Alpha Beta Risk and Stock Returns—A Decomposition Analysis of Idiosyncratic Volatility with Conditional Models

The variance of stock returns is decomposed based on a conditional Fama–French three-factor model instead of its unconditional counterpart. Using time-varying alpha and betas in this model, it is evident that four additional risk terms must be considered. They include the variance of alpha, the variance of the interaction between the time-varying component of beta and factors, and two covariance terms. These additional risk terms are components that are included in the idiosyncratic risk estimate using an unconditional model. By investigating the relation between the risk terms and stock returns, we find that only the variance of the time-varying alpha is negatively associated with stock returns. Further tests show that stock returns are not affected by the variance of time-varying beta. These results are consistent with the findings in the literature identifying return predictability from time-varying alpha rather than betas.