The evidence on the relation between idiosyncratic risk and future market return is at odds with the theory in Merton (1987). We argue that this is because conventional idiosyncratic risk measures are too noisy that consequently camou?age the true pricing relation suggested by the theory in empirical tests. To reduce the noise, we employ a random portfolio approach to construct an alternative aggregate idiosyncratic risk measure. Due to a high correlation between the noise components of the conventional idiosyncratic risk measure and our portfolio idiosyncratic risk measure, we include both measures simultaneously in a predictive regression, in which the conventional idiosyncratic risk measure helps to further reduce the noise in our portfolio idiosyncratic risk measure. We ?nd that both variables are signi?cant and jointly predict returns on the market with an adjusted R2 of 2%. Our results are very robust to all conventional control variables, sample periods, the size deciles