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

Unconditional alphas are biased when conditional beta covaries with the market risk premium (ldquo;market-timingrdquo;) or volatility (ldquo;volatility-timingrdquo;). We demonstrate an additional bias (ldquo;overconditioningrdquo;) that can occur any time an empiricist estimates risk using information, such as a realized beta, that is not available to investors ex ante. Calibrating to U.S. equity returns, volatility-timing and overconditioning can plausibly impact alphas more than markettiming, which has been the focus of prior literature. To correct market- and volatility-timing biases without overconditioning, we show that incorporating realized betas into instrumental variables estimators is effective. Empirically, instrumentation reduces momentum alphas by 20-40%. Overconditioned alphas overstate performance by up to 2.5 times. We explain the sources of both the volatility-timing and overconditioning biases in momentum portfolios