Unsophisticated Arbitrageurs and Market Efficiency: Overreacting to a History of Underreaction?

• DOI: http://doi.org/10.1111/1475-679X.12070
• Author: JONATHAN A. MILIAN
• Date: 01 March 2015
• Published date: 01 March 2015

DOI: 10.1111/1475-679X.12070

Journal of Accounting Research

Vol. 53 No. 1 March 2015

Printed in U.S.A.

Unsophisticated Arbitrageurs

and Market Efficiency: Overreacting

to a History of Underreaction?

JONATHAN A. MILIAN

∗

Received 6 March 2013; accepted 17 October 2014

ABSTRACT

Prior research has documented that arbitrage activity significantly reduces or

eliminates stock market anomalies. However, if anomalies arise due to unso-

phisticated investors’ behavioral biases, then these same biases can also ap-

ply to unsophisticated arbitrageurs and thereby disrupt the arbitrage process.

Consistent with a disruption in the arbitrage process for the post-earnings

announcement drift anomaly, I document that the historically positive auto-

correlation in firms’ earnings announcement news has become significantly

negative for firms with active exchange-traded options. For these easy-to-

arbitrage firms, the firms in the highest decile of prior earnings announce-

ment abnormal return (prior earnings surprise), on average, underperform

the firms in the lowest decile by 1.59% (1.43%) at their next earnings an-

nouncement. Additional analyses are consistent with investors learning about

the post-earnings announcement drift anomaly and overcompensating. This

study suggests that unsophisticated attempts to profit from a well-known

∗School of Accounting, Florida International University.

Accepted by Christian Leuz. I thank Ryan Ball, Abhijit Barua, Marcus Burger (AAA discus-

sant), William Cready, R. David McLean (AFA discussant), Jeffrey Pontiff, Changjiang Wang,

two anonymous reviewers, and seminar participants at the 2013 South Florida Accounting

Research Conference, a brown bag workshop at Florida International University, the 2014

Annual Meeting of the American Finance Association, and the 2014 Annual Meeting of the

American Accounting Association. An online appendix to this paper can be downloaded at

http://research.chicagobooth.edu/arc/journal-of-accounting-research/online-supplements.

175

Copyright C, University of Chicago on behalf of the Accounting Research Center,2014

176 J.A.MILIAN

anomaly can significantly reverse a previously documented stock return

pattern.

JEL codes: G10; G12; G14; M40; M41

Keywords: Arbitrage; market efficiency; post-earnings announcement drift;

anomalies

1. Introduction

Academic research has documented an extensive set of stock return

predictors or anomalies (Green, Hand, and Zhang [2013]). In his review

of stock market anomalies, Schwert [2003] argues that increased arbitrage

activity should cast doubt on whether these anomalies can persist. Con-

sistent with this argument, recent research finds that many of the most

well-known anomalies no longer present profitable trading opportunities

(e.g., Chordia, Subrahmanyam, and Tong [2014], Green, Hand, and

Soliman [2011], Richardson, Tuna, and Wysocki [2010]). While this recent

research is consistent with the notion of an increasingly efficient market

in which arbitrageurs eliminate profitable trading opportunities, it is not

clear that attempts to profit from a well-known anomaly must always drive

stock prices to fundamental values. For it is possible that, if imperfections

(e.g., behavioral biases) allow anomalies to arise in the first place, then

these same forces can also apply to the arbitrage process.

Attempts to arbitrage well-known anomalies will not necessarily drive

stock prices to fundamental values because the trading strategies for ex-

ploiting these anomalies are based on relative values rather than absolute

or fundamental values.1Because these trading strategies are not based

on estimates of fundamental value, an arbitrageur relying solely on these

strategies never knows the extent of the mispricing, if any.2This inherent

uncertainty regarding the magnitude of the mispricing requires the

arbitrageur to understand the price impact, if any, of other arbitrageurs

using the same or similar strategy. Determining the price impact of other

arbitrageurs is a difficult problem and likely subject to the same behavioral

biases that can create mispricing. For example, an unsophisticated arbi-

trageur may exhibit overconfidence from his knowledge of the anomaly,

and/or he may exhibit conservatism in assessing the amount of capital

1In this paper, I use the term arbitrage to refer to trading activity that attempts to profit

from a believed mispricing. I do not take a position on whether there is an actual mispricing,

and I do not take the position that arbitrage activity requires both long and short positions

(e.g., some investors are only able to take long positions).

2In this paper,arbitrageurs are investors whose trading activities are influenced by the trad-

ing strategies found in academic research on stock market anomalies. The sophistication of

these arbitrageurs can vary greatly, from sophisticated arbitrageurs with unbiased estimates of

fundamental value and unbiased estimates of the price impact of other arbitrageurs to unso-

phisticated arbitrageurs relying solely on the findings in potentially dated academic research.

UNSOPHISTICATED ARBITRAGEURS AND MARKET EFFICIENCY 177

invested by other arbitrageurs attempting to profit from the anomaly.3

Thus, just as mispricing can stem from unsophisticated investors, there

is the potential for unsophisticated arbitrageurs to disrupt the arbitrage

process.

Stein [2009] and Lundholm [2008] present theoretical models where

some arbitrageurs use trading strategies based solely on relative values

(i.e., these arbitrageurs do not consider fundamental values). They show

that, when this type of arbitrage activity becomes too aggressive, these ar-

bitrageurs can cause the opposite of the expected return pattern instead

of eliminating the pattern. Similarly, Lo [2004] argues that, in an adaptive

market, a trading strategy will undergo cycles of profit and loss depending

on the magnitude of the profit opportunities and the amount of capital

invested in the trading strategy. Motivated by these theoretical models and

given that we live in an imperfect world, I hypothesize that the return pat-

tern from a well-known anomaly can significantly reverse over a nontrivial

period of time due to an overcrowding of unsophisticated arbitrageurs in

that trading strategy.4

To test my hypothesis, I study one of the main features of the post-

earnings announcement drift (hereafter, PEAD) phenomenon. More

specifically, I examine the autocorrelation in earnings announcement news

for firms with active exchange-traded options.5This setting increases the

likelihood of detecting an overcrowded trade for several reasons. First, the

PEAD anomaly is one of the most well-known anomalies. Second, firms with

active exchange-traded options are easier to arbitrage. Third, a short-return

window following the subsequent earnings announcement is an ideal time

to test for overcrowding in the PEAD trading strategy (i.e., a reversal of the

PEAD return pattern).

The subsequent earnings announcement is an attractive period because

the abnormal returns per unit of time are greatest to the PEAD strategy

at that time (e.g., Bernard and Thomas [1989], Freeman and Tse [1989]).

Given this well-known aspect of PEAD, arbitrage activity is potentially at its

maximum just prior to the subsequent earnings announcement. Thus, a

reversal of the PEAD return pattern following the subsequent earnings an-

nouncement can occur for two reasons. First, because a significant amount

of fundamental information is released at the earnings announcement, fun-

damental traders can more easily correct mispricing created by the unso-

phisticated arbitrageurs. Second, price pressure in the direction opposite

3Overconfidence and conservatism are examples of two psychological biases used to ex-

plain investor underreaction and overreaction in securities markets (e.g., Barberis, Shleifer,

and Vishny [1998], Daniel, Hirshleifer, and Subrahmanyam [1998]).

4In a departure from the Stein [2009] model, rather than assuming that each arbitrageur

makes an unbiased estimate of the arbitrage activity by others, my hypothesis requires that

unsophisticated arbitrageurs consistently underestimate the arbitrage activities of others.

5I refer to the relation between the current earnings announcement abnormal return and

either the prior earnings announcement abnormal return or the prior earnings surprise as

the autocorrelation in earning announcement news.