the range -180 to +180 degrees. When the actual phase value is outside this range, the phase value is increased or decreased by a multiple of 360 degrees to put the phase value back within the -/+ 180-degree range. This is called “phase wrap” and results in the appearance of a zig-zag line, but each 360 degree line segment jump is actually a continuation of the previous line segment.
- Examples of the time domain output of the various filters are shown using price charts of the daily S&P 500 stock index closing values for 2018 and 2019, which includes 503 trading days.

Double moving average (DMA) is a time series forecasting and process control method that uses two single moving averages to estimate the mean and trend of time series that contain linear trends ^{2}. The double moving average set of equations is:

where N is the number of input data points, i.e., the moving average length N (N > 1), included in the two single moving averages used to calculate the double moving average, and x(t) represents the price at integer time t. The derivation of the double moving average equations is shown in Appendix 1.

The double moving average generates three main outputs: an estimate of the mean y_{0}(t) at time step t, an estimate of the linear trend y_{1}(t) at time step t, and a mean prediction y_{0}^(t) made at time step t for the next time step t+1. The linear trend prediction y_{1}^(t) for the next time step t+1 is the same as the linear trend estimate y_{1}(t), since a double moving average does not model non-linear trends.

The single moving average (MA) equations shown above are in FIR (non-recursive) form. The filter coefficients have equal value 1/N. The IIR (recursive) form, which requires proper initialization, is:

Note that a single moving average actually has two outputs: an estimate of the mean and a mean prediction for the next time step, but the mean prediction is the same as the mean estimate, since a single moving average does not model trends.

The double moving average mean filter y_{0}(t) is a type of FIR low pass filter, i.e., it passes frequencies below the cutoff frequency f_{c} and attenuates frequencies above the cutoff frequency. The value N determines the cutoff frequency, which is inversely proportional to N (the cutoff period P_{c} is proportional to N). The filter coefficients sum to 1.0.

FIR mean filter difference equation:

IIR mean filter difference equation (requires proper initialization):

**Example:** Double moving average mean filter with length N = 10

Passes frequencies below the -3 dB (half power) cutoff frequency f_{c} of approximately 0.0734, which corresponds to a cutoff period P_{c} of approximately 13.6 time samples. Completely suppresses frequencies of 0.1, 0.2, 0.3, 0.4, and 0.5, which correspond to periods of 10, 5, 3.3333, 2.5, and 2 time samples, respectively. (Suppression occurs because, for example, the average value of a 10 time-sample period sine wave over 10 time samples is zero, the average value of two 5 time-sample period sine waves over 10 time samples is zero, etc.) There is a magnitude peak above 1.0 (i.e., 0 dB) at a period of approximately 27 time samples.

The double moving average linear trend filter y_{1}(t) is a type of FIR bandpass filter. The filter has a center (also called “resonant”) frequency f_{0}, corresponding to a center period P_{0}, which passes at maximum power. The value N determines the center frequency f_{0}, which is inversely proportional to N (the center period P_{0} is proportional to N). The filter coefficients sum to 0.0.

FIR linear trend filter difference equation:

IIR linear trend filter difference equation (requires proper initialization):

**Example:** Double moving average linear trend filter with length N = 10

The center frequency f_{0} is approximately 0.0417, which corresponds to a center period P_{0} of approximately 24 time samples. The filter completely suppresses frequencies of 0.1, 0.2, 0.3, 0.4, and 0.5, which correspond to periods of 10, 5, 3.333, 2.5, and 2 time samples, respectively.

The following S&P 500 daily price chart shows the double moving average mean (dashed blue line) and linear trend (solid blue line) for filter length N = 10. The single moving average mean (dashed red line) for filter length N = 10 is shown for comparison.

The amplitude of the linear trend filter output is proportional to the local slope of the price, i.e., the greater the amplitude, the steeper the slope, although the output can be affected by the presence of cycles and non-linear trends.

Trading signals using double moving average mean and linear trend filters can potentially be generated, for example, when:

- the price crosses above (buy) or below (sell) the mean line
- the mean line reaches a local crest (sell) or trough (buy)
- the linear trend line crosses above (buy) or below (sell) the zero line
- the linear trend line reaches a local crest (sell) or trough (buy)

or by a combination of these conditions.

The graph below illustrates the concepts of amplitude, crest, and trough:

Double linear weighted moving average (DLWMA) is a modified form of double moving average that uses linear weighted moving averages instead of moving averages to estimate the mean and linear trend. The double linear weighted moving average set of equations is:

where N is the number of input data points, i.e., the linear weighted moving average length N (N > 1), included in the two single linear weighted moving averages used to calculate the double linear weighted moving average, and x(t) represents the price at integer time t. The derivation of the double linear weighted moving average equations is shown in Appendix 2.

The double linear weighted moving average generates three main outputs: an estimate of the mean y_{0}(t) at time step t, an estimate of the linear trend y_{1}(t) at time step t, and a mean prediction y_{0}^(t) made at time step t for the next time step t+1. The linear trend prediction y_{1}^(t) for the next time step t+1 is the same as the linear trend estimate y_{1}(t), since a double linear weighted moving average does not model non-linear trends.

The single linear weighted moving average (LWMA) equations shown above are in FIR (non-recursive) form. The filter coefficients are linearly weighted with the greatest weights placed on the most recent input values. The IIR (recursive) form, which requires proper initialization, is:

Note that a single linear weighted moving average actually has two outputs: an estimate of the mean and a mean prediction for the next time step, but the mean prediction is the same as the mean estimate, since a single linear weighted moving average does not model trends.

The double linear weighted moving average mean filter y_{0}(t) is a type of FIR low pass filter, i.e., it passes frequencies below the cutoff frequency f_{c} and attenuates frequencies above the cutoff frequency. The value N determines the cutoff frequency, which is inversely proportional to N (the cutoff period P_{c} is proportional to N). The filter coefficients sum to 1.0.

FIR mean filter difference equation:

IIR mean filter difference equation (requires proper initialization):

**Example:** Double linear weighted moving average mean filter with length N = 10

Passes frequencies below the -3 dB (half power) cutoff frequency f_{c} of approximately 0.0894, which corresponds to a cutoff period P_{c} of approximately 11.2 time samples. There is a magnitude peak above 1.0 (i.e., 0 dB) at a period of approximately 24 time samples.

The double linear weighted moving average linear trend filter y_{1}(t) is a type of FIR bandpass filter. The filter has a center (also called “resonant”) frequency f_{0}, corresponding to a center period P_{0}, which passes at maximum power. The value N determines the center frequency f_{0}, which is inversely proportional to N (the center period P_{0} is proportional to N). The filter coefficients sum to 0.0.

FIR linear trend filter difference equation:

IIR linear trend filter difference equation (requires proper initialization):

**Example:** Double linear weighted moving average linear trend filter with length N = 10

The center frequency f_{0} is approximately 0.05, which corresponds to a center period P_{0} of approximately 20 time samples.

The following S&P 500 daily price chart shows the double linear weighted moving average mean (dashed blue line) and linear trend (solid blue line) for filter length N = 10. The single linear weighted moving average mean (dashed red line) for filter length N = 10 is shown for comparison.

Trading signals using double linear weighted moving average mean and linear trend filters can potentially be generated in a similar manner to those described for double moving average mean and linear trend filters.

Double exponential smoothing (DES) is similar to the double moving average, except that it uses exponential smoothing instead of moving averages to estimate the mean and linear trend ^{3}. The double exponential smoothing set of equations is:

where α is the exponential smoothing constant (0 <= α <= 1) used in the two single exponential smoothings used to calculate the double exponential smoothing, and x(t) represents the price at integer time t. The derivation of the double exponential smoothing equations is shown in Appendix 3.

Double exponential smoothing generates three main outputs: an estimate of the mean y_{0}(t) at time step t, an estimate of the linear trend y_{1}(t) at time step t, and a mean prediction y_{0}^(t) made at time step t for the next time step t+1. The linear trend prediction y_{1}^(t) for the next time step t+1 is the same as the linear trend estimate y_{1}(t), since double exponential smoothing does not model non-linear trends.

The single exponential smoothing (ES) equations shown above are in IIR (recursive) form, which requires proper initialization. The filter smoothing constant α is applied to the current input value and (1 – α) is applied to the previous filter output value. The FIR (non-recursive) form is:

Note that single exponential smoothing actually has two outputs: an estimate of the mean and a mean prediction for the next time step, but the mean prediction is the same as the mean estimate, since single exponential smoothing does not model trends.

The double exponential smoothing mean filter y_{0}(t) is a type of IIR low pass filter, i.e., it passes frequencies below the cutoff frequency f_{c} and attenuates frequencies above the cutoff frequency. The value of the exponential smoothing constant α determines the cutoff frequency, which is proportional to α (the cutoff period P_{c} is inversely proportional to α).

IIR mean filter difference equation (requires proper initialization):

**Example:** Double exponential smoothing mean filter with exponential smoothing constant α = 0.1772

The filter has about the same -3 dB (half power) cutoff frequency f_{c} of approximately 0.0734 (cutoff period P_{c }of approximately 13.6 time samples) as a double moving average filter with length N = 10. There is a magnitude peak above 1.0 (i.e., 0 dB) at a period of approximately 48 time samples.

The double exponential smoothing linear trend filter y_{1}(t) is a type of IIR bandpass filter. The filter has a center (also called “resonant”) frequency f_{0}, corresponding to a center period P_{0}, which passes at maximum power. The value of the exponential smoothing constant α determines the center frequency f_{0}, which is proportional to α (the center period P_{0} is inversely proportional to α).

IIR linear trend filter difference equation (requires proper initialization):

**Example:** Double exponential smoothing linear trend filter with exponential smoothing constant α = 0.1772

The center frequency f_{0} is approximately 0.0313, which corresponds to a center period P_{0} of approximately 32 time samples.

The following S&P 500 daily price chart shows the double exponential smoothing mean (dashed blue line) and linear trend (solid blue line) with smoothing constant α = 0.1772. The single exponential smoothing mean (dashed red line) with smoothing constant α = 0.1772 is shown for comparison.

Trading signals using double exponential smoothing mean and linear trend filters can potentially be generated in a similar manner to those described for double moving average mean and linear trend filters.

The alpha-beta (α-β) filter is used for object tracking in track-while-scan radar systems, based on a linear motion model ^{4}. The function of the tracking filter is to process noisy position measurement inputs into “smoothed” position and velocity estimate outputs. The alpha-beta tracking filter set of equations is:

where α is the position smoothing constant, β is the velocity smoothing constant, and x(t) is the observed position of the object (or price in this case) at integer time t. Note that the alpha-beta filter position estimate is analogous to the mean estimate and the velocity estimate is analogous to the linear trend estimate of the other filters described above. The α and β smoothing constants are subject to the following stability constraints:

The alpha-beta tracking filter generates three main outputs: an estimate of the position y_{0}(t) at time step t, an estimate of the velocity y_{1}(t) at time step t, and a position prediction y_{0}^(t) made at time step t for the next time step t+1. The velocity prediction y_{1}^(t) for the next time step t+1 is the same as the velocity estimate y_{1}(t), since the alpha-beta tracking filter does not model acceleration and higher order maneuvers.

Various alpha-beta filter smoothing constant relationship equations have been developed to calculate optimal values, based on an assumed underlying process model that approximates the dynamic behavior of the target or on a set of filter design objectives, such as providing good transient response and small noise and prediction error ^{5} ^{6}. They include:

Notes:

- Discounted least squares error (critically damped) smoothing constants α and β produce results equivalent to double exponential smoothing if

- The alpha tracking filter, which only estimates position, is comparable to single exponential smoothing and is closely related to the one-state steady-state Kalman filter, where the single state is position. Similarly, the alpha-beta tracking filter is closely related to the two-state steady-state Kalman filter, where the two states are position and velocity
^{7}.

Alpha-Beta Position Tracking Filter Frequency Response (α = 0.29896, β = 0.05295)

The alpha-beta position tracking filter y_{0}(t) is a type of IIR low pass filter, i.e., it passes frequencies below the cutoff frequency f_{c} and attenuates frequencies above the cutoff frequency. The α and β smoothing constant values determine the cutoff frequency of the filter.

IIR position tracking filter difference equation (requires proper initialization):

**Example:** Alpha-beta position tracking filter using random acceleration-based smoothing constants α = 0.29896 and β = 0.05295 The filter has a -3 dB (half power) cutoff frequency f_{c} of approximately 0.0769 (cutoff period P_{c} of approximately 13-time samples), similar to that of a double moving average mean filter with length N = 10. There is a magnitude peak above 1.0 (i.e., 0 dB) at a period of approximately 33-time samples.

The alpha-beta velocity tracking filter y_{1}(t) is a type of IIR bandpass filter. The filter has a center (also called “resonant”) frequency f_{0}, corresponding to a center period P_{0}, which passes at maximum power. The α and β smoothing constant values determine the center frequency f_{0} of the filter.

IIR velocity tracking filter difference equation (requires proper initialization):

**Example:** Alpha-beta velocity tracking filter using random acceleration-based smoothing constants α = 0.29896 and β = 0.05295

The center frequency f_{0} is approximately 0.04, which corresponds to a center period P_{0} of approximately 25 time samples, similar to that of a double moving average linear trend filter with length N = 10.

The following S&P 500 daily price chart shows the alpha-beta position (dashed blue line) and velocity (solid blue line) tracking filter using random acceleration-based smoothing constants α = 0.29896 and β = 0.05295.

Trading signals using alpha-beta position and velocity tracking filters can potentially be generated in a similar manner to those described for double moving average mean and linear trend filters.

For a time series with an underlying second order process, assuming that the current linear trend (velocity) y_{1}(t) is locally constant and using the same time step convention as is used for the one time-step predictions above, mean (position) predictions y_{0}^ at future integer time steps can be made at time step t, using the following equation:

One measure that can be used to evaluate the appropriate filter length or smoothing constant values to use with a particular time series is to calculate the root mean square error (RMSE) of the one time-step predictions of the filter over a sample of observations. The one time-step prediction error x_{e}(t) at each time step t is the difference between the input value x(t) at time step t and the prediction y_{0}^(t-1) made for time step t at the previous time step t-1:

The root mean square error over a sample of N observations is:

In general, the filter length or smoothing constant values that produce the minimum RMSE can be helpful in determining a useful setting. Unlike filters that are modeled on first order processes, filters modeled on second order processes will usually have a non-trivial minimum RMSE value when applied to financial time series. However, values that minimize RMSE may not necessarily correspond to maximum trading profitability. In addition, the value that minimizes RMSE in one sample of observations will not necessarily be the same in a different sample, due to the volatility, non-normality, and non-stationarity usually observed in financial time series.

While mean (position) filters modeled on second-order processes are able to follow input time series that contain a locally constant linear trend (velocity) with less lag compared to filters modeled on first-order processes, if the input time series contains a non-linear trend (acceleration or higher-order maneuver), for example, second-order mean (position) filter estimates will lag the input.

Second-order process linear trend (velocity) filters are bandpass filters that are “tuned” to a specific center frequency or period, based on the filter coefficients, with an associated phase response. As a result, if the input time series contains a cycle with a period that is *less* than the center period of the filter, the filter output will crest (trough) *after* the input time series cycle crest (trough). Conversely, if the input time series cycle period is *greater* than the center period, the filter output will crest (trough) *before* the input time series crest (trough). This behavior can be observed in the linear trend (velocity) filter outputs in the S&P 500 daily price charts.

Since financial time series are non-stationary with means and variances that change over time, the use of filters with fixed parameters will not perform well at all times for trading purposes. As a result, filter coefficients that are “fitted” to a particular portion of a time series history will not necessarily produce good results in the future.

I would like to thank Larry Stabile for reviewing this article and providing many helpful comments and suggestions.

For a second order process input with mean *a*, linear trend *b*, and normally distributed random noise ε(t):

a single moving average of length N estimates the mean value at each time step t over the last N observations. Assuming for a moment that ε(t) = 0, the mean estimates MA_{1}(t) form a straight-line ramp with slope *b* and lag (N – 1)/2 relative to x(t):

A single moving average MA_{2}(t), also of length N, of the mean estimates MA_{1}(t) forms a straight-line ramp with slope *b* and lag (N – 1)/2 parallel to MA_{1}(t):

Letting the mean filter output y_{0}(t) = *a* + *b**t and the linear trend filter output y_{1}(t) = *b*:

and solving the two equations for mean y_{0}(t) and linear trend y_{1}(t) gives:

For a second order process input with mean *a*, linear trend *b*, and normally distributed random noise ε(t):

a single linear weighted moving average of length N estimates the mean value at each time step t over the last N observations. Assuming for a moment that ε(t) = 0, the mean estimates LWMA_{1}(t) form a straight-line ramp with slope *b* and lag (N – 1)/3 relative to x(t):

A single linear weighted moving average LWMA_{2}(t), also of length N, of the mean estimates LWMA_{1}(t) forms a straight-line ramp with slope *b* and lag (N – 1)/3 parallel to LWMA_{1}(t):

Letting the mean filter output y_{0}(t) = *a* + *b**t and the linear trend filter output y_{1}(t) = *b*:

and solving the two equations for mean y_{0}(t) and linear trend y_{1}(t) gives:

For a second order process input with mean* a*, linear trend *b*, and normally distributed random noise ε(t):

single exponential smoothing with smoothing constant α estimates the mean value at each time step t. Assuming for a moment that ε(t) = 0, the mean estimates ES_{1}(t) form a straight-line ramp with slope *b* and lag (1 – α)/α (with an initial transient (1- α)^{t} that goes to zero as t increases) relative to x(t):

Single exponential smoothing ES_{2}(t), also with smoothing constant α, of the mean estimates ES_{1}(t) forms a straight-line ramp with slope *b* and lag (1 – α)/α (with an initial transient (1- α)^{t} that goes to zero as t increases) parallel to ES_{1}(t):

Letting the mean filter output y_{0}(t) = *a* + *b**t and the linear trend filter output y_{1}(t) = *b*:

and solving the two equations for mean y_{0}(t) and linear trend y_{1}(t) gives:

Notes:

- See this post for further background on the discussion below and see here for some details on simple trend-following systems ↩
- Brown, R. G.,
*Smoothing, Forecasting, and Prediction of Discrete Time Series*, Prentice Hall, 1962 ↩ - Brown, R. G.,
*Smoothing, Forecasting, and Prediction of Discrete Time Series*, Prentice Hall, 1962 ↩ - Benedict, T. R., and Bordner, G. W., “Synthesis of an Optimal Set of Radar Track-While-Scan Smoothing Equations”,
*IRE Transactions on Automatic Control*, AC-7 (4), 27-32, July 1962. ↩ - Navarro, A. M., “General Properties of Alpha Beta and Alpha Beta Gamma Tracking Filters”, Report PHL 1977-02, Physics Laboratory, National Defense Research Organization, Netherlands, January 1977. ↩
- Kalata, P. R., “The Tracking Index: A Generalized Parameter for α-β and α-β-γ Target Trackers”,
*IEEE Transactions on Aerospace and Electronic Systems*, AES-20 (2), 174-182, March 1984. ↩ - Painter, J. H., Kerstetter, D., and Jowers, S., “Reconciling Steady-State Kalman and Alpha-Beta Filter Design”,
*IEEE Transactions on Aerospace and Electronic Systems*, AES-26 (6), 986-990, November 1990. ↩

Trend-Following Filters: Part 1/2 was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>P-Hacking Via Academic Finance Research Conferences was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>- Manoela N. Morais and Matthew R. Morey
- Journal of Investing
- A version of this paper can be found here

This research is an update to “**Documentation of the File Drawer Problem in Academic Finance Journals**” published by the same authors in the Journal of Investment Management in 2018. A summary of that article can be found here. The “file drawer problem” refers to the idea that journal editors are predisposed to accepting articles for publication, only if they contain statistically significant results. Since editors are motivated by improving journal impact numbers and citation counts, this bias is not surprising. Articles with significant results are more likely to be cited and thus improve journal impact. Articles with nonsignificant results end up hidden away in the researchers’ *file drawer* and not submitted anywhere at all. Putting numbers to the problem in academic journals, the authors reported only 2.1% of 29 finance journals published nonsignificant results. Five of those 29 journals published no studies with insignificant results. This update examines the degree to which finance conferences exhibit a similar pattern.

- Is there a significant file drawer problem with respect to academic financial conferences?

- YES. The file drawer problem was observed to be at least as serious at finance conferences as it is in finance journals. The authors constructed a database of 3,425 empirical articles presented at the annual Financial Management Association for 5 years. The FMA is the largest academic conference by number of papers. Each paper examined was a stand-along research article. Roundtables, panel sessions, pedagogy series and debates were not included. Of the 3,425 articles, only 14 (or 0.41%) had nonsignificant results over the five year period. This is in comparison to the 2.1% of articles published in academic journals. It also appears that the problem within the FMA intensified between 2014 and 2018. Stunning.

As with journal publications, this article provides evidence that the file drawer problem is alive and well with respect to academic financial research conferences. It appears that potential presenters should avoid submitting analyses that have nonsignificant results otherwise risk rejection by the conference. As a result, conference attendants see a biased set of research presentations comprised of only those papers that exhibit statistical significance. The important question here how much this bias contributes to the use of p-hacking or datamining practices in order to achieve significant results. We have seen increasing attention paid to the practice of p-hacking, datamining, and other “bad habits” and the negative impact they have on the credibility of the discipline.

In 2017, Campbell Harvey (his Presidential Address for the Am Finance Assoc) took the issue one step further into the *intentional* misuse of statistics in empirical research. He defines intentional p-hacking as the practice of reporting only significant results when the researcher has conducted a myriad of statistical methods, empirical approaches or data manipulation. The underlying motivation for the use of such practices is the desire to be published in a world where finance journals are biased towards publishing significant results almost exclusively. The underlying risk to p-hacking and datamining, especially in the investments area, is the identification of significant results when they are likely just random events. Since random events by definition, do not repeat themselves in a predictable manner, the investment results are likely to fail on a going-forward basis. *Datamining and p-hacking go a long way in explaining why investment strategies fail out-of-sample, or even worse when they are implemented in the real world.*

This criticism can now be extended to finance conferences.

The file drawer problem is a publication bias where journal editors are much more likely to accept empirical papers with statistically significant results than those with statistically nonsignificant results. As a result, papers that have nonsignificant results are not published and relegated to the file drawer, never to be seen by others. In a previous paper, Morey and Yadav (2018) examined the file drawer problem in finance journals and found evidence that strongly suggests that such a publication bias exists in finance journals. In this follow-up study, we examine the prevalence of the file drawer problem at finance conferences. As such we are the first article in finance that we know of to attempt such an analysis. To do this, we examine every single empirical paper presented at the annual Financial Management Association (FMA) conference from 2014–2018. In an examination of 3,425 empirical papers, we found less than 0.5% of these papers had statistically nonsignificant results. These results suggest that there is also a significant file drawer problem at finance conferences.

P-Hacking Via Academic Finance Research Conferences was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>A Curious Combination: Momentum Investing, Tesla, and November 9th was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>“The plural of anecdote is not data”

I’ve used this quote to discount the validity of a single observation to explain much of anything. That observation is true. Yet the real quote, attributed to Stanford researcher Ray Wolfinger, is the following:

“the plural of anecdote is data”.

Ray Wolfinger

Every data point has a story and sometimes that story can illuminate a larger truth.

I think the anecdote of Tesla’s recent stock surge this year gives us some insight into the Momentum Factor, namely that stocks like Tesla that have already surged in price are emotionally impossible to own for those of us not day trading on Robinhood. And for good reason: they can fall out of favor fast! The potential for these massive price corrections and the psychological toil of owning them helps explain the return premium associated with the Momentum Factor. Tesla’s recent stock volatility and the emotions it triggers not only makes it a worthy poster child for momentum stocks but also provides some insight into the differences across both momentum factors and momentum funds. And dare I add when looking at the price action of similar stocks on November 9th, it is a warning on what may yet still be on the horizon.

The traditional academic “momentum” moniker most simply applies to stocks that have performed the best over the past year. These stocks over various time periods and across markets, both in and out of sample, have exhibited excess risk-adjusted returns as well documented on this blog (here is an example) as well as many others ^{1}. Equally well documented is the ability of momentum stocks to drop like a stone. In fact, on November 9^{th} of this year, one of the sharpest price reversals for these stocks in the last couple of decades occurred. Yet the event passed largely unnoticed by the general public (outside of some by the #fintwit community and modest coverage in the Wall Street Journal).

The scatter plot above captures this extreme relative move in the momentum factor on November 9th. The -14.5% return of the Dow Jones U.S. Thematic Market Neutral Momentum Index was almost 15 standard deviations from the norm ^{2}. Bloomberg’s US Pure Momentum Portfolio factor was down a more modest 4% or 4 standard deviations from the norm. Since 1999, the most significant daily drop in price was a meager 7.5% for the Dow’s on March 23rd, 2000, and a 1.7% drop for Bloomberg’s factor on 1/09/09. Hmmm, coming out of the Internet Bubble and Great Financial Crisis the Momentum Factor experienced much more than just a daily reversal. This is a well-documented period of gut-wrenching drawdowns for the factor ^{3}. French’s data goes back much further than the 01/01/2000 start of the other two factor indices and records 5 days exceeding a 10% drop, mostly in the 30s during the Great Depression ^{4}. Again, the largest drawn down in the Momentum Factor’s history also occurred over this time period and the proximity of the large daily reversals should give us pause.

And what about the large performance differences across the factors for this date? What first appears to be minor differences in both how and when to calculate the factor has major repercussions for returns. The Momentum Factor attempts to neutralize swings in the market by going long these momentum stocks and short out-of-favor stocks that have done poorly. But different quants calculate that factor differently. Ken French of Dartmouth sorts daily to calculate the Fama-French Daily Momentum Factor and combines both big company and small company portfolios to go long and short momentum. Bloomberg uses an implicit factor model using multivariate cross-sectional regression analysis designed to zero out exposure to other factors, including the market. Dow Jones sorts stocks based on 12 months returns within various sectors in attempt to minimize industry bets. French uses market value weights. To avoid idiosyncratic risk, Bloomberg uses the square root of market value when determining weights. Dow Jones uses equal weighting and rebalances quarterly.

Even momentum definitions can differ. Although momentum enjoys considerable consensus on what it means, namely 6 to 12 months of relative strong performance with an adjustment for well documented short term (up to a month) reversals, this also can lead to differences in returns. French-Fama’s factor uses returns starting 251 days back (roughly 12 months) and stopping 21 days back (roughly 1 month) to avoid short-term reversals. Bloomberg goes back 54 weeks and stops 2 weeks back. Dow Jones just goes back 52 weeks with no adjustment for short-term reversals.

Definitions aside, the differences in returns of the long-short measurements of the Momentum Factor also translates into differences in returns to long-only Exchange Traded Funds (i.e., ETFs) and mutual funds trying to capture the momentum strategy’s excess returns. As shown in the table below, on November 9^{th} most, but not all, of the listed funds dropped with the factor indexes while the U.S. Market, as measured by Vanguard’s Total Stock Market ETF <VTI> was up 1.25%.

Performance differences across funds have been especially stark recently. For example, from when the Momentum Factor began to suffer recently on September 2^{nd} through December 15^{th}, the largest Momentum ETF, iShares MSCI USA Momentum Factor <MTUM> was up only 1.9% whereas the Vanguard U.S. Momentum Factor ETF was down 3.5% while the US market, as measured by Vanguard’s Total Stock Market ETF <VTI> was up 6.5%. These performance differences, although not as glaring, also appear in other periods of poor momentum strategy returns. Details matter.

Note in my table, I include the returns of ARK Innovation ETF <ARKK> as well as Tesla and “Jon’s Bubble” stock portfolio. Let me admit the sad back story about why I did.

Back on September 9^{th} I proudly wrote to my clients that Tesla’s then drop in price may reflect a long-overdue correction.

I quote:

In my article on “Price” from earlier this year, I shared this graph constructed by Morgan Stanley analyst Adam Jonas as a humble admission that the then-current price of Tesla may prove to be way off in hindsight but, like all stock prices, was likely the best guess of value at the time. The future movement of stocks are just too hard to predict. Even after dropping 33% since the end of the month, Tesla’s stock price is still at a split-adjusted $1,651, up nearly 400% from the date of the article and over 3X’s his bull case.

Note my emphasis on past performance as a set-up in explaining why Tesla was overpriced. Ugh. I went on to reassure them that although I was not a stock picker, I stay clear of stocks like Tesla that trade at “crazy” valuations as part of my value bias when constructing stock portfolios. ^{5} I named Zoom, DocuSign, Peloton, and Square as similarly overpriced stocks despite booming businesses and great products. I then gloated that as a group, those 5 stocks were on average down 17.5% in the previous 3 days and we owned none of them.

*Yep, I got that one wrong. *

Tesla closed December 18th at $695 or a split-adjusted $3,475, more than double from when wrote my letter and up over 10 times since Adam Jones wrote his article declaring a potential upside of only 50% (and downside of 97%!). The group of 5 stocks which I now call my Bubble Portfolio together were up nearly 20% since my letter, well outperforming the market’s ^{6} otherwise stellar returns of 6.5% over the same time period ending December 15^{th}.

I picked the 4 additional stocks as examples along with Tesla of well-known success stories that also had little actual earnings and “crazy” valuations. What I didn’t factor in was that I was also creating the perfect (with hindsight!) Momentum Fund. Over the 11 months through October (remember, most measurements of momentum drop the latest month as stocks tend to revert from shorter-term movements ^{7}. My basket of 5 stocks was up 304% ^{8}. Tesla stock itself was up 488%.

As the table above shows, other Momentum Funds have had much smaller percentages of these companies but do have large exposures to Apple, a worthy momentum stock but hardly one of the market’s best-performing stocks. It is the biggest and when the fund also uses the market value as a criterion for position size, you see the effect. ^{9}

Next, take a look at ARK Innovation ETF <ARKK>, the hot fund for 2020. It first appears to be a momentum fund in disguise. I assume they construct their portfolios more thoughtfully than I did when creating my Bubble Portfolio, but the recent performance patterns are uncanny.

This begs the question, are Momentum Funds innovator funds in disguise? Certainly, not all momentum funds qualify if my 5 stocks are a proxy of any kind. Methodology and definitional differences explain much of the differences between Momentum Factors and Funds, especially the role market cap plays in weightings, but the idiosyncratic timing of rebalancing seems to have an even larger impact, at least recently. Granted, the most popular momentum fund holdings today look like a who’s who list of stay-at-home, order in, and the “hope for a vaccine” stocks: Apple, Amazon, Mirati Therapeutics, and Nvidia. But these stocks will eventually roll out to be replaced by other market favorites. For instance, last September when momentum ETFs took it on the chin as interest rates rose, their portfolios were dominated by REITs and Utilities.

Again, I want to use Tesla as an antidote to help dissect the long- and short-term success of momentum strategies. The Momentum Factor I believe acts as both efficient compensation for risk and as a tool to profit from common mispricing (gasp, market inefficiencies) due to well-established behavioral heuristics. A better understanding of this dynamic keeps me invested in the strategy even though I believe another correction is coming. My disgust with Tesla’s continued escalation solidifies my awareness that my biases to shy away from these types of stocks are deep and the pain of owning them, even via an ETF, is real.

Although I’m still climbing, the initial steps out of this deep-rooted bias against momentum were also arduous. I’m a product of Gene Fama’s Financial Theory course, TA’d at one time by both Cliff Asness of AQR fame, a firm built with a momentum foundation, and Wes Gray of Alpha Architect, the author of The Book on momentum investing who also hosts this blog. At the time, 1992, Fama was co-chairing Asness’s dissertation on momentum’s unexplained persistence to generate excess risk-adjusted returns ^{10}. He undoubtedly thus wasn’t naïve to the factor. By then, the empirical evidence supporting the outperformance of those stocks that have performed the best in the last 12 months (not including the first month) had been published by Narasimhan Jedadeesh ^{11}. Yet, it didn’t make our reading list. In fact, Jegadeesh (1990) was only barely mentioned in Fama’s 1991 seminal survey of attacks on market efficiency, Efficient Capital Markets: II, which concludes, “…the new research on the predictability of long‐horizon stock returns from past returns is high on drama but short on precision.”

It seems Fama had his biases, too.

But like the factor return itself, the evidence for employing momentum strategies kept compounding. Corey Hoffstein of Newfound Research provides a nice summary of the path of acceptance through both time periods and markets here. Eventually, even Fama and his prolific counterpart Ken French (2017) ^{12} “somewhat reluctantly” accepted momentum as a worthy factor for explaining the cross-section of stock returns. Although trained to recognized that supposed patterns in stock prices were illusions to those weaker minds seeking order in the reality of randomness ^{13}, eventually (with the help of Wes/Jack…thank you!), I, too, succumbed to the evidence. But it was hard, especially when looking under the hood to see the stocks these momentum ETFs owned. But general acceptance of the data hasn’t translated into an acceptance of the theory behind the data.

Modern Portfolio Theory has evolved in its broader efforts to explain differences in returns across stocks. From the vantage point of an efficient market assumption, Bill Sharpe constructed a world where investors look only for compensation for risk tied to their current portfolios (e.g., CAPM). Robert Merton’s world saw investors willing to hedge their current and future consumption with a variety of factors (e.g., Intertemporal CAPM or ICAPM). And Lu Zhang more recently argued for an investment world where differences in expected return are driven by firms’ decisions to invest (Investment CAPM) instead of investors’ desire to hedge. Momentum’s tendency to crash like it did on November 9^{th} and other periods favor viewing the excess returns generated by the Momentum Factor as fair compensation to disruptions in future consumption a la’ ICAPM. But my experience indicates it is also compensation for my stomach aches and sleepless nights. I’ll wait for someone else to build that fact into a workable pricing model.

Investing in a fund that owns stocks like Tesla let alone owning the stocks outright isn’t easy but why doesn’t the knowledge that these companies provide excess returns act as a tonic? Or why not alleviate the side-effects of momentum investing with Pepto Bismol and sleeping pills? In other words, why do the premium and my stomach aches persist? Behavioral heuristics also seems to have a role.

Anchoring is the tendency of mere mortals to place too much emphasis on the first piece of information we receive. Although I had an unbiased view of Tesla at the start of the year, I saw the analyst Adam Jonas give the stock an upside for 2020 of $500 as reasonable. No surprise that when Tesla reached a split-adjusted $2,000, I was incredulous.

We also place a greater value on avoiding a big loss over capturing a big gain. I can’t imagine buying any of my bubble stocks, including Tesla, right now ^{14}. Our tendency towards loss aversion makes us overly fear the second half of the idiom “pigs get fat and hogs get slaughtered” so much that we never fatten our portfolios.

But hogs many of these stocks become and a subsection of the investor community (again, see Robinhood) seem morbidly obese. “One more thin mint?” The momentum factor also seems to capture the tendency to believe that success is based on skill versus luck and breeds overconfidence and rationalizations like claiming Tesla could be the next Amazon.

Yes, Amazon’s similar valuation was once scoffed at, too. But rightfully so even with hindsight. Amazon shares dropped 94% between December 1999 and September 2001 even though its sales nearly tripled in the ensuing two years. It wasn’t until 2007 and sales had increased over 600% before it regained its stock price from the end of 1999.

In short, Tesla’s stock performance makes me squirm. Back in September I let my clients know that I thought the valuation was crazy. But TSLA doesn’t care what I think and doubled yet again. It takes all the strength than I can muster to invest in stocks like Tesla that have already skyrocketed in price, and even then I outsource the task to momentum ETFs. It also takes a higher expected return to attract investors. So far this year, many, but certainly not all, momentum funds exceeded those high expectations. The devil is in the details on why some versus others have performed well, but the results show up in the holdings: those weighted most toward stocks of companies experience product innovation and growth even in the face of COVID-19 have smoked the market.

Will these stocks likely tumble back to earth in a flame at some point. History tells us yes. And history tells us that November 9^{th} was an almost unprecedented extreme rotation out of momentum and major moves are typically clustered. Three antidotes certainly don’t translate into data, but given that the other large reversals occurred coming out of The Great Depression, The Internet Bubble and The Great Financial Crisis when the momentum factor suffered some of its largest drawdowns does make one pause. Having already feasted plenty from the trough, let’s hope momentum factors and funds will rotate out of the current crop of market darlings this time and into the new hot stocks that I seem equally mentally programmed to want to avoid.

Notes:

- see especially the blogs at Newfound Research and AQR ↩
- implying this distribution is anything but normal! ↩
- See Table 8.5 of the book Quantitative Momentum ↩
- As of publishing, French hasn’t updated his data for November ↩
- Although direct indexing more easily allows for tax-loss write-offs, I more typically use ETFs and only use individual stocks when trying to manage around legacy assets or professional risk. ↩
- well, Vanguard’s definition of the market, the ETF (VTI) ↩
- see
**Asness, C. (1994), “Variables that Explain Stock Returns,” Ph.D. Dissertation, University of Chicago.**An adapted and extended version of this paper can be found at AQR here. ↩ - rebalanced on 12/31/2019 and 09/02/2020 ↩
- Note that SPDRs S&P 1500 Momentum Tilt ETF as S&P requires a certain amount of profitability prior to even entering the universe for consideration. Tesla only just qualified. ↩
**Asness, C. (1994), “Variables that Explain Stock Returns,” Ph.D. Dissertation, University of Chicago.**An adapted and extended version of this paper can be found at AQR here. ↩**Jegadeesh, Narasimhan, 1990, Evidence of Predictable Behavior of Security Returns, The Journal of Finance, 45 (July), 881-898**↩-
**Fama, Eugene F., and Kenneth R. French, 2017, Choosing Factors, forthcoming, Journal of Financial Economics.**↩ - see A Random Walk Down Wall Street, written by Burton Gordon Malkiel ↩
- In fact I did when I outsourced the task to my Momentum ETFs ↩

A Curious Combination: Momentum Investing, Tesla, and November 9th was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Investing Based on Who you Follow on Social Media? A Real Thing? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>- Manuel Ammannt and Nic Schaub
*Management Science,*2020- A version of this paper can be found here

We have written in the past about the links between social media, investing and future stock returns ( here, here, and have a full chapter covering the topic in our book). As we turn to social media for our friendships, entertainment, confirmation bias, and news, it’s little surprise that active traders would begin using it as a potential source of sentiment information and/or as a way to ‘talk their book.’ That investors are turning to these new sources for information isn’t particularly shocking, however, these developments may become more informative going forward as smaller investors have been re-entering the market. In this paper, the authors ask:

- Do individual investors rely on investment-related Internet postings when making investment decisions?
- Do postings help individual investors identify investment strategies that deliver superior performance in the future?
- Are there cross-sectional differences in the relation between comments posted by traders and the trading behavior of followers?

The research team analyzed a leading European social trading platform, the sample is made up of about 30,000 comments from traders with replicating transactions of followers, which amounts to €234 million over the time period from January 2013 to December 2014, the authors find:

- YES- The posting of comments is associated with a significant increase in the trading activity of followers. In fact, if a trader posted a comment yesterday, today’s net investments of followers in the shared trading strategy increase by about 6% compared to the average daily net investments for the same portfolio (and higher activity lasts for about 3 weeks). Additionally, when looking at the tone of comments, a one standard deviation increase in the fraction of positive words is associated with a significant increase in net investments of followers by about 4% on average.
- NO- Neither the posting of comments nor the tone of comments have predictive power for the future performance of traders’ portfolios. Additionally, trades of followers executed after the posting of comments deliver about the same performance as trades of followers executed on all other days. Both types of trades tend to underperform common benchmarks.
- YES- A highly significant reaction following the posting of comments for small investors but no reaction for large investors. This suggests that it is mainly unsophisticated individuals who rely on investment-related Internet postings when making investment decisions.

The authors perform a number of robustness checks confirming the results.

Investors hunting for an edge will turn anywhere and the less sophisticated investor can be convinced that they “know” something by finding an “expert” on a social media platform to guide them to higher returns. This paper suggests that it is primarily unsophisticated individuals who rely on the opinions of others shared on social media platforms when making investment decisions, but there is not much evidence that online postings help those unsophisticated individuals improve their investment quality.

Many people share investment ideas online. This study investigates whether individual investors trade on investment-related Internet postings. We use unique data from a social trading platform that allows us to observe the shared portfolios of traders, their posted comments, and the replicating transactions of followers. We find robust evidence that followers increasingly replicate shared portfolios of traders after the posting of comments. However, postings do not help followers identify portfolios that deliver superior performance in the future. In a cross-sectional analysis, we show that it is mainly followers who are typically considered to be unsophisticated who trade after comment postings.

.

Investing Based on Who you Follow on Social Media? A Real Thing? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Is Size a Useful Investing Factor or Not? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>In their 2018 study, “Fact, Fiction, and the Size Effect,” (Summary) Ron Alquist, Ronen Israel, and Tobias Moskowitz, members of the research team at AQR Capital Management, concluded that there is no strong empirical evidence to support a size premium. However, they did add that size can be an important factor for explaining mutual fund returns and that other factors, such as value, tend to be more powerful among smaller stocks—which is not supportive of there being a small-cap versus large-cap effect but might be a reason to overweight small-cap stocks in long-only constrained factor portfolios. Extending the 2018 *Journal of Financial Economics* paper, “Size Matters, if You Control Your Junk,” by Clifford Asness, Andrea Frazzini, Ronen Israel, Tobias Moskowitz, and Lasse Pedersen, they then “saved” the size effect by demonstrating that it is made much stronger (and implementation costs are reduced) when size is combined with the newer common factors of profitability, quality and defensive (low beta). Alquist, Israel, and Moskowitz noted:

“Controlling for quality resurrects the size effect after the 1980s and explains its time variation, restores a linear relationship between size and average returns that are no longer concentrated among the tiniest firms, revives the returns to size outside of January and simultaneously diminishes the returns to size in January—making it more uniform across months of the year, and uncovers a larger size effect in almost two dozen international equity markets, 30 where size has been notably weak. These results are robust to using nonmarket-based size measures, making the size premium a much stronger and more reliable effect after controlling for quality.”

The above findings are consistent with those of Mikheil Esakia, Felix Goltz, Ben Luyten and Marcel Sibbe, authors of the study “Size Factor in Multifactor Portfolios: Does the Size Factor Still Have Its Place in Multifactor Portfolios?” (Summary) published in the Winter 2019 issue of *The Journal of Index Investing*. They concluded: “Our results suggest that the size factor improves model fit, delivers a significant positive premium in the presence of other factors, and contributes positively to the performance of multifactor portfolios. Omitting the size factor has substantial cost to investors, which often exceeds that of omitting other popular factors.” They also observed that size is included as an explanatory factor in all major asset pricing models (three-, four-, five- and q-factor). Confirming their conclusion, in their 2015 study “A Five-Factor Asset Pricing Model,” Eugene Fama and Ken French found that spanning regression tests on the size factor produces reliable intercepts with respect to the other factors, suggesting it has explanatory power over returns not captured by them.

David Blitz and Matthias Hanauer contribute to the literature on the size premium with their September 2020 paper “Settling the Size Matter.” For the U.S. their data sample covered the period July 1963 to December 2019 (Fama-French/AQR data) or January 1967 to December 2019 (q-factor data), which are the longest periods for which all the required data series are available. They also considered international samples, with data from July 1990 to December 2019 (Fama-French data) or July 1993 to December 2019 (AQR data). All portfolios are capitalization weighted, and all returns are in U.S. dollars. Following is a summary of their findings, which are consistent with the papers discussed above:

- The U.S. size premium was 0.19% per month with a t-statistic of 1.68, weakly significant at the 10% confidence level. However, this size premium drops to an insignificant 0.08% after adjusting for market beta exposure.
- The U.S. size premium remained absent when additionally controlling for the classic value and momentum factors, but jumped to 0.22% per month (t-stat = 2.06) when adding the new Fama-French factors of profitability and investment. The main driver of this boost was a highly significant negative loading on the profitability factor, RMW (which is highly correlated with the quality factor, QMJ, from the 2018 paper “Quality Minus Junk” by Clifford Asness, Andrea Frazzini and Lasse Pedersen).
- Replacing profitability with the QMJ factor resulted in a highly significant 0.42% per month size premium (t-stat = 3.98), driven by a strong negative loading on the QMJ factor. This confirms the AQR conclusion of restoring the size premium when controlling for junk. Even stronger results were found when using the q-factor model.

- For international stock markets, size also loads negatively on quality factors, and the size premium improves once controlling for quality, though it remains statistically indistinguishable from zero.
- In the U.S. the added value of SMB in time-series regressions is entirely driven by the short side of quality factors. There is no size premium when controlling for the long side of quality factors.

Despite these findings, like the authors of the previously mentioned studies, Blitz and Hanauer concluded:

“This result does not imply that investors should generally strive for size neutrality, in particular when it comes to long-only factor strategies. … The fact that other factors, such as value, tend to be stronger in the small-cap space may justify a structural overweight in small-cap stocks even if the size premium itself is zero.”

They added:

“Thus, a tilt towards small-cap stocks in long-only factor strategies can serve as a powerful catalyst for unlocking the full potential of these other factors.”

They concluded:

“For long-only investors, this means that an overweight in small-cap stocks may be desirable even if there is no size premium because small-cap stocks can serve as a powerful catalyst for unlocking the full potential of other factors, such as value and momentum. The higher expected return from targeting other factors in the small-cap space has to be balanced against the systematic risk that comes along with small-cap exposure, in particular the risk of small-cap stocks, in general, lagging the capitalization-weighted index by a substantial amount or for a prolonged period of time.”

Having reviewed the research findings, we can also review the evidence from live, systematic small-cap mutual funds—the true test of a realizable size premium.

Based on their research, Dimensional uses screens in its fund construction rules to eliminate lottery and “junky” stocks (that is, penny stocks, recent IPOs, stocks in bankruptcy, and small stocks with high investment and low profitability). In addition, since 2013 Dimensional has incorporated screens for profitability. It added a screen for high investment in 2019. The table below shows the simulated returns to each market category. Note how exclusions improve returns.

By reviewing the results of Dimensional’s small-cap funds, we can determine if there has still been a small-cap premium, controlling for junk (and profitability), that investors could have captured, not only in the U.S. but also in developing and emerging markets.

So that we can use all live funds, we will examine the more than 21-year period from January 1999 through August 2020 ^{1}.

For the more than the 21-year period from January 1999 through August 2020, in each case there was an annualized size (small) premium, ranging from 1.8% to as much as 4.4%. These results are over the period where supposedly the size premium had disappeared (though in “Size Matters, if You Control Your Junk,” the authors do show slight improvement in the post-2000 period relative to the initial period after Banz published his paper), but importantly, these results were after screens that attempt to eliminate small, junky stocks. These results were net of not only expense ratios but all implementation costs, while index returns do not include any costs that are incurred by live funds. Long live the size premium (controlling for junk)!

Notes:

- Full disclosure: My firm, Buckingham Strategic Wealth, recommends Dimensional funds in constructing client portfolios. ↩

Is Size a Useful Investing Factor or Not? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Placement Agents In Private Equity, Are They Any Good? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>- Matthew D. Cain, Stephen B. McKeon, and Steven Davidoff Solomon
- Journal of Financial and Quantitative Analysis
- A version of this paper can be found here

The authors attempt to explain the drivers of the dramatic increase in the use of placement agents in private equity that has occurred since the early 1990s. The discussion is framed around two competing hypotheses: Are agents simple influence peddlers or do they represent a value proposition to GPs in search of information and/or certification of reputation? Interestingly, this research finds support for both. Using a database of 32,526 investments in 4,335 PE funds, the authors can uniquely lay claim to results specific to a universe of entirely professional investors.

- What is the value proposition for using a placement agent (PA) in private equity?
- Under what conditions is a general partner (GP) likely to employ a placement agent?
- Does the use of placement agents result in higher returns for investors?

- Placement agents generally provide services to general partners that effectively reduce the cost of information searches and reduce the required labor as the fund-raising process moves forward. For example: (1) PAs are well able to identify sources of capital from a deep bench of institution investor contacts; (2) PAs are also a reliable source of information on the current state of market conditions as they relate to fund-raising including fee structures, distribution rights, governance issues, clawback provisions and so on; (3) they often assist in creating the ‘narrative’ for GP’s intended use of funds and in the preparation of marketing materials; (4) PAs may act as facilitators for investor meetings and communications between GPs and LPs; and (5) they provide valuable assistance with due diligence. The newer the GP, the more likely is the GP to take advantage of some or all of the services of placement agents. For those unfamiliar with the relationship structure, Figure 1 provides a graphical representation what is typical between GPs, LPs, the Fund, and PAs.

2. The decision to use a PA is driven by a myriad of reasons. primarily driven by characteristics internal to the GP, the authors document that PAs are associated with larger Funds and with Fund of Fund (FOF) structure types on the LP side. The later result is somewhat surprising as FOFs embed 3 levels of intermediation: in addition to the PA, intermediation is also practiced by the FOF and the PE fund that invests in the portfolio companies. Not exactly a value-add proposition. However, when combined with the expectation that PAs are more closely affiliated with complex fund-raisings it does seem less disconcerting. For example, the authors find that GPs domiciled in different countries than LPs are more likely to agents experienced with cross-country norms and standards. Public pensions and endowments apparently have a lower likelihood to use agents, perhaps due to the predominance of consultant advice among those organizations. The authors find PAs are used more often during periods of higher inflows to the PE asset class (see chart below), With respect to fund type, buyout funds are more likely than venture or real estate funds to use PAs. This was pronounced if the fund had a greater diversity of LP countries of origin. Same relationship if the fund is either at it’s initial offering or otherwise early in the sequence of offerings. However, the use of agents is lower among GPs with US headquarters. All in all, it appears that the evidence is consistent with two hypotheses. First, the authors present data supporting the idea that PAs perform an important role in the information sourcing and certification/due diligence portions within the fund-raising process. However, the finding that PA affiliated funds are increasingly associated with poor returns leads to a different, more troubling conclusion. The authors explain:

We document further evidence supporting

investor capture and influence peddlingamong certain placement agents. We find that the strength of investor– agent relationships is negatively correlated with returns. In other words, the higher frequency with which an LP invests in funds affiliated with a given placement agent, the worse the returns are for that LP.

*3*. NO. The analysis of the relationship between fund returns and placement agents tested the difference between equally weighted IRRs for fund with PAs and those without PAs. They are sorted on fund type, investor type and geographic location of GP to LP. For all conditions, IRRs were higher for funds without agents than for funds with at least one agent. Take a look. The details are not pretty if one is a placement agent.

However, the authors also present evidence that investors in agent affiliated funds exhibit lower volatility and lower drawdowns. Perhaps PAs contribute to the tradeoff between risk and return and should be viewed with that lens.

As the first study to identify the characteristics of LPs/GPs using placement agents and the resulting returns to investors to affiliated funds with and unaffiliated funds, it implies context to policy makers and regulators. For example, an outright ban on agents may produce negative, although unintended, consequences. Top-tier agents may indeed provide value to investors in terms of providing information and due diligence, as well as a conduit to mitigate return volatility.

Intermediation in private equity involves illiquid investments, professional investors, and high information asymmetry. We use this unique setting to empirically evaluate theoretical predictions regarding intermediation. Using placement agents has become nearly ubiquitous, but agents are associated with significantly lower abnormal returns in venture and real estate funds, consistent with investor capture and influence peddling. However, returns are higher for buyout funds employing a top-tier agent and for first-time real estate and venture funds employing an agent, and are less volatile for agent-affiliated funds, consistent with a certification role. Our results suggest heterogeneous motives for intermediation in the private equity industry.

Placement Agents In Private Equity, Are They Any Good? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Buying Quality: Is the Juice Worth the Squeeze? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>What is a yield-hungry investor supposed to do in this environment? Increasing the allocation to equities seems like the only choice for most investors, leaving alternatives like private equity aside. However, the outlook for equities is also not rosy given high valuations in the US and poor demographics in most developed and many emerging markets. Economic growth depends on healthy demographics. And there is also the rising amount of debt in society, which is bound to have negative consequences on growth at some point.

The most frequent argument to escape this dire outlook is to focus on high-quality companies with sustainable growth, defensible business models, high profitability, and low leverage. Intuitively, using our quick-reaction, i.e., “system one,” thinking style, this advice sounds rational. It isn’t until we kick in our rational brain, i.e., “system two,” where we can question seemingly simple and clear advice. Such great stocks are likely to be expensive as they are highly appealing to most investors, and high-profit margins tend to be disrupted by new market entrants.

Although we can not forecast how high-quality stocks will perform in the future, we can certainly evaluate their historical performance. In this short research note, we will evaluate high-quality companies through the lens of quality-themed ETFs in the US.

We focus on all quality ETFs in the US, which broadly come in two flavors: pure quality and quality income. The stock selection process varies significantly across ETF issuers as there is no standard definition for quality. However, it tends to be multi-metric approaches that include ratios like earnings stability, leverage, and profitability.

We observe that the assets under management in quality and quality income ETFs have almost doubled between 2018 and 2020. However, it is worth highlighting that the aggregate amount of assets of slightly under $30 billion represents a fraction of the capital allocated to other smart beta categories. For example, investors have allocated approximately $70 billion to low volatility ETFs, which is surprising given that this factor only became popular post the global financial crisis in 2009. Even more surprising is that more than $200 billion are invested in growth ETFs, despite there being almost zero academic support on this investment style having any useful characteristics like generating outperformance or reducing risk.

**SELECTING QUALITY ETFS**

Investors can select ETFs qualitatively, quantitatively, or apply a combination of both approaches. A qualitative approach is to simply search for ETFs that contain terms like “Quality” or “Defensive” in their name, which results in less than 15 ETFs in the US that charge an average of 16 basis points (bps) per annum. It is worth noting that one product from iShares dominates this list with an 85% share of the assets under management.

Similarly, there are less than 10 quality income ETFs and two of these have an 82% market share. The average management fee is 32 bps, i.e. double the fee of quality-only products. The high fees are explained by quality income ETFs being primarily bought by income-loving retail investors, who are not particularly price-sensitive.

A quantitative approach to selecting quality ETFs would be to take a quality factor and regress the universe of all ETFs against that. Naturally, this requires defining the quality factor in the first place. In this analysis, we will use the profitability factor from the Fama-French five-factor model, i.e. also called robust minus weak (RMW), which measures the operating profitability of companies.

Somewhat surprisingly, quality and quality income ETFs do not feature particularly high factor betas to the profitability factor. In fact, the betas of long-term US government bonds, gold, and growth ETFs are approximately the same. The low betas of quality and quality income products can be attributed to ETF issuers using several metrics in the stock selection process versus solely focusing on profitability.

**PERFORMANCE OF QUALITY ETFS**

Next, we construct equal-weighted indices for quality and quality income ETFs, which highlight that both significantly underperformed the S&P 500 in the period from 2005 to 2020. Investors might question if management fees explain the underperformance. However, the management fees have become almost marginal in recent years and the underperformance has steadily been expanding, which implies different forces at work.

It is interesting to note that there was very little differentiation between quality and quality income, despite substantially different stock selection processes. Furthermore, a portfolio comprised of the 30% of stocks featuring the highest profitability would have outperformed all three indices, albeit before transaction costs.

**REDUCING RISK WITH QUALITY ETFS**

However, quality-themed products are not bought for outperformance, but for risk reduction. If quality ETFs reduced maximum drawdowns during stock market crashes, then they fulfilled their primary purpose and can be considered accretive for investors’ portfolios.

Unfortunately, neither quality nor quality income ETFs had significantly lower maximum drawdowns during the global financial crisis of 2009 or the more recent COVID-19 crisis of 2020, which resulted in lower risk-adjusted returns compared to the S&P 500. In contrast, the portfolio comprised of highly profitable stocks achieved meaningful reductions in drawdowns in both crisis periods.

**SECTORAL BIASES OF QUALITY ETFS**

In order to further evaluate the underperformance of the quality-themed ETFs, we investigate if there are sectoral biases compared to the S&P 500. We observe that quality ETFs had minor overweights to healthcare and consumer staples stocks and underweights to consumer discretionary and financials.

In contrast, the sectoral biases of quality income ETFs were significantly different, which is explained by the focus on high dividend-yielding stocks with quality characteristics. Specifically, there is a large overweight to industrials and basic materials and underweight to technology stocks. The latter is intuitive as many technology companies do not pay dividends, which makes them rank low when measured by their dividend yield.

Given the different sectoral biases of quality and quality income ETFs, it is surprising that they performed so similarly. The underperformance of quality income ETFs to the S&P 500 is simply explained by the underweight in the technology sector as this was one of the best-performing sectors in the period from 2000 to 2010.

The underperformance of quality ETFs is more difficult to explain as there is no underweight to technology stocks. However, a closer inspection shows that there is a much lower weight to the best-performing stocks, i.e. Facebook, Apple, Amazon, Netflix, Microsoft, and Google (FAANMG). A significant portion of the returns of the S&P 500 over the last decade can be attributed to these few stocks and having less exposure to these generated a large tracking error.

**FURTHER THOUGHTS**

Although the exposure to the FAANMG stocks was low in quality ETFs, some of these like Microsoft or Google can be considered high-quality stocks due to attractive operating margins and low leverage. However, what makes these companies unique is that they have become quasi-monopolies that face little disruption from new entrants. Although not impossible, it is currently difficult to imagine a firm that takes down Amazon given its massive scale.

It is interesting to contemplate building a portfolio of new monopoly companies (the ticker NeMo still seems available) with quality characteristics. However, these wonderful companies do come at high valuations and the risk of government interventions, which is becoming a larger risk as these companies are becoming more and more powerful.

**RELATED RESEARCH**

- Using Quality to Separate Good and Bad Value Stocks
- Picking Profitable Companies Can Be Unprofitable
- Integrated Value, Growth & Quality Portfolios
- Quality Factor: How to Define It?

Buying Quality: Is the Juice Worth the Squeeze? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Global Factor Performance: December 2020 was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>- Standardized Performance
- Factor Performance
- Factor Exposures
- Factor Premiums
- Factor Attribution
- Factor Data Downloads

Notes:

- free access for financial professionals ↩

Global Factor Performance: December 2020 was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Early Female Investors, More Independent than Previously Thought? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>- Graeme G. Acheson; Gareth Campbell; Áine Gallagher and John D. Turner
*Economic History Review,*2020- A version of this paper can be found here

When we think of the investing community of the late 19th Century and early 20th Century, our minds might immediately think of characters such as Rich Uncle Pennybags ^{1}. It turns out that Uncle Pennybags should be joined, if not replaced, by “Rich Aunt Stuffed-Pockets”. Scholars have documented the rise of women investing during the nineteenth century but this paper focuses on answering two important questions about the development of female investors:

- How did this phenomenon progress into the twentieth-century?
- Whether women shareholders over a century ago behaved differently from their male counterparts?

By analyzing the shareholder constituencies of railways ^{2}, which were the largest public companies at the time and a popular investment among the middle class, the authors find:

- Women were playing an important role in financial markets in the early twentieth century: there is evidence of the growing importance of women shareholders from 1843, when they made up about 11 percent of the Great Western Railway shareholder base, to 1920 when they constituted about 40 percent of primary shareholders. By the early twentieth century, women represented 30 to 40 percent of shareholders in each railway company in our sample, which is in line with estimates of the number of women investing in other companies at this time.
- At a time when joint shareholdings were fairly common,
- Women were much more likely to be solo shareholders than men, with 70 to 80 percent of women investing on their own, compared to just 30 to 40 percent of men. When women participated in joint shareholdings, there was no discernible difference as to whether they were the lead shareholder or the secondary shareholder, whereas the majority of men took up a secondary position in their joint shareholdings.
- Women were more likely than men, and solo investors more likely than joint shareholders, to invest locally. This suggests that while men may have used joint investments as a way of reducing the risks of investing at a distance, women preferred to maintain their independence even if this meant focusing more on local investments.
- Male and joint shareholders were more likely than female and solo shareholders to hold multiple railway stocks. This could imply that men were using joint shareholdings as a means of increasing diversification. In contrast, women may have been prioritizing independence, even if it meant being less diversified.

These findings provide evidence that women shareholders were acting independently by choosing to take on the sole risks and rewards of share ownership when making their investments as a single shareholder as opposed to sharing the risks and rewards via a joint shareholding. The conclusions of this paper paints a more nuanced picture of how we should think about female investors in the past.

The early twentieth century saw the British capital market reach a state of maturity before any of its global counterparts. This coincided with more women participating directly in the stock market. In this paper, we analyze whether these female shareholders chose to invest independently of men. Using a novel dataset of almost 500,000 shareholders in some of the largest British railways, we find that women were much more likely to be solo shareholders than men. There is also evidence that they prioritized their independence above other considerations such as where they invested or how diversified they could be.

Notes:

Early Female Investors, More Independent than Previously Thought? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Profitability Factor Details: Taxable Income is Tied to Future Profitability and Returns was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Following is a summary of his findings:

- Profitability, as measured by the ratio of gross profits to assets, has roughly the same power as the book-to-market ratio (a value measure) in predicting the cross-section of average returns.
- Surprisingly, profitable firms generated significantly higher returns than unprofitable firms despite having significantly higher valuation ratios (for instance, higher price-to-book ratios).
- Profitable firms tend to be growth firms, meaning they expand comparatively quickly. Gross profitability is a powerful predictor of future growth as well as of earnings, free cash flow, and payouts.
- The most profitable firms earned returns 0.31 percent per month higher on average than the least profitable firms (t-stat = 2.49).
- The abnormal return (alpha) of the profitable-minus-unprofitable return spread relative to the Fama-French three-factor model was 0.52 percent per month (t-stat = 4.49).
- The returns data were economically significant, even among the largest, most liquid stocks.
- Gross profitability has more power in predicting the cross-section of returns than earnings-based measures of profitability.
- Controlling for profitability dramatically raises the performance of value strategies, especially among the largest, most liquid stocks. Controlling for book-to-market ratio improves the performance of profitability strategies. Controlling for profitability provides less help for other value strategies because, while book-to-market is negatively correlated with profitability, other value metrics (such as price-to-cash-flow and enterprise-value-to-EBITDA, or earnings before taxes, interest, depreciation, and amortization) are positively correlated with profitability.
- While the more profitable growth firms tend to be larger than less profitable growth firms, the more profitable value firms tend to be smaller than less profitable value firms.
- Strategies based on gross profitability generate value-like average excess returns even though they are actually growth strategies.
- Because both gross-profit-to-assets and book-to-market ratios are highly persistent, the turnover of both the profitability and value strategies is relatively low.
- Strategies built on profitability are growth strategies, so they provide an excellent hedge for value strategies. Adding profitability on top of a value strategy reduces the strategy’s overall volatility.

Building on Novy-Marx’s work, in their 2020 study “ On the Conjoint Nature of Value and Profitability,” Sunil Wahal and Eduardo Repetto showed that combining the two strategies, tilting exposure to the two factors, in long-only portfolios improved the performance of value strategies.

Bradley Blaylock, Bradley Lawson, and Michael Mayberry contribute to the profitability literature with their study “ Taxable Income, Future Profitability, and Stock Returns,” which was published in the July-August 2020 issue of the Journal of Business, Finance, and Accounting. They examined how taxable income relates to future performance. They measured performance along three different dimensions: (1) future pretax cash flows, (2) future pretax book income, and (3) future ‘Street’ pretax earnings. Their data sample covered the period 2002 to 2016. They regressed one, two, and three-year-ahead future performance measures on taxable income and controlled for either pretax book income or its components (i.e., cash flows and accruals).

Following is a summary of their findings:

- Taxable income was positively associated with future pretax cash flows, pretax book income, and Street pretax earnings over a three-year horizon. It ceased to be a reliable signal of future performance by year t+4.
- A one standard deviation increase in taxable income predicted a 9.2% to 24.7% increase in future performance for year t+1.
- There was a significantly positive association between taxable income and analysts’ future pretax forecasts across all time horizons—taxable income not only predicts future pretax performance but also influences analysts’ expectations of future performance.
- There is no significant association between taxable income and future forecast errors—analysts efficiently utilize taxable income as a useful signal of multiple performance measures and employ these signals in their forecasting process.

Their findings led Blaylock, Lawson and Mayberry to conclude:

Overall, our results are consistent with taxable income being a signal of firms’ fundamental values. That is, higher taxable income predicts stronger future performance.

They added:

We find a significantly positive association between taxable income and analysts’ future pretax forecasts, consistent with taxable income influencing future earnings expectations.

The research demonstrates that profitability provides incremental explanatory power to the cross-section of returns while also providing a premium that has been persistent, pervasive around the globe, robust to various definitions, and implementable (low turnover). In addition, adding exposure to the profitability factor provides a portfolio diversification benefit, as it has exhibited low to negative correlation to the market beta, size, value, and momentum factors. Such benefits are why fund families such as AQR, Alpha Architect, Avantis, BlackRock, Bridgeway, and Dimensional incorporate the strategy into portfolio construction design. ^{1}

Notes:

- (Full disclosure: My firm recommends funds from the AQR, Avantis, BlackRock, Bridgeway, and Dimensional fund families in client portfolios.) ↩

Profitability Factor Details: Taxable Income is Tied to Future Profitability and Returns was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>A Short Research Library Outlining Why Traditional Stock Picking is Challenging was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>And while we can never say that one approach always dominates another approach, we can make general arguments for and against different approaches based on empirical evidence and common sense. For example, on average, voodoo investing is less repeatable and transparent than evidence-based systematic approaches. ^{1}

What follows is a short summary of research that Jack and I put together that outlines why traditional discretionary stock-picking, on average, is a poor idea. ^{2} Sure you can win, but the odds aren’t in your favor. If you are exploring stock picking, or have clients who claim to be Warren Buffett, we recommend you sit down and review the materials discussed below.

If you still walk away with a desire to play the game, go for it. As a recovering member of the stock-picking anonymous club, I emphathize with those who are confident in their ability to be “the one” that bucks the trend. I just don’t think it is a great idea.

We’ll break this short library of articles/research into 3 sections:

- The challenge of individual buy and hold stock return distributions:
*most stocks fail, miserably.* - The empirical evidence outlining the performance of active stock-pickers:
*the vast majority add no value, only noise and costs.* - The ability for systems to replicate (with less bias!) the capabilities of active stock-pickers:
*machines can do it cheaper and more efficiently.*

- Do stocks outperform treasury bills?
- Almost all the stock market gains come from a small subset of stocks, so stock picking is extremely difficult!! A crazy statistic in this paper: most stocks have worse returns (lifetime buy and hold performance) than holding cash!

- The Risk of Owning an Individual Stock
- Key statistic: 73% of individual stocks experience a drawdown of 50%+ over their lifetime.

- One Way to Beat the Market. Be Different!
- Randomly selecting small portfolios of stocks is a great way to lose relative to a broad-based index.

- Luck versus Skill in the Cross-Section of Mutual Fund Returns
- Finding skill among stock-pickers is not impossible, however, the costs of entry are so high that investors rarely win after fees.

- Active Management in Mostly Efficient Markets
- Similar to above, it is possible to find successful active stock-pickers, but the chances are bleak.

- On Persistence in Mutual Fund Performance
- Maybe you find a winning stock picker, but did they get there on purpose? Unlikely. And can they continue to win? Unlikely.

- SPIVA Scorecards
- If you’re an active stock picker, this is a great way to feel depressed about your prospects of success.

- Superstar Investors
- Finding skill among stock-pickers is not impossible, however, the costs of entry are so high that investors rarely win after fees.
- A fun article that ties back to the paper above and adds some flavor.

- Buffett’s Alpha
- Even the great Warren Buffett can be replicated, in many respects, via a computer algorithm.

Not necessarily. The world is full of trade-offs and nothing is ever free. We must always face expected benefits and expected costs.

Here is a basic workflow of how I would consider this question, if asked:

- Currently, market-cap passive funds follow a process that deliver an extremely low cost exposure to a portfolio of relatively expensive, mega-cap stocks, which have done very well, recently.
- However, historically, portfolios of relatively expensive and extremely large stocks (i.e., passive indexes in their current form) deliver lower returns and lower volatility than portfolios of stocks that are cheaper, have high momentum, and/or are outside of the mega-cap market.
- If your financial goal over the next 20 years is to have a decent return with lower volatility — and you value the ability to closely track the markets on a day-to-day basis — passive market-cap Indexes are great.
- If your financial goal over the next 20 years is to have higher returns — and you are willing to take on more volatile short-run performance that deviates from the general markets — passive indexes may not be the best solution.
- Of course, costs always matter. So if we want to go down the #4 route and seek the higher return, higher volatility objective, we’ll need to focus on strategies that deliver the desired exposures affordably and efficiently. Otherwise, maybe #3 isn’t a bad option.

Market-cap indexes are not a panacea and active investing is not necessarily a bad idea, but high costs can ruin almost any investment party. Moreover, just like we should avoid pitches that suggest there is an active strategy that can beat the market, consistently, we should avoid any sales pitch that 1) quote’s Bill Sharpe for social proof purposes and 2) makes the following the claim: ^{3}

Check this out: We have this

awesome market-cap weighted passive indexinvestment strategy that earnshigher returns with lower riskthan these loser active strategies, comes at~zero cost, and you can buy it ininfinite supplywithout market impacts.What could go wrong?

If one would like to explore the various arguments of passive versus active in more detail, we recommend you read the following deep dive on the topic via Prof. Geoff Warren:

Good luck!

Notes:

- “voodoo” investing is not an actual investment approach. It is a made up term that serves as a catch-all for approaches that are completely ad-hoc and ridiculous. In short, voodoo investing is typically practiced by people who have a Robinhood account. Just joking… ↩
- akin to playing a poker hand with a 2 of clubs and a 7 of hearts in a Texas Hold ’em tournament. ↩
- Rick Ferri, I attribute this sales pitch to you. Semper Fi! lol ↩

A Short Research Library Outlining Why Traditional Stock Picking is Challenging was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>DIY Asset Allocation Weights: December 2020 was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Request a free account here if you want to access the site directly.

Exposure Highlights (**bold **implies a month over month change): ^{1}

- Full exposure to domestic equities
**.** **Full exposure to international equities.****Partial exposure to REITs.****Partial exposure to commodities.**- Full exposure to long-term bonds.

Notes:

DIY Asset Allocation Weights: December 2020 was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Mutual Fund Trading When No One Is Watching: It’s Not Pretty was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>- Alexander Eisele, Tamara Nefedova, Gianpaolo Parise, Kim Peijnenburg,
- Journal of Financial Economics
- A version of this paper can be found here

As equity trading moves to less regulated markets and off of exchanges across the world, mutual fund families have increasingly taken advantage of this opportunity to reallocate trades. Fund families are able to offset opposite trades of their affiliated funds within an internal market referred to as “cross-trading” (CT). In theory, because we don’t observe it directly, cross-trades have the effect of reallocating performance between and among various funds. How does this reallocation occur? When coordinated at the fund family level, for example, funds can avoid liquidations at firesale prices—selling at full price internally; and through the discretionary ability to set a price beneficial to one “trader” at the expense of another—for example pricing a cross-trade at the highest bid price instead of the average bid/ask. There is little direct empirical evidence in the current literature because the data is not detailed in regulatory filings. As a result, research is handicapped by the fact that funds disclose their holdings at the end of the quarter without disclosing activity that occurs throughout the quarter. This research uses the ANcerno ^{1} database which includes 12 years of trade-level equity transactions from a large number of US mutual funds. It is the first study to identify and define cross-trades directly. The authors define a cross-trade as a mirror transaction that occurs within the same fund family; occurring in the same stock and in the same quantity; at the same minute of the same day at the same price, but traded in the opposite direction.

- Are cross-trades by mutual funds opportunistically priced?
- Can those cross-trades be mitigated by increased regulation and monitoring?

- YES. Figure 1 presented below, is descriptive of the potential for the strategic or opportunistic pricing of cross-trades. Stricter empirical tests confirm the hypothesis that if CTs are used to price opportunistically, then we should see higher effective spreads when compared to similar open exchange markets. The authors report that under conditions of minimal monitoring, CTs exhibited a 42 basis point spread higher than that of matching open market trades. Apparently, the execution prices of CTs deviate more from the mid-price than comparable transactions in public markets. In addition, the authors report that CTs are retroactively priced, set either to the highest or lowest price of the day. This type of backdating process permits the largest performance reallocation among the trading funds or other trading counterparties. The effect is 4 times more likely to be executed at the exact high or low daily price when compared to open exchanges, indicative of backdating to the point in time when the price move was at it’s most extreme. The authors report CTs are more likely to occur between funds with higher fees, funds with liquidity shortfalls, and with younger funds. The losing counterparties tend to be funds suffering persistent outflows. All in all, it seems that CTs do indeed reflect discretionary pricing that acts to reallocate performance from distressed funds to funds that are valuable in one way or another, or in need of liquidity relief.
- YES. When compliance and monitoring efforts are enhanced then the 42 bp spread drops to 3bps. It seems that fund families utilize CTs when monitoring is weak, while discretionary pricing effectively disappears with stronger monitoring policies.

This research provides insights into the regulatory debate on the implications of off exchange trading venues for investors. Asset managers argue that internal crossing reduces transaction costs, fire-sale impacts and liquidity constraints, thus a beneficial feature of off-exchange trading options. Regulators, while recognizing the dampening effect on costs of transactions and fire-sales, CTs that are not adequately monitored impose unfair penalties on some investors.

This paper explores how mutual fund groups set the price of in-house transactions among aﬃliated funds. We collect a data set of four million equity transactions and compare the pricing of trades crossed internally (cross-trades) with that of twin trades executed with external counterparties. While cross-trades should reduce transaction costs for both trading parties, we find that the price of cross-trades is set strategically to reallocate performance among sibling funds. Furthermore, we provide evidence that a large number of cross-trades are backdated. We discuss the implications for the literature on fund performance and the current regulatory debate.

Notes:

- (also known as Abel Noser Solutions), ↩

Mutual Fund Trading When No One Is Watching: It’s Not Pretty was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>What Matters to Individual Investors? Evidence from the Horse’s Mouth was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>- James Choi and Adriana Robertson
- Journal of Finance, 2020
- A version of this paper can be found here

Finance literature is abundant with theories. As academics, we like to think these theories foster behaviors and choices by investors, which in turn translate into asset prices. To test these theories, scholars typically try to infer the validity of these assumptions by examining outcomes. The authors in this study follow a different and more direct approach: they survey a nationally representative sample of 1,098 U.S. individuals in the RAND American Life Panel to find out how well leading academic theories describe the way they decided:

- What fraction of their portfolio to invest in equities,
- Their beliefs about actively managed mutual funds,
- and their beliefs about the cross-section of individual stock returns.

The authors find:

- EQUITY SHARE OF PORTFOLIO:
- 48% of employed respondents say that the amount of time left until their retirement is a very or extremely important factor in determining the current percentage of their investible financial assets held in stocks, and 36% of all respondents say the same about the amount of time left until a significant non-retirement expense.
- Health risk (47% of all respondents), labor income risk (42% of employed respondents), and home value risk (29% of homeowners) are frequently rated as very or extremely important.
- Lack of knowledge about how to invest (36% of all respondents), and lack of a trustworthy adviser (31% of all respondents).
- Needing to have enough cash on hand to pay for routine expenses (47% of all respondents) and concern that stocks take too long to convert to cash in an emergency (29% of all respondents).
- Personal experience of living through stock market returns and personal experience investing in the stock market are rated as very or extremely important by 27% and 26% of respondents.
- Concern about economic disasters as a very or extremely important factor (45% of all respondents).

Although many factors ( out of 34 in the survey) appear to determine portfolio equity shares, only six principal components explain 54% of the variance in whether they were rated as very or extremely important. These components can be roughly interpreted as corresponding to neoclassical asset pricing factors: return predictability and retirement savings plan defaults; consumption needs, habit, and human capital; discomfort with the market; advice; and personal experience.

2. ACTIVE MANAGEMENT:

- The belief that the active fund would give them a higher average return than a passive fund (51% of those who purchased an active fund)
- The recommendation of an adviser (48% of active investors).
- A fund having outperformed the market in the past (46% of active investors).
- A hedging motive—the belief that the active fund would have lower unconditional expected returns than the passive fund but higher returns when the economy does poorly (27% of active investors).
- Personal experience of living through stock market returns and personal experience investing in the stock market are rated as very or extremely important by 27% and 26% of respondents.
- Concern about economic disasters as a very or extremely important factor (45% of all respondents).

3. CROSS SECTION OF INDIVIDUAL RETURNS:

- Not consistent with historical data, 28% of respondents expect value stocks to normally have lower expected returns than growth stocks, a proportion not statistically distinguishable from the 25% who believe the reverse.
- Consistent with historical data, more respondents (24%) expect high-momentum stocks to normally have higher expected returns than low-momentum stocks instead of the reverse (14%)
- 44% percent expect value stocks to normally be less risky than growth stocks, while only 14% believe the opposite.
- 25% percent expect high-momentum stocks to normally be riskier, while 14% expect them to be less risky.

Despite the fact that survey methodologies can of course have weaknesses such as survey respondents might not be highly motivated to give accurate responses and the meaning of each response category (e.g., “very important”) probably differs across respondents, the ordinal ranking of importance and agreement ratings is informative.

We survey a representative sample of U.S. individuals about how well leading academic theories describe their financial beliefs and decisions. We find substantial support for many factors hypothesized to affect portfolio equity share, particularly background risk, investment horizon, rare disasters, transactional factors, and fixed costs of stock market participation. Individuals tend to believe that past mutual fund performance is a good signal of stock‐picking skill, actively managed funds do not suffer from diseconomies of scale, value stocks are safer and do not have higher expected returns, and high‐momentum stocks are riskier and do have higher expected returns.

What Matters to Individual Investors? Evidence from the Horse’s Mouth was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Using “Quality” to Separate Good and Bad Value Stocks was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>However, after years of holding such stocks without much performance to show for, the realization sets in that these cheap stocks reflect structurally impaired businesses. The stock is not mispriced and market expectations are not wrong, it is simply a dying business that is on the way to bankruptcy. Another name for these stocks is “value traps.”

How can the systematic value investor minimize the chance of a value trap? Investors have several tools at hand to avoid these siren stocks and one common approach is to rank cheap stocks by another metric, effectively creating a multi-factor portfolio. Ideally, these other factors feature low or negative correlations to Value, where Momentum and Quality represent the most popular choices.

In this short research note, we will contrast Value & High Quality (our favored style) versus Value & Low Quality across stock markets. (Please note that the Quantitative Value Index, which was developed by Alpha Architect, specifically seeks to leverage quality metrics to improve a generic systematic value strategy. You can read more about that here. My piece is related to this concept but I approach it in a simple way to make a basic point about the potential benefits of incorporating quality into a value strategy)

We focus on all stocks in the US, Europe, and Japan with a market capitalization larger than $1 billion. We utilize a sequential model to first rank all stocks by value using an equal-weight combination of price-to-book and price-to-earnings multiples and then rank the residual universe by quality using a combination of debt-over-equity and return-on-equity ratios. At each step, 30% of the stocks are selected, which results in concentrated portfolios on the long and short side. Given that we rank for high and low quality, this approach generates four portfolios: cheap and high quality, cheap and low quality, expensive and high quality, and expensive and low quality.

We can highlight the fundamental differences by contrasting the long portfolio of the multi-factor combinations, which shows a lower debt-over-equity and a higher return-on-equity ratio for the cheap and high-quality stocks, as per definition.

Intuitively, cheap and low-quality stocks should be cheaper than cheap and high-quality stocks, which is the case when using median price-to-book multiples, but not for price-to-earnings (PE).

It is somewhat unusual to observe that investors seem to pay higher PE multiples for companies with worse fundamentals, however, this can be explained by different sector biases. Both portfolios are heavily exposed to financials, but the portfolio comprised of cheap and low-quality stocks has an almost 30% allocation to real estate and utility stocks, which represent highly leveraged companies that tend to trade at above-average PE multiples.

Theoretically, value traps should be detracting from the performance of the value factor, therefore excluding these should result in better returns. However, the performance of the long-short value factor and the value & high-quality combination in the US were approximately the same in the period between 1989 and 2018. (results are different, internationally).

The value & low quality portfolio performed worse than the factor on a stand-alone basis, as expected, but it seems that the cheap stocks with average-quality characteristics outperformed those with high-quality features.

Next, we calculate the CAGRs for the three scenarios in the US, Europe, and Japan, which highlights positive excess returns from the value factor across regions over the last three decades. Naturally, these returns were not distributed equally and were largely negative over the last decade, but that is another discussion.

However, more interestingly, we observe that in Europe and Japan the value & high-quality combination significantly outperformed the value factor. It is difficult to explain why this approach was less successful in the U.S., but should not be regarded too critically as financial markets are noisy. The threshold for quantitative approaches to be of interest is that a methodology should have a sound economic foundation and should work on average, but not necessarily in each market or over too short time periods.

Finally, we calculate the risk-adjusted returns for the three scenarios, which shows that focusing value & high quality resulted in the highest risk-return ratios across markets. Given that the return for the factor combination was lower than for the value factor in the US implies lower volatility when including quality metrics, which is intuitive. Cheap stocks tend to be companies in trouble, but when leverage is low and profitability moderate, then it might be more temporary than structural issues.

It is also worth noting that the value & high-quality combination experienced much lower maximum drawdowns than cheap stocks. In the US the maximum drawdown, which occurred during the tech bubble in 1999, only reduced from 66% to 63%, but from 65% to 46% in Europe, and from 83% to 34% in Japan.

Factor investing is like cooking. There are millions of plants, but only a few are edible and relevant for our kitchen. Some like potatoes or rice can be eaten as a stand-alone meal, but result in a rather bland eating experience. Mixing these up with herbs and spices produces a much more delicious and balanced dish.

Quality on its own is not an attractive factor as it is difficult to make a case that investors should be earning positive excess returns for holding stocks featuring low leverage and high profitability. The factor is more useful as a filter, similar to the Size factor, although that is currently being hotly debated in otherwise calm academic circles.

However, even if focusing on high-quality cheap stocks has generated more attractive returns than cheap stocks on their own, the performance still largely represents that of the Value factor. No amount of herbs or spices will cover that up.

How Alpha Architect Builds a Value and High Quality Portfolio

The recipe and reason for adding Momentum and Value

Improving the Odds of Value: II

Value Factor: Comparison of Valuation Metrics

Using “Quality” to Separate Good and Bad Value Stocks was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>An Easy Way to Simplify and Improve the Shiller CAPE Ratio as a Prediction Tool was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>- Thomas K. Philips and Adam Kobor
- Journal of Portfolio Management
- A version of this paper can be found here (slides here)

Shiller’s (1998) original CAPE ratio (the cyclically adjusted price of an equity index/10 year average of real earnings) used to predict long term equity returns, like every online recipe, has been improved over the years by various reviewers. A number of substitutes for real earnings have been proposed and analyzed including national income + product account earnings; revenue + cash flow; and past earnings weighted by revenues. Using a 10-year average in any or all of these alternative formulations has the effect of reducing noise and estimates earnings over a full business cycle. The author of this article produces superior results to previous attempts using only one year’s quarterly earnings and revenues. A vastly simpler approach.

- How do they do it?

- There are essentially 3 components in the simplified CAPE model. A major attraction of this article is the detailed description of the methodology used to construct and test the model.

- The authors document that a
**nonlinear filter**used on quarterly earnings each year is effective at reducing noise and unwanted characteristics of the earnings series. It is apparent from the data that the worst quarter of each year contributes to the skewness and kurtosis of the earnings series. The worst quarter is substantially different than the other 3 in that its volatility, skewness, and kurtosis are significantly higher. Therefore, the authors discard the worst quarter in each year, add the 3 quarters together and multiply by 4/3 to standardize to the level of earnings. This transformation produces an estimate of earnings over 3 quarters (E3) contains approximately one-half of the volatility of E or CAE (cyclically adjusted earnings) alone. Additional attributes of E3 include reduced bias and variance forecasts. The authors report adding a quadratic term (E/P)2 produces a larger R2. - Seasonality or other time variations in corporate profitability and margins are addressed using a second, separate model based on the sale-to-price (S/P) ratio. The authors hypothesize margins will mean-revert given competitive pressures. Perhaps a low S/P ratio could provide information about a decline in future earnings growth or a high level of profitability not contained in earnings. Adding a quadratic term (S/P)2 to (S/P) more completely approximates the observed nonlinear nature between equity index (SP500, in this case) returns and valuation ratios.
- The final piece of the simplified CAPE is the weighting scheme applied to the above 2 components E3/P, (E3/P)2, and S/P, (S/P)2 to create a composite model and forecast. Weights of the components are calculated as the inverse proportion of their forecast error variances. The approach of combining two univariate models in this manner is preferable as they are consistent with economic justification as separate variables, at least in the author’s opinion.
- Summary stats are presented in Exhibit 15 below. Note that the composite or simplified CAPE produces the most attractive performance profile, especially when compared to the original Shiller formulation.

The contribution of this research lies in the transformation of the original formulation of the CAPE ratio that is not only more effective at reducing noise, but actually produces more accurate out-of-sample forecasts of the long-run returns of the equity index. (here is another example of how to use CAPE)

Professor Robert Shiller’s cyclically adjusted price/earnings ratio (CAPE) has proven to be a powerful descriptor, as well as a useful predictor, of long-term equity returns in the United States and many global markets. CAPE uses a 10-year average of real earnings to simultaneously filter noise in earnings and to estimate corporate profitability over a business cycle. In this article, the authors simplify the CAPE methodology by separating the filtering of noise from the detection of cyclicality in earnings. They filter noise by discarding the worst quarter’s earnings in each year, allowing them to use one year’s earnings instead of 10, and proxy temporal variation in profit margins using the sales-to-price ratio. In addition, they account for an empirical nonlinearity in the relationship between valuation ratios and equity market returns. They combine the output of two models, one based on earnings and the other on sales, to create a robust forecast of 10-year forward returns. In out-of-sample tests, their technique increases the correlation between out-of-sample-forecasts and realizations from 0.69 to 0.87, reduces the standard deviation of the forecast error for the 10-year returns of the S&P 500 relative to CAPE by 40%, and linearizes the relationship between forecast and realized returns.

An Easy Way to Simplify and Improve the Shiller CAPE Ratio as a Prediction Tool was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Trend Following Research: Breaking Bad Trends was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Research into momentum continues to demonstrate its persistence and pervasiveness, in, as well as across, factors. Recent papers have focused on trying to identify ways to improve the performance of momentum strategies.

- The 2015 study “Momentum Has Its Moments”, found that momentum strategies can be improved on by scaling for volatility—targeting a specific level of volatility, reducing (increasing) exposure when volatility is high (low).
- The 2016 study “Idiosyncratic Momentum: U.S. and International Evidence” found that results could be improved, reducing the risk of momentum strategies, by removing the return component due to market beta. (summary here).
- The 2019 study “Extreme Absolute Strength of Stocks and Performance of Momentum Strategies,” found that eliminating stocks with the most extreme past returns from the eligible universe signiﬁcantly reduced the volatility of portfolios while modestly increasing the average return in most cases, improving the risk-adjusted-performance. Doing so also alleviated the problem of momentum crashes and rendered momentum strategies proﬁtable in the post-2000 era, a period during which momentum appeared to have vanished (due to momentum’s crash in April 2009). (summary here).
- The 2020 study “Opposites Attract: Combining Alpha Momentum and Alpha Reversal in International Equity Markets,” found that an integrated investment approach that combines the trading strategies of momentum and reversal is a superior strategy than either individually. (summary here)

The most recent attempt to improve on momentum strategies comes from Ashish Garg, Christian L. Goulding, Campbell R. Harvey, and Michele G. Mazzoleni , authors of the June 2020 study “Breaking Bad Trends.” They begin by noting that going long during sustained bull markets—or short during sustained bear markets—tends to be a good bet under such a strategy. However, trends eventually break down and reverse direction (called either corrections or rebounds). At and after these breaks trend following tends to place bad bets because trailing returns can reflect an older, inactive trend direction. “Faster trend signals (e.g., only a few months of trailing returns), rather than solving the problem, increase the tendency of placing bad bets because faster signals often reflect noise instead of a true turn in trend.” They called this the “Achilles heel” of trend investing. They attempted to find a way to mitigate the negative impact of breaks, or turning points—defining a turning point for an asset as a month in which its slow (longer lookback horizon) and fast (shorter lookback horizon) momentum signals differ in their indications to buy or sell. They sought to determine if these turning points were informative (predictive) of future returns.

To accomplish that objective, the authors partitioned an asset’s return history into four observable phases—Bull (slow and fast signals both +), Correction (slow signal +/fast signal -), Bear (slow and fast signals both -), and Rebound (slow signal -/fast signal +). When the signals agree, the dynamic strategy is the same as the static strategy. When the signals disagreed, they observed the historical evidence to determine if the fast signal was informative of future returns or not. They did this for each of the 55 individual assets in their database. They then used this information to specify an implementable dynamic trend-following strategy that adjusts the weight it assigns to slow and fast time-series momentum signals after observing market breaks (Corrections or Rebounds). That different markets behave differently is an interesting idea.

They explained:

“We say that an asset is at a turning point in month m if the signs of its slow and fast signals disagree. The basic idea is that if the average return over a shorter period is pointing in a different direction than the average return over a longer period (say, up versus down), then the market may have encountered a break in trend (say, from downtrend to uptrend). If a trend break has indeed occurred, then slower signals prescribe bad bets (e.g. shorting the market based on an older downward trend when the market is recently trending up). On the other hand, if disagreements reflect noise in fast signals rather than true trend breaks, then faster signals prescribe bad bets.”

Their dynamic strategy works in the following intuitive manner. If historical returns tend to be positive after Corrections (when the slow strategy goes long and the fast strategy goes short), then the dynamic strategy tilts away from the FAST signal. If historical returns tend to be positive after Rebounds (when the slow strategy goes short and the fast strategy goes long), then the dynamic strategy tilts toward FAST. If historical returns are negative after such states, then the direction of the tilt reverses. If the estimate is noisy, then there is shrinkage to a no-information signal. Their “framework supports dynamic blending of two time-series momentum strategies having slow and fast momentum signals.”

Their data sample included 55 futures, forwards, and swaps markets across four major asset classes: 12 equity indices, 10 bond markets, 24 commodities, and 9 currency pairs. Their sample begins in 1971 for some assets, adding each asset when its return data become available through 2019. Their time series of returns is based on holding the front-month contract (or 1-month forward or 10-year swap) and swapping to a new front contract as its expiration date approaches. Their slow signal is a fixed lookback window size of 12 months of prior returns and goes long one unit if the trailing 12-month return is positive; otherwise, it goes short one unit. The fast signal is the average of the prior 2 months of returns.

Following is a summary of their findings:

- As we would intuitively expect, there is a negative relationship between the number of turning points that an asset experiences and the risk-adjusted performance of its 12-month trend-following strategy. This holds across a diverse collection of assets from different asset classes and also carries over to multi-asset portfolios of trend-following strategies.
- For a multi-asset trend-following portfolio normalized to have 10% annualized volatility over the last 30 years, a one-standard-deviation increase in the average number of breaking points per year (+0.45) is associated with a decrease of approximately 9.2 percentage points in its annual portfolio return.
- Turning points and return volatility are uncorrelated—the number of turning points per asset per year is approximately uncorrelated with return volatility: 0.02 correlation. High or low volatility can appear during periods of sustained uptrend or downtrend (bull or bear markets) as well as at and after turning points.
- For assets with six or more turning points within a year, median returns to static trend following are negative. For assets with 8 or more turning points within a year, the vast majority of returns to static trend following are negative with annualized Sharpe ratios below −1.0 on average across assets.
- The number of breaking points helps explain the deterioration of trend-following performance in more recent years (as discussed in the 2019 study “You Can’t Always Trend When You Want”- Summary)— six of the most recent 10 years are in the top one-third over the last 30 years when ranked by the highest-to-lowest average number of turning points. An increase in turning points means a decrease in sustained periods of a trend.
- Trend-following strategies that react dynamically to asset turning points improve the performance of multi-asset trend-following portfolios, especially in months after asset turning points, which have become more frequent in recent years.
- Multi-asset static trend generates approximately 7.5% annualized average return over the 30-year evaluation period, yet only 1.8% in the most recent decade. Dynamic trend generates a 4.3% average return in the recent decade, which is more than double the 1.8% generated by the static trend, and the bulk of those gains are from returns harvested after turning points.

While the results are both intuitive and impressive, the following cautions are worth noting.

- The authors didn’t provide any data showing the statistical significance of their findings. Thus, we cannot make any observations about its significance.
- They allocated equal weight to each asset’s value within its asset class and equal weight to each asset class across the four asset classes. This leads to the results being dominated by commodities and equities. Thus, we don’t know if the results are truly pervasive. And we don’t know if the results are robust to value weighting.
- As if almost always the case, we don’t know how different strategies they tried, and perhaps failed with, before “uncovering” one that worked.
- And finally, the period of 30 years is not that long.

The dynamic trend strategy studied by Garg, Goulding, Harvey, and Mazzoleni has intuitive appeal. Multiple metric (or ensemble) strategies have been demonstrated to add value in many areas. For example, in their 2020 study “Is (Systematic) Value Investing Dead?” – Summary Ronen Israel, Kristoffer Laursen and Scott Richardson of AQR Capital Management showed that a diversified (equal-weighted) combination across individual value metrics (such as p/b, p/e, ev/s, ev/cf) generated a strongly positive risk-adjusted return (t-stats well above conventional levels)—demonstrating the benefits of using an ensemble approach versus one single metric. AQR also uses multiple signals in their managed futures strategies (a short-term or fast signal, an intermediate-term signal, and a long-term reversal signal). In addition, the idea that different markets behave differently is an interesting idea. Hopefully, we will see future research explore this concept in greater depth.

Editor’s note: Trend following is an interesting concept that allows investors to shape portfolio outcomes in unique ways to achieve different financial objectives. However, it is important to note that no amount of financial engineering will eliminate the difficult journey investor’s must face when utilizing trend following strategies. Hence the reason we often say, Trend Following is the epitome of no pain no gain.

Trend Following Research: Breaking Bad Trends was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Do Analysts Exploit Factor Anomalies when recommending stocks? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>- Li Guo, Frank Weikai Li, K.C. John Wei
- Journal of Financial Economics
- A version of this paper can be found here

Do analysts actively exploit anomalies when they recommend stocks? Do analysts’ research efforts contribute to efficiency in the equity markets? Good questions. This research clarifies the relationship between established stock return anomalies and analyst recommendations. Given that anomalies are so well-documented and so well-known, and if analysts are “sophisticated informed and unbiased”, it makes sense that they should be willing and able to take advantage of them. However, if analysts are “biased and uninformed” they may make recommendations inconsistent with these anomalies. As a result of ignoring anomalies they may represent a significant friction in the market and significantly contribute to mispricing. The research completed in this paper examines long-short portfolios of 11 anomalies including net stock issuance (NSI), composite equity issuance (CEI), total accruals (Accrual), net operating assets (NOA), asset growth (AG), investment to assets (IA), gross profitability (GP), return on assets (ROA), momentum (MOM), ﬁnancial distress (Distress), and Ohlson O-score (O-score). The 11 anomalies were combined into two composites—PERF (Distress, O-score, MOM, GP, and ROA) and MGMT (NSI, CEI, Accrual, NOA, AG, and IA). The sample covered the period 1993-2014.

- Do analyst recommendations and changes in recommendations contain information consistent with anomaly signals?
- Are analyst recommendations biased with respect to anomaly signals?
- Is the market reaction stronger for sophisticated/unbiased analysts?
- Were the results robust to risk adjustments and alternative explanations?

- NO. Analysts more often than not issue recommendations inconsistent and contradictory to the predictions of anomalies, especially for those related to equity issuance and investment. The long/short spread for the MGMT composite was -0.55, significant at 1%. More specifically and as shown in Panel A of Table 3 below: stocks on the short side had more favorable recommendations than those on the long side. For MGMT, the value of the recommendation for the shorts was 4.07 and 3.52 for the longs. Similar results were found for all but 2 of the anomalies included in the MGMT composite. The data tells a difference story for the PERF composite. Analyst recommendations were consistent with anomaly predictions for the PERF anomalies, with the value for the short side at 3.71 and 3.89 for the long. Although this represents a significant result, it is small when compared to the MGMT anomalies. Results did not change when the authors examined
*changes*in recommendations. For MGMT anomalies, upgrades were more likely for stocks on the short side and downgrades were more likely for stocks on the long side. For the MGMT composite, the value for upgrades was 0.02 and 0.06 for downgrades, with the difference significant at the 1% level, although economically small. Apparently, analysts are quite active in revising their recommendations on anomaly stocks, however, the change in opinion is*opposite*of that predicted by the anomalies. WEIRD huh? - YES. The alphas from L/S portfolios are larger for portfolios for which analyst recommendations are contradictory to the anomaly predictions, especially for anomalies in the PERF composite. The L/S PERF composite returned a risk-adjusted alpha of 1.57% for the contradictory case. The L/S PERF composite returned an alpha of 0.90% for portfolios formed for recommendations that were consistent with anomaly predictions. The difference of 0.67% between the two types of recommendations (inconsistent vs. consistent) was significant at the 1% level. Individual anomalies performed similarly to the composite, in the range of 0.43% to 0.65%, all significant. The picture for anomalies in the MGMT composite is very different. The alphas between consistent and inconsistent portfolios are small, positive, and are not significant. There were 2 exceptions: Accruals returned a difference of 0.54% and 0.52% for IA, both significant. For both PERF and MGMT anomalies returns from the short side of the inconsistent portfolios were amplified.
- YES. The authors develop and test a method for identifying “sophisticated and unbiased”, i.e.
*skilled*analysts. Please refer to the paper for a description as it is beyond the scope of this summary. In any case, the research shows that skilled analysts who exploit anomaly predictions in the recommendations is a very small set of all analysts. They tend to be sell-side analysts who use quantitative research and elicit stronger returns around announcement of recommendations. As a result, those stocks followed by skilled analysts of this sort have muted anomaly returns, but are not sufficiently followed such that the return predictability is eliminated entirely. - YES. The authors find that results hold for 6 other prominent anomalies including idiosyncratic volatility, maximum daily returns, part 12-month turnover, cash flow duration, losers minus winners, and market beta and were robust to firm size, institutional ownership, investor sentiment and 3-factor risk adjustments.

This research clarifies the relationship between analysts and predictable returns of anomaly stocks and buttress the argument that analysts are likely important contributors to mispricing in the equity markets and help explain the persistence of the returns from anomalies in the equity market. Apparently analysts do not make full use of information provided by anomaly signals and frequently contradict them. In other words, if you want to be the genius analyst on wall street, screen for anomalies first then write your research. Of course, the time period is a bit dated at this point. Because of the massive shift from active to passive and from discretionary to systematic, it would be interesting to see how things have changed since 2014.

We examine the value and eﬃciency of analyst recommendations through the lens of capital market anomalies. We ﬁnd that analysts do not fully use the information in anomaly signals when making recommendations. Analysts tend to give more favorable consensus recommendations to stocks classified as overvalued and, more important, these stocks subsequently tend to have particularly negative abnormal returns. Analysts whose recommendations are better aligned with anomaly signals are more skilled and elicit stronger recommendation announcement returns. Our findings suggest that analysts’ biased recommendations could be a source of market friction that impedes the eﬃcient correction of mispricing.

Do Analysts Exploit Factor Anomalies when recommending stocks? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Should Treasury Bills Be The Risk-Free Asset in Asset Pricing Models? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Blitz then asked if the choice of the one-month Treasury is misspecified. If it is, and the true risk-free asset is a longer-maturity Treasury bond, what are the implications? One implication is that the equity risk premium would be much smaller, helping to resolve the so-called equity risk premium puzzle.

Blitz began his analysis by noting that if the true risk-free rate were a longer-term Treasury, it leads to the testable prediction that low-beta (high-beta) stocks should then exhibit positive (negative) bond betas. For example, if the equity beta is 0.7, the predicted bond beta is 0.3; if the equity beta is 1.3, the predicted bond beta is -0.3. In other words, if we subtract 1 from the equity beta, the predicted bond beta is equal to the remaining equity beta with the sign flipped—we should see an inverse linear relationship between equity betas and bond betas. Prior research, including the 2014 study “Interest Rate Risk in Low-Volatility Strategies,” the 2016 study “Understanding Defensive Equity,” and the 2017 studies “Interest Rate Exposure of Volatility Portfolios” and “Equity Portfolios with Improved Liability-Hedging Benefits,” found that stocks with low equity betas exhibit positive bond betas. In other words, low-beta stocks—which tend to be large, mature, profitable, and dividend-paying firms—are bond-like stocks.

To determine the best fit for the riskless rate, Blitz built value-weighted returns for 10 industry portfolios, 10 portfolios sorted on size, 10 portfolios sorted on operating profitability, 10 portfolios sorted on investment (one-year change in total assets), 10 portfolios sorted on earnings-to-price, 10 portfolios sorted on cash-flow-to-price, 10 portfolios sorted on dividend yield and the portfolio of zero-dividend stocks, 10 portfolios sorted on accruals (change in operating working capital), 10 portfolios sorted on net share issues, 10 portfolios sorted on residual variance (past 60 days) and 10 portfolios sorted on market beta (past 60 months). This yielded a total of 121 well-diversified portfolios as test assets. For the risk-free rate, Blitz considered 2-year, 5-year, 7-year, 10-year, and 30-year Treasuries. His sample period spanned more than half a century, from July 1963 to December 2018.

Following is a summary of his findings:

- There is a strong inverse linear relation between the estimated equity and bond betas; that is, the higher the equity beta, the lower the bond beta, and vice versa—portfolios with equity betas below 1 have positive bond betas, portfolios with equity betas above 1 have negative bond betas, and portfolios with a beta of 1 have a zero bond beta.

- The fit of the regressions is very strong, with adjusted R-squared levels ranging from 73% to 80%. and estimated intercepts are all statistically indistinguishable from zero.
- The slope coefficients are all negative, and highly statistically significant, with t-statistics of about -20, ranging from -0.40 for the 30-year bond asset to -1.54 for the 2-year bond asset.
- The coefficient that comes closest to the -1 level predicted is the -0.92 estimated slope for 5-year bonds, which also has the highest correlation.

As a test of robustness, the results were consistent over three subperiods of about the same length: July 1963 to December 1981, January 1982 to December 2000, and January 2001 to December 2018. The first subperiod is characterized by rising interest rates and hence low bond returns. The other two subperiods are characterized by high bond returns owing to falling interest rates. The explanatory power was consistently high, with R-squared levels ranging from over 75% in the middle subperiod to over 47% in the most recent subperiod. The best fit for the risk-free asset was for 2-year bonds in the first subsample, 7-year bonds in the middle subsample, and between 2- and 5-year bonds in the last subsample.

As a further test of robustness, Blitz examined whether the results for the U.S. market carry over to the main markets outside the United States—the United Kingdom, Japan, and the Eurozone. The universe consisted of all stocks in either the S&P Broad Market Index or FTSE Index at each point in time, giving an average of 482 stocks for the United Kingdom, 1,284 for Japan, and 861 for the Eurozone. The sample period is from January 1986 to December 2018 for the United Kingdom and Japan and, because of the introduction of the euro, from January 1999 to December 2018 for the Eurozone. Blitz found similar inverse relations between equity and bond betas in those markets as in the United States, as well as high correlations and intercepts that were all statistically indistinguishable from zero. For the United Kingdom and the Eurozone, the best fit for the risk-free security was the 10-year bond. For Japan, the 2-, 5- and 7-year maturities had similar results.

These findings led Blitz to conclude:

“The data are not only highly supportive of the theoretically predicted implications of a misspecified risk-free asset but also enable us to pinpoint the most appropriate choice for the risk-free asset as a bond with a maturity of about 5 years.”

Blitz found strong evidence that the risk-free rate used in asset pricing models is misspecified, as the empirical evidence provides support for intermediate-term Treasuries as the more appropriate benchmark. In addition to the empirical evidence, economic theory posits that the one-month rate is not a riskless rate for investors with horizons beyond that term. His findings help explain at least part of the equity risk premium puzzle. In addition, the evidence helps explain the performance of low-beta stocks.

Should Treasury Bills Be The Risk-Free Asset in Asset Pricing Models? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>DIY Asset Allocation Weights: November 2020 was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>Request a free account here if you want to access the site directly.

Exposure Highlights (**bold **implies a month over month change): ^{1}

- Full exposure to domestic equities
**.** **No exposure to international equities.**- No exposure to REITs.
- No exposure to commodities.
- Full exposure to long-term bonds.

Notes:

DIY Asset Allocation Weights: November 2020 was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>How Do You Think the Global Market Portfolio Has Performed from 1960-2017? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

]]>- Ronald Doeswijk, Trevin Lam and Laurens Swinkels
- The Review of Asset Pricing Studies, 2019
- A version of this paper can be found here

This paper complements Doeswijk, Lam, and Swinkels’ 2014 paper, which documents the historical composition of the market portfolio. Doeswijk, Lam, and Swinkel stopped their research in building the “market portfolio,” but left the work of the market portfolios historical returns undone. In this post, the original authors pick up where they left off and work on finding the returns of the market portfolio they had previously identified. The market portfolio, all assets held by financial investors around the globe, is comprised of ten market-capitalization-weighted asset classes organized in five asset class categories: equities (public equities and private equity ^{1}), government bonds (government bonds, inflation-linked bonds, and emerging market bonds), non-government bonds (investment grade credits, high yield, and leveraged loans), real estate, and commodities. (see here for a discussion from Jon Seed on the Global Market Portfolio).

The authors ask the following questions:

- What is the average compound real return and standard deviation for the global market portfolio from 1960 to 2017?
- What is the average compound real return of the global market portfolio during expansions and recessions?
- What is the average compound real return of the global market portfolio during inflationary and deflationary periods?

By constructing a total return series (gross of transaction costs, taxes and management fees), the authors find:

- The global market portfolio realizes an average compounded real return of 4.45%, with a standard deviation of annual returns of 11.2% from 1960 until 2017, gross of trading costs, taxes, and/or management fees. The arithmetic average real return of the market portfolio is 5.05%.
- The average annual real return of the market portfolio in expansions is a statistically significant 9.68 percentage points higher than the return in recessions.
- In the inflationary period from 1960 to 1979, the average real return is 2.77 percentage points below the return in the disinflationary period from 1980 to 2017, but this gap is statistically insignificant.

This study is interesting because of the following:

- The market portfolio is relevant for studying financial markets, in the sense that the market portfolio reflects the entire opportunity set of investors
- The market portfolio matters for asset pricing studies
- It is an estimate of the average return that financial investors have potential achieved since 1960

We create an annual return index for the invested global multiasset market portfolio. We use a newly constructed unique data set covering the entire market of financial investors. We analyze returns and risk from 1960 to 2017, a period during which the market portfolio realized a compounded real return in U.S. dollars of 4.45%, with a standard deviation of annual returns of 11.2%. The compounded excess return was 3.39%. We publish these data on returns of the market portfolio, so they can be used for future asset pricing and corporate finance studies.

Notes:

- listed private equity returns are available starting 1994. Prior to 1994, the index contained only public equity returns. At his time, private equity weighted about 1.5%, and prior to that 0.8% in the overall market portfolio. ↩

How Do You Think the Global Market Portfolio Has Performed from 1960-2017? was originally published at Alpha Architect. Please read the Alpha Architect disclosures at your convenience.

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