Idiosyncratic risk and the cross-section of stock returns: the role of mean-reverting idiosyncratic volatility

A key prediction of the Capital Asset Pricing Model (CAPM) is that idiosyncratic risk is not priced by investors because in the absence of frictions it can be fully diversified away. In the presence of constraints on diversification, refinements of the CAPM conclude that the part of idiosyncratic risk that is not diversified should be priced. Recent empirical studies yielded mixed evidence with some studies finding positive correlation between idiosyncratic risk and stock returns, while other studies reported none or even negative correlation. We examine whether idiosyncratic risk is priced by the stock market and what are the probable causes for the mixed evidence produced by other studies, using monthly data for the US market covering the period from 1980 until 2013. We find that one-period volatility forecasts are not significantly correlated with stock returns. The mean-reverting unconditional volatility, however, is a robust predictor of returns. Consistent with economic theory, the size of the premium depends on the degree of 'knowledge' of the security among market participants. In particular, the premium for Nasdaq-traded stocks is higher than that for NYSE and Amex stocks. We also find stronger correlation between idiosyncratic risk and returns during recessions, which may suggest interaction of risk premium with decreased risk tolerance or other investment considerations like flight to safety or liquidity requirements. We identify the difference between the correlations of the idiosyncratic volatility estimators used by other studies and the true risk metric the mean-reverting volatility as the likely cause for the mixed evidence produced by other studies. Our results are robust with respect to liquidity, momentum, return reversals, unadjusted price, liquidity, credit quality, omitted factors, and hold at daily frequency.