Conditional Risk and Performance Evaluation: Volatility Timing, Overconditioning, and New Estimates of Momentum Alphas

Abstract

Unconditional alpha estimates are biased when conditional beta covaries with market risk premia (“market-timing”) or volatility (“volatility-timing”). We demonstrate an additional bias (“overconditioning”) that can occur any time an empiricist uses a risk proxy not in the investor information set — for example when asset payoffs are nonlinear and the conditional loading is proxied by contemporaneous realized beta. Calibrating to U.S. equity returns, volatility-timing and overconditioning plausibly impact alphas much more than market-timing, which has been the focus of prior literature. A variety of instrumental variables estimators using realized betas can substantially correct market- and volatility-timing biases, while eliminating overconditioning. Empirically, appropriate instrumentation reduces momentum alphas by 20-40 % relative to unconditional, whereas overconditioned alphas overstate performance by up to 2.5 times. Volatility-timing inflates unconditionally estimated momentum alpha because the formationperiod market return (i) positively predicts holding-period beta (Grundy and Martin, 2001) and (ii) negatively predicts holding-period market volatility (French, Schwert, and Stambaugh,