Short‐Selling Risk

• Author: JOSEPH E. ENGELBERG,MATTHEW C. RINGGENBERG,ADAM V. REED
• DOI: http://doi.org/10.1111/jofi.12601
• Date: 01 April 2018
• Published date: 01 April 2018

THE JOURNAL OF FINANCE •VOL. LXXIII, NO. 2 •APRIL 2018

Short-Selling Risk

JOSEPH E. ENGELBERG, ADAM V. REED, and MATTHEW C. RINGGENBERG∗

ABSTRACT

Short sellers face unique risks, such as the risk that stock loans become expensive

and the risk that stock loans are recalled. We show that short-selling risk affects

prices among the cross-section of stocks. Stocks with more short-selling risk have

lower returns, less price efficiency, and less short selling.

“Some stocks are hard to borrow. Herbalife is not, especially, but it is risky

to borrow ...IfCarl Icahn were tolaunch a tender offer, say, it might get

a lot more expensive to short Herbalife, and the convertible trade would

become considerably less fun.”

—Matt Levine, Former Investment Banker, BloombergView (2014)1

SHORT SELLING IS A RISKY BUSINESS.SHORT SELLERS must identify mispriced

securities, borrow shares in the equity lending market, postcollateral, and pay a

loan fee each day until the position closes. In addition to the standard risks that

many traders face, such as margin calls and regulatory changes, short sellers

also face the risk of loan recalls and the risk of changing loan fees. To date, the

literature has viewed these risks as a static cost to short sellers, and empirical

∗Joseph E. Engelberg is at Rady School of Management, University of California, San Diego,

Adam V. Reed is at Kenan-Flagler Business School, University of North Carolina. Matthew C.

Ringgenberg is at David Eccles School of Business, University of Utah. The authors thank Ken

Singleton (the editor), an anonymous associate editor, and two anonymous referees, Tom Boulton,

Wes Chan, Itamar Drechsler,David Goldreich, Charles Jones, Juhani Linnainmaa, Paolo Pasquar-

iello, Burt Porter, David Sovich, and Anna Scherbina; participants at the 2012 Data Explorers Se-

curities Financing Forum in New York, the 2013 IMN Beneficial Owner’sInternational Securities

Lending Conference in New Orleans, the 2013 RMA/UNC Securities Lending Institutional Con-

tacts Academic and Regulatory Forum, the 6th Annual Florida State University SunTrust Beach

Conference, the 2014 Financial Intermediation Research Society conference, the 2014 LSE Con-

ference on the Frontiers of Systemic Risk Modelling and Forecasting, the 2014 Western Finance

Association annual meeting, the BlackRock WFA preconference, the 2014 BYU Red Rock Finance

Conference, and the 2015 Wharton/Rodney L. White Center Conference on Financial Decisions and

Asset Markets; and seminar participants at Washington University in St. Louis, the University of

Michigan, the University of Cambridge, and the University of California – Irvine. We also thank

Markit for providing equity lending data. All errors are our own. The authors do not have any

conflicts of interest, as identified in the Journal of Finance’s Disclosure Policy.

1Levine, Matt, 2014, What happened to Herbalife yesterday? BloombergView,February 4.

DOI: 10.1111/jofi.12601

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papers have shown that static impediments to short selling significantly affect

asset prices and efficiency.2The idea in the literature is simple: if short selling

is costly, short sellers may be less likely to trade, and as a result prices may

be biased or less efficient (e.g., Miller (1977), Diamond and Verrecchia (1987),

Lamont and Thaler (2003)).

In this paper, we examine the costs of short selling from a different per-

spective. Specifically, we show that the dynamic risks associated with short

selling result in significant limits to arbitrage. In particular, stocks with more

short-selling risk have lower future returns, less price efficiency, and less short

selling.

Consider two stocks—A and B—that are identical in every way except for

their short-selling risk. Specifically, stock A and stock B have identical funda-

mentals as well as identical loan fees and number of shares available today,

but future loan fees and share availability are more uncertain for stock B than

for stock A; that is, there is considerable risk that future loan fees for stock B

will be higher and future shares of stock B will be unavailable for borrowing.

Since higher loan fees reduce the profits from short selling and limited share

availability can force short sellers to close their position before the arbitrage

is complete, a short seller would prefer to short stock A because it has lower

short-selling risk. In this paper, we present the first evidence that uncertainty

regarding future short sale constraints is a significant risk, and we show that

this risk affects trading and asset prices.

The short-selling risk we describe has theoretical underpinnings in several

existing models. For example, in D’Avolio (2002b)andDuffie,G

ˆ

arleanu, and

Pedersen (2002), short-selling fees and share availability are a function of

the differences of opinion between optimists and pessimists, and short-selling

risk emerges as these differences evolve. As noted by D’Avolio (2002a, p. 279),

“ . . . a short seller is concerned not only with the level of fees, but also with

fee variance.” Accordingly, we focus on the variance of lending fees as our

natural proxy for short-selling risk. To get the best possible measure of this

proxy, we project the variance of lending fees on several equity lending market

characteristics and firm characteristics. We then use fitted values from this

forecasting model (ShortRisk) as our measure of short-selling risk.3

Using this measure, we examine whether short-selling risk affects arbitrage

activity. If short-selling risk limits the ability of arbitrageurs to trade and

2To test the impact of impediments to short selling, existing studies examine a wide variety of

potential measures of short sale constraints including regulatory action (Jones (2008), Diether,Lee,

and Werner (2009), Battalio and Schultz (2011), Boehmer,Jones, and Zhang (2013)), institutional

ownership (Asquith, Pathak, and Ritter (2005), Nagel (2005)), the availability of traded options

(Figlewski and Webb (1993), Danielsen and Sorescu (2001)), and current loan fees (Jones and

Lamont (2002), Cohen, Diether, and Malloy (2009)). However, all of these are static measures of

short sale constraints (i.e., they examine how conditions today constrain short sellers), while we

focus on the dynamics of short selling constraints (i.e., we examine how the risk of changing future

constraints impacts short sellers).

3Our results are robust to using alternate measures of short-selling risk, including the uncon-

ditional historical variance of loan fees for each stock. These results are shown in the Internet

Appendix, which is available in the online version of this article.

Short-Selling Risk 757

correct mispricing, then it should be related to returns, market efficiency, and

short-selling activity. We find that it is. First, we show that our short-selling

risk proxy is related to future returns: a long-short portfolio formed based

on ShortRisk earns a 9.6% annual five-factor alpha. Next, in a Fama and

MacBeth (1973) regression framework we confirm the return predictability of

short-selling risk after controlling for a variety of firm characteristics. We also

consider the Stambaugh, Yu, and Yuan (2015) mispricing measure (MISP)and

find that MISP’s ability to predict returns is greatest among stocks with high

short-selling risk. Thus, higher short-selling risk appears to limit the ability

of arbitrageurs to correct mispricing, and as a result these stocks earn lower

future returns.4

We next test whether increases in short-selling risk are associated with de-

creases in price efficiency. We examine the Hou and Moskowitz (2005) measure

of price delay and find that short-selling risk is associated with significantly

larger price delay, even after controlling for current loan market conditions

(Saffi and Sigurdsson (2011)); a one-standard-deviation increase in ShortRisk

is associated with a 6.8% increase in price delay. Thus, the risk of future short-

selling constraints is associated with decreased price efficiency today, inde-

pendent of short constraints that may exist at the time a short position is

initiated.

Of course, if short-selling risk is truly a limit to arbitrage, then we would

expect this risk to affect trading activity, especially for trades with a long

expected time to completion.5Ofek, Richardson, and Whitelaw (2004, p. 329)

note thatthe “...difficulty of shorting mayincrease with the horizon length,

as investors must pay the rebate rate spread over longer periods and short

positions are more likely to be recalled.” To test this prediction, we turn to one

of the only cases in which mispricing and the expected holding horizon of a

trade can be objectively measured ex ante. Specifically, we examine deviations

between stock prices and the synthetic stock price implied from put-call parity.

Ofek, Richardson, and Whitelaw (2004) and Evans et al. (2009) show that

deviations between the actual and synthetic stock price often imply that a

short seller would short sell the underlying stock and purchase the synthetic

stock, with the expectation that the two prices will converge upon the option

expiration date. Accordingly, we measure mispricing using the natural log of

the ratio of the actual stock price to the implied stock price (henceforth put-

call disparity) as in Ofek, Richardson, and Whitelaw (2004), and we examine

whether short sellers trade less on mispricings when short-selling risk is high

and when the option has a long time to maturity. We find that they do. In

particular, arbitrageurs short significantly less when short-selling risk is high,

and as a result there is more mispricing today. Moreover, both of these effects

are significantly larger for long-horizon trades.

4This result is consistent with models of limits to arbitrage. For example, the model in Shleifer

and Vishny (1997) predicts that stocks that are riskier to arbitrage will exhibit greater mispricing

and have higher average returns to arbitrage.

5We thank an anonymous referee and the Editor for suggesting this point.