We test the limits of arbitrage argument for the survival of irrationality-induced financial anomalies by sorting securities on their individual residual variability as a proxy for idiosyncratic risk – a commonly asserted limit to arbitrage – and comparing the strength of anomalous returns in low versus high residual variability portfolios. We find no support for the limits of arbitrage argument to explain undervaluation anomalies (small value stocks, value stocks generally, recent winners, and positive earnings surprises) but strong support for the limits of arbitrage argument to explain overvaluation anomalies (small growth stocks, growth stocks generally, recent losers, and negative earnings surprises). Other tests also fail to support the limits of arbitrage argument for the survival of overvaluation anomalies and suggest that at least some of the factor premiums for size, book-to-market, and momentum are unrelated to irrationality protected by limits to arbitrage

This paper tests whether the persistence of the momentum and reversal effects is the result of idiosyncratic risk limiting arbitrage. Idiosyncratic risk deters arbitrage, regardless of the arbitrageur’s diversification. Reversal is prevalent only in high idiosyncratic risk stocks, suggesting that idiosyncratic risk limits arbitrage in reversal mispricing. This finding is robust to controls for transaction costs, informed trading, and systematic relations between idiosyncratic risk and subsequent returns. Momentum is not related to idiosyncratic risk. Momentum generates a smaller aggregate return than reversal, so the findings along with those in related studies suggest that transaction costs are sufficient to prevent arbitrageurs from eliminating momentum mispricing

Previous studies have shown that high short interest stocks have low subsequent returns. We test whether the persistence of this effect is due to costs limiting arbitrage. The arbitrage cost that we focus on is idiosyncratic risk which, regardless of the arbitrageur’s level of diversification, deters arbitrage activity. Consistent with costly arbitrage, we find that among high short interest stocks a one standard deviation increase in idiosyncratic risk predicts a more than 1% decline in monthly returns. Moreover, idiosyncratic risk does not predict returns across low short interest stocks, and short interest does not predict low returns across low idiosyncratic risk stocks. Our results are robust to commonly used proxies for both transaction costs and short sale constraints