This paper examines the impact of idiosyncratic risk on the cross-section of weekly stock returns from 1963 to 2006. I use an exponential GARCH model to forecast expected idiosyncratic volatility and employ a combination of the size e§ect, value premium, return momentum and short-term reversal to measure relative mispricing. I ?nd that stock returns monotonically increase in idiosyncratic risk for relatively undervalued stocks and monotonically decrease in idiosyncratic risk for relatively overvalued stocks. This phenomenon is robust to various subsamples and industries, and cannot be explained by risk factors or ?rm characteristics. Further, transaction costs, short-sale constraints and information uncertainty cannot account for the role of idiosyncratic risk. Overall, these ?ndings are consistent with the limits of arbitrage arguments and demonstrate the importance of idiosyncratic risk as an arbitrage cost.