Tail Risk in Momentum Strategy Returns

Abstract

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.