 The risk theory says that Value stocks are inherently riskier due to a loading on an unknown distress factor. Since they are riskier, investors should demand a higher rate of return for taking on additional risk. Under this model, the value premium will continue to exist as long as investor risk preferences stay the same; however, if investor risk preferences change and they are willing to take on additional risk for a lower rate of return (unlikely!), the value premium would go away. ^{2}.
 The LSV behavioral theory is a mispricing theory that claims that investors incorrectly extrapolate past growth rates (behavioral error) and cause value stocks to be underpriced, and growth stocks to be overpriced–this causes the future higher (lower) returns to value (growth) stocks. ^{3}
So what’s the answer? A new paper entitled, “Interpreting Factor Models,” says it best:Another possibility is that investors consistently held priors that size and booktomarket ratios were proxies for systematic risk and, as a result, attached higher discount rates to stocks with these characteristics. … If this is the case, then the patterns we have observed in the data should not be repeated in the future.
In short, nobody really knows. We would argue that there is a mix of all three ideas going on at the same time. As more investors learn about an investment approach that previously had higher returns (value investing), the expected returns to that approach may diminish in the future (implication of the characteristic theory), if arbitrage constraints are minimal. ^{6} The rest of the article is broken into three sections:We argue that tests of reducedform factor models and horse races between “characteristics” and “covariances'” cannot discriminate between alternative models of investor beliefs.
 A dive into the characteristic versus risk debate.
 An examination of what this means for a longonly value investor
 A review of live portfolios with a breakdown of factors and characteristics
Do Portfolio Factors or Characteristics Drive Expected Returns?
Most in finance are aware of the value premium: Historically, cheap stocks have outperformed expensive stocks (based on some price to fundamental). Below is a chart from a simulation exercise which highlights the performance of cheap vs. expensive portfolio simulations from 1963 to 2013. One of the original papers on the value premium topic was Fama and French in 1993. In their paper, they find that there are three factors (the market, size, and value proxied by Mkt_rf, SMB, and HML) that explain the crosssection of stock returns. More important to this discussion, they suggest that value is a risk factor, as value firms covary with one another. In their story, the covariance matters, and is why the loading on HML is important. ^{7} But what are some implications of this theory? Directly from FF 1993:In other words, the HML loading can be used to estimate future expected returns. A higher loading implies a higher amount of risk, which implies a higher rate of expected return. This is exactly the type of interpretation we often hear from DFA advisors, many of whom have been taught by Fama and French. But the factor approach (and the reliance on regression slopes to make decisions) is not a panacea and has plenty of holes like any other approach. We have discussed in detail, an alternative explanation to risk being the driver of the value premium is the LSV behavioral theory. The LSV theory suggests that investors over extrapolate data, causing prices to sometimes deviate from fundamentals and limits to arbitrage prevent these mispricings from being “arbitraged” away. It is important, for this discussion, to note that the argument between the risk and LSV behavior camps does not focus on whether or not the return premia of value and small firms can be explained by a factor model–they agree it can. However, they argue whether the factors represent an economically relevant risk or mispricing that is costly to exploit. However, there is a 3rd explanation for the value premium, which is also a “mispricing” based argument–the premium is simply driven by characteristics (not covariances, or factors). In other words, your HML loading does NOT matter, but your portfolio booktomarket ratio does matter.The regression slopes and the historical average premiums for the factors can then be used to estimate the (unconditional) expected return for the portfolio.
Why Characteristics Matter: The Theory
This theory was proposed by Kent Daniel and Sheridan Titman in 1997, in their paper titled “Evidence on the Characteristics of Cross Sectional Variation in Stock Returns.” ^{8} ^{9} This is a wellwritten paper. The introduction very clearly states what the paper will test, and what they find:So what this paper is trying to argue is that after controlling for characteristics, factor exposures (i.e., factor “loadings”) don’t tell us much about expected returns. In other words, if an investor is calculating “HML loadings” as a means to tell them something about future returns, they should stop this practice. Instead, investors should identify the booktomarket ratio of their portfolio, which will be much more predictive of expected returns. Before digging into Daniel and Titman’s 1997 Journal of Finance paper, I will quote and use a few images from their 1998 Journal of Portfolio Management paper, which nicely explains their argument. This paper can be found here and a working paper (used below) can be found here. Consider that we have 3 stocks: A, B, and C. Here are the assumed facts about these securities:In contrast, this article addresses the more fundamental question of whether the return patterns of characteristicsorted portfolios are really consistent with a factor model at all. Specifically, we ask (1) whether there really are pervasive factors that are directly associated with size and booktomarket; and (2) whether there are risk premia associated with these factors. In other words, we directly test whether the high returns of high booktomarket and small size stocks can be attributed to their factor loadings.Our results indicate that (1) there is no discernible separate risk factor associated with high or low booktomarket (characteristic) firms, and (2) there is no return premium associated with any of the three factors identified by Fama and French (1993), suggesting that the high returns related to these portfolios cannot be viewed as compensation for factor risk…Once we control for firm characteristics, expected returns do not appear to be positively related to the loadings on the market, HML, or SMB factors.
 Stock A and stock B have the same B/M ratio
 Stock A has a higher HML loading () than stock B.
 Stock C has a higher B/M ratio than stock B.
 Stock B and stock C have the same HML loading ().
Why Characteristics Matter: The Evidence
In the 1997 paper, the authors form 45 portfolios to test their idea that characteristics are better than factors (covariances). The form portfolios employing a 3way split. They first split firms into 3 groups on both size and B/M, yielding 9 portfolios. Within each of the 9 portfolios, they then split firms into five groups based on their HML loading, yielding 45 portfolios. Table IV of the 1997 paper highlights shows the 45 portfolios, first split on size and B/M, and then on HML. ^{10} How does one go about testing the characteristic model against the factor model when characteristics and factors are so correlated? ^{11} The authors build what they call characteristic balanced portfolios based on HML loadings. ^{12} For each of the 9 portfolios split on size and B/M, the authors go long the top two portfolios on the HML loadings and short the bottom two portfolios on the HML loadings. In the end, each portfolio has similar characteristics, such as size and B/M ratios, but the HML dimension is allowed to vary. ^{13} What would the factor model predict versus the characteristics model predict for these portfolios? The factor model would suggest the following: The L/S portfolio should have positive expected returns because the portfolios are long the high HML firms and short the low HML firms.
 Alpha should be zero because the Fama and French 3factor model will pick up the variation in returns via a higher HML loading.
 The L/S should have flat expected returns because the portfolios are formed with similar characteristics (Size and B/M).
 Alpha could be positive because the 3factor model may fully not pick up the variation in returns due to characteristics.
 Characteristic Balanced: Long high HML firms and short low HML firms, controlling for characteristics
 Factor Balanced: Long high B/M firms and short low B/M firms, controlling for factor loadings (market, size, and value).
 Controlling for characteristics, factor loadings do not matter.
 Controlling for loadings, characteristics do matter.
Fama and French Fight Back
Why is everyone still using factor models in 2017? Well, the debate didn’t end with Daniel and Titman 1997. In 2000, James Davis, Eugene Fama, and Ken French (DFF) came to defend factor models. Their paper is titled, “Characteristics, Covariances, and Average Returns: 19291997.” ^{14} DFF run similar tests as the DT paper, but over a longer time cycle. A minor portfolio construction change is made, by creating 27 portfolios, as opposed to 45. Similar to DT, DFF first split the universe into 9 portfolios based on size and B/M ratios. Next, for each of the 9 portfolios split on size and B/M, the authors split the firms into 3 groups along the HML loadings–this leads to 27 portfolios. Within each of the 9 portfolios sorted on size and B/M, DFF go long the high HML firms and short the low HML firms. As a reminder, here is that the two models would predict (from above): The factor model would say the following: The mean monthly return should be positive, as the portfolios are long the high HML firms and short the low HML firms.
 The mean alpha should be zero, as the 3factor model should pick up the variation in returns via a higher HML loading.
 The mean monthly return should be zero, as the portfolios are formed by controlling for the characteristics (Size and B/M).
 The mean alpha should be positive, as the 3factor model may fully not pick up the variation in returns due to characteristics.
Out of Sample Studies to Settle the Factors Versus Characteristics Debate
Two additional studies conduct the same tests, out of sample, by using returns from Japan and the U.K. Here is the abstract from a 2001 paper titled, “Explaining the CrossSection of Stock Returns in Japan: Factors or Characteristics” by Kent Daniel, Sheridan Titman, and K. C. john Wei.Here is the abstract from a 2007 paper titled, “UK Evidence on the Characteristics versus Covariance Debate” by Edward Lee, Weimin Liu, and Norman Strong.Japanese stock returns are even more closely related to their booktomarket ratios than are their U.S. counterparts, and thus provide a good setting for testing whether the return premia associated with these characteristics arise because the characteristics are proxies for covariance with priced factors. Our tests, which replicate the Daniel and Titman [1997] tests on a Japanese sample, reject the Fama and French [1993] threefactor model, but fail to reject the characteristic model.
So in two outofsample datasets, the evidence is in favor of the characteristic model. ^{15} What do we make of all this? First off, factor models are just that– a model. It should be pointed out that many still examine and give weight to the beta of a portfolio, which is built upon the covariance of the portfolio relative to the variance of the market. A higher beta should imply higher returns–we know that is not necessarily the case. Additionally, saying that the HML loading of a portfolio is unrelated to the B/M of the portfolio is untrue as well–the HML factor creates a long/short portfolio return by sorting stocks on B/M! So in the end, it is hard to ascertain which is 100% correct. In the end, both characteristics and loadings probably matter when explaining the crosssection of stock returns. But how does this affect a longonly value investor? Below I examine this question directly.We evaluate the Fama–French threefactor model in the UK using the approach of Daniel and Titman (1997) to determine whether characteristics or covariance risk better explains the size and value premiums. Across all three factors, we find that return premiums bear little relationship to the corresponding loadings. We show that small and value stocks earn higher returns irrespective of their return covariance. Our study contributes to the existing literature by reporting original findings on the Fama–French threefactor model in the UK and by reporting results that complement existing evidence from similar studies in the USA and Japan.
I’m Not From the Ivory Tower: How Does This Affect Me and My Clients?
While the analysis above is an academic debate within long/short portfolios, what are the implications for a longonly investor who is interested in a particular investment approach, such as Value and Momentum investing? Below I examine this in the context of a Value investor by allowing portfolios to be split into ValueGrowth Deciles by two methods: The previous HML loading.
 The B/M ratio.
VW Returns: 7/1/1973 – 12/31/2016
As seen in the image above, the CAGRs for the portfolios increase for both the HML deciles and the B/M deciles as one moves from Growth to Value firms (left to right). This highlights that using both characteristics (B/M) and factors (HML loadings) to create Value portfolios worked in the past, as the Value decile outperformed the Growth decile. For most longonly investors, it would be hard to argue, given the evidence in our charts and the papers above, that sorting a portfolio on characteristics is a bad way to form value portfolios. Across each decile, the correlation between the portfolios formed on B/M and HML loadings are high and range between 0.86 and 0.925. It should be noted that the high B/M and HML decile portfolios (both VW and EW) have a tracking error relative to the SP500 of at least 10%, so these are portfolios that would not be used by many professional money managers (too much career risk!). Subperiod analysis is done and shown in the below reference–it is generally found that characteristics performed better in the original DT sample period (7/1/197312/31/2016), whereas forming portfolios on HML performed better (especially for the VW portfolios) in the period thereafter (1/1/199412/31/2016). ^{19} But given that we have the data, what are the loadings of the Value portfolios formed either by sorting on B/M ratios or by HML loadings? Below we show the 4factor loadings over the entire time period tested above (7/1/197312/31/12016):4Factor Regression  
Alpha (Annual)  MKT_RF  SMB  HML  MOM  
High HML VW  4Factor  0.00  1.17  0.10  0.60  0.00 
pvalue  0.8907  0.0000  0.0574  0.0000  0.9542  
High B/M VW  4Factor  0.00  1.05  0.04  0.78  0.15 
pvalue  0.7484  0.0000  0.2746  0.0000  0.0000  
High HML EW  4Factor  0.00  1.12  0.36  0.58  0.00 
pvalue  0.9423  0.0000  0.0000  0.0000  0.9055  
High B/M EW  4Factor  0.02  1.01  0.25  0.71  0.15 
pvalue  0.7484  0.0000  0.0000  0.0000  0.0000 
The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. These regression estimates highlight that portfolios formed by exante sorting on either B/M ratios or HML loadings have similar expost HML loadings themselves! Again, all of this makes sense–the HML factor is a long/short portfolio formed by sorting firms on size and B/M! So while one can debate whether or not it is optimal to form a portfolio using factors or characteristics, we highlight above that in the past, the two methods end up yielding similar results for a longonly investor. Thus, when assessing potential portfolios or investments, such as ETFs and mutual funds, one can examine both the loadings from a factor regression and the characteristics of the underlying portfolio (easier to interpret than regression outputs). This can be important for the analysis by advisors on certain funds. Let’s say as an advisor, you want to assess a fund that claims to sort firms on P/E ratios. ^{20} Well, almost by construction, sorting firms on P/E will most likely (but not always) lead to a lower HML, or “value” loading, than another fund that sorts on B/M. ^{21} So does this mean that the P/E fund is not a value fund as it doesn’t have a high HML loading? Not necessarily; and one way to ascertain what the P/E fund is doing is to examine the characteristics of the portfolio. Similarly, how can one assess a multifactor fund? Without tools to assess the portfolio, it can be tough to decide. Let’s examine a live portfolio and highlight both the factor loadings and the overlap to the academic value portfolio formed on characteristics. We will then discuss a new tool we plan to launch soon, which will help advisors assess the characteristics of an ETF or even a portfolio of ETFs.
Examination of a live portfolio
To examine both the factor loadings, as well as the portfolio characteristics, I chose the Vanguard’s VTV ETF. A huge “value” ETF known to most professional investors. To examine the factor loadings, I use the online tool, PortfolioVisualizer. A link can be found here and an image of the factor loadings to VTV is shown below: As can be seen above, the fund’s loadings are 0.97 on the market, a negative 0.19 loading on SMB, and a positive 0.27 loading on HML–all are significant. Since this is a value fund, where the positions are mainly valueweighted (marketcap weighted), these loadings make sense–market beta ~ 1 as it marketcap weights large stock positions, a negative size loading as it invests in large stocks, and a positive HML loading as it is a Value fund. So nothing surprising here. Next, we examine this same ETF using our Visual Active Share tool–an explanation of this tool can be found here. Our tool allows an investor to analyze a fund from a characteristicsbased framework as opposed to a regression/factorbased framework. On the image above, each circle represents an underlying stock, with the size of the circle representing the weight of the stock within the ETF. The xaxis ranks all nonmicrocap stocks on P/B (inverse of B/M), while the yaxis ranks all stocks on size. As shown above, VTV is a larger cap fund, as the holdings are ~ 75th percentile and higher, which a huge emphasis on the largest stocks in the universe. The Fund seems to have little relationship with P/B, as the dots are spread out across the spectrum of cheap/expensive. Let’s dig further. How does VTV compare to “academic” value portfolios, formed on characteristics? Within the visual active share tool, we have the academic characteristic portfolios prebuilt (start typing “academic” and they’ll show up). Below we add the academic bottom decile on P/B (inverse of B/M), where a lower P/B indicates a firm is cheaper. We also add Vanguard’s SP500 ETF, VOO to view the index holdings. As can be seen above, the VTV and VOO ETFs (Value and SP500) hold very similar positions. The fee difference is 0.02%, so one can’t really complain about the funds being too similar (you aren’t paying for any differentiation). Also, one notices that these funds are different than the academic characteristicbased P/B portfolio. This makes sense–Vanguard gives investors access to the marketcap portfolio, for a very cheap price. They are not trying to be that different than the market, and by doing so, have helped many investors. But clearly, this fund is not the same as the characteristicbased academic portfolio. Our Visual Active Share tool can be helpful to visually view the differences between live funds and the characteristicbased academic portfolio. ^{22} Bottom line: We’re building out a capability for investors to assess portfolios based on characteristics, as opposed to factors.Conclusion
We started this discussion by highlighting the perpetual debate regarding the value premium–risk or mispricing? We introduced an alternative way of viewing the world via characteristicsbased asset pricing. The main takeaways are the following: There is a clear academic debate about whether higher returns to value and small firms are driven by factors or characteristics. There is decent evidence to suggest that both models have legs to stand on, and this has an implication for the future expected return to the value premium. However, it should be noted that the two are clearly related–the HML is formed by sorting firms on size and B/M, so an HML loading has some relation to the B/M characteristic. We don’t necessarily take a side here, but rather highlight that one can examine both loadings and characteristics to assess a fund.
 When assessing the returns to value paper portfolios, sorting on either factors or characteristics yielded a similar result from a CAGR and expost factor loading perspective. Thus, examining current characteristics of portfolios is not a bad idea.
 We walked through an example of a value fund and highlighted our Visual Active Share tool, which allows investors to visually view underlying stocks along different characteristics.
Notes:
 Note — a 4th explanation of the value premium is that it was a chance result, and is unlikely to be found out of sample. However, the outofsample data contradicts this idea. Value and Momentum have been found to work (almost) everywhere. ↩
 Note, or if investors decide to purchase value stocks, regardless of risk, this could diminish the premium ↩
 discussed here ↩
 We believe the largest cost of arbitrage is tracking error risk, which is further explained in this paper on “Interpreting Factor Models.“ ↩
 This can be viewed as mispricing theory, or maybe not. ↩
 “Fact, Fiction, and Valueinvesting” also outlines the argument that there probably isn’t a catchall explanation for factor premiums. ↩
 As a reminder, a stock’s market Beta is a measure of the firm’s covariance with the market, divided by the variance of the market. ↩
 I highly recommend everyone read the entire paper. ↩
 A great replication and explanation of this paper, as well as the source code, was done by Alex Chinco and can be found here. ↩
 A pretty version of this analysis is here. ↩
 (see table below from 1998 paper). ↩
 This term is used in the 1998 JPM paper, but is instructive so I use it here. ↩
 Again, this portfolio sort is possible because there are groups of cheap smallcap value stocks that have high HML betas and there are groups of cheap smallcap value stocks that have low HML betas. ↩
 Note the dates are included in the title of the paper–a big chunk of the paper is devoted to highlighting that the Daniel and Titman results are very specific to the time period tested in the DT paper — 19731993. ↩
 Here is a paper that examines mutual fund portfolios using characteristicbased benchmarks–this is one way to assess mutual funds and ETFs. ↩
 Regression of excess stock returns against the marketrisk free, SMB, HML, and MOM factors. ↩
 Manager Fees and transaction costs would lower the returns to each of the decile portfolios ↩

EW Returns: 7/1/1973 – 12/31/2016
↩ 
VW Returns: 7/1/1973 – 12/31/1993
EW Returns: 7/1/1973 – 12/31/1993
VW Returns: 1/1/1994 12/31/2016
EW Returns: 1/1/1994 12/31/2016
↩  Note we are big fans of Enterprise Multiples, as shown in our analysis here and here. ↩
 Assuming that P/E and B/M are not 100% correlated when it comes to sorting firms, this P/E fund will most likely have a lower HML loading. ↩
 While this is a nice tool, we have had two common requests from those using the tool:
 Can we simply get summary statistics (characteristics) of the ETFs
 Can we see the overlap and summary characteristics of a portfolio of ETFs
We are working on building these tools out now! The new tools will allow advisors to view the average characteristics of the ETFs–an example being the average Enterprise multiple being 10% for fund A and 6% for the Sp500. We will do this by calculating the valueweighted average for each characteristic. The second tool will allow advisors to build a portfolio of ETFs, and then view the overall overlap (relative to some index) as well as the average characteristics (P/E, Momentum, expense ratio, etc.) of the portfolio. So in total, we will have three tools that will allow advisors to better assess the characteristics of ETFs and portfolios of ETF. ↩