WHAT'S IN A NAME? A CAUTIONARY TALE OF PROFITABILITY ANOMALIES AND LIMITS TO ARBITRAGE

• Author: H. Zafer Yüksel,R. Jared DeLisle,Gulnara R. Zaynutdinova
• Date: 01 May 2020
• DOI: http://doi.org/10.1111/jfir.12208
• Published date: 01 May 2020

The Journal of Financial Research Vol. XLIII, No. 2 Pages 305–344 Summer 2020

DOI: 10.1111/jfir.12208

WHAT’S IN A NAME? A CAUTIONARY TALE OF PROFITABILITY

ANOMALIES AND LIMITS TO ARBITRAGE

R. Jared DeLisle

Utah State University

H. Zafer Yüksel

University of Massachusetts Boston

Gulnara R. Zaynutdinova

West Virginia University

Abstract

The recent literature investigating profitability anomalies defines profitability in

various ways (i.e., gross, operating, and cash based). We show that limits to arbitrage

are associated with returns of gross and cash‐based operating profitability anomalies,

suggesting mispricing. In contrast, returns from the operating profitability strategy

have no relation with barriers to arbitrage and exhibit no evidence of mispricing.

Additionally, we show that the differential effects of limited arbitrage‐related

mispricing of gross and cash‐based operating profitability anomalies are attributable

to their respective correlations with selling, general, and administrative (SG&A)

expense and accruals anomalies. We find that SG&A return predictability, like that

of accruals, is related to limits to arbitrage. These findings suggest that investors and

researchers should proceed with caution when searching for return predictability by

redefining profitability measures.

JEL Classification: G11, G12, M41

I. Introduction

Since the advent of the efficient market theory, researchers have been documenting

cross‐sectional anomalies where selected firm or security characteristics appear to have

stock return predictability (for a copious list of anomalies, see Harvey, Liu, and

Zhu 2016). Although rational asset pricing theory suggests that return predictability is

The authors thank Ahmed Baig, Naomi Boyd, Ruiyuan Chen, Mine Ertugrul, Xin Gao, Ann Marie Hibbert,

George Jiang, Januj Juneja, Hayden Kane, David Kenchington, Alex Kurov, Jordan Neyland, Eric So, Ben

Sopranzetti, Ozgur Ince, and Chi Wan for helpful comments and suggestions. They also thank participants and

their discussants in the 2019 Financial Management Association European conference (Xin Liu, discussant),

2019 Financial Markets and Corporate Governance conference (Haozhi (Rachel) Huang, discussant), 2019

American Accounting Association Mid‐Atlantic regional meetings (dialogue session), 2018 American

Accounting Association annual conference (Jenny Zha Giedt, discussant), 2018 Global Finance Association

annual meetings (Demir Bektic, discussant), and 2018 Financial Management Association annual meetings

(Dustin Snider, discussant). The usual disclaimer applies.

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© 2020 The Southern Finance Association and the Southwestern Finance Association

related to systematic risk premia, it is also possible that predictability occurs because of

market mispricing. Mispricing in a completely efficient market should be quickly

corrected by rational arbitrageurs who wish to profit from less sophisticated or

uninformed investors who price assets in a manner that does not reflect fundamental

value. However, as Shleifer and Vishny (1997) explain, if there are barriers or limits

to arbitrage, mispricing will persist and the flow of wealth to sophisticated arbitrageurs

will be delayed. This delay then gives the appearance of return predictability.

Conversely, limits to arbitrage should be unrelated to an anomaly’s return

predictability if the future returns are due to systematic risk premia.

One of the asset pricing anomalies that has recently gained attention is the

profitability anomaly. An interesting characteristic of this accounting‐based anomaly

is that profitability can be defined in many ways, depending on the economic or

accounting rationale. For example, Novy‐Marx (2013) formally documents the gross

profitability anomaly, Ball et al. (2015) demonstrate an operating profitability

anomaly, and Ball et al. (2016) show a cash‐based operating profitability anomaly.

Given the proliferation of profitability measures in the search for improved

anomalous return prediction, it is in the interest of researchers and investors alike

to determine whether the anomalous returns based on various profitability measures

are related to limits to arbitrage and, hence, market mispricing. Although the

literature contains many empirical studies linking anomaly predictability and limits

to arbitrage, the profitability anomaly is largely overlooked.

1

Furthermore, to the

best of our knowledge, no studies examine the effects of limits to arbitrage among

various definitions of profitability. Thus, we focus on three profitability anomalies—

gross, operating, and cash‐based operating—and investigate the relation between

their return predictability and limits to arbitrage.

2

These measures are incrementally

different from each other by small, but crucial, accounting adjustments, particularly

selling, general, and administrative (SG&A) expenses and accruals. Consequently,

limits to arbitrage may have different effects across the return predictability of the

three anomalies. In fact, our empirical results support this differential effect.

Specifically, we find that limits to arbitrage contribute to the return predictability of

both the gross and cash‐based operating profitability anomalies, but not the operating

profitability anomaly.

We begin our study by verifying that the three profitability anomalies exist in

our sample period using both Fama–MacBeth (1973) cross‐sectional regressions and

hedge portfolio analyses, thus confirming the findings of previous studies (Novy‐Marx

2013; Ball et al. 2015, 2016).

3

Next, we examine the effect of limits to arbitrage

1

For example,return predictability related to firmcharacteristicssuch as earnings (Mendenhall 2004), book‐to‐

market equity ratio (Ali, Hwang, and Trombley 2003), accruals (Mashruwala, Rajgopal, and Shevlin 2006), asset

growth (Lam and Wei 2011), cash holdings (Li and Luo 2016), momentum (Arena, Haggard, and Yan 2008), and

S&P 500 index membership (Wurgler and Zhuravskaya 2002) have been linked to limits to arbitrage.

2

We concentrate on measures that change the definition of profitability only in the numerator and avoid

measures that differ in both the numerator and the denominator, such as the measure in Fama and French (2015),

which is operating profitability less interest expense scaled by book equity. However, in unreported results, an

operating probability measure analogous to the Fama and French (2015) definition (operating profitability less

interest expense scaled by total assets) yields similar results to that of the Ball et al. (2015) measure.

306 The Journal of Financial Research

on stock return predictability based on each profitability measure (i.e., the impact of

limits to arbitrage on profitability‐associated hedge portfolio returns). If limits to

arbitrage deter profitability from being fully priced, we expect the return predictability

associated with profitability measures to be stronger (weaker) for stocks with larger

(smaller) limits to arbitrage. Our proxies for limits to arbitrage include arbitrage

risk (idiosyncratic volatility) and a composite index of various arbitrage costs,

including bid–ask spread, Amihud (2002) illiquidity measure, firm size, trading

volume, institutional ownership (both number of institutions and total percentage of

outstanding shares owned), and analyst coverage.

4

When examining the individual effects of arbitrage risk and arbitrage costs,

portfolio analyses reveal surprising differences in the effect of limits to arbitrage on the

return predictability across different profitability measures. Specifically, we find that

both arbitrage risk and arbitrage costs play an important explanatory role in the risk‐

adjusted returns to long–short strategies based on gross and cash‐based operating

profitability, which suggests that limits to arbitrage impose significant barriers to

exploiting the mispricing associated with these two firm characteristics. In sharp

contrast, we find no relation between any of our proxies for limits to arbitrage and the

return predictability of operating profitability. The results from Fama–MacBeth (1973)

cross‐sectional regressions support all the findings of the portfolio analyses. Taking

all the evidence together supports the hypothesis that limits to arbitrage contribute to

the return predictability of gross and cash‐based profitability, but not that of operating

profitability.

We further examine the roles of underlying accounting treatments (i.e.,

differing definitions of profitability) as potential causes of the differential effects of

limits to arbitrage on the return predictability of the profitability anomalies. In contrast

to simple gross profit, operating profit is obtained by subtracting the cost of goods sold

and SG&A expenses, excluding research and development (R&D) expenditures, from

revenue (Ball et al. 2015). Recent studies document that SG&A expenses represent

investments in organizational capital that affect stock returns and firm value (Lev and

Radhakrishnan 2005; Anderson et al. 2007; Eisfeldt and Papanikolaou 2013; Ball

et al. 2015). Banker et al. (2019) find that SG&A expenses are mispriced and have

return predictability in the cross‐section of stock returns. Furthermore, cash‐based

operating profitability excludes accounting accruals from operating profit (Ball

et al. 2016). Studies such as Sloan (1996) show that accruals have return predictability.

However, Mashruwala, Rajgopal, and Shevlin (2006) show that stocks with extreme

accruals are associated with high arbitrage risk, making an accruals‐based hedge

strategy unattractive to arbitrageurs (Lev and Nissim 2006; Ali et al. 2008). Thus,

mispricing due to each accounting component of the profitability ratios could be

contributing to their overall return predictability. To explore this possibility, we further

examine the relation between limits to arbitrage, SG&A expenses, accruals, and the

3

Hedge portfolio refers to a portfolio that executes a strategy long in a firm characteristic deemed high and

short in a firm characteristic deemed low.

4

We follow Ali, Hwang, and Trombley (2003), Mashruwala, Rajgopal, and Shevlin (2006), Lam and Wei

(2011), and Lam, Wei, and Wei (2017) in defining arbitrage costs and arbitrage risk.

307A Cautionary Tale of Profitability Anomalies