1. Throughout the article our focus is on the examination of cross-sectional momentum and how mutual funds attempting to capture cross-sectional momentum are able to benefit their investors. We leave the study of time-series momentum or momentum in asset classes other than equity outside the scope of this article.
2. To be fair, all factors may experience long periods of less-than-stellar performance when investors would have been better off investing in the benchmark. If the momentum factor is characterized by sharp drawdowns, other factors such as value may have long periods of underperformance without high negative skewness. As we write this article, many value managers have experienced a decade-long period of subpar performance over which the theoretical long–short value factor (HML) has averaged an annualized −3.1% return in the 10 years ending December 2016.
3. Our study focuses on mutual funds. We are not claiming that no market participants have benefited from momentum. In fact, some highly skilled hedge fund managers are able to benefit from momentum. Ironically, the fact that mutual funds are not benefiting from momentum exposures likely means that these mutual funds are acting as a source of the premium to the hedge fund industry.
4. In the first article of the Alice in Factorland series (Arnott, Kalesnik, and Wu, 2017) we show that investors are routinely unable to capture most factor premia. Mutual fund managers deliver only about half of the value premium and, quite strikingly, almost none of the momentum premium. We expand on that finding in this article with a more detailed examination of momentum funds. In the second article of the series (Arnott, Clements, and Kalesnik, 2017), we show that those who dismiss smart beta strategies as merely a collection of factor tilts miss the rich nuances of some of these strategies, and in so doing, perform a disservice to investors. We show this by replicating smart beta strategies using theoretical long–short factor portfolios and find they delivered much worse investment outcomes than the paper portfolios—even before trading costs, which would be incurred in live replications of the strategies. We also find that a “smart” smart beta strategy is far more than a collection of its factors. In the third article of the series, we demonstrate mean reversion in fund performance. This finding implies that investors who follow the common practice of firing underperforming managers and replacing them with recently outperforming managers tend to lose from such performance chasing. Another important take away of the article is that fund-return mean reversion is largely driven by factor valuation cycles. Indeed, knowing a fund’s past factor exposures and current factor valuations can be useful in identifying future winners; this relationship has correlations ranging to above 25% for subsequent one-year relative performance.
5. Although cross-sectional momentum was first documented in the academic literature fairly recently, traders have been following momentum strategies for centuries in various forms of technical analysis. A good example is the candlestick chart, which Japanese traders speculating in rice futures used at least as far back as the 17th century.
6. Cross-sectional momentum in equities was first documented by Jegadeesh and Titman (1993), Asness (1994), and Carhart (1997). These authors showed that stock performance on the horizon of several months up to a year tends to continue into subsequent months, and that this factor should be a part of the standard toolkit in explaining cross-sectional equity performance. Subsequent studies by Rouwenhorst (1998), Griffin, Ji, and Martin (2003), Liew and Vassalou (2000) and Chui, Titman, and Wei (2010) have demonstrated that the momentum effect is robust internationally. Moskowitz and Grinblatt (1999) have documented an industry momentum effect. Asness, Liew, and Stevens (1997) and Bhojraj and Swaminathan (2006) have demonstrated the momentum effect for country equity indices. The momentum effect has also been demonstrated for other asset classes: Arnott and Pham (1993), Kho (1996), and LeBaron (1999) for currencies; and Erb and Harvey (2006) and Gorton, Hayashi, and Rouwenhorst (2008) for commodities. Apart from cross-sectional momentum, Moskowitz, Ooi, and Pedersen (2012) have documented time-series momentum.
7. Risk-based explanations for momentum have, to this point, been less developed in the literature. Perhaps one of the more convincing risk-based explanations is offered by Harvey and Siddique (2000), who provide evidence that skewness risk is associated with a premium. This evidence suggests negatively skewed momentum is responsible, tying its positive return premium to its negative skewness. In other words, it works well most of the time, as recompense for its horrible crashes. Conrad and Kaul (1998) also offer a risk-based interpretation of momentum, demonstrating that the momentum return comes mostly from the differences in the long-run average returns of stocks, not the time-series effect. This outcome is inconsistent with the behavioral-based explanations of Barberis, Shleifer, and Vishny (1998), Daniel, Hirshleifer, and Subrahmanyam (1998), and Hong and Stein (2000). The risk-based interpretation of these results is that if certain stocks are riskier than others and consistently deliver a higher risk premium, they will be picked up by a momentum strategy. Unfortunately, later studies such as Jegadeesh and Titman (2001, 2002) have failed to replicate their findings and therefore attribute the original result to complications of using a boot-strapping econometric technique. Chordia and Shivakumar (2002) argue that momentum profits can be explained by stock return predictability arising from macroeconomic variables, suggesting a possible role for time-varying expected returns. Grinblatt and Moskowitz (2004) point out the relation between tax-loss selling and the momentum effect. And finally, Lou, Polk, and Skouras (2017) show that momentum profits accrue entirely overnight and explain this phenomenon as the “clientele effect.”
8. Evidence suggests the slow reaction to news, both positive and negative, could be due to a conservativism bias in human information processing (Barberis, Shleifer, and Vishny, 1998). Such a bias could explain both the initial underreaction when good news is announced and the overreaction of investors in continuing to push a stock’s price higher or lower following the direction of the momentum. Several studies, such as Chan, Jegadeesh, and Lakonishok (1996) and Chordia and Shivakumar (2002), find a strong return associated with earnings momentum, confirming that a lot of the momentum return is earned around earnings announcements. Earnings momentum and price momentum are such related anomalies that Novy-Marx (2015) recently argued that earnings momentum fundamentally subsumes price momentum.
9. Overconfidence in psychology is defined as a type of miscalibration of the accuracy of success probability (Brenner et al., 1996; Dawes and Mulford, 1996; Fischhoff, Slovic, and Lichtenstein, 1977; and Slovic, Fischhoff, and Lichtenstein 1980). Sources of overconfidence are grouped into cognitive and motivational categories (Keren, 1997, and Griffin and Tversky, 1992). Overconfidence bias is also extensively studied in the behavioral economics and finance literature, including implications of this bias on trading volume (Biais, Glosten, and Spatt, 2005), information processing in markets (Odean, 1998), and corporate actions, such as mergers and acquisitions activity (Roll, 1986).
10. We observe that these three widely cited papers, all which describe behavioral foundations for momentum, appeared shortly before standard momentum began to fail in the United States.
11. Except where otherwise noted, we are referring to standard momentum, which measures performance over the past 12 months, excluding the latest month, and we are choosing the best-performing 30% of stocks for our long portfolio and the worst-performing 30% for our short portfolio, while controlling for size.
12. Sharpe ratio comparisons mask the propensity of momentum strategies to suffer from momentum crashes; the cross-sectional momentum strategy is negatively skewed, while the value and small-cap strategies have historically exhibited positive skewness. Japan is a notable exception. Momentum does not work in the Japanese market. We will touch on the unique situation of Japan in more detail in a later section.
13. Because momentum is viewed as one of the strongest and most pervasive investment factors, academics tend to include it in empirical studies of multi-factor models along with other widely studied factors, such as value and size. Asness (1994) and Carhart (1997) were among the first to advocate controlling for momentum in empirical research.
14. Sharpe ratios of the small-cap, value, and momentum factors in the US region for the 1927–2016 period are 0.23, 0.38, and 0.49, respectively. To compare the US region to the other geographic regions, we report statistics for the 1990–2016 period in Figure 1.
15. Arnott, Kalesnik, and Wu (2017) document the performance gap by comparing the respective performances of the momentum funds (with positive momentum exposure) and the contrarian funds (with negative momentum exposure). In using this method, we acknowledge the possibility that the gap could arise because the contrarian funds perform materially better than implied by their negative momentum exposure. Furthermore, if the momentum exposure of the funds we measure is very noisy, then the measured factor premium would be significantly downward biased. The detailed study of the gap in this article addresses these concerns.
16. A regression-based factor model may not be the best tool to adjust fund performance for momentum exposure because it is not clear that momentum is a risk factor. The literature mostly agrees that mispricing interpretation is more plausible as the cause of the momentum premium and that the momentum stock characteristic is the driver of return. Thus, a Daniel et al. (1997) (DGTW) model-style attribution may provide more accurate fund momentum exposure measurement and fund performance attribution. The drawback of the DGTW model is that it requires access to fund holdings. Because our main purpose in including the factor exposure is to validate that momentum funds do indeed have higher momentum loadings among the selected groups, we view the less accurate method as still being appropriate.
17. The −1.4% a year underperformance is calculated using equally weighted fund/month observations. If at each point in time we equally weighted the funds and computed this equally weighted portfolio, it would underperform −4.1% a year.
18. In Panel A of Table 2, we report measures of fund sensitivity to market, small-cap, value, and momentum factors using observed fund returns in the full sample. The factor sensitivity of funds is estimated using multivariate regression. No doubt, using the full sample introduces a look-ahead bias into estimation of fund factor sensitivities, but also makes factor sensitivity estimations more precise. In Panel B of Table 2, we report measures of the correlation of fund value-add relative to the benchmark with the momentum factor, again using the full sample.
19. We find it puzzling many observers expect positive alphas net of Fama–French three-or-more factor attribution tests. Fees and trading costs will show up in these alphas, as will other forms of implementation shortfall (Arnott, 2006). A multi-factor alpha of zero is a win. A positive multi-factor alpha is a big win. A more realistic exercise could be to use an alternative factor-model specification in which factor returns are adjusted for the implementation shortfall.
20. We also display the factor sensitivities of the funds to confirm that our selection process yields the desired outcome; each of the groups has the highest loading on the factor it seeks to capture.
21. Other studies, for example, Korajczyk and Sadka (2004) and Novy-Marx and Velikov (2015), using different assumptions, find a similar order of magnitude in trading cost estimates. Further, we find that these estimated trading costs match remarkably well the realized factor-return shortfalls we observed in the first article in this series, Arnott, Kalesnik, and Wu (2017).
22. This is constructed in the conventional fashion. Stocks are ranked based on trailing 12-month performance, excluding the most recent month; this is our momentum metric. The factor-return time series is constructed by computing the performance difference of a long portfolio, consisting of 30% of the market with the best momentum, capitalization weighted, relative to a short portfolio consisting of 30% of the market with the worst momentum, also capitalization weighted. The portfolio is reconstituted monthly, leading to just under 10% turnover each month for both the long and the short portfolios. No adjustment is made for transaction costs, missed trades, cost of leverage, cost of borrowing stock for the short portfolio, fees, and so forth.
23. Credit for this finding goes to Engin Kose and his colleagues during his PhD program Long Chen and Ohad Kadan, who explore this idea in detail in the 2012 working paper “Fresh Momentum.”
24. These average results are based on 89 years of data, with over 1,000 starting portfolios on both the long and the short sides, so the smoothness of this line is deceptive. Every starting month will be different, as will be the trajectory over the subsequent three years.
25. See Arnott, Beck, and Kalesnik (2016a,b).
26. More generally, as first documented by DeBondt and Thaler (1987), a stock, on average, experiences short-term mean reversion on a monthly horizon, then momentum on the horizon of up to a year, and then mean reversion on the horizon larger than a year and strongest over 2 to 3 years. The mean reversion we observe on the horizon above one year, as shown in Figure 3, is strongly related and largely subsumed by value as documented by Beck et al. (2017). Most of these 89 years of data are before standard momentum was “discovered” by academe, and before it lost its efficacy in even the early months.
27. Chen, Kadan, and Kose (2012) argue a more efficient way of momentum investing. Conditioning momentum on longer-term return performance creates a more profitable momentum strategy. We are adopting this idea in our fresh and stale momentum definitions.
28. Traditional cap-weighted indices weight companies in proportion to their capitalization, overweighting companies as they become overpriced and underweighting as they become cheap, leading to a return drag (Arnott et al., 2014, and Treynor, 2005). Fundamental Index strategies select and weight companies in proportion to the size of a company’s business (e.g., cash flows, sales, book value of equity, dividends + buybacks, number of employees, etc.). This weighting scheme is unrelated to prices and therefore does not suffer from a similar return drag as does a cap-weighted index. It also assigns larger weight to larger companies, which are usually large cap and highly liquid, resulting in capacity similar to that of the cap-weighted benchmark.
29. The Fundamental Index category now spans an estimated quarter-trillion USD in assets globally—so large that other authors could include Fundamental Index without risk of criticism, and thus we should be accorded the same privilege.
Aked, Michael, and Max Moroz. 2015. “The Market Impact of Passive Trading.” Journal of Trading, vol. 10, no. 3 (Summer):5–12.
Arnott, Robert D. 2006. “Implementation Shortfall.” Financial Analysts Journal, vol. 62, no. 3 (May/June):6–8.
Arnott, Robert D., Noah Beck, and Vitali Kalesnik. 2016a. “To Win with ‘Smart Beta’ Ask If the Price Is Right.” Research Affiliates (June).
———. 2016b. “Timing ‘Smart Beta’ Strategies? Of Course! Buy Low, Sell High!” Research Affiliates (September).
Arnott, Robert D., Noah Beck, Vitali Kalesnik, and John West. 2016. “How Can ‘Smart Beta’ Go Horribly Wrong?” Research Affiliates (February).
Arnott, Robert D., Mark Clements, and Vitali Kalesnik. 2017. “Why Factor Tilts Are Not Smart ‘Smart Beta.’” Research Affiliates (May).
Arnott, Robert D., Jason Hsu, Jun Liu, and Harry Markowitz. 2014. “Can Noise Create the Size and Value Effects?” Management Science, vol. 61, no. 11 (October):2569–2579.
Arnott, Robert D., Vitali Kalesnik, and Lillian Wu. 2017. “The Incredible Shrinking Factor Return.” Research Affiliates (April).
Arnott, Robert D., and Tan Pham. 1993. “Tactical Currency Allocation.” Financial Analysts Journal, vol. 49, no. 5 (September/October):47–52.
Asness, Clifford. 1994. “Variables That Explain Stock Returns.” Doctoral dissertation, University of Chicago.
Asness, Clifford, John Liew, and Ross Stevens. 1997. “Parallels between the Cross-Sectional Predictability of Stock and Country Returns.” Journal of Portfolio Management, vol. 23, no. 3 (Spring):79–87.
Barberis, Nicholas, Andrei Shleifer, and Robert Vishny. 1998. “A Model of Investor Sentiment.” Journal of Financial Economics, vol. 49, no. 3 (September):307–343.
Beck, Noah, Shingo Goto, Jason Hsu, and Vitali Kalesnik. 2017. “The Duality of Value and Mean-Reversion.” In Portfolio Construction, Measurement, and Efficiency edited by John B. Guerard, Jr. Switzerland: Springer International Publishing:229–238.
Bhojraj, Sanjeev, and Bhaskaran Swaminathan. 2006. “Macromomentum: Returns Predictability in International Equity Indices.” Journal of Business, vol. 79, no. 1(January):429–451.
Biais, Bruno, Larry Glosten, and Chester Spatt. 2005. “Market Microstructure: A Survey of Microfoundations, Empirical Results, and Policy Implications.” Journal of Financial Markets, vol. 8, no. 2 (May):217–264.
Brenner, Lyle, Derek Koehler, Varda Liberman, and Amos Tversky. 1996. “Overconfidence in Probability and Frequency Judgments: A Critical Examination.” Organizational Behavior and Human Decision Processes, vol. 65, no. 3 (March):212–219.
Carhart, Mark. 1997. “On Persistence in Mutual Fund Performance.” Journal of Finance, vol. 52, no. 1 (March):57–82.
Chan, Louis, Narasimhan Jegadeesh, and Josef Lakonishok. 1996. “Momentum Strategies.” Journal of Finance, vol. 51, no. 5 (December):1681–1713.
Chen, Long, Ohad Kadan, and Engin Kose. 2012. “Fresh Momentum.” Washington University in St. Louis working paper.
Chordia, Tarun, and Lakshmanan Shivakumar. 2002. “Momentum, Business Cycle, and Time-Varying Expected Returns.” Journal of Finance, vol. 57, no. 2 (April):985–1019.
Chui, Andy, Sheridan Titman, and John Wei. 2010. “Individualism and Momentum around the World.” Journal of Finance, vol. 65, no. 1 (February):361–392.
Conrad, Jennifer, and Gautam Kaul. 1998. “An Anatomy of Trading Strategies.” Review of Financial Studies, vol. 11, no. 3 (July):489–519.
Daniel, Kent, Mark Grinblatt, Sheridan Titman, and Russ Wermers. 1997. “Measuring Mutual Fund Performance with Characteristic-Based Benchmarks.” Journal of Finance, vol. 52, no. 3 (July):1035–1058.
Daniel, Kent, David Hirshleifer, and Avanidhar Subrahmanyam. 1998. “Investor Psychology and Security Market Under- and Overreactions.” Journal of Finance, vol. 53, no. 6 (December):1839–1885.
Dawes, Robyn, and Matthew Mulford. 1996. “The False Consensus Effect and Overconfidence: Flaws in Judgment or Flaws in How We Study Judgment?” Organizational Behavior and Human Decision Processes, vol. 65, no. 3 (March):201–211.
Erb, Claude, and Campbell Harvey. 2006. “The Strategic and Tactical Value of Commodity Futures.” Financial Analysts Journal, vol. 62, no. 2 (March/April):69–97.
Fama, Eugene, and Kenneth French. 1993. “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics, vol. 33, no. 1 (February):3–56.
Fischhoff, Baruch, Paul Slovic, and Sarah Lichtenstein. 1977. “Knowing with Certainty: The Appropriateness of Extreme Confidence.” Journal of Experimental Psychology: Human Perception and Performance, vol. 3, no. 4 (November):552–564.
Gorton, Gary, Fumio Hayashi, and Geert Rouwenhorst. 2008. “The Fundamentals of Commodity Futures Returns.” Yale International Center for Finance working paper.
Griffin, Dale, and Amos Tversky. 1992. “The Weighing of Evidence and the Determinants of Confidence.” Cognitive Psychology, vol. 24, no. 3 (July):411–435.
Griffin, John, Xiuqing Ji, and Spencer Martin. 2003. “Momentum Investing and Business Cycle Risk: Evidence from Pole to Pole.” Journal of Finance, vol. 58, no. 6 (December):2515–2547.
Grinblatt, Mark, and Tobias Moskowitz. 2004. “Predicting Stock Price Movements from Past Returns: The Role of Consistency and Tax-Loss Selling.” Journal of Financial Economics, vol. 71, no. 3 (March):541–579.
Harvey, Campbell, and Akhtar Siddique. 2000. “Conditional Skewness in Asset Pricing Tests.” Journal of Finance, vol. 55, no. 3 (June):1263–1296.
Hong, Harrison, and Jeremy Stein. 1999. “A Unified Theory of Underreaction, Momentum Trading, and Overreaction in Asset Markets.” Journal of Finance, vol. 54, no. 6 (December):2143–2184.
Jegadeesh, Narasimhan, and Sheridan Titman. 1993. “Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency.” Journal of Finance, vol. 48, no. 1 (March):65–91.
———. 2001. “Profitability of Momentum Strategies: An Evaluation of Alternative Explanations.” Journal of Finance, vol. 56, no. 2 (April):699–720.
———. 2002. “Cross-Sectional and Time-Series Determinants of Momentum Returns.” Review of Financial Studies, vol. 15, no. 1 (January):143–157.
Keren, Gideon.1997. “On the Calibration of Probability Judgments: Some Critical Comments and Alternative Perspectives.” Journal of Behavioral Decision Making, vol. 10, no. 3 (September):269–278.
Kho, Bong-Chan. 1996. “Time-Varying Risk Premia, Volatility, and Technical Trading Rule Profits: Evidence from Foreign Currency Futures Markets.” Journal of Financial Economics, vol. 41, no. 2 (June):249–290.
LeBaron, Blake. 1999. “Technical Trading Rule Profitability and Foreign Exchange Intervention.” Journal of International Economics, vol. 49, no. 1 (June):125–143.
Liew, Jimmy, and Maria Vassalou. 2000. “Can Book-to-Market, Size, and Momentum Be Risk Factors That Predict Economic Growth?” Journal of Financial Economics, vol. 57, no. 2 (August):221–245.
Lou, Dong, Christopher Polk, and Spyros Skouras. 2017. “A Tug of War: Overnight versus Intraday Expected Returns.” Working paper (March).
Moskowitz, Tobias, and Mark Grinblatt. 1999. “Do Industries Explain Momentum?” Journal of Finance, vol. 54, no. 4 (August):1249–1290.
Moskowitz, Tobias, Yao Hua Ooi, and Lasse Heje Pedersen. 2012. “Time Series Momentum.” Journal of Financial Economics, vol. 104, no. 2 (May):228–250.
Novy-Marx, Robert. 2015. “Fundamentally, Momentum Is Fundamental Momentum.” NBER Working Paper No. w20984 (February).
Odean, Terrance. 1998. “Are Investors Reluctant to Realize Their Losses?” Journal of Finance, vol. 53, no. 3 (October):1775–1798.
Roll, Richard. 1986. “The Hubris Hypothesis of Corporate Takeovers.” Journal of Business, vol. 59, no. 2 (April):197–216.
Rouwenhorst, Geert. 1998. “International Momentum Strategies.” Journal of Finance, vol. 53, no. 1 (February):267–284.
Slovic, Paul, Baruch Fischhoff, and Sarah Lichtenstein. 1980. “Facts and Fears: Understanding Perceived Risk.” In Societal Risk Assessment: How Safe Is Safe Enough? edited by Richard Schwing and Walter Albers, General Motors Research Laboratories. Boston, MA: Springer:181–216.
Treynor, Jack. 2005. “Why Market-Valuation-Indifferent Indexing Works.” Financial Analysts Journal, vol. 61, no. 5 (September/October):65–69.