Tail Risk in Momentum Strategy Returns

Momentum strategies exhibit rare but dramatic losses (crashes), which we show are a result of the leverage dynamics of stocks in the momentum portfolio. When the economy is in a hidden turbulent state associated with a depressed and volatile stock market, the short-side of the momentum portfolio becomes highly levered, and behaves like a call option on the market index portfolio, making momentum crashes more likely. We develop a hidden Markov model of the unobserved turbulent state that affects the returns on the momentum strategy and the market index portfolios. We find that the use of a combination of Normal and Student-t distributions for the hidden residuals in the model to construct the likelihood of the realized momentum and market index returns dramatically improves the models ability to predict crashes. The same variable that forecasts momentum crashes also forecasts the correlation between momentum strategy and value strategy, two of the benchmark investment styles often used in performance appraisal of quant portfolio managers. The correlation is conditionally negative only when the probability of the economy being in a turbulent state is high. The conditional correlation is zero otherwise, which is two thirds of the time. Half of the negative value-momentum relation is due to leverage dynamics of stocks in the momentum strategy portfolio. The other half is due to a hidden risk factor, likely related to funding liquidity identified in Asness et al. (2013), which emerges only when the economy is more likely to be in the turbulent state. We thank Torben Andersen, Raul Chhabbra, Randolph B. Cohen, Zhi Da, Gangadhar Darbha, Ian DewBecker, Francis Diebold, Robert Engel, Bryan T. Kelly, Robert Korajczyk, Jonathan Parker, Prasanna Tantri, Viktor Todorov, Lu Zhang, and the participants of seminars at the Becker-Friedman 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, and the 2016 Value Investing Conference at Western University, for helpful comments on the earlier versions of the paper. Special thanks to Lu Zhang for providing us 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: [email protected]. Ravi Jagannathan, Finance Department, Kellogg School of Management, Northwestern University and NBER; E-mail: [email protected]. Soohun Kim, Finance Area, Georgia Institute of Technology; E-mail: [email protected]. 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. A majority of quantitative fund managers employ momentum as a component of their overall strategy, and even fundamental managers appear to incorporate momentum in formulating their trading decisions. Notwithstanding their inherent simplicity, momentum strategies have been profitable across many asset classes and in multiple geographic regions. Over our sample period of 1044 months from 1927:01 to 2013:12, our baseline momentum strategy produced monthly returns with a mean of 1.18% and a standard deviation of 7.94%, generating an annualized Sharpe ratio of 0.52. Over this same period the market excess returns (Mkt-Rf) had annualized Sharpe Ratios of 0.41 and the CAPM alpha is 1.52%/month (t=7.10). While the momentum strategy’s average risk adjusted return has been high, the strategy has experienced infrequent but large losses. The historical distribution of momentum strategy returns is highly left skewed. Consistent with the large estimated negative skewness, over our sample there are eight months in which the momentum strategy has lost more than 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.” Asness et al. (2013) provide extensive cross-sectional evidence on momentum effects. Chabot et al. (2014) find the momentum effect in the Victorian era UK equity market. Our baseline 12-2 momentum strategy, described in more detail later, ranks firms based on their cumulative returns from months t−12 through t−2, and takes 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 same period, the SMB and HML factors by Fama and French (1993) had annualized Sharpe Ratios of 0.26 and 0.39, respectively, and the Fama and French three-factor alpha is 1.76%/month (t=8.20). From 1967:01 to 2013:12, the I/A and ROE factors by Hou et al. (2015) achieved annualized Sharpe Ratios of 0.81 and 0.77, respectively, the Hou et al. (2015) four-factor alpha of momentum strategy returns is 0.39%/month (t = 1.07). Lastly, the annualized Sharpe Ratios of CMW and WMA factors in Fama and French (2015) are 0.41 and 0.57, respectively, and the associated five-factor alpha is 1.34%/month (t=4.03). The t-statistics are computed using the heteroskedasticity-consistent covariance estimator by White (1980).