Even though investors' view of risk is generally regarded as related to the downside of the return distribution the CAPM beta is still a widely used measure of systematic risk. A number of studies compare the empirical performance of CAPM beta and downside beta in explaining the variation in...

We show analytically that the cross-sectional relation between idiosyncratic volatility estimated as the variance of the residuals in a single factor model and expected stock return may be represented by a truncated parabola that opens to the left and has horizontal axis. This relation is...