Return reversals, idiosyncratic risk, and expected returns

The empirical evidence on the cross-sectional relation between idiosyncratic risk and expected stock returns is mixed. We demonstrate that the omission of the previous month s stock returns can lead to a negatively biased estimate of the relation. The magnitude of the omitted variable bias depends on the approach to estimating the conditional idiosyncratic volatility. Although a negative relation exists when the estimate is based on daily returns, it disappears after return reversals are controlled for. Return reversals can explain both the negative relation between value-weighted portfolio returns and idiosyncratic volatility and the insignificant relation between equal-weighted portfolio returns and idiosyncratic volatility. In contrast, there is a significantly positive relation between the conditional idiosyncratic volatility estimated from monthly data and expected returns. This relation remains robust after controlling for return reversals.