The Limits of the Limits of Arbitrage

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Review of Finance (2010) 14: 157–187 doi: 10.1093/rof/rfp018 Advance Access publication: 4 October 2009

The Limits of the Limits of Arbitrage
ALON BRAV1 , J.B. HEATON2 and SI LI3
Professor of Finance, Duke University Fuqua School of Business; 2 Partner, Bartlit Beck Herman Palenchar & Scott LLP; 3 Assistant Professor of Finance, Wilfrid Laurier University School of Business and Economics Abstract. 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. JEL Classification: G11, G12, G14 1

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1. Introduction
Empirical asset pricing tests of the predictions of the Sharpe-Lintner CAPM often result in model falsification. Small stocks earn returns that are higher than predicted (see Banz, 1981), as do recent winners (see, e.g., Chan et al., 1996), value stocks (see, e.g., Lakonishok et al., 1994), and stocks of companies with positive earnings surprises (see, e.g., Ball and Brown, 1968; Bernard and Thomas, 1990). Growth We thank Ray Ball, Nick Barberis, Zahi Ben-David, Peter Bossaerts (the editor), Michael Brandt, Markus Brunnermeier, George Constantinides, Campbell Harvey, Dong Hong, Ron Kaniel, Reuven Lehavy, Jon Lewellen, Mark Loewenstein (a discussant), Toby Moskowitz, Doron Nissim, Per Olsson, Matthew Rothman, Darren Roulstone, Ronnie Sadka, Richard Thaler, Mohan Venkatachalam, Mitch Warachka, two anonymous referees, and seminar participants at the Seventh Maryland Finance Symposium, the Securities and Exchange Commission Office of Economic Analysis, Duke University, Hebrew University, Interdisciplinary Center, Herzlyia, Israel, Northwestern University and Vanderbilt University for helpful comments. Please address correspondence to Brav at Fuqua School of Business, Duke University, Box 90120, Durham, North Carolina 27708–0120, email: brav@duke.edu. Heaton acknowledges that the opinions expressed here are his own, and do not reflect the position of Bartlit Beck Herman Palenchar & Scott LLP or its attorneys. Li acknowledges financial support from the Social Sciences and Humanities Research Council of Canada. C The Authors 2009. Published by Oxford University Press [on behalf of the European Finance Association]. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

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stocks, recent losers, and negative earnings surprises earn returns that are lower than predicted (see, e.g., Ritter, 1991; Barberis and Huang, 2008; Ball and Brown, 1968; Bernard and Thomas, 1990; Chan et al., 1996). Researchers in behavioral finance argue that asset pricing anomalies result from the influence of unmodeled irrational behavior on security prices (see, for example, the extended discussion in Barberis and Thaler (2003) of the above anomalies). The behavioral claim is controversial. First, rational behavior is just one of several assumptions used to derive the tested asset pricing models. Model falsification might result from the failure of an assumption other than the...
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