The Momentum Gap and Return Predictability
Southern Methodist University (SMU) – Cox School of Business
May 17, 2015
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Momentum strategies have historically delivered large alphas, yet they also displayed significant time-variation that is not very well understood. I document that expected momentum profits vary negatively with the formation period return difference between past winners and losers, which I term the momentum gap. A one standard deviation increase in the momentum gap predicts a 1.29% decrease in the monthly momentum return after controlling for existing predictors. I find consistent results across 21 international stock markets. Following the simple real-time strategy of investing in momentum only when the momentum gap is below the 80th percentile generates monthly returns of 1.28%.
The Momentum Gap And Return Predictability – Introduction
The profitability of momentum strategies, as documented by Jegadeesh and Titman (1993), is an important asset pricing anomaly because it implies high variability of marginal utility across states of nature and does not appear to compensate for bearing systematic risk (Fama and French (1996)). At the same time, returns to momentum strategies exhibit significant time-variation. While there is a large literature on the cross-sectional determinants of momentum profits, we know much less about this time-variation.1 In this paper, I document a new and significant determinant of variation in expected momentum profits. I then use these results to shed light on the source of the momentum anomaly.
I find that expected momentum profits vary negatively with the formation period return difference between past winners and losers, which I term the momentum gap. The average adjusted return of my baseline momentum strategy varies monotonically from 2.23 percent per month, when the lagged momentum gap is small, to -0.13 percent per month, when the lagged momentum gap is large. The predictive power of the momentum gap remains economically and statistically significant after controlling for market return, market volatility, and market illiquidity.2 Conditional on these controls, a one standard deviation increase in the momentum gap is associated with a 1.29 percent decrease in the monthly adjusted return of the momentum strategy. My regression-based tests employ a bootstrap methodology to ensure that the inferences are robust to the predictive regression biases highlighted in Stambaugh (1999) and Ferson, Sarkissian, and Simin (2003). The momentum gap has significant predictive power for both the long and short legs of the momentum trade, ruling out the possibility that the results are driven by the infrequent yet large-scale reversals of past losers documented by Daniel and Moskowitz (2013).
A recent emphasis in the return predictability literature is on the out-of-sample performance of predictors (Campbell and Thompson (2007); Welch and Goyal (2007)). Even though momentum strategies are popular, I am not aware of any comprehensive study on the out-of-sample performance of momentum predictors. I examine the out-of-sample predictive power of the momentum gap and other predictors in the literature using the same method, time period, and estimation frequency. Formal tests show that the momentum gap has significant out-of-sample predictive power. In fact, it delivers the highest out-of-sample among the predictors I examine. Conditional momentum strategies using the momentum gap in real time yield substantially higher Sharpe ratios and lower skewness than the unconditional strategy.
I set out three hypotheses to explain the negative relation between expected momentum profits and the momentum gap. Hypothesis 1 is that the empirical relation is spurious. While robust in the panel of U.S. stocks, it could simply be the outcome of data snooping. Hypothesis 2 is that the momentum gap’s predictive power is driven by its relation to the business cycle. Once macroeconomic variables known to predict returns are accounted for, the momentum gap will lose its predictive power. Hypothesis 3 is that momentum is a mispricing phenomenon, and that the momentum gap reflects the degree to which arbitrageurs are trading the strategy.3 For example, if momentum is due to under-reaction, then more arbitrageurs exploiting the situation will lead to less under-reaction and a larger momentum gap. As a result, a large momentum gap indicates the presence of many arbitrageurs and near-complete convergence of prices to fundamental values, thereby explaining why the trade is less profitable going forward.
I find no evidence to support Hypothesis 1 or Hypothesis 2. Using a sample of international stocks from the 21 largest markets excluding the U.S., I find a negative relation between expected momentum returns and the momentum gap in 20 of the countries, statistically significant in 13. In no country is the relation significantly positive. Moreover, the momentum gap holds its predictive power in the presence of the dividend yield, default spread, term spread, short-term interest rate, and industrial production growth. In contrast, none of the macroeconomic variables predict momentum returns after controlling for the momentum gap.
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