Financial Analysts Journal Volume 67 Number 4 ©2011 CFA Institute The Limits to Arbitrage Revisited: The Accrual and Asset Growth Anomalies Xi Li and Rodney N. Sullivan, CFA Using idiosyncratic volatility as a proxy for arbitrage costs, the authors found that the highly publicized accrual and asset growth anomalies exist because of high barriers to arbitrage, occurring predominantly in the universe of stocks with higher arbitrage risks. Therefore, investors who seek to profit from the accrual and asset growth anomalies must bear greater uncertainty in outcomes than was previously understood. hat such straightforward, well-publicized The importance of our investigation is bolstered asset pricing anomalies as the accrual (Sloan by recent research that demonstrates the adverse 1996) and asset growth (Cooper, Gulen, and impact of IVOL on effective arbitrage (e.g., Pontiff T Schill 2008) effects are seemingly over- 2006). Exploring the influence of IVOL on extracting looked by investors and that these anomalies could anomalous returns sheds light on investors’ ability persist for years despite the abundance of research to profit from any associated mispricing. In particu- describing them is puzzling. In our study, we lar, our model tests whether the accrual and asset sought to understand the extent to which the anom- growth anomalies exist in association with high alous returns associated with these two effects can IVOL. That is, do the accrual and asset growth anom- be attributed to higher arbitrage risks that arise from alies exist among stocks with higher or lower levels the lack of close substitutes. We focused on the of IVOL? If the predictive power of either or both of accrual and asset growth effects because both have these anomalies is stronger among stocks with high been shown to affect future returns negatively and IVOL, then doubt would be cast on whether at least are used extensively by active managers, yet the some of their usefulness in predicting returns is persistence of the return link is not well understood attributable to the significant impact of arbitrage despite their widespread adoption in practice. Fol- costs (as measured by IVOL). lowing prior research, we used idiosyncratic vola- tility (IVOL) from the Fama–French (1992) model to measure arbitrage risk. By doing so, we aimed to Limits to Arbitrage determine whether the anomalous accrual and asset Our study expands the extensive body of research growth effects are largely present among those that explores limits to arbitrage (e.g., Pontiff 1996, stocks with higher IVOL, a group with meaning- 2006; Shleifer and Vishny 1997). Pontiff (2006) sep- fully higher costs to arbitrage. If so, then such arated arbitrage costs into two types: transaction increased difficulty in arbitraging away their prof- costs and holding costs. These two costs clearly itability may explain their persistence, even after hinder the ability of arbitrageurs to reduce mispric- becoming widely known. ing through corrective trading. Transaction costs are incurred when positions are opened or closed Xi Li is a managing partner at XL Partners, Boston, and are proportional to initiating or terminating and a visiting scholar at Boston College. Rodney N. arbitrage positions, including bid–ask spreads, Sullivan, CFA, is head of publications at CFA Institute, market impact, commissions, and dollar volume. Charlottesville, Virginia. As reported here and in the prior literature, the accrual and asset growth anomalies can be found Editor’s Note: Rodney N. Sullivan, CFA, is editor of in infrequently (annually) rebalanced portfolios the Financial Analysts Journal. He recused himself and their return predictive power can last as long from the referee and acceptance processes and took as three years (Sloan 1996; Cooper et al. 2008). Thus, no part in the scheduling and placement of this transaction costs are unlikely to create significant article. See the FAJ policies section of cfapubs.org limits to arbitrage, even if they are strongly related for more information. to the predictive power of these two anomalies. 50 www.cfapubs.org ©2011 CFA Institute The Limits to Arbitrage Revisited Proportional to the amount of time the arbi- In seeking to explain the persistence of the trage position is held, holding costs include interest returns associated with the accrual and asset on margin requirements, short-sale costs (e.g., a growth anomalies, we also sought to determine haircut on a short-sale rebate rate), and the risk of whether these anomalies arise from investor mis- holding a position with high IVOL. When con- pricing or from systematic market risk. This dis- fronted with holding a position with high IVOL, tinction is of paramount importance to investors. If investors are less willing to engage in arbitrage the anomalies are related to systematic risk, then, because such a position is costly to hedge. This in the spirit of the capital asset pricing model and situation occurs when the position has no close the efficient market hypothesis, the excess returns substitutes that can be used for hedging. If the arbi- can be viewed as fair compensation to investors for trageur cannot perfectly hedge the undesired risk of bearing that risk. But if the mispricing is driven by the arbitrage position, then arbitrage involves an imperfection (e.g., investor irrationality) con- unwanted risk. Therefore, among the various hold- nected with the anomaly, then the excess returns ing costs, idiosyncratic volatility is of particular are likely to be ephemeral as investors come to importance to arbitrageurs and thus serves as our understand their cognitive error and arbitrage 2 focus in measuring the relevant arbitrage costs. away any excess returns. To further understand how IVOL relates Investors’ willingness to try to arbitrage anom- directly to arbitrage costs, consider the practice of alous returns is contingent on the expectation that arbitraging asset mispricing. In an ideal, riskless excess returns will represent fair compensation for arbitrage, the arbitrageur uses a zero-cost arbitrage bearing related arbitrage risks. Given that investors portfolio, with long and short positions, that fully allocate a smaller portion of their portfolio to high- hedges market risk and idiosyncratic risk, leaving IVOL assets than to low-IVOL assets, the excess only the desired mispricing effect. In other words, returns associated with a particular anomaly may the arbitrageur seeks stocks that are highly nega- very well persist over time because the excess tively correlated along the mispriced dimensions returns likely come with greater risk and uncertainty and highly positively correlated (perfect substi- in outcomes. To the extent that anomalous returns tutes) along other, undesired dimensions. The are concentrated in high-IVOL stocks, an arbitrageur absence of such perfect substitutes in real markets can expect to earn abnormal returns only by bearing makes arbitraging the desired mispricing effect higher undiversified risks. A strong, positive rela- imperfect and rather risky. Thus, in practice, the tionship between the return predictive power of the impact of IVOL makes the complete hedging away two anomalies and IVOL suggests an explanation of of undesired risk impossible. The higher the IVOL, their return predictive power that is consistent with the more difficult (and costly) the arbitrage effort. market mispricing and market efficiency as con- strained by the limits to arbitrage. In short, a stronger Idiosyncratic volatility poses an important risk anomaly mispricing signal associated with higher even for those who seek to exploit anomalies IVOL means that arbitrageurs face higher invest- through infrequent portfolio rebalancing and rela- ment risk and, thus, higher arbitrage costs. tively low transaction costs. In reality, high IVOL means that arbitrageurs remain exposed to the risk that any targeted mispricing may jump adversely Accruals and Asset Growth in the short term, forcing them to liquidate their Recent research has examined the viability of such positions prematurely because of high leverage or simple, fundamental anomalies as accruals and capital constraints. asset growth.3 For the asset growth effect, research Although intuitively IVOL might seem to be findings generally suggest that periods of signifi- relevant only to the undiversified arbitrageur, in cant asset expansion or capital expenditures tend fact, the diversification of the arbitrageur is irrele- to be followed by periods of negative abnormal vant with respect to the arbitrageur’s willingness to stock returns. A central debate is about whether the invest in a mispriced asset. That is, all risk-averse asset growth effect can be attributed to mispricing investors allocate a smaller portion of their portfolio or to systematic risk. On the one hand, advocates to high-IVOL assets given a certain level of expected of the mispricing explanation argue that investors return, irrespective of the number of securities in overreact to past information about positive asset the portfolio or the portfolio’s level of diversifica- growth by extrapolating the past growth rate into tion. This result can be seen in Treynor and Black future periods.4 Stock returns attenuate when (1973) and Pontiff (2006), who studied the invest- investors are disappointed by the mean reversion ment allocation of arbitrageurs in a mean–variance of asset growth rates (see, e.g., Lakonishok, Shleifer, portfolio optimization framework.1 and Vishny 1994). July/August 2011 www.cfapubs.org