Idiosyncratic volatility, returns, and mispricing: No real anomaly in sight

Recent empirical evidence has shown that the relationship between idiosyncratic volatility and a stock's expected return depends on the pricing of the stock: it is negative among overvalued stocks and positive among undervalued ones. We provide both theoretical and numerical evidence that this risk-return relationship might be driven purely by mathematical properties of return distributions. Using a simulation-based approach, we document that even in completely random samples, the correlation between idiosyncratic risk and mean returns depends on the ex-post estimation of abnormal returns.