Managing the risk of the low risk anomaly

Betting-against-risk (BAR) anomaly portfolios formed on past beta and idiosyncratic / total volatility produce large CAPM alphas. But these return spreads are well explained by the Fama--French six-factor model (FF6). Operating profitability, investment, and momentum factors subsume the low-risk anomaly. However, risk-managed versions of the same low-risk anomalies are substantially more puzzling. Specifically, risk management increases the Sharpe ratio in 29 out of 30 cases examined and increases risk-adjusted returns for all BAR portfolios. Splitting the sample by lagged volatility, risk factors explain returns only after months of high volatility. All BAR long-short portfolios earn abnormal profits following low-volatility months. By splitting the total variance of each BAR factor into systematic and idiosyncratic components, the later drives the gains of timing risk. The negative predictive relation of volatility and BAR profitability is hard to reconcile with leverage constraints and lottery demand, the leading extant theories of low-risk effects