The Causal Effect of Limits to Arbitrage on Asset Pricing Anomalies

• DOI: http://doi.org/10.1111/jofi.12947
• Author: DAVID HIRSHLEIFER,YONGQIANG CHU,LIANG MA
• Published date: 01 October 2020
• Date: 01 October 2020

THE JOURNAL OF FINANCE •VOL. LXXV, NO. 5 •OCTOBER 2020

The Causal Effect of Limits to Arbitrage on Asset

Pricing Anomalies

YONGQIANG CHU, DAVID HIRSHLEIFER, and LIANG MA∗

ABSTRACT

We examine the causal effect of limits to arbitrage on 11 well-known asset pricing

anomalies using the pilot program of Regulation SHO, which relaxed short-sale con-

straints for a quasi-random set of pilot stocks, as a natural experiment. We find that

the anomalies became weaker on portfolios constructed with pilot stocks during the

pilot period. The pilot program reduced the combined anomaly long–short portfolio

returns by 72 basis points per month, a difference that survives risk adjustment with

standard factor models. The effect comes only from the short legs of the anomaly

portfolios.

OVER THE LAST SEVERAL DECADES, finance researchers have discovered

many cross-sectional asset pricing anomalies, whereby predetermined security

characteristics predict future stock returns.1Such patterns can derive from ei-

ther rational risk premia or market mispricing. The mispricing explanation is

consistent with the idea that limits to arbitrage delay the flow of wealth from

irrational to sophisticated investors (Shleifer and Vishny (1997)). In contrast,

if return predictability is the result of rational risk premia that compensate

investors for bearing factor risk, limits to arbitrage should not affect expected

returns.

An interesting question that arises is whether, to the extent that return

anomalies reflect mispricing, such anomalies are persistent because limits

to arbitrage prevent sophisticated investors from trading profitably against

∗Yongqiang Chu is with the Belk College of Business, University of North Carolina, Charlotte.

David Hirshleifer is with the Merage School of Business, University of California at Irvine and

NBER. Liang Ma is with the Darla Moore School of Business, University of South Carolina. For

helpful comments and suggestions, we thank Wei Xiong (the editor); an anonymous associate ed-

itor; two anonymous referees; Karl Diether; Lukasz Pomorski; Jeffrey Pontiff; Lin Sun; and par-

ticipants at the 2016 Rodney L. White Center for Financial Research Conference on Financial

Decisions and Asset Markets at Wharton and the 2017 American Finance Association Meetings.

This research has received financial support from the Moore School Research Grant Program.

The authors have read The Journal of Finance disclosure policy and have no conflicts of interest

to disclose.

Correspondence: Liang Ma, Department of Finance, Darla Moore School of Business, University

of South Carolina, 1014 Greene Street, Columbia, SC 29208; e-mail: liang.ma@moore.sc.edu.

1Harvey, Liu, and Zhu (2016) provide a comprehensive list of variables that can predict cross-

sectional stock returns.

DOI: 10.1111/jofi.12947

© 2020 the American Finance Association

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them. However, it is empirically challenging to capture pure variations in lim-

its to arbitrage that exclude variations in other economic forces that might

affect risk premia or mispricing. In this paper, we study the causal effect of

limits to arbitrage on 11 well-known asset pricing anomalies, namely, the mo-

mentum, gross profitability, asset growth, investment to assets, return on as-

sets, net operating assets, accruals, net stock issuance, composite equity is-

suance, failure probability, and O-score anomalies. These 11 anomalies, which

were the focus of Stambaugh, Yu, and Yuan (2012) in their study of sentiment

and anomalies, survive after adjusting for the Fama–French three factors. Ex-

amining the causal effect of limits to arbitrage on these anomalies provides

insight into the extent to which well-known return anomalies derive from risk

versus mispricing.

It is difficult to identify the causal effect of limits to arbitrage as we seldom

observe them, or pure variations in them, directly. Accordingly, existing liter-

ature often relies on firm characteristics, such as idiosyncratic volatility, size,

and stock liquidity, as proxies for limits to arbitrage. However, these proxies

are likely to be correlated with risk. For example, size has been offered as the

basis for a risk factor in the three-factor model of Fama and French (1993), and

volatility can be a risk measure in models with limited diversification such as

settings with costs of trading or asymmetric information. This raises the pos-

sibility that effects attributed to limits to arbitrage may actually be due to

rational risk premia.

Here we offer a pure test of the causal effect of limits to arbitrage on asset

pricing anomalies. Short-sale constraints are one of the most important limits

of arbitrage (e.g., Jones and Lamont (2002), Lamont and Thaler (2003), Nagel

(2005), Gromb and Vayanos (2010)). Research on the effect of short-sale con-

straints on asset prices relies mainly on indirect proxies such as breadth of

ownership (Chen, Hong, and Stein (2002)), institutional ownership (Asquith,

Pathak, and Ritter (2005), Nagel (2005), Hirshleifer, Teoh, and Yu (2011)), firm

size (Ali and Trombley (2006), Israel and Moskowitz (2013)), short interest

(Asquith, Pathak, and Ritter (2005)), and shorting cost estimated from stock

borrowing and lending behavior (Geczy, Musto, and Reed (2002), Jones and La-

mont (2002), Drechsler and Drechsler (2014)). Several of these proxies may be

correlated across stocks or over time with variations in factor risk.

We exploit a natural experiment—the Rule 202T pilot program of Regula-

tion SHO (hereafter the pilot program)—to identify the causal effect of limits

to arbitrage, and in particular short-sale constraints, on asset pricing anoma-

lies. Regulation SHO was adopted by the Securities and Exchange Commission

(SEC) in July 2004. Among stocks in the Russell 3000 index as of June 2004,

the pilot program designated every third stock ranked by average daily trad-

ing volume (in the prior year) on each of NYSE, Amex, and NASDAQ as pilot

stocks. The pilot program then removed short-sale price tests on this quasi-

randomly selected group of pilot stocks. Prior to Regulation SHO, the specific

form of short-sale price tests differed across stock markets. NYSE/Amex im-

posed the uptick rule, which only allowed a short sale to be placed on a plus

tick or a zero-plus tick, whereas NASDAQ imposed the bid price test, which

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did not allow short sales at or below the (inside) bid when the inside bid was

at or below the previous inside bid. From May 2, 2005 to August 6, 2007, the

pilot stocks on NYSE/Amex were exempted from the uptick rule and those on

NASDAQ were exempted from the bid price test. The pilot program therefore

made it easier to short sell pilot stocks relative to nonpilot stocks. Because the

assignment of pilot and nonpilot firms is quasi-random, the program provides

an ideal setting to examine the causal effect of short-sale constraints on asset

pricing anomalies. The bid price test for NASDAQ stocks is not very restric-

tive (see Diether, Lee, and Werner (2009) and discussion in Section I), and a

significant fraction of trading volume in NASDAQ-listed stocks is executed on

ArcaEx and INET, which do not enforce the bid price test. We therefore ex-

clude NASDAQ stocks and only include pilot and nonpilot stocks traded on

NYSE/Amex in our main analysis.

We examine two main hypotheses regarding the differential performance of

pilot versus nonpilot anomaly portfolios during the pilot period of Regulation

SHO. The first is that the anomalies become weaker for pilot firms relative

to nonpilot firms during the pilot period. During the pilot period, arbitrageurs

could more easily short pilot stocks to construct arbitrage portfolios, which

should reduce mispricing. It follows that the return spread of arbitrage portfo-

lios should decline for pilot stocks relative to nonpilot stocks.

To test the first hypothesis, for each asset pricing anomaly we construct

long–short portfolios with pilot and nonpilot stocks separately. Specifically, we

first sort all pilot stocks into deciles according to the return-predicting charac-

teristic and calculate the anomaly returns as the return differences between

the highest performing decile based on existing anomaly evidence (the long

leg) and the lowest performing decile (the short leg). We then do the same

with all nonpilot stocks. In a difference-in-differences framework, we find that

the anomalies were much weaker in long–short portfolios constructed using

pilot stocks during the pilot period. The effect is statistically significant in

five of the 11 anomalies. When the 11 anomalies are combined in a joint

test, the effect is both statistically and economically significant. The pilot pro-

gram reduced the anomaly returns by 72 basis points per month, or 8.64%

per year.

The second hypothesis is that the decrease in anomaly returns for pilot

stocks during the pilot period comes mostly from the short-leg portfolios. In

general, anomaly returns can come from either overpriced short legs or under-

priced long legs. A loosening of short-sale constraints should reduce profitabil-

ity of short-leg arbitrage portfolios. Using the same difference-in-differences

framework, we find that the returns of short-leg portfolios constructed with pi-

lot stocks were significantly and substantially higher during the pilot period,

that is, short strategies became less profitable. In contrast, there is no signifi-

cant effect of the pilot program on long-leg portfolios.

We next consider two additional hypotheses. First, the difference in anomaly

returns between pilot and nonpilot stocks should vanish after the ending

of the pilot program, with the disappearance of the difference in short-sale