Welcome A Hidden Markov Model of Momentum

We develop a two-state hidden Markov model where the process driving market returns transitions between turbulent and calm states. A cross-sectional momentum strategy embeds a call option on the market, inducing a state-contingent convex relation between market and momentum returns. In turbulent states, the short side of the momentum strategy has high beta and convexity with respect to the market, as a result of higher effective leverage of the past-loser securities, making momentum crashes more likely. A momentum timing strategy based on this model avoids momentum crashes and achieves superior out-of-sample risk-adjusted performance. We thank Torben Andersen, Raul Chhabbra, Randolph B. Cohen, Zhi Da, Gangadhar Darbha, Ian DewBecker, Francis Diebold, Robert Engel, Bryan T. Kelly, Robert Korajczyk, Tyler Muir, Jonathan Parker, Marco Sammon, Prasanna Tantri, Viktor Todorov, Lu Zhang, and the participants of seminars at the BeckerFriedman Institute Conference honoring Lars Hansen at the University of Chicago, the Fifth Annual Triple Crown Conference in Finance, Fordham University, the Indian School of Business, London Business School, London School of Economics, Nomura Securities, Northwestern University, the Oxford-Man Institute of Quantitative Finance, the Securities and Exchange Board of India, Shanghai Advance Institute for Finance, Shanghai Jiao Tong University, the SoFiE Conference, the University of Virginia, the WFA meetings, the 2016 Value Investing Conference at Western University, and the AFA meetings, for helpful comments on the earlier versions of the paper. Special thanks to Lu Zhang for providing us with time series data on q-factor model. We alone are responsible for any errors and omissions. †Kent Daniel, Finance and Economics Division, Graduate School of Business, Columbia University and NBER; E-mail: kd2371@columbia.edu, Ravi Jagannathan, Finance Department, Kellogg School of Management, Northwestern University and NBER, ISB, SAIF; E-mail: rjaganna@kellogg.northwestern. edu, Soohun Kim, Finance Area, Georgia Institute of Technology; E-mail: soohun.kim@scheller.gatech. edu. Price momentum can be described as the tendency of securities with relatively high (low) past returns to subsequently outperform (underperform) the broader market. Long-short momentum strategies exploit this pattern by taking a long position in past winners and an offsetting short position in past losers. Momentum strategies have been, and continue to be popular among traders. The majority of quantitative fund managers employ momentum as a component of their overall strategy, and even fundamental managers appear to incorporate momentum when formulating their trading decisions. Notwithstanding their inherent simplicity, momentum strategies have been profitable across many asset classes and in multiple geographic regions (Asness et al., 2013; Chabot et al., 2014). Over our sample period from 1927:01 to 2017:12 (1,092 months), our baseline momentum strategy produced monthly returns with a mean of 1.17% and a standard deviation of 7.80%, generating an annualized Sharpe ratio of 0.52. Over this same period, the market excess return (Mkt-Rf) had an annualized Sharpe ratio of 0.43. Momentum’s CAPM alpha is 1.53%/month (t=7.43). While the momentum strategy’s average risk adjusted return has been high, the strategy has experienced infrequent but large losses. As Chabot et al. (2014) document, this Swaminathan (2010) shows that most quantitative managers make use of momentum. He further estimates that about one-sixth of the assets under management by active portfolio managers in the U.S. large cap space is managed using quantitative strategies. In addition, Jegadeesh and Titman (1993) motivate their study of price momentum by noting that: “. a majority of the mutual funds examined by Grinblatt and Titman (1989; 1993) show a tendency to buy stocks that have increased in price over the previous quarter. ” Badrinath and Wahal (2002) show that institutions behave as momentum traders when entering new positions, but as contrarians otherwise. In our baseline 12-2 momentum strategy, described in more detail later, we rank firms in U.S. based on their cumulative returns from months t−12 through t−2, and take a long position in the value-weighted portfolio of the stocks in the top decile, and a short position in the value-weighted portfolio of the bottom decile stocks. Over the period from 1927:01 to 2017:12, Fama and French’s (1993) SMB and HML factors had annualized Sharpe Ratios of 0.23 and 0.38, respectively, and the Fama and French three-factor alpha for momentum is 1.75%/month (t= 8.63). From 1967:01 to 2016:12, Hou et al.’s (2015) I/A and ROE factors achieved annualized Sharpe ratios of 0.79 and 0.73, respectively, the Hou et al. (2015) four-factor alpha for momentum is 0.43%/month (t = 1.24). Lastly, from 1963:07 to 2017:12, the annualized Sharpe ratios of Fama and French’s (2015) RMW and CMA factors are 0.39 and 0.50, respectively, and the associated five-factor alpha for momentum is 1.38%/month (t = 4.37). The t-statistics are computed using White’s (1980) heteroskedasticity-consistent covariance.