Arbitrage Risk and Book to Market Ratio

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Journal of Financial Economics 69 (2003) 355–373

Arbitrage risk and the book-to-market anomaly$
Ashiq Alia,*, Lee-Seok Hwangb, Mark A. Trombleya
a

Eller College of Business, Public Administration, University of Arizona, Tucson, AZ 85721, USA b College of Business Administration, Seoul National University, Seoul, South Korea Received 24 August 2001; received in revised form 4 April 2002; accepted 21 March 2003

Abstract This paper shows that the book-to-market (B/M) effect is greater for stocks with higher idiosyncratic return volatility, higher transaction costs, and lower investor sophistication, consistent with the market-mispricing explanation for the anomaly. The B/M effect for high volatility stocks exceeds that for the low volatility stocks in 20 of the 22 sample years. Also, volatility exhibits significant incremental power beyond transaction costs and investor sophistication measures in explaining cross-sectional variation in the B/M effect. These findings are consistent with the Shleifer and Vishny (1997) thesis that risk associated with the volatility of arbitrage returns deters arbitrage activity and is an important reason why the B/M effect exists. r 2003 Elsevier B.V. All rights reserved. JEL classification: G11; G14 Keywords: Arbitrage risk; Book-to-market; Mispricing; Transaction costs; Investor sophistication

1. Introduction Numerous studies show predictable returns over three to five years for portfolios long in high book-to-market (B/M) stocks and short in low B/M stocks The comments of Bill Horace, George Jiang, Chris Lamoureux, the workshop participants at Duke University, the University of Oregon, and an anonymous referee are gratefully acknowledged. The analyst estimates data used in this study were provided by I/B/E/S under its program to encourage research on earnings expectations. Professors Ali and Trombley acknowledge financial support provided by the University of Arizona Eller College of Business and Public Administration Faculty Development Fund and by Ernst and Young. *Corresponding author. Tel.: +1-520-621-3765. E-mail address: ashiq@u.arizona.edu (A. Ali). 0304-405X/03/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0304-405X(03)00116-8 $

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A. Ali et al. / Journal of Financial Economics 69 (2003) 355–373

(e.g., Rosenberg et al., 1984; Fama and French, 1992; Lakonishok et al., 1994). Two competing explanations for this exist. First, the return to B/M-based portfolio strategies represents compensation for risk, as suggested by Fama and French (1992, 1993, 1997). Second, the return to B/M-based portfolio strategies results from systematic mispricing of extreme B/M securities. Studies supporting the mispricing explanation show that market participants underestimate future earnings for high B/M stocks and overestimate future earnings for low B/M stocks (La Porta et al., 1997; Skinner and Sloan, 2002).1 If the B/M effect represents mispricing due to systematic bias in expectations, then why don’t professional arbitrageurs exploit this opportunity and quickly eliminate the mispricing? Shleifer and Vishny (1997) argue that arbitrage is costly and any systematic mispricing would not be quickly and completely traded away in situations where arbitrage costs exceed arbitrage benefits. They further argue that risk due to the volatility of arbitrage returns (hereafter arbitrage risk) deters arbitrage activity and is likely to be an important reason why the B/M effect exists. Our study empirically examines their prediction and in doing so provides additional evidence to discriminate between the risk and mispricing explanations for the B/M effect. Arbitrage resources are concentrated in the hands of a relatively few specialized and poorly diversified traders. These arbitrageurs are risk averse and are concerned about the idiosyncratic risk of their portfolios. Thus, Shleifer and Vishny (1997) predict that volatility will deter arbitrage activities. If the B/M...
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