Eugene Fama, the 2014 co-recipient of the Nobel Prize in Economics and father of the efficient market hypothesis, and his equally well-credentialed co-author, Ken French, have summarized the academic research on momentum as follows: 1

Eugene Fama and Ken French

The premier anomaly is momentum.

When the greatest empirical finance researchers suggests momentum is the leading academic anomaly, we take note. Fama and French make this statement because the empirical research on the momentum effect is compelling. For example, academic researchers have examined stock data going back over 200 years and identified a significant and robust historical performance record. 2 As natural skeptics, we have independently verified many of the empirical results associated with momentum. Momentum is well grounded, historically. And while we never want to invest in a strategy simply because it has a great backtest, we believe that the momentum anomaly is a sustainable active investment strategy. We believe the strategy can persist because the returns are 1) driven by innate human bias, and 2) following the strategy is difficult because of enhanced volatility and career risk considerations.

We minimize deeply ingrained human bias by following a systematic approach to security selection, which protects us from our own behavioral errors. Our tools do not necessarily need to be complex, but they do need to be systematic.  We contend with volatility and career risk by educating investors on the long-term horizon required to be a successful momentum investor. We refuse to appease those with short horizons by “diluting” our Quantitative Momentum Index. Hence, our strategy is concentrated and follows an evidence-based methodology. In the end, we cannot guarantee long-term success, but our index process does promise one thing: a high-conviction momentum strategy that is grounded in our years of research and development.

Note: For those who want to dive right into the specifics of the Quantitative Momentum Indexes, information is available below:

An Introduction to the Quantitative Momentum Index

Our Quantitative Momentum (QM) process has a straightforward mission:

  • Identify the most effective way to systematically capture the momentum premium.

Our mission involves two core beliefs:

  • Momentum investing works over the long-haul and is driven by a predictable underreaction to positive news/fundamentals.
  • The strategy needs to be focused (i.e., 50 stocks or less) and anti-closet index.

We document our complete research findings in our book, Quantitative Momentum.

The book has been well received by the investment community, for example: 3

“Systematic momentum investing, as opposed to its complementary cousin value, has not gotten the investor attention it deserves. Wes and Jack fix this problem. Anyone interested in systematic investing should read this book and add more tools to their repertoire.”

Cliff Asness, Ph.D., Managing and Founding Principle of AQR

“Anyone who is using, studying or incorporating momentum will find a wealth of information in the pages of Quantitative Momentum

Chris Geczy, Ph.D., Founder and CEO of Forefront Analytics

Quantitative Momentum is the story of momentum-based stock selection algorithms. Wes and Jack lucidly explain how and why these systems work.”

Narasimhan Jegadeesh, Ph.D. Dean’s Distinguished Chair in Finance at Goizueta Business School

In 2012, Alpha Architect partnered with a multi-billion dollar family office and turned our dream to deliver affordable active management into a reality. At the time, we were focused on our Quantitative Value strategy. However, in the course of our extensive research and development efforts we created a momentum strategy that complemented our value strategy. In the end, we boiled down our momentum process into five sequential steps (depicted in Figure 1):

  1. Identify Universe: Our universe generally consists of mid- to large-capitalization U.S. exchange-traded stocks.
  2. Core Momentum Screen: We rank stocks within our universe based on their past twelve-month returns, ignoring the first month.
  3. Momentum Quality Screen: We screen high momentum stocks on the “quality” of their momentum—we focus on stocks with a “smoother” return path towards their high momentum status.
  4. Seasonality Screen: We take advantage of certain seasonal aspects applicable to momentum investing, which determines the timing of our rebalance.
  5. Invest with Conviction: We seek to invest in a concentrated portfolio of stocks with the highest quality momentum. This form of investing requires disciplined commitment, as well as a willingness to deviate from standard benchmarks.

Step 1–Identify the Investable Universe: Mid- and Large-Caps

The first step in the QM investing process involves setting boundaries on the universe for further screening.  There are several reasons we place such limits around the stocks to consider. A critical aspect involves liquidity, which is related to the size of the stocks under consideration. In general, if we include stocks that are too small, the possibility of large price moves on small volume can lead to significantly overstated theoretical returns relative to actual returns.  In other words, if we include small stocks in our universe, the back-tested results may generate phenomenal returns, but these returns may be unobtainable in the real world, even when operating with small amounts of capital.

In order to honestly assess and reliably implement the QM approach, we eliminate all stocks below the 40th percentile breakpoint of the NYSE by market capitalization. As of December 31, 2014, the 40th percentile corresponded to a market capitalization of approximately $1.9 billion.  Our universe also excludes ADRs, REITS, ETFs, and firms without 12 months of return data.

In summary, our investment universe contains liquid companies with at least one year of return data.

Step 2–Core Momentum Screen: Buy Past Winners

In basketball, if a player has made a few shots in a row, the player is described as having a “hot hand;” in finance parlance, this player has “momentum.” But can basketball players actually exhibit momentum? Originally, the evidence seemed to reject such a theory, as outlined in a 1985 paper by Thomas Gilovich, Robert Vallone and Amos Tversky. 4 For decades, the theory of a hot hand in sports was considered a myth. The question appeared settled. However, recent working papers by Andrew Bocskocsky, John Ezekowitz and Carolyn Stein in 2013 5, and Brett S. Green and Jeffrey Zwiebel in 2013 6, now show that the hot hand probably exists in basketball and also in baseball.

The intellectual journey to identify momentum in sports is similar to the attempts to identify momentum in stocks. Initially, stock momentum was deemed a myth because the efficient market hypothesis considered this approach to be impossible. Academics laughed at the idea. But contravening evidence began to mount…and mount…and mount. Today, no one is laughing. Serious evidence-based investors and academic researchers can no longer consider momentum heresy.

But how does one calculate momentum?

When testing momentum in stock returns, we need to first identify the time period over which we will calculate the momentum variable. Below we summarize the main academic research findings for three different look-back momentum calculation periods:

  • Short-Term Momentum (1-month) – exhibits a reversal in returns 7
  • Long-Term Momentum (3 to 5 years) – exhibits a reversal in returns 8
  • Intermediate-Term Momentum (6-12 months) – exhibits a continuation in returns 9

In short, both short-term and long-term momentum signal a future reversal in returns. In other words, one can expect these stocks to underperform. However, intermediate-term momentum provides a continuation of returns−the so-called “hot-hand”−and these stocks tend to outperform. We focus on this momentum measurement for Step 2. A simple hypothetical image to describe the intermediate-term momentum strategy can be found below:

Charts presented are for illustrative purposes only.

To examine how the momentum portfolios have performed, we use Ken French’s data in our book (here is a link to the data description). The results shown below are gross of any fees and run from 1/1/1927 to 12/31/2014, and examine the value-weight returns to the top and bottom decile momentum portfolios formed every month on their cumulative 12 month past returns, ignoring the last month (a.k.a.12_2 momentum) 10.

Performance figures contained herein are hypothetical, unaudited and prepared by Alpha Architect, LLC; hypothetical results are intended for illustrative purposes only. Past performance is not indicative of future results, which may vary. Index returns are for illustrative purposes only and do not represent actual fund performance. Index performance returns do not reflect any management fees, transaction costs, or expenses, which would reduce returns. Indexes are unmanaged and one cannot invest directly in an index. Source: Gray and Vogel. Quantitative Momentum. Hoboken: John Wiley and Sons, 2015. Period is from 1927 to 2014.

Big picture — buying the highest momentum stocks over the past nine decades was a great idea (on paper!). Note that the low-momentum decile portfolio, had a negative return over the same time period.

In general, the momentum premium decays as the rebalance frequency decreases, as we highlight here (e.g., monthly rebalanced portfolios beat annually rebalanced portfolios). However, costs increase with rebalance frequency. 11 Thus, consistent with the law of diminishing returns, there is a point at which the momentum benefits of frequent rebalancing are overcome by costs. As a compromise, we examine a “sweet spot” 3-month rebalance for the portfolio analysis that employs overlapping portfolios. 12

As shown in the image above, a generic momentum screen outperforms the passive market index based on annualized returns. However, a generic momentum portfolio also has more volatility and a larger drawdown. In the next step, we seek to identify techniques to minimize the extra volatility and drawdowns associated with momentum strategies.

Step 3–Momentum Quality Screen: The Path Matters

Step 1 helps us identify a universe that is expected to be reasonably liquid, and Step 2 examines the results for our first screen−the core momentum screen. In Step 3 we seek to identify the quality of momentum associated with the stocks from Step 2.

The details for calculating momentum quality are complex, but the intuition is simple. Consider two hypothetical momentum stocks: Stock A is a biotechnology company, Stock B is a Big Box Store, and both companies have a 200% return over the past 12 months. However, assume A and B have vastly different paths to 200 percent returns.

  • Buzzing Biotech: Stock A’s returns were 0% for 11 months, but just recently Stock A was granted an FDA approval for a new drug and the stock shot up 200%.
  • Boring BigBox: Stock B has returned 0.80% each day, on average, for the past 250 days, and has generated a 200% return.

Stock A and Stock B are both considered momentum stocks, but Buzzing Biotech’s path is much different from Boring BigBox’s path. So-called “path dependency” matters, if momentum is driven by an investor bias referred to as “limited attention.” For example, Buzzing Biotech’s FDA approval will likely be covered by the media and be highly available to investors, thus rapidly driving the company’s price to efficient levels. However, Boring BigBox is delivering news that is consistently better than market expectations over a longer period, and because the attention to Boring BigBox is limited, this good news is slow to be incorporated into market prices.

Below we graphically depict a hypothetical example of 2 “high” momentum stocks. 13 14

Graphic is for illustrative purposes only.

Although testing the “limited attention” hypothesis in the context of momentum is challenging, we’re lucky that finance professors have been hard at work. In a 2014 paper titled, “Frog-in-the-Pan: Continuous Information and Momentum,” Zhi Da, Umit Gurun, and Mith Awarachka find that high momentum firms with smooth, or “high-quality” momentum, tend to do better than those firms with choppy low-quality momentum. The results are summarized in Figure 3, which shows three-factor alpha estimates for long/short high-quality (“continuous”) and low-quality (“discrete”) momentum portfolios over various rebalance frequencies. 15 16

The Quantitative Momentum Investing Philosophy_Da, Gurun and Warachka

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.

Recall that the proverbial frog-in-the-pan sits in a pool of water whose temperature is gradually increasing. Because the change in temperature is so slow, the frog has limited attention to the rising heat and he slowly boils to death. Similarly, investors have limited attention to the ongoing flow of uneventful, but reliable information, arriving continuously in small amounts regarding a stock.

To calculate “frog-in-the-pan” momentum, the authors classify each daily return as either positive or negative (or zero in some cases). In general, a high-quality momentum stock should have a higher percentage of positive return days compared to a choppier stock. 17 We conduct our own analysis of the frog-in-the-pan variable and incorporate this variable into our Quantitative Momentum Index. In our context, we use the frog-in-the-pan measure to identify stocks from Step 2 that have high-quality momentum. We split the portfolio of high generic momentum stocks into high-quality momentum and low-quality momentum. The portfolio is value-weighted and rebalanced quarterly using over-lapping portfolios. The returns shown below are gross of any fees and run from 1/1/1927 – 12/31/2014.

Performance figures contained herein are hypothetical, unaudited and prepared by Alpha Architect, LLC; hypothetical results are intended for illustrative purposes only. Past performance is not indicative of future results, which may vary. Index returns are for illustrative purposes only and do not represent actual fund performance. Index performance returns do not reflect any management fees, transaction costs, or expenses, which would reduce returns. Indexes are unmanaged and one cannot invest directly in an index. Source: Gray and Vogel. Quantitative Momentum. Hoboken: John Wiley and Sons, 2015. Period is from 1927 to 2014

The results highlight that focusing on the high momentum stocks with quality momentum can improve CAGR, Sharpe and Sortino ratios.

Step 4–Seasonality Screen: Premiums Vary Over Time

Steps 1 through 3 focus on momentum stocks with quality momentum. Step 4 further enhances our Quantitative Momentum system by incorporating seasonality effects that have been documented in momentum strategy research. 18 Some of the most compelling research on this subject is found in a 2007 paper titled, “Causes and Seasonality of Momentum Profits,” published in the Financial Analyst Journal by Richard Sias. Professor Sias shows that window-dressing (i.e., when institutions buy stocks that have performed well so they can report ownership of “winning” stocks for quarter-end reports) and tax incentives at year-end drive momentum seasonality effects.

Professor Sias summarizes his results:

“…the average monthly return to a momentum strategy for U.S. stocks was found to be 59 bps for non-quarter-ending months but 310 bps for quarter-ending months…investors using a momentum strategy should focus on quarter-ending months…”

Sias’s paper focuses on long/short momentum portfolios, but the conclusions regarding momentum seasonality can be incorporated into our long-only Quantitative Momentum system. Below we show the spread between the high and low momentum portfolios month-to-month from 1/1/1927 – 12/31/2014, gross of any fees. 19 It is important to not we are showing the average monthly return to the difference between the high and low momentum portfolios (a long/short portfolio).

Performance figures contained herein are hypothetical, unaudited and prepared by Alpha Architect, LLC; hypothetical results are intended for illustrative purposes only. Past performance is not indicative of future results, which may vary. Index returns are for illustrative purposes only and do not represent actual fund performance. Index performance returns do not reflect any management fees, transaction costs, or expenses, which would reduce returns. Indexes are unmanaged and one cannot invest directly in an index. Source: Gray and Vogel. Quantitative Momentum. Hoboken: John Wiley and Sons, 2015. Period is from 1927 to 2014.

One notices that the spread between the high and low momentum portfolios is (in general) the highest in quarter-ending months (comparing the returns within each quarter). 20  We test our quality momentum strategy, but vary the start date of the portfolios. In the figure below, we compare a quarterly rebalanced portfolio that incorporates seasonality effects by rebalancing near the beginning of quarter-ending months (column 1) 21 to a portfolio to a portfolio that ignores seasonality (column 2). The returns show below are from 1/1/1927 – 12/31/2014 and are gross of any fees.

Performance figures contained herein are hypothetical, unaudited and prepared by Alpha Architect, LLC; hypothetical results are intended for illustrative purposes only. Past performance is not indicative of future results, which may vary. Index returns are for illustrative purposes only and do not represent actual fund performance. Index performance returns do not reflect any management fees, transaction costs, or expenses, which would reduce returns. Indexes are unmanaged and one cannot invest directly in an index. Source: Gray and Vogel. Quantitative Momentum. Hoboken: John Wiley and Sons, 2015. Period is from 1927 to 2014.

As the table above shows, forming the portfolio to exploit seasonality effects within momentum stocks yields higher CAGR, Sharpe, and Sortino ratios.

Step 5–Invest with Conviction: Focused Quantitative Momentum Factor Exposure

Steps 1 through 4 systematically identify stocks with the highest quality momentum and take advantage of momentum seasonality. We believe we have identified a form of momentum investing that intelligently incorporates the best research on the subject into a coherent and pragmatic investment approach. But we can easily destroy the benefits of a reasonable investment process by mismanaging portfolio construction and “diworsifying” our active momentum exposure. Charlie Munger, at the 2004 Berkshire Hathaway Annual Meeting, is quoted as saying, “The idea of excessive diversification is madness…almost all good investments will involve relatively low diversification.” Charlie Munger is right: to the extent you believe you have a reliable method of constructing a high alpha “active” portfolio, less diversification is desirable.

In the spirit of Munger’s sage advice, we construct our portfolios to hold around 50 securities, on average.

Consider our typical process:

  1. Identify Universe: We typically generate ~ 1,000 names in this step of the process.
  2. Core Momentum Screen: Select the top decile of firms on their past momentum, or 100 stocks.
  3. Momentum Quality Screen: Select high-momentum firms with smoothest momentum, 50 stocks or 50%.
  4. Seasonality Screen: Rebalance the portfolio near the beginning of quarter-end months.
  5. Invest with Conviction: We invest in our basket of 50 stocks with the highest quality momentum.

Our Quantitative Momentum Index has the following construction details:

  • Equal-weight construction
  • Quarterly rebalanced
  • 25% sector/industry constraint
  • Pre-trade liquidity requirements

We don’t like to emphasize historical performance, because we believe process is paramount. However, if you’d like to see the hypothetical performance we suggest you review our index educational materials, which are available here.

Why Isn’t Everyone a Concentrated Systematic Momentum Investor?

We believe our Quantitative Momentum Index process is evidence-based and has a chance to outperform the market over the long-haul on a risk-adjusted basis. But while all of this may sound promising, one must consider a simple question:

If this is so easy, why aren’t all investors doing it?

In addition to the fact that building and implementing a momentum portfolio is non-trivial, there are two key reasons why our approach to momentum is simple but challenging:

  1. Momentum investing is inherently more volatile than passive equity investing.
  2. High-conviction momentum investing is loaded with career risks and the chance of suffering long stretches of relative underperformance.

Many professionals shy away from momentum investing because the return path is volatile and deviations from standard benchmarks are extreme. For example, from 1974 to 2016 the standard deviation of the market (S&P 500) was 15.30%, whereas the standard deviation of the domestic Quantitative Momentum Index is 25.15%. The Quantitative Momentum Index is inherently volatile.

But the pain doesn’t end there, the Quantitative Momentum Index is designed to be very different from the passive indexes. The tracking error of the Quantitative Momentum Index versus the S&P 500 is over 17%. In other words, prepare for major deviations from standard benchmarks and multiple opportunities to get fired as an asset manager.

The ability to withstand short-term pain is required to pursue a high-conviction momentum strategy, but the rewards for a disciplined investor are the hopeful upside expected returns.


In the short-run, most of us simply cannot endure the pain that momentum investing strategies impose on our portfolios and our psyches. It is simply too difficult. Furthermore, for those in the investment advisory business, providing a strategy with the potential for multi-year underperformance is akin to career suicide. 22 And yet, at Alpha Architect, we explicitly focus on a high-conviction momentum investing philosophy because the evidence for outperformance is so striking and robust. Why would we risk such career suicide? Our hope is that we can educate investors with the appropriate temperament on what it takes to achieve long-term investment success as a momentum-investor. It is not easy, and it is not for everyone, but for those rare souls who understand the discipline required, our systematic momentum investment process allows investors to simply “follow the model” and avoid behavioral biases that can poison even the most professional and independent fundamental momentum investors.

Buy Stocks with the Highest Quality Momentum

— Wesley R. Gray and Jack R. Vogel, co-CIOs Alpha Architect

Information on our Quantitative Momentum Indexes is available here.

Here are some specific research/educational materials:

The Quantitative Momentum book, outlines the details associated with steps 2, 3, and 4 if you’d like to learn more about the process.

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  1. Fama, E. and K. French, 2008, Dissecting Anomalies, The Journal of Finance, 63, pg. 1653-1678.
  2. Geczy, C. and M. Samonov, 212 Years of Price Momentum, University of Pennsylvania Working Paper, accessed 10/31/2015
  3. The recommendations are directed towards the quality of the book and are not an endorsement of advisory services provided by Alpha Architect, LLC or affiliates. Alpha Architect does not know if the recommenders approve or disapprove of its services. The recommendations were chosen from a list of formal recommendations based on if the author had a PhD or not.
  4. Gilovich, E., R. Vallone, and A. Tversky, 1985, The Hot Hand in Basketball: On the Misperception of Random Sequences, Cognitive Psychology, 17, pg. 295-314.
  5. Bocskocsky, A., J. Ezekowitz, and C. Stein, 2014, The Hot Hand: A New Approach to an Old “Fallacy”, working paper, accessed 11/15/15
  6. Green, B. S., and J. Zwiebel, 2015, The Hot-Hand Fallacy: Cognitive Mistakes or Equilibrium Adjustments? Evidence from Major League Baseball, working paper, accessed 11/15/15
  7. Lehman, B. N., 1990, Fads, Martingales, and Market Efficiency, The Quarterly Journal of Economics, 105, pp. 1-28 and Jegadeesh, N., 1990, Evidence of Predictable Behavior of Security Returns, The Journal of Finance, 45, pp. 881-898.
  8. DeBondt, W. F., and R. Thaler, 1985, Does the Stock Market Overreact?, The Journal of Finance, 40, pp. 793-805.
  9. Jegadeesh, N., and S. Titman, 1993, Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency, The Journal of Finance, 48, pp. 65-91.
  10. Note: we exclude last month’s returns to minimize the short-term momentum reversal effect
  11. We highlight arguments regarding trading costs in a few blog posts here, here, and here.
  12. We use overlapping portfolios. An example of a 3-month hold portfolio would be as follows: on Jan 1, buy the top decile and hold until March 31; on Feb 1, buy the top decile and hold until April 30; on March 1, buy the top decile and hold until May 31. So the portfolio return during March would be the equal-weighted basket of the stocks added on Jan 1, Feb 1, and March 1.
  13. Note, Stock A and Stock B drawn here are not “Buzzing BioTech” and “Boring BigBox” described above–h.t. to G for the close reading!
  14. Note — we are not great artists!
  15. Da, Z., U. G. Gurun, and M. Warachka, 2014, Frog in the Pan: Continuous Information and Momentum, Review of Financial Studies, pp. 1-48.
  16. Figure 3 also highlights that the alpha for a long/short momentum strategy decreases as the holding period increases (less rebalances). A similar result is found for long-only portfolios in many academic papers.
  17. The exact variable used is ID = sign(momentum over past 12 months ignoring last month)*(%negative-% positive)
  18. Sias, R., 2007, Causes and Seasonality of Momentum Profits, Financial Analyst Journal, 63, pp. 48-54.
  19. We again use overlapping quarterly-rebalanced value-weight portfolios
  20. While the January finding in the paper is interesting (low momentum outperforms high momentum in January), attempting to trade on this can be difficult to implement. As such, we do not include this in our Quantitative Momentum screening methodology.
  21. This portfolio is rebalanced at the close on the last trading day of February, May, August, and November.
  22. High conviction momentum can be combined with high conviction value strategies to help mitigate portfolio risk.