Idiosyncratic Risk, Costly Arbitrage, and the Cross-Section of Stock Returns

TLDR: In this paper, the authors test a new cross-sectional relation between expected stock return and idiosyncratic risk implied by the theory of costly arbitrage and find that average stock returns monotonically increase (decrease) with idiosyncratic risks for undervalued (overvalued) stocks.

Abstract: We test a new cross-sectional relation between expected stock return and idiosyncratic risk implied by the theory of costly arbitrage. If arbitrageurs find it more difficult to correct the mispricing of stocks with high idiosyncratic risk, there should be a positive (negative) relation between expected return and idiosyncratic risk for undervalued (overvalued) stocks. We combine several well-known anomalies to measure stock mispricing and proxy stock idiosyncratic risk using an exponential GARCH model for stock returns. We confirm that average stock returns monotonically increase (decrease) with idiosyncratic risk for undervalued (overvalued) stocks. Overall, our results support the importance of idiosyncratic risk as an arbitrage cost.