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The Limits of the Limits of Arbitrage

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.