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 (market timing) or volatility (volatility timing). We demonstrate an additional bias (overconditioning) 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 market timing, 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.

► Volatility timing can significantly bias unconditional alpha estimates.
► Nonlinear payoffs bias alphas if beta estimates are outside investor information.
► Instrumenting with realized betas is effective in reducing alpha bias.
► Momentum betas are low when expected volatility is high.
► Conditional momentum alphas are 25 basis points lower than unconditional alphas.