A Critique of Momentum Anomalies

Abstract

This paper offers theoretical, empirical, and simulated evidence that momentum regularities in asset prices are not anomalies. Within a general, frictionless, rational expectations, risk-based asset pricing framework, riskier assets tend to be in the loser portfolios after (large) increases in the price of risk. Hence, the risk of momentum portfolios usually decreases with the prevailing price of risk, and their risk premiums are approximately negative quadratic functions of the price of risk (and the market premium) theoretically truncated at zero. The best linear (CAPM) function describing this relation unconditionally has exactly the negative slope and positive intercept documented empirically.

Predictability Concentrates in Bad Times. And so Does Disagreement

“…Risk proxies are the ones typically related to the cross-section of asset returns. For stock returns in particular, examples include the stocks' estimated market betas (Sharpe, 1964;Lintner, 1965); the firm's size, value, investment, or profitability (Fama and French, 2015); and realized returns (Jegadeesh and Titman, 1993;de Oliveira Souza, 2019a).…”

“…Under the hypothesis that past returns are risk proxies (de Oliveira Souza, 2019a;Berk et al, 1999), time series momentum (Moskowitz et al, 2012) should also increase in bad times. This explains why time series momentum is stronger in bad times, for example (Cujean and Hasler, 2017).…”