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Stock Market Anomalies, Risk Factors, and Premiums

     Returning to the discussion about the efficient market hypothesis discussed in chapter six, let’s take a more in depth look at the question of how good stock markets are at pricing investment securities. Despite extensive evidence that the U.S. stock markets are highly efficient, there have been hundreds of studies that have documented long-term historical anomalies that seem to contradict the efficient market hypothesis. Many practitioners that attempt to outperform markets have historically been described as using “quantitative” strategies, but more recently other terms like “fundamental indexing,” “smart beta,” and other terms1 have been promoted to describe funds that attempt to outperform markets using various screens using factors, or risk premiums.

     There have been so many factors of various types identified in the academic literature that the term factor zoo is commonly used (John Cochrane coined the term “zoo of factors” in 2011).2 Campbell Harvey and Yan Liu have a publicly posted spreadsheet of the over 500 research papers documenting factors that have been documented, organized by date of publication.3

     Arguably, factor and style research originate from William Sharpe’s suggestion that market correlation (represented by “beta”) explained equity returns, which was named the capital asset pricing model (CAPM). In other words, the higher the beta, the higher the risk and expected return.

     Other researchers were also working simultaneously on theories to explain stock performance. Jack Treynor, John Lintner, and Jan Mossin were among those developing models (building off the work of Harry Markowitz) suggesting stock performance was related to the overall stock market. Some credit Fisher Black with identifying low risk as another factor in 1972.4 Black developed another version of CAPM (called Black CAPM) that does not assume the existence of a riskless asset (which is used to calculate returns in the CAPM).

     Barr Rosenberg was also among the first to document other factors correlated with returns (around 1974).5 Stephen Ross and Richard Roll developed a separate model in 1976 called the arbitrage pricing theory (APT), which argued that stock market factors (like GDP growth and inflation) can be constructed so that they represent macroeconomic influences.6 Some credit Narasimhan Jegadeesh and Sheridan Titman for documenting outperformance of a momentum strategy in 19937 and Mark Carhart is credited by many for documenting momentum as a stock factor in 1997.8

     In 1992 Eugene Fama and Kenneth French published a paper titled “The Cross-Section of Expected Stock Returns” which concluded that in addition to the overall stock market risk (or beta), book value to market price (or value) and market capitalization (small size) helped explain stock market returns.9 Fama and French later expanded to five factors (adding profitability, and investment patterns) in a paper published in 2015.10

     Fama and French’s 1992 paper had a profound impact in the academic community and made headlines in part because Fama was a long-time champion of CAPM. Based on CAPM, a stock that moves less than the market would have a low beta and lower expected return, while more volatile stocks have beta above one and higher expected returns. But Fama and French’s newer data suggested that there was a lot more going on with stocks than just beta (confirming what others had been documenting). Thus newer models were developed with the addition of other factors. Investment products that attempt to take advantage of any pricing inaccuracies have been introduced in many forms, using numerous names and terms. The term “smart beta” derives from Sharpe’s market “beta” and expands to other factors.

     Rob Arnott founded Research Affiliates in 2002 and creating “RAFI” indexes that intend to generate excess returns relative to market cap weighted indexes. Charles Schwab launched a series of mutual funds based on the RAFI indexes in April 2007 and they recently claimed the “fundamental indexes” had outperformed market cap indexes in the U.S. and international markets (by 50 to 220 basis points per year). Their funds deviate from full market weighting based on market cap by using a strategy based on fundamental measures, which they argue has proven to be a beneficial. They pointed out that value strategies actually underperformed growth over that period, making the fundamental indexes performance even more impressive. They argued the performance implies the other factors used in the indexes (size or popularity) helped to improve performance for the period.11

     Researchers that discover anomalies or styles that would have produced superior returns (based on historical data) have two choices. They can go public and seek recognition for discovering the technique; or they can attempt to use the technique to try to earn excess returns. Some do both, but arguably at this point, the probability of finding anomalies that haven’t been discovered or aren’t related to other anomalies has diminished significantly. Yet, given that hundreds of anomalies or risk factors have been identified in recent decades, perhaps there are some significant factors, or unique situations in different locations or scenarios that remain undiscovered.

     An example of an anomaly that was discovered, but not well documented in the academic community until later, is momentum investing.12 Ironically, I joined Plexus Group in 1998 when the firm was well established with dozens of prominent clients, but Plexus’ first client for its main product was Driehaus Capital Management, founded by Richard Driehaus (considered the father of momentum investing) in 1982. Another early momentum investor was Nicholas Applegate Capital Management, which was founded in 1984 (and was one of my clients at Plexus Group).

     While the existence of anomalies is generally well accepted, the question of whether investors can exploit them to earn superior returns in the future is debatable. Investors evaluating anomalies and factors should keep in mind that some anomalies that existed historically, later stopped working, and of course, there is no guarantee others will persist in the future. If they do persist, transactions costs may prevent outperformance in the future. Investors should also consider tax effects in their taxable portfolios when evaluating stock strategies. Anomalies that have existed over the longest time frames and have been confirmed to exist in international markets and out of sample periods are the most persuasive.

     Initially, many argued that value stocks and small cap stocks are riskier and thus have higher returns. But others (including supporters of behavioral finance) disagree that the outperformance is related to risk, and subsequently many other factors have also been identified that seem to have less of a logical connection with a risk argument. Many (myself included) are skeptical that many of the factors can be expected to produce any extra return above appropriate benchmarks, net of costs. Bruce Jacobs and Kenneth Levy were also skeptical of investors’ ability to benefit from so called smart beta strategies in a 2015 paper titled “Smart Beta: Too Good to be True?“13

     It's common for money to flow into strategies that attempt to exploit anomalies and this in turn can cause the anomaly to shrink, or disappear. A May 2018 article by Bloomberg estimated that over 20% of ETF assets from 2014-2018 were in smart beta funds.14 Vanguard also recently began offering “factor investing” options.15 Further, even anomalies that do persist may take decades to pay off. John West and Jason Hsu also warn that investors’ poor timing (see Chapter 11) likely completely negates alpha from smart beta or factor investing.16. Check also my recent post Who Knows?

     Investors evaluating historical data should also consider the potential pitfalls of "data mining" (more on that in Chapter 25). When searching large amounts of data, correlations between variables may occur randomly and therefore may have no predictive value. A possible example is the fact that the DJIA through 1995 had never had a down year in any year ending in 5. 2005 had a slight loss, but a positive return with dividends, while most indexes were down in 2015.

1. Simon Constable writing in early 2019 discussed the term "quantamental" - "an investment strategy that combines a fundamental approach to investing with a quantitative one" in "What Is ‘Quantamental’ Investing?" Wall Street Journal, April 7, 2019
2. See "Now we have a zoo of new factors" at
and "To address these questions in the zoo of new variables" at
3. Campbell Harvey, Yan Liu, "A Census of the Factor Zoo" March 25, 2019
4. For instance, on page 18 of "Credit Suisse Global Investment Returns Yearbook 2018" Elroy Dimson, Paul Marsh, Mike Staunton summarize factor investing and mention Black.
5. See “Factor Investing and Asset Allocation: A Business Cycle Perspective”, Vasant Naik, Mukundan Devarajan, Andrew Nowobilski, Sébastien Page, Niels Pedersen, December 2016
6. "The Arbitrage Theory of Capital Asset Pricing," S.A. Ross, Journal of Economic Theory, December 1976
7. "Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency" Narasimhan Jegadeesh and Sheridan Titman The Journal of Finance, March 1993
8. On Persistence in Mutual Fund Performance, Mark M. Carhart, The Journal of Finance, March 1997
9. “The Cross-Section of Expected Stock Returns.” Fama, Eugene F. and Kenneth R. French. Journal of Finance, June 1992.
10. “A Five-Factor Asset Pricing Model” Fama, Eugene F., and Kenneth R. French, Journal of Financial Economics, April 2015
11. "A Decade of Results" The Past, Present, and Future of Fundamental Index® Strategies
12. For a summary of momentum see Corey Hoffsteinon, Two Centuries of Momentum, March 23, 2018
13. Smart Beta: Too Good to be True? Bruce I. Jacobs, Ph.D. Kenneth N. Levy , The Journal of Financial Perspectives, July 2015
14. "Investors Can Miss the Forest for the Smart Beta Trees" Nir Kaissar, May 7, 2018
16. John West, Jason Hsu, "The Biggest Failure in Investment Management: How Smart Beta Can Make It Better or Worse" October 2018

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Table of Contents and Launch Site

Last update 3/16/2020. Copyright © 2019-2020 Gary Karz. All rights reserved.
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