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This is to certify that the
dissertation entitled

ESSAYS ON ARBITRAGE ACTIVITIES

presented by

Umit Gurkan Gurun

has been accepted towards fulfillment
of the requirements for the

Ph.D. degree in Finance

 

   

Pro ssors Signatdre

10 ”a? 0700:7/

Date

MSU is an Afi‘innative Action/Equal Opportunity Institution

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LIBRARY

Michigan State

University

 

 

PLACE IN RETURN Box to remove this checkout from your record.
TO AVOID FINE return on or before date due.
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DATE DUE

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6/01 cJCIRC/DateDuo.p65«p.15

ESSAYS ON ARBITRAGE ACTIVITIES
By

Umit Gurkan Gurun

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Finance

2004

 

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In the SECOnd

ABSTRACT

ESSAYS ON ARBITRAGE ACTIVITIES

By

Umit Gurkan Gurun

This study contains two chapters. In the first chapter, we provide new insights to the
visibility hypothesis of Miller (1977), who argues that increased attention to a given stock
should attract and convince more investors to buy the stock. We argue that stocks with
low substitutability risk are more likely to experience abnormal trading activity when
their prices deviate from fundamentals and postulate that the abnormal trading activities
may signal the intentions of the traders, presumably arbitrageurs. Thus, in an economy
where short selling is restricted, stocks with close substitutes are more likely to be
“visible” when they are underpriced. We present empirical evidence that substitutability
risk can explain the high-volume return premium documented by Gervais, Kaniel, and

Mingelgrin (2001).

In the second chapter, we show that cross sectional differences of momentum profits
across 31 countries can be explained by market intelligence measures such as investor
sophistication and earnings management severeness. We present three novel findings:
First, momentum is more pronounced in countries that have severe earnings management
practices, suggesting that momentum is not due to market under reaction due to earnings
related information. Second, momentum strategies appear to be profitable in countries

that have more sophisticated investors. And third, the growth rate of momentum

strateg)"S VOL
suggesting thiz

investors. OVL’

risk is the pric
and Zhou (2i?

trading costs.

 

strategy’s volatility (exploitability risk) is positively related to investor sophistication,
suggesting that momentum strategies are riskier in markets dominated by sophisticated
investors. Overall our empirical evidence is consistent with the notion that exploitability
risk is the price of momentum profits, and complements the findings of Lesmond, Schill,
and Zhou (2004), who show that stocks that generate momentum profits have higher

trading costs.

To my uncle Nevzat Kip (1944-2000)

iv

lam Salem

I
professor 6- I
queSlIOIISs Ihi
comminee m"
Schroder for
acknowledge 3
Finance DEPL‘A‘
ideas. Profess
helped me de\

I feel extreme

 

during my dm
Altsu for prm'
can eXpress r
Dalgin, Dagh
Oguzhan Ku
encouragemer
Lew but not
Sema Gurun .
ml heme. I a]
home in US.
had courage 1

IOI her infirm-

ACKNOWLEDGEMENTS

I am grateful for the excellent guidance and support of my committee chair and mentor,
Professor G. Geoffrey Booth. Without his insightful comments and thought provoking
questions, this dissertation would not be completed. I would also like to thank my
committee members, Professor Richard Baillie, Kirt Butler, Charlie Hadlock and Mark
Schroder for their help and continued support throughout my studies. I would like to
acknowledge many fruitful discussions with other faculty and fellow doctoral students of
Finance Department at MSU. They provided an excellent environment for nurturing new
ideas. Professor Gautam Kaul, Tamer Cavusgil, and Mitchell Warachka’s comments
helped me develop my ideas.

I feel extremely fortunate to have received support from many other people before and
during my doctoral studies. My primary debts are to Professor Veday Akgiray and Celal
Aksu for providing me an opportunity to study finance. There are no words with which I
can express my deepest appreciation to my friends and mentors Salim Buge, Burak
Dalgin, Daghan Erbakan, Omer Erdem, Emre Gurkan, Mustafa Kamasak, Ali Koo,
Oguzhan Kulekci, Volkan Muslu, and Bulent Yildirim for their support and
encouragement.

Least but not last, I thank my family - Ayse Gurun, Muzaffer Gurun, Jale Gurun, and
Sema Gurun - for their incredible patience and continued support while I was away from
my home. I also thank Elizabeth Booth, Mike Booth, and Matt Booth for making me feel
home in US. Without my farmly in Turkey and US. standing behind, I would not have
had courage to write this dissertation. Finally, I am indebted to my fiancee Ayfer Seyfi

for her inspiration, patience and unqualified love that kept me emotionally alive.

w
I

llST OF TAB
LIST OF FIGI.

INTRODL'CT‘.

l.

Does 1“
Return

lntrodu

The Lit

 

Limite |
Trading
The .\lk
Genera
Assets
Inx'estr:
Constr.
SOlUtic
Empin'
Empiri
Dania

POnfi)

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

INTRODUCTION

1.

1.1

1.2

1.2.1

1.2.2

1.3

1.3.1

1.3.2

1.3.3

1.3.4

1.3.5

1.3.6

1.4

1.4.1

1.4.2

1.4.3

1.4.4

Does Fundamental Risk of Arbitrage Explain the High-Volume
Return Premium?

Introduction

The Literature

Limited Arbitrage

Trading Volume Literature

The Model

General Setup

Assets

Investors and Their Investment Opportunity Sets
Constraints of the Arbitrageur

Solution of the Arbitrageur’s Problem
Empirical Implications of the Solutions
Empirical Tests

Data and Methodology

Portfolio Formation and Returns
Measure of Substitutability Risk

Measure of Divergence of Opinions

vi

viii

xii

10

10

10

ll

13

15

22

24

24

26

28

29

1.4.6
1.4.7

1.4.8

1.6

APPENDIX 1

.\1ea.<t.
Tests
Relatii
Expla:
Econo
Investi

Conch

 

BIBLIOGRAI
3- Tests (
and St
2.1 Intro-Jr
3-3 Relatei
2.3 Model
2.4 Empirf
2.4.1 Data
2.4.2 \"ariat
2.43 H} POI
2.5 COneI‘
APPEXDIX ‘

1.4.5

1.4.6

1.4.7

1.4.8

1.5

1.6

Measure of Other Risk Factors

Tests

Relationship between Size and Substitutability Risk

Explanatory Power of the EM Ratio

Economic Significance of Arbitrageur’s Profits and High-Volume
Investing as a Hedge Fund Strategy

Conclusion

APPENDIX 1 TABLES AND FIGURES FOR CHAPTER 1

BIBLIOGRAPHY REFERENCES FOR CHAPTER 1

2. Tests of Competing Theories of Momentum: Market Intelligence
and Statistical Arbitrage

2. 1 Introduction

2.2 Related Literature

2.3 Model

2.4 Empirical Setup

2.4.1 Data

2.4.2 Variables

2.4.3 Hypotheses, Tests, and Results

2.5 Conclusion

APPENDIX 2 TABLES AND FIGURES FOR CHAPTER 2

BIBLIOGRAPHY REFERENCES FOR CHAPTER 2

vii

30

31

35

37

37

39

42

66

73

73

76

8O

83

83

84

91

104

106

157

TABLES F 01
Table 1.1

Table 1.2

Table 1.3

Table 1.4

Table 15

Table 1.6.1

 

 

 

LIST OF TABLES

TABLES FOR CHAPTER 1

Table 1.1

Table 1.2

Table 1.3

Table 1.4

Table 1.5

Table 1.6.1

Table 1.6.2

Descriptive Statistics for the Daily CRSP Sample 42
Zero Investment Portfolio Formation Strategy for the Daily CRSP
Sample 44
Empirical Distribution and Sample Statistics for the 20-day Net
Returns of the High Volume and Low Volume and Market

Portfolios Using the Daily CRSP Sample 46
Descriptive Statistics of Substitutability Risk Estimates 48
All companies - SURE Model of High- and Low-volume

Portions of the Zero Investment Portfolios Using the Daily

CRSP Sample. 50
Original Sample, All companies. Wald test results of the

SURE Model that Regresses High- and Low-volume Portions

of the Zero Investment Portfolios Using the Daily CRSP Sample. 52
Buying/Selling Pressure Control Sample, All companies.

Wald Test Results of the SURE Model That Regresses High-

and Low-volume Portions of the Zero Investment Portfolios

Using the Daily CRSP Sample. 55

viii

Table 1.7-1

Table 1.7.2

Table 1.8.1

Table 1_8_3

Table 1.7.1

Table 1.7.2

Table 1.8.1

Table 1.8.2

Original Sample, Large Size Companies. Wald Test Results

of the SURE Model That Regresses Hi gh- and Low-volume

Portions of the Zero Investment Portfolios Using the Daily

CRSP Sample 57
Buying/Selling Pressure Control Sample, Large Size Companies.
Wald Test Results of the SURE Model That Regresses Hi gh-

and Low-volume Portions of the Zero Investment Portfolios

Using the Daily CRSP Sample Panel A: Estimated Slope

Differences. 59
Original Sample, Small and Medium Size Companies Wald

Test Results of the SURE Model That Regresses High- and
Low-volume Portions of the Zero Investment Portfolios Using

the Daily CRSP Sample Panel A: Estimated Slope Differences. 61
Buying/Selling Pressure Control Sample, Small and

Medium Size Companies. Wald Test Results of the SURE

Model That Regresses High- and Low-volume Portions

of the Zero Investment Portfolios Using the Daily CRSP Sample 63

TABLES FOR CHAPTER 2

Table 2.1

Table 2.2.1

Table 2.2.2

Sample Dates and Number of Companies and
Descriptive Country Specific Information 108
Momentum Profits for Some Countries: Australia-India 111

Momentum Profits for Some Countries: Ireland-Norway 113

ix

Table 2.2.3
Table 2.3.1
Table 2.4.1.1
Table 2.4.1.2
Table 2.4.2.1
Table 2.4.2.2

Table 2.4.3.1

Table 2.4.4.1
Table 2.4.4.2

Table 2.5

 

Table 2.2.3

Table 2.3.1

Table 2.4.1.1

Table 2.4.1.2

Table 2.4.2.1

Table 2.4.2.2

Table 2.4.3.1

Table 2.4.3.2

Table 2.4.4.1

Table 2.4.4.2

Table 2.5

Table 2.6

Table 2.7.1

Table 2.7.2

Table 2.7.3

Table 2.7.4

Table 2.7.5

Table 2.8.1

Table 2.8.2

Table 2.8.3

Table 2.8.4

Momentum Profits for Some Countries: Pakistan-US
Variables

Statistical Arbitrage Tests for 3/ 1/3 Momentum Strategies
Summary Statistics for 3/1/3 Momentum Portfolios
Statistical Arbitrage Tests for 6/1/6 Momentum Strategies
Summary Statistics for 6/1/6 Momentum Portfolios
Statistical Arbitrage Tests for 9/1/9 Momentum Strategies
Summary Statistics for 9/1/9 Momentum Portfolios
Statistical Arbitrage Tests for 12/1/12 Momentum Strategies
Summary Statistics for 12/1/12 Momentum Portfolios
Correlation Matrix for the Variables Described in Table 2.9
and Reported in Table 2.3

Momentum Profits and Asset Price Comovement
Momentum Profits of 3/1/3 Strategy and Its Determinants
Momentum Profits of 6/1/6 Strategy and Its Determinants
Momentum Profits of 9/1/9 Strategy and Its Determinants
Momentum Profits of 12/1/12 Strategy and Its Determinants
Momentum Profits of 6/1/6 Strategy and Its Determinants
(with Investor Protection)

Risk of 3/1/3 Momentum Strategy and Its Determinants
Risk of 6/1/6 Momentum Strategy and Its Determinants
Risk of 9/1/9 Momentum Strategy and Its Determinants

Risk of 12/1/ 12 Momentum Strategy and Its Determinants

115

117

121

123

125

126

128

129

131

132

134

135

136

138

139

140

141

142

143

144

145

 

Table 2.9

Table 2.10

 

‘ Table 2.9 Data description and sources 146

Table 2.10 Statistical Arbitrage 152

xi

FIGURES F(

Figure 1.1

FIGL'RES Ft"

Figure 2.1.1

 

LIST OF FIGURES

FIGURES FOR CHAPTER 1

Figure 1.1 Time Sequence for Sample Selection.

FIGURES FOR CHAPTER 2

Figure 2.1.1 Statistical Arbitrage Tests of 3/1/3 Momentum Strategy
Figure 2.1.2 Statistical Arbitrage Tests of 6/1/6 Momentum Strategy
Figure 2.1.3 Statistical Arbitrage Tests of 9/1/9 Momentum Strategy

Figure 2.1.4 Statistical Arbitrage Tests of 12/1/12 Momentum Strategy

xii

65

154

155

156

157

1 Does

Premium?

1,1 lntror

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both scholar:
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Chapter 1

1 Does Fundamental Risk of Arbitrage Explain the High-Volume Return

Premium?

1.1 Introduction

Although information content of past trading volume has been intensely scrutinized by
both scholars and practitioners in various contexts, there is little consensus about its
usefulness in predicting future returns. This article examines the relationship between
substitutability risk and trading volume, and proposes a new interpretation of abnormal

trading activities.1

Our main argument is analogous to the ‘substitution hypothesis’ of Scholes (1972), who
maintains that the availability of close substitutes for individual assets is essential for
obtaining efficient prices. When securities have perfect substitutes, deviations from
fundamentals provide risk-free profit that can be eliminated by competitive arbitrageurs
immediately.2 On the contrary, when there are no perfect (or close) substitutes, rational
investors may be reluctant to trade against mispricing because risk aversion limits their

aggressiveness and they therefore have to bear fundamental risk (Shleifer(2000)).

In the first part of this paper, we present a model in which investors are more likely to
engage in arbitrage activities when securities have perfect (or close) substitutes. This

happens for two reasons. First, return from arbitrage activities of stocks with perfect

 

' Substitutability risk is also called as arbitrage risk (Wurgler and Zhuravskaya (2002)) or
fundamental risk of arbitrage (Shleifer (2000)).

2 A perfect substitute is an asset (or portfolio) with identical cash flows in all states of the
world.

substitutes IS

.. - l
posmonS 1“

with imperb

 

substitutes 31
EVCII if there
bypass profit
work Of Cm

\tealth- and

 

 

 

assets in a

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substitutes is higher than that of with imperfect substitutes. Second, investors take larger
positions in these stocks since they are less subject to substitutability risk than the ones
with imperfect substitutes. Furthermore, in our model, when assets without perfect
substitutes are underpriced, investors can still eliminate deviations from fimdamentals
even if there are short-selling constraints, but when such assets are overpriced, investors
bypass profit opportunities. Methodologically, the model builds on and complements the
work of Gromb and Vayanos (2002), who characterize the conditions under which
wealth- and margin-constrained arbitrageurs provide liquidity of perfectly substitutable
assets in a segmented market. Our model extends their framework to imperfect

substitutes.

The empirical evidence presented in the second part of the paper indicates that portfolios
that are close substitutes to market portfolio are likely to experience abnormal trading
activity. We choose to work with portfolios of assets rather than individual securities for
two reasons. First, much research suggests that it is almost impossible to identify perfect
(or even close) substitutes for a given stock (Roll( 1988), Wurgler and Zhuravskaya
(2002)). Second, any method for finding the best substitutes is subject to the criticism of
data mining. Whereas individual assets may not have close substitutes, a diversified
portfolio may be considered a close substitute for the market portfolio by construction,

assuming that the latter is always correctly priced.

The results suggest that the substitutability hypothesis can explain an anomaly
documented by Gervais, Kaniel, and Mingelgrin (2001): Stocks that experience
abnormally high (low) trading volumes over a day tend to appreciate (depreciate) over

the course of the following month. They found that the return premium of high-volume

 

stocks 0V9r
announcemet
volume and
h}pothesis 01
will reflect tl‘
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stocks over low-volume stocks cannot be explained by information effects (firm
announcements), liquidity, momentum and short-term interactions between trading
volume and returns. To account for this return premium, they suggest the visibility
hypothesis of Miller (1977). That is, when there are short-selling constraints, stock prices
will reflect the valuations of optimists but not pessimists, because the latter simply refrain
from the market as opposed to selling short, which is what they would do in an
unconstrained setting. In other words, investors typically only consider the assets they
hold when making their sell decisions. Therefore, the decision about which asset to sell
does not convey much information to the market, since it is usually interpreted as
liquidity motivated. In buying an asset, however, the selection is limited to the number of
assets in the market, so buy orders convey more information than sell orders do. As a

result, large buy trading volumes should have a positive price impact.3

Although Miller’s visibility hypothesis can explain why attention towards a given stock
results in a subsequent price increase, it says nothing about why those particular stocks
became attractive in the first place. We argue that stocks with close substitutes are more
likely to gain investors’ attention, because investors believe that those particular stocks
are less likely to be mispriced, and even if they are mispriced, mispricing will be
eliminated immediately. On the one hand, as our model suggests, the elimination of
mispricing should make underpriced stocks especially attractive, since any investor
(including current stockholders) can buy them. On the other hand, the elimination of

mispricing for overpriced stocks should have limited effect since only the current

 

3 Similar arguments are made by Arbel and Strebel (1982), Chan and Lakonishok (1993),
and Mayshar (1983).

 

stockhOlderS

from shortin

In other wor
when they at
Miller's visil
try to answe
deviations fr
activities? \V
Based on em
(2001) (here
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stockholders can sell them when the lack of perfect substitutes prevents other investors

from shorting these assets.

In other words, all else being equal, stocks with close substitutes are likely to be visible
when they are underpriced, so the substitution hypothesis of Scholes (1972) complements
Miller’s visibility hypothesis, which is the main message of this study. Specifically, we
try to answer the following questions: Does substitutability makes it easier to capture
deviations from fundamentals or new information, thereby cause unusually high trading

activities? Which stocks suddenly become more visible?

Based on empirical tests, we first confirm and then extend the findings of Gervais et a1.
(2001) (hereafter GKM) by showing that substitutability risk indeed can explain the
return premium difference between stocks that experience a positive shock and that of a
negative shock in their trading activities. The statistical significance of substitutability
risk disappears for the portfolios of large size companies around the tenth trading day, but
it remains to be significant for portfolios of small and medium firms. This supports our
conjecture that deviations from fundamentals are more likely for stocks without perfect
(or close) substitutes. Deviations from fundamentals in large companies are more likely
to be identified sooner than an opportunity in stocks of small and medium companies,
because large companies are followed by more analysts and by a larger investor
(presumably arbitrageur) base. Substitutability of the stocks of large companies increases
investors’ interest and trading volume (visibility), which will reduce the possibility and
duration of mispricing. Because small size firms are less visible to a large number of
competitive arbitrageurs in a short period, price corrections take longer time. The

relationship between size and substitutability risk also confirms Merton (1987)’s

argun‘lent 3b
' |
interpretatio:
|

releases) an
I
extreme tray

other explan.

This study it
and trading ‘.
the fund-arm
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argument about the cost of information gathering. The results are robust to other possible
interpretations of trading volume, such as announcement affects (new information
releases) and difference of opinion among investors.4 Therefore, we conclude that
extreme trading activities are more likely to be explained by substitutability risk than

other explanations.

This study mainly contributes to two different streams of the literature: limits to arbitrage
and trading volume. First, it provides further empirical evidence that investors care about
the fundamental risk of arbitrage (substitutability risk), which means that imperfect
substitutes are indeed a limit to arbitrage (Shleifer and Vishny (1997)). The idea that the
risk associated with volatility of arbitrage deters arbitrage activity also has implications
for other well documented anomalies, such as the book-to-market (B/M) effect (Ali et al.
(2003)). We also find that the high-minus-low factor (Fama and French (1992)) can
account for part of the high—volume premium, but its explanatory power is not as great as
that of substitutability risk. Finally, this research supports the findings of Wurgler and
Zhuravskaya (2002), who postulate that demand curves of stocks incorporate
substitutability risk. Second, our approach relates extreme trading volumes to the most
fundamental motive of trading, arbitrage and its limits. Therefore, the results may shed
light on trading activities that cannot be explained by announcement affects, difference of

opinion or liquidity.

The rest of paper is organized as follows. The next section reviews recent works on the
return-volume relationship and the limits of arbitrage. The following sections introduce

the model and present the results of empirical tests. We then discuss the economic

 

4 Gervais et a1. (2001) rule our liquidity as an explanation for the high-volume premium,
so we do not control for that factor explicitly.

signlfiCanC‘

conclusionf
1.2 The
1.2.1 Lim

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(2003) prov

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fundamental
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significance of substitutability risk for the high-volume premium puzzle and offer

conclusions.
1.2 The Literature
1.2.1 Limited arbitrage

Recent works have raised the issue of limits to arbitrage, such as noise trader risk and
transactions costs, and claim that the time it takes to reach fundamental values may be
substantially longer than it should be in an efficient market.5 Shleifer (2000) and Barberis

(2003) provide excellent surveys of the limited arbitrage literature.

Obviously, the major risk of arbitrage strategies is substitutability risk (or the
fundamental risk of arbitrage), since it is almost impossible to find a perfect substitute.
Studies that scrutinize the effects of fundamental risk include Roll (1988), Froot and
Dabora (1999) and. Wurgler and Zhravskaya (2002). These works mainly show that
assets are far from having a perfect substitute and question the effect of limited arbitrage
on the elasticity of demand curves. Kyle (1985) shows that it is not possible to distinguish
price effects between private information and supply shocks. Consequently, studies that
tests the slope of the demand curve (i.e., effects of substitutability risk) focus on a subset
1

of specific large supply shocks whose source can be identified as uninformed by the

market participants. Examples include large block trades (Scholes (1972), Holthausen et

 

5 Shleifer and Vishny (1997) show that the agency problem between professional
arbitrageurs and investors imposes an indirect wealth constraint that reduces arbitrageurs’
ability to exploit opportunities. Theoretical works on short selling restrictions include
Littner (1969), Miller (1977), and Jarrow (1980), among others. On the empirical side,
Chen, Hong, and Stein (2002), Geczy, Musto, and Reed (2002), Mitchell, Pulvino and
Stafford (2002), and Jones and Lamont (2001) provide evidence that short selling
restrictions exist in financial markets. In contrast, D’Avolio (2002) shows that short-
selling costs may not be economically significant. Noise trader risk is discussed by
DeLong et a1. (1990).

a1, (1990)). :

(1986)).

hiourtnod
combined \\
arbitrage. E:
assets have
121302), Liu
studies, arbi
positions ag;
they quuida:
constraints r
aF‘Proach co:

substitutabili

1.2.2 Trad
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6 .
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al. (1990)), seasoned equity offerings (Loderer et al. (1991)) and index changes (Shleifer

(1986)).

In our model, imperfectly substitutable assets that are traded in segmented markets
combined with wealth and margin constraints constitute the major frictions that limit
arbitrage. Effects of wealth and margin constraints on arbitrageurs’ demand for risky
assets have been scrutinized in many recent studies including Gromb and Vayanos
(2002), Liu and Longstaff (2003), Xiong (2001), and Kyle and Xiong (2001). In these
studies, arbitrageurs reduce asset price volatility and provide liquidity by taking risky
positions against noise trading. Yet, when an unfavorable shock causes capital losses,
they liquidate positions. Furthermore, in combination with wealth constraints, margin
constraints prevent arbitrageurs engaging in some of the arbitrage opportunities. Our
approach contributes to this literature by adding another dimension, the effect of asset

substitutability on the arbitrageur’s portfolio choice problem.
1.2.2 Trading volume literature

There is a considerable trading volume literature. Market participants often follow
volume data, which presumably convey information about future price movements
because it is believed that trading volume shows the degree of disagreement on the
fundamental prices.6 In the finance literature, trading volume not only is used as a proxy
for information but also is a sign of the degree of information asymmetry among the

investors (divergent opinions).7

 

6 Earlier works on trading volume is surveyed in Karpoff(1986).

7 Theoretical work on the relationship between difference of opinion and trading volume
includes Harris and Raviv (1993) and Shalen (1993).The major message of these studies
is that dispersion can contribute to the positive correlation between volume and absolute

Volume in
Theorellcall:
constant r31
information

andpficesre

volume bCCO

Trading V011
(19781,). If

available sec
representativ
processes. Ir
determined p
of the aggro»:
lie. change

characterizat

\
Price change
ghanges.

 

One recent
trading VOILI’

 

 

Volume includes both liquidity-driven trading and information-driven trading.
Theoretically speaking, if it is assumed that liquidity trading comes to the market at a
constant rate, then the price change of stocks should be caused mainly by new
information arriving in the market.8 If trading volume is linked to the information flow
and prices reflect investors’ use of this information, then a relationship between price and

volume becomes a very convincing argument.9

Trading volume plays a minor role in conventional models of asset pricing (e.g., Lucas
(1978)). If markets are complete or can be completed through dynamic trading of
available securities (as in Kreps (1982)), then asset prices evolve as if there were a single
representative agent, even when there are several agents with different tastes and income
processes. In this environment, the resulting allocation is optimal, and asset prices are
determined purely by the aggregate risk. Trading in the market only reflects the allocation
of the aggregate risk and the diversification of individual risks among investors. Volume
(i.e. change in demand) provides no additional information about prices, given the

characterizations of aggregate risk.

 

price changes, and as well as the positive correlation among consecutive absolute price
changes.

8 One recent work related to this study examined the effect of earnings announcements on
trading volume. Bamber and Cheon (1995) find that when these announcements are
accompanied by large volume but small price changes, they tend to be followed by price
increases.

9 Two branches of literature study the price-volume relationship. The first, which
develops rational expectation models with private information flows and noise or
liquidity traders (Admati and Pfeiderer (1990); Foster and Viswanathan (1990); Kyle
(1985)), suggests a positive relation between information arrival and trading volume. The
second branch views information flow as a latent variable that affects trading volume and
focuses on the popular mixture of distribution hypothesis (Bollerslev and Jubinski
(1999);Clark (1973); Epps and Epps (1976); Harris (1986); Karpoff (1986); Lamoureux
and Lastrapes (1990); Smirlock and Starks (1985); Richardson and Smith (1994);
Tauchen and Pitts (1983); Tauchen and Pitts (1983))

 

In models \
Heaton and
equilibrium

heterogeneit
priced in tile
the risk prei
investors vvi'

investors.

In the tradin,
Campbell c1
information \
the informar
pal'tiCiPants.
mOVEmemS
(buy) Orders
Prices ShOUL
(infomation
(inCreaSe) in
trading 8cm

maI'ICEI par“.k

 

In models with an incomplete asset market setting (e.g., Campbell and Kyle (1993);
Heaton and Lucas ( 1993); Wang (1993)), both aggregate and individual risk affect
equilibrium prices, and the behavior of prices crucially depends on the nature of investor
heterogeneity. In these models, trading volume conveys information about how assets are
priced in the market. For example, Wang (1993) maintains that noise traders can affect
the risk premium only under asymmetric information, which means that less informed
investors will demand additional premium for the risk of trading against better informed

investors.

In the trading volume literature, tangential to our study are works by Blume et al. (1994),
Campbell et a1. (1993), and Wang (1994). Blume et al. (1994) show that when quality of
information cannot be deduced from prices, volume can be used to differentiate quality of
the information. Therefore volume can be regarded as a learning tool by market
participants. Wang (1994) categorizes trading motivation and its relation to price/volume
movements into two classes: speculative trades and hedging trades. Speculators’ sell
(buy) orders reflect negative (positive) private information about future payoffs therefore
prices should continue to decrease (increase) after their information revealing process
(information content of volume). Hedgers’ sell (buy) orders reflect a temporary reduction
(increase) in the stock price (noninfonnational volume).10 In our context, abnormal
trading activity can be regarded as a signal of arbitrage related trades and therefore

market participants can use them as learning tools.

 

'0 In support of these arguments, Llorente et al. (2002) find that in periods of heavy
volume, stocks with a high degree of speculative trading tend to have a positive return
autocorrelation and stocks with a low degree of speculative trading tend to exhibit a
negative return autocorrelation.

1.3 The
1.3.1 Gen

Consider an
and an arbit
Investors ca
Examples 1:
invested as
segmented 1‘
3 go-betvvu

arbitrageur 1*
1.3.2 Asst-

AII agents c,

“her-65! is ;
lndependEm .

bounded Sup;

 

'- The lefo I”:

1.3 The Model
1.3.1 General Setup

Consider an economy in which three different types of investors (investor A, investor B,
and an arbitrageur) trade two risky assets (A and B) and a risk-free asset in T+1 periods.
Investors can only invest in different subsets of the market due to some market frictions.
Examples include institutional constraints, such behavioral biases as familiarity with
invested assets, home bias, and information gathering costs (Merton (1987)). The
segmented market assumption is required to define a role for the arbitrageur, who acts as
a go-between for the segmented investors. With access to both market segments,

arbitrageur has better risk sharing opportunities than either investor.
1.3.2 Assets

All agents can invest in the risk-free asset. Investors A and B can invest in only one of
the risky assets (A and B, respectively), whereas the arbitrageur can invest in both of the

risky assets. Assets A and B are in zero net supply and pay off only in period T.ll
Assets are perfectly substitutable, that is, their payoffs are identical and equal to

261,

T
t=0
where 6t is a random variable revealed in period t. It is assumed that the 61 are

independent and identically distributed, and distribution is symmetric around zero on the

bounded support [—313 ]. In other words, the payoffs cannot go below or above a certain

 

11 The zero net supply assumption means that the market will be cleared at all times, that
is any sell by investor i (i=A,B) will be bought by the arbitrageur, or vice versa.

10

limit. The In

 

become imp

Price of ass.

premium), (,

$1.! : I:

The risk-free

 

net supply .
risky assets
assumption
dsmand for 1

13.3 In“,

Investor A ‘
cash flOWs, 1

Both investt

reSpecri‘.elV

LTI(\V1‘T)Z

limit. The bounded support assumption ensures that margin constraints on arbitrageurs

become important in certain states of the world.

Price of asset i is denoted by pit in period t, and excess return per share of asset i (risk

premium), ¢i t , is represented as
9

T t
¢i,t :Et 258 _piJ 2255 ‘17” ,(i=A,B).
5:0 5:0

The risk-free asset has an exogenous return equal to one. Perfect substitutability and zero
net supply assumptions ensure that the arbitrageur holds opposite positions in the two
risky assets and hedges risks associated with assets’ payoffs. Later, we will relax the
assumption of perfectly substitutability and focus on the change in the arbitrageur’s

demand for risky assets.
1.3.3 Investors and Their Investment Opportunity Sets

Investor A can only invest in asset A and the risk-free asset, and investor B can only
invest in asset B and the risk-free asset. It is assumed that assets A and B have identical
cash flows, so their prices should be the same at all times unless different shocks change

propensity of investors to hold the assets.

Both investors and the arbitrageur are competitive and have initial wealth, Win and wo,

respectively. They all maximize the expected utility of period T wealth,

Ui(wi,T): ‘9.“ Wu .

11

In each PFri

asset p500”
111-101 ('11!

The coeffici
11%le IIIgII.
period t- l i~
emphasize t‘:
the supply s}
I: .. .T‘l . {\I
For example
lead to devi
Shocks, inve-
exPloit the p
wealth, She ,

The CI'IIICa] 1

 

 

In each period t > 1, investors i (i=A,B) receive an endowment that is correlated with the

asset payoff (5,). We assume that the endowment of investors A (B) in period t is

lit-15: Fur-15)-

The coefficient UH measures the extent to which the endowment covaries with 5b When
u,-, is high, the covariance is high, and thus the willingness of investor i to hold asset i in

period t—l is low. We refer to u,_] as the “supply shock” of investor i in period t—l to

emphasize that it negatively affects investor demand in that period.’2 For the base case,

the supply shock u, is deterministic and identical in all periods, that is, u, = uo for t= 0,
1, .. ,T—l. All uncertainty is resolved in period 1.

For example, shocks can be interpreted as correlated noise trades caused by herding that
lead to deviations from the fundamental price temporarily. Due to different supply
shocks, investors A and B will have different propensities to hold the assets. Since they
cannot trade with each other because of the segmented market, only the arbitrageur can
exploit the price wedge created by these shocks. Intuitively, if the arbitrageur has infinite
wealth, she will be able to absorb shocks in all periods and make risk free profit by

longing asset A and shorting asset B.

The critical implication of the opposite supply shock assumption for the model is that

investors A and B incur different shocks. The arbitrageur does not have any endowment,

 

’2 To be consistent with the zero net supply assumption, the endowments can be
interpreted as positions in a different but correlated asset. This specification of
endowments is quite standard in the literature (Gromb and Vayanos (2002), O’Hara
(1995)). As shown in Gromb and Vayanos (2002), the assumption of equal shocks is for
simplicity and do not change the conclusions.

12

‘r 41".“

so she is no

 

shocks to (11
words, She

circumstanc
The merits \

receives a r

 

 

 

shock. The
Willing to St
buy. Throui

provides liq
1.3.4 Con

The arbitra;
The margir
In the me1
the im'estn
investors a:
long mm
arbitraSEUr
occur in th
of the mar

i .
n a gIVEU

so she is not affected by the supply shock directly. However, the difference of the supply
shocks to different segments of the market provides her an indirect endowment. In other
words, she exploits price discrepancies between assets A and B, which arise from the

circumstances described above. One can think of arbitrageur as a go-between.

The merits of this model can best be understood by an example. Suppose that investor A

receives a positive supply shock (u0>0), in which case investor B receives a negative

shock. The arbitrageur buys asset A (underpriced asset) from the investor A, who is
willing to sell, and sells asset B (overpriced asset) to the investor B, who is willing to
buy. Through this transaction the arbitrageur makes a profit and at the same time

provides liquidity to the other investors.
1.3.4 Constraints of the Arbitrageur

The arbitrageur is subject to not only a budget constraint but also a margin constraint.
The margin accounts can be thought of as collateral to insure possible losses. Collateral
in the form of long positions in other assets are risky positions and may create losses for
the investment house who acts as custodian for the arbitrageur. Therefore, in practice,
investors are often required to keep a cash amount in their margin accounts rather than a
long position in another asset. It is assumed that the margin constraint requires
arbitrageur to have enough cash (not other stocks) to cover the maximum loss that can
occur in the margin account. This implies that her ability to invest is limited by the value
of the margin account. In particular, she may be unable to eliminate a price discrepancy

in a given period, even if she knows that the discrepancy will disappear in the next

13

 

period. L811"

without a m
L61 XL! (1611
margin acco

I1.1+l

The requiret

._/ _
ill—IA!

 

Where \1'[ dc
- - |
negativity c(

default. Not}

later, we “'1

Fina”): the 2

Max

x4 [9x

"-91 T-

to

14] t 1

period. Later, we will relax this assumption and solve the arbitrageur’s problem with and

without a margin constraint for perfectly and imperfectly substitutable assets.

Let Xi“ denote the number of shares in asset i in period t, and let Vit be the value of the

margin account for asset i. We have

Vi,1+1 : Vi,t + xi,t (pi,t+l — pi,t),1=A,B.

The requirement that Vim Z 0 implies that

W: : VA! + VBt Z maX(xA,z(pA,z _ pA,t+l ))+max(x8,t(p8,t ‘p3,1+1))

pA,r+l p8,t+l

where w denotes the arbitrageur’s wealth in period t. In other words, imposing the non-
negativity constraint on the sum of each margin account ensures that arbitrageurs never
default. Notice that the margin constraint is symmetric for both long and short positions.

Later, we will change this assumption and completely restrict short sales in certain cases.

Finally, the arbitrageur’s problem becomes:

Max E0U(WT)

x x
A,t ’ B,t
t=..0 ,1 T-1

subject to the dynamic wealth constraint,

wr+l : W, + Z xi,t(pi,t+l _pi,t) f0? t : Oala°°9T_1

i=A,B

and the margin constraint,

l4

Wt 2 2 max (xi,t (17),, —pi,t+l)),

i=A,B P1,:+1

1.3.5 Solution of the Arbitrageur’s Problem

In this section, the arbitrageur’s demand is characterized under different assumptions.
Specifically, we focus on four situations: (1) no margin constraints and perfectly
substitutable assets, (2) margin constraints and perfectly substitutable assets, (3) no
margin constraints and imperfect substitutes, and (4) margin constraints and imperfect

substitutes.

The general equilibrium solution for investors A and B and the arbitrageur’s portfolio
selection problem for perfect substitutes is provided in Gromb and Vayanos (2002). Our
interest lies in the relationship between arbitrageurs demand and assets substitutability,
therefore we briefly summarize their main results for perfect substitutes and then focus

on how substitutability affects the arbitrageur’s demand.
Case I: No margin constraints and perfect substitutes

Gromb and Vayanos (2002) show that, in equilibrium, due to the symmetry of the set up

and perfect substitution, opposite supply shocks will induce opposite risk premiums:

(¢A,t _ ¢A,t+l) = _(¢B,t _ ¢B,r+1) : (¢t — ¢t+1),

the arbitrageur will buy Xt shares of asset A and sell Xt shares of asset B to satisfy the

zero net supply assumption (market clearance). Therefore, in the absence of margin

constraint, the arbitrageur’s wealth constraint reduces to

15

.‘ 2 II,
I'I‘HJ I

That is, the
substitutes '
amounts in '.
ofthe arbitr;

place in the
Case II: Ma
If assets at
arbitrageur f
not bear an).

that

II” +1 2 ‘17

 

 

wt+l = wt +xr(¢r _ ¢r+l +5r+1) —xt(—¢t +¢r+l +61+1),

wt+l = Wt + 2xr(¢t - ¢t+1)

That is, the wealth increase does not involve any risk because the assets are perfect
substitutes to each other. The arbitrageur absorbs all the shocks and invests infinite
amounts in asset A and B as long as the price wedge is positive. In equilibrium, existence
of the arbitrageur keeps prices at their fundamental levels at all times, and no trading take

place in the market unless there is mispricing in either assets.
Case II: Margin constraints and perfect substitutes

If assets are perfectly substitutable, the zero net supply assumption ensures that

arbitrageur holds opposite positions in the two risky assets (x, = x Ar = —xB,) and does

not bear any risk. Similar to the previous case, the arbitrageur’s wealth constraint implies

that

Wt+1 : Wt +2xr(¢t —¢r+1),

Furthermore, the margin constraint of the arbitrageur implies that

Wt 2 max(x, (—¢t + ¢r+l — 51+1))+ rrsiax(—x, (¢t _ ¢r+l _ 61+1))

6H1 1+1

=> w. 2 231391 + max(x.(—¢, + ¢...>)+ max(— x.(¢. — an)

16

U

'4".

l/\
[\L

that is, the
asset payof:

all uncertair

to the arbitr.

In other \v.
arbitrageur

constraint. It

If the uncert
Shoe that th
0n the arbitr;
the PTOfitab

COml‘varable '

 

Lonssmff (:1
larger) and “I

\\hen 'rl : ‘l

wt
:>x

is —
26 —2 (¢1_¢r+l),

 

that is, the margin constraint reduces arbitrageurs ability to exploit opportunities when

asset payoffs are more volatile and the arbitrageur has less wealth. Since we assume that

all uncertainty is resolved at time 1, the value of the price wedge,(¢t — ¢r+1)’ is known

to the arbitrageur. As long as (Q -— ¢t +1) > 0, she invests up to the financial constraint.

In other words, if the prices are known to converge to each other over time, the
arbitrageur uses all her resources to exploit this opportunity. Due to the margin

constraint, however, the price wedge does not converge to 0 at all periods as in Case I.

If the uncertainty is resolved over time rather than at time 1, Gromb and Vayanos (2002)
show that the arbitrageur’s demand for risky assets depends not only on expected return
on the arbitrage opportunity but also the covariance between the arbitrageur’s wealth and
the profitability of investment opportunities. The interpretation of their result is
comparable to the findings of Shleifer and Vishny (1997), Xiong (2001), and Liu and
Longstaff (2003)’s findings under different setups: Due to the uncertainty of shocks, the
arbitrageur may lose some wealth if the price wedge increases (mispricing becomes
larger) and this reduction in wealth prevents her from exploiting more valuable arbitrage

opportunities.

W

 

When x, = — I
25 —2 (¢1_¢r+l)

is used in the wealth constraint, we get

17

.~ :: W
u1+1 I

of price we
invests more
Case III: N
Assume that
the price vs
3.58.61 \VIII bc‘

llllCS‘lOr :\ \\

but they “‘11

 

invests in

constraint rec

Ivtfl 2 11

that 15’ She is

Strategy. In

emCiem Prit

considered It

L‘nder thesg

OptileatiQn

5

Wm = W that is, the profit of arbitrageur depends on the evolution

'6_-(¢. —¢,.1>’

 

of price wedge. As it decreases over time, the arbitrageur’s wealth increases, and she

invests more in the next period.

Case 111: No margin constraints and imperfect substitutes

Assume that asset A does not have a perfect substitute. If a positive shock hits investor A,
the price wedge between the new price and the efficient price will become ¢, , and the

asset will be underpriced by ¢, . In the absence of a perfect substitute, the arbitrageur and

investor A will have the same investment opportunity set (asset A and the risk-free asset)
but they will have different expectations about the value of asset A. The arbitrageur
invests in A by using risk-free asset as the other leg of the arbitrage. Her wealth

constraint reduces to

Wt+1 : wt +xt(¢t _¢t+l + 5H1),

that is, she is subject to the volatility of asset A’s payoff.

The payoff volatility represents the fundamental (substitutability) risk involved in this
strategy. In the certainty case, the arbitrageur knows that the price will converge to its
efficient price at time T, but due to uncovered fimdamental arbitrage risk, she can be

considered to be a speculator as opposed to an arbitrageur.

Under these assumptions, the arbitrageur’s problem reduces to a mean-variance

Optimization problem, and the demand of the arbitrageur becomes

18

a:

it
al

1

Notice that
decreases. I
strategy inv
risky. so the
the substitu

variability oi

 

On the one 1

“I“ be deter
Uncertainty 1

the arbitrag.

x ___ (¢t — ¢r+l)
‘ a Var(6)'

 

Notice that as arbitrageur’s risk aversion (or) increases, the demand for the risky asset
decreases. Risk aversion was irrelevant in the previous cases because the arbitrage
strategy involved no risk. However, imperfect substitutes cause that strategy to become

risky, so the solution incorporates this effect. The arbitrageur is compensated for taking

the substitutability risk by the expected return, (¢, —¢,+l). Not surprisingly, the

variability of cash flows reduces the demand, as it does in case 11.
On the one hand, if the uncertainty is resolved in period 1, the return from this strategy

will be deterministic and equal to the numerator (€15, — (4,”) . On the other hand, if the

uncertainty of supply shocks is resolved gradually, further return uncertainty is added to

the arbitrageur’s strategy and show up in the numerator of the demand expression as
(¢r _ E(¢r+l )) .

The intuition is similar to that discussed in case II: The possibility of a larger price wedge
in the next period causes the arbitrageur to hedge against this risk and reduce her demand
in the current period (DeLong et a1. (1990)). The reduction in demand is not caused by a

margin requirement as in case 11, but by the risk of imperfect substitutes.

These results confirm the findings of Wang (1994), who demonstrates that large trading
volume induces positive (negative) return autocorrelations when the primary motive for
trading is speculation (liquidity). The arbitrageur that invests in imperfect substitutes is

similar to the speculator in Wang (1994). Since the price discrepancy cannot be

19

 

eliminated 1

(B) will COI

Case IV: M.

positive autt

lfa positive
efficient pri

constraint or

 

“141 — 11
In other \\'0
rePresents t1

cover the m;

eliminated immediately at all periods due to imperfect substitution, the price of asset A
(B) will continue to increase (decrease) until time T. In other words, there should be a

positive autocorrelation on the returns of assets in which the arbitrageur invests.
Case IV: Margin constraints and imperfect substitutes

If a positive shock occurs for investor A, the price wedge between the new price and the
efficient price will become ¢ , that is asset A is underpriced by ¢t' The wealth

constraint of the arbitrageur reduces to

WM] : Wt +xt (¢t — ¢t+l + 5H1) (1)

In other words, she is subject to the volatility of asset A’s payoff and that volatility
represents the ftmdamental risk involved in this arbitrage strategy. Moreover, the margin
constraint of the arbitrageur implies that she holds enough funds in her margin account to

cover the maximum loss that she can face:

wt 2 max(xt (_¢l + ¢t+l _ 6r+l))

 

6I+l
SW, 23—- — x {W ¢l+l)
:>x _ wt
’__ 2
6 — ¢1 + (+1 ()

When (1) and (2) are combined, we get

20

~ : W,
”1+1 1
1.1-hen a neg

case, the we

11‘ 2 11“, 1

+1

 

 

 

A comparisti
the next per
(negative), t
IOVerpriced 1
S.‘Tnmetric f.
the assets,

OPPOFTUDitie
fea‘Sible trad
It may be OI
becomes p 0
demands 11C

TCSUII is n01

\

_ W 1+ (514-1 + (¢t _ ¢t+l))
T _ (3)
(6 _ (¢t — ¢r+l ))

 

wt+l I

When a negative shock occurs for investor A, asset A becomes overpriced by ¢t . In this

case, the wealth constraint and margin constraint imply that

(—5t+1 + (¢t _ ¢t+l ))
1 + __ (4)
(6 _ (¢t _ ¢r+l ))

 

Wm : W1
A comparison of (3) and (4) reveals us the arbitrageur’s demand difference, depending on
the next period’s payoff and the risk premiums. If the next periods payoff is positive
(negative), the wealth of the arbitrageur increases more when the asset is underpriced
(overpriced) than when it is overpriced (underpriced). Notice that the margin constraint is
symmetric for both long and short positions. If the arbitrageur is restricted from shorting
the assets, she can only invest in underpriced assets and must bypass the profit
opportunities when assets are overpriced. In that case, the equation (2) and (3) give the

feasible trading strategy and wealth process respectively.

It may be optimal for the arbitrageur not to execute her strategy if the next period payoff
becomes positive (negative) when the asset is overpriced (underpriced). In that case, she
demands nothing at all periods and lets the mispricing exist until time T. In fact, this

result is not surprising because of the conservative margin requirement.
1.3.6 Empirical Implications of the Solutions

All these cases present the effects of limits to arbitrage and their effects on the trading

activities of arbitrageurs. It may not be possible to distinguish case I from case IV,

21

because if :1
situations. I
This is panl

spectrum of

The similari
11982) is in:
arrival of ne
if traders bt
speculative 1
that they sla-
happens due
requirements
mainly origi

PFOduct of in

Cases 11 and
fully absorb
depends on .
aversion COe:
demand fOr ri
Proposition
th

ere Will be .

’he reguired l

 

because if all mispricing is eliminated instantaneously, there should be no trade in either
situations. Therefore, no trade argument becomes equivalent to no arbitrage condition.
This is particularly striking since cases I and IV represent the extreme situations in the

spectrum of the arbitrageur’s ability to absorb shocks.

The similarity between the no-trade result of this model and that of Milgrom and Stokey
(1982) is interesting. The latter is often used to argue that in ongoing security markets the
arrival of new information cannot generate trade. The usual intuition for this claim is that
if traders begin with a Pareto optimal allocation of resources, then any trade is for
speculative purposes, so the willingness of one trader to make a trade indicates to others
that they should not accept the other side of the trade. In our context, lack of trade
happens due to high limits of arbitrage (imperfect substitutes and conservative margin
requirements) rather than information asymmetry. Yet, the similarity of predictions
mainly originates from the segmented market assumption, which is essentially a by-

product of information asymmetry.

Cases 11 and III produce an observationally equivalent result since the arbitrageur fails to
fully absorb the supply shock. The comparison of arbitrageur’s demand in these cases
depends on the level of financial constraint imposed on the arbitrageur and the risk
aversion coefficient. Two propositions can now be stated with respect to arbitrageurs’

demand for risky assets.

Proposition 1 (no trade — no arbitrage): If the limits of arbitrage are strong enough,
there will be no attempt to eliminate possible mispricing and arbitrageurs will not provide
the required liquidity to the market. In a frictionless market, the existence of arbitrageurs

ensures no mispricing. In both cases, there will be no arbitrage-related demand for assets.

22

 

Propositior
increases th
boosts arbt

volume.

We test the
by GKM (2
ilovv) volu:
postulate 111..
argument c
visibility ant1

visible than

information

Investors tra
rebalancing

Opportunity

arh

 

 

Proposition 2 (risky arbitrage): Any mispricing in assets with close substitutes
increases the interest among competitive arbitrageurs (increased visibility) and therefore
boosts arbitrageurs’ demand for risky asset, which is revealed as abnormal trading

volume.

We test the second proposition to explain the high-volume premium puzzle documented
by GKM (2001). As discussed before, GKM (2001) find that periods of extremely high
(low) volume tend to be followed by positive (negative) excess returns, and they
postulate that this pattern depends on increased stock visibility or lack of thereof. Their
argument can explain increased returns but not the relationship between increased
visibility and increased trading activity. Is there any factor that makes some stocks more
visible than others? lDoes substitutability makes it easier to capture mispricings or new

information, thereby causing unusually high trading activities?

Investors trade for at least two reasons: portfolio rebalancing and speculation. Portfolio
rebalancing trades may be triggered by many factors, such as changes in investment
opportunity sets, investment objectives, and liquidity needs. Speculative trades are
mainly based on heterogeneity in beliefs or information sets. We argue that neither
motive can be the reason for the increased visibility and trading activity that may explain
high volume premium unless the need for trades due to the above factors is positively

correlated among all investors.

Only arbitrage trades, the very basic motivation to trade, can be positively correlated if
there is enough competitive arbitrageurs in the market and if they do not face significant
limits to arbitrage. This argument is the flip side of the correlated noise trades and

associated noise trader risk (DeLong et al. ( 1990)). One can think of groups of investors

23

 

   
  
  
  
 

A and B a-
Shocks that
distinguish

(Shleifer (2’

depends on
investment
arbitrageurs

increase its

We use dat.
betvveen Au.E
interval betvv
50 trading d

trading Illlerv

Each lumen-a.
last day_ The
volume is in
Wading V011”

Stock if its I

 

 

A and B as noise traders in their segmented markets, which receive correlated supply
shocks that make their trades positively correlated. In this sense, it is not possible to
distinguish arbitrageurs from noise traders unless the direction of supply shocks is known
(Shleifer (2000)). From this perspective, substitutability risk is related to noise trader risk
and it is systematic, and therefore should be priced. Arbitrageurs’ demand for risky assets
depends on the degree of substitutability risk (deviation from the fimdamental values),
investment horizon, risk aversion, and margin constraints. Therefore, provided that
arbitrageurs are competitive, their interest in a certain asset may be strong enough to

increase its visibility via abnormal trading activities.
1.4 Empirical Tests
1.4.1 Data and Methodology

We use data from Center for Research in Security Prices (CRSP) on NYSE stocks
between August 1963 and January 2001. The sample is constructed by splitting the time
interval between August 15, 1963, and .Ian 31, 2001, into 188 nonintersecting intervals of
50 trading clays.‘3 We avoid using the same day of the week as the last day in every

irading interval by skipping a day in between each of these intervals.

Each interval is split into a reference period, the first 49 days, and a formation period, the
last day. The reference period is used to determine how unusually large or small trading
volume is in the formation period. The number of shares traded is used as the measure of
trading volume.'4 In a given trading interval, a stock is classified as a high (low) volume

stock if its formation period volume is in the top (low) 10 percentile of 50 daily

 

’3 We follow GKM’s method but our test period is five years longer than theirs.
’4 The results were not affected when dollar volume is as a trading activity measure.

24

 

s l

1
volumes- I
statistics ab

high volurm

At the end c
trading volt
portfolios 1“
stocks. The

suLsequent ‘

All NYSE c
Which 50mg
merger. a do
you prior to
the NYSE at
some Point i
10 COmpan}.
market Capit
[lift-“Ugh eigh
one are EXCI

abOVe.

 

volumes.ls Methods and the terminology we used are illustrated in Figure 1. Descriptive
statistics about the sample are summarized in Table 1.1. Overall we end up with 30,832

high volume and 32,148 low volume stocks.

At the end of each formation period (the formation date), we form portfolios based on the
trading volume classification of stocks for that interval. We construct zero investment
portfolios by shorting low-volume stocks and taking long positions in high-volume
stocks. The portfolios are held without any rebalancing over the test period, that is, the

subsequent 1 to 20 trading days.

All NYSE common stocks are considered in any given trading interval except those for
which some data was missing. We also removed (1) any stocks that experienced a
merger, a delisting, partial liquidation, or a seasoned equity offering during or within one
year prior to the formation period; (2) stocks with less than one year of trading history on
the NYSE at the start of an interval; and (3) stocks whose price fell below five dollars at
some point in the reference period. Also, we divided the sample in three parts according
to company size and calculated the return on high— and low-volume stocks. The firms in
market capitalization deciles nine and ten are classified as large, those in deciles six
through eight as medium, and those in deciles two to five as small firms. Firms in decile
one are excluded from the sample because most do not survive the filters described

above.

 

15 GKM uses the highest (lowest) 5 stocks as opposed to top (bottom) 10 percentile. Our
approach increases the sample size, which allows us to obtain better substitutability risk
estimates of portfolios using the market portfolio as a substitute. The descriptive statistics
of our sample is slightly different from those of GKM because of the modified method
and the data period.

25

 

1.4.2 Port

At each forr
for a total of
a total of on
(low) \'Olun'
formation p.

to 20 days.
The test peril
5}'NRI : I

tne hypothes

 

1.4.2 Portfolio Formation and Returns

At each formation date, a zero investment portfolio is formed by taking a long position
for a total of one dollar in all high-volume stocks in a size group, and a short position for
a total of one dollar in all low-volume stocks in that same group. Each stock in the high
(low) volume category is given equal weight. The position taken at the end of the
formation period in each trading interval 1’ is not rebalanced for the whole test period of 1

to 20 days.
The test period returns of the long position are denoted by Rih (Ril), and the net position

by NRi = Rih - Ril. For the reasons explained later, we use the last 184 periods to test

the hypothesis that the average net returns of this strategy over all 184 trading intervals,

NR, are positive:

__ 1 184
NR =—8—ZZ]VR1.

i=1

Note that, in any given interval, only stocks that experience a large enough trading
volume shock (positive or negative) are included in the zero investment portfolio. In this
respect, this portfolio formation approach is similar to Cooper (1999). The zero
investment portfolios are also similar to those used by Conrad et a1. (1994) in that the
high-volume side of the position requires an investment of exactly one dollar, whereas

the low-volume side of the position generates exactly one dollar at the outset.

The cumulative returns of high-volume, low-volume and zero investment portfolios are
summarized in Table 1.2. Table 1.3 presents descriptive statistics for cumulative returns

of the high-volume and low-volume portfolios. Overall, our results confirm the high

26

 

 

volume pre
different m
volume 510‘

volume ret .

    

Finally. “‘6
period to c
cumulative

In the discu:
sample. A]:
infomiation,
or earnings

period, For t
1984. More
interval in o

Oflhese filte

 

 

volume premium documented by GKM (2001) for a longer data period using slightly
different methods. The cumulative return differential between high-volume and low-
volume stocks is positive and statistically greater than zero. Furthermore, the high-

volume return premium is more apparent for small than large companies.

Finally, we replicate the same analysis by skipping one more day after the formation
period to control for possible short-term buy/sell pressures that can influence the
cumulative returns. Results are not significantly different from the findings in Table 1.2.
In the discussion of results, we will compare this buy/sell control sample with the original
sample. Also, in order to control for further possible announcement effects (new
information), we follow GKM’S method and eliminate stocks that experienced a dividend
or earnings announcement one day before, the day of, or one day after the formation
period. For this purpose, we used I/B/E/S actuals database, which has data available after
1984. Moreover, the five most extreme observations are removed from each trading
interval in order to eliminate the effects of outliers. The results are not affected by either

of these filters.

Before we attempt to reconcile the high-volume premium documented in Table 1.2, we
must define the measures used for certain well-documented risk factors, measures of

difference of opinion, and substitutability risk.

27

 

 

1.4.3 Me;

l

The substitr

regression r

where i: I—
.f- ‘ -
R; cones;

approach v.

effects on d

The intuitio

arbitrageurs

 

short Sl in ’
is assumed

that [here 3‘
peTfC‘CI SUI):
Wmiller ant

Well‘diVerSi

residu318 as

FOI each hi;

and the Star

 

1.4.3 Measure of Substitutability Risk

The substitutability risk of a portfolio (P) is measured at time t as the standard error of the

regression and sum of the squared residuals of the following OLS:
P f _ m _ f
Ri _Ri —IB(R1' Ri)+8i’
where i= t—l , t—2, ..., t—k (k determines the estimation window length).

Rif corresponds to risk free rate and R,- represents to market return at time 1. Thls

approach was used by Wurgler and Zhuravskaya (2002), who analyze substitutability

effects on demand curve elasticity.l6

The intuition behind this approach is based on the zero investment portfolio created by
arbitrageurs. The implied zero investment strategy is, for every $1 long in portfolio P:
short $1 in T-bills, short 8 B in market portfolio, and long 8 B in T-bills. In other words, it
is assumed that market should be a close substitute for any diversified portfolio, provided
that there are enough stocks in the portfolio. On an individual stock basis, finding a
perfect substitute is almost impossible as shown by many studies (e.g., Roll (1988),
Wurgler and Zhuravskaya (2002)). Yet, the market should be a perfect substitute for any
well-diversified portfolio by construction. We interpret the standard deviation of the OLS

residuals as the denominator of the Sharpe ratio.

For each high-volume and low-volume portfolios, we calculate the variance of residuals

and the standard error of regression by using the previous 150, 200, and 250 days.17 In

 

‘6 We also used companies with closest B/M and Size in the same industry as close
subsitutes in addition to market portfolio. The results are essentially the same.

28

#4..- ‘e—

 

order to Ck
and focus

substitutalo

 

between 11'
stocks haV

less signifi

l.4.4 .‘lc

    
   
 

A possible
differ morfi
for this f:
h)pothesiz
10 aIInOUn

|
the returns
POSiIi\'e 5k
mOre Prom

SugOeSt ne

Opinion:

 

i order to compare the effects of measurement changes, we discard the first four periods
and focused on the last 184. Descriptive statistics for empirical distributions of
substitutability are reported in Table 1.4. A comparison of substitutability risk difference
between high-volume and low-volume stocks supports our conjecture that high—volume
stocks have lower substitutability risk (Table 1.4 - Panel C), but, the difference becomes

less significant as the estimation period decreases.
1.4.4 Measure of Divergence of Opinions

A possible explanation of the observed return premium is that opinions among investors
differ more for high-volume portfolios than low-volume portfolios.‘8 In order to control
for this factor, we employ two measures suggested by Chen et al. (2001), who
hypothesize that managers with some discretion over the disclosure of information prefer
to announce good news immediately and allow bad news to emerge slowly. In that case,
the returns of such companies should reflect asymmetries that can be captured by the
positive skewness of the distribution. They also show that positive skewness should be
more pronounced for firms that receive attention from fewer analysts. Therefore, they
suggest negative skewness of empirical distributions as a measure for difference of

opinion:

 

SK, = — n(n-1)3IZZR;3
(n—1)(n—2)(ZR;)

/2’

 

17 We also calculated substitutability risk using two-day and three-day returns but the
results were unaffected.

'8 Analyst coverage and difference between analyst estimates (Diether et al.(2002)) are
the two most commonly used measures of difference of opinion. Because of the time
interval in our study, we do not use these.

29

is

where RP r
and n “I“

{Queuing l

n, represcr
idea of the

likely to be
1.4.5 Me

In order tr
eKamined 1
(Small min
and Titmai
5‘ Winner 0
fOI’matiOn

liqllidity (

differential

N
Sam C

‘r' a
._ Se

 

where Rp represents the sequence of demeaned daily returns of the portfolios for period t,
and n represents the number of days before the formation period. They also use the

following measure, which is based on the second moments of the empirical distributions:

“(m -1) 2sz
DUVAL, = log DOW” ;

(nd _1)Z sz
k UP J

‘

 

V

 

 

nu represents the number of “up” days, and nd represents the number of “down” days. The
idea of the DUVAL (down-to-up volatility) measure is similar to skewness, but it is less

likely to be affected by the extreme returns. '9
1.4.5 Measure of Other Risk Factors

In order to control for various risk factors suggested in the literature, we use those
examined by F ama and French (1992), book-to-market (high minus low, HML) and size
(small minus big, SMB ).20 Also, to control for possible momentum effects (Jegadeesh
and Titman (1993)), we use an indicator variable that represents whether a portfolio was
a winner or loser portfolio with respect to the market for 50,100, and 250 days before the
formation period. Using the Trade and Quote (TAQ) database, GKM (2001) show that
liquidity (Arnihud and Mendelson (1986)) is not a possible explanation for the return
differential between high-volume stocks and low-volume stocks. Therefore, we do not

control for the liquidity factor.

 

'9 We report the results for skewness (SK). The results with DUVAL are essentially the
same.
20 See http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

30

 

1.4.6 T68

We argue
substitutab
fundament.
systematic
average re‘
low-vol um

puzzle.

in order to
following I

the disturb.

 

be correlat

“‘3 a1 j

1.4.6 Tests

We argue that higher systematic risk requires a higher expected return and that
substitutability risk is systematic, so it should be priced when assets deviate from
fimdamentals. Furthermore, if abnormal trading activity is a proxy for positive shifts in
systematic substitutability risk, then a positive trading volume shock should precede large
average return. Therefore, the return differential between responsiveness of high- and
low-volume portfolios to changes in systematic risk should explain the high-premium

puzzle.

In order to test the effect of systematic risk difference on return differential, we use the
following equation system. The seemingly unrelated regression method (SURE) allows
the disturbance terms for the high- and low-volume portfolios in each trading interval to

be correlated.“

R,” = em + eHMR,“ + flHSSMB, + eHHHML, + ,BHOMzsof’ +
flHSKSKrH + flHAA‘tH + 5rH (5)

R,” = em + em R,“ + ,BLSSMB“ + ,8”, mm, + ,BLOMZSOf +
flLSKSKrL + IBLAALr + 5f (6)

In these equations, t=5,..,188; i=1 ..20; and

H
R” = cumulative i day return on the equally weighted high volume portfolio;

 

2' We also used OLS to estimate the given system, but differences between the methods
do not affect the conclusions.

31

R: =CU]
H _ .
A ,— star
period (sul
L _ - ‘.
{'1 t— 5131

period (sul

 

 

 

 

Rirm : C L11
S.\IB,= r
HML, =

”2 \"OIH

daFS befo

3K3”, 5

before the

In this se-
SecuI’IIIeS
Securities
Fur-{berm

coefficieI

N

.. OtiCe
(”manor

L
R” = cumulative i day return on the equally weighted low volume portfolio;
AH, = standard error of the regression in Section 1.4.3 for 250 days before the formation
period (substitutability risk measure for high volume portfolio) 22;

AL, = standard error of the regression in Section 1.4.3 for 250 days before the formation

period (substitutability risk measure for low volume portfolio);

R “m = cumulative market return for the corresponding test period;
511le Fama-French size factor for the corresponding test period;
HA/[Lt = Fama-French book-to-market (B/M) factor for the corresponding test period;

M25031, M250,L = 1 if high (low) volume portfolio outperformed the market for 250

days before the formation period, 0 otherwise (momentum factor); and

SKtH, SK}: negative skewness of the high (low) volume portfolio for 250 days

before the formation period.

In this setting, the low-volume portfolio is a benchmark for a portfolio of correctly priced
securities, and the high-volume portfolio represents a portfolio of possible mispriced
securities. Therefore, we expect to estimate a significant BRA and an insignificant BLA.
Furthermore, because we are particularly interested in the difference among the

coefficients of systematic risks due to other factors, we test the following hypotheses:

 

22 Notice that the substitutability risk is estimated by using the returns before the
formation period. This information is available at the formation date.

32

Hypothesis 1: There is no market risk difference between high-volume and low-volume

portfolios, or

firm — flLM = 0-

Hypothesis 2: Size differences do not explain the return differential of high-volume and

low-volume portfolios, or ,BHS — ,BLS = 0.

Hypothesis 3: B/M differences do not explain the return differential of hi gh-volume and

low-volume portfolios, or flHH — ,8“, = 0.

Hypothesis 4: Momentum risk differences do not explain the return differential of high-

volume and low-volume portfolios, or [3H0 — ,BLO = 0.

Hypothesis 5: Difference of opinion differences do not explain the return differential of

high-volume and low-volume portfolios, or ,8ng — flLSK = 0.

Hypothesis 6: Substitutability risk differences do not explain the return differential of

high-volume and low-volume portfolios, or flHA — ,BLA = 0.

Main results are presented in Table 1.5 and two points should be noted. First, confirming
F ama and French (1992), market, size and book-to-market factors are significant for both
high- and low-volume portfolios, but difference of opinion is not significant for both.
Second, the coefficients for momentum and substitutability risks are significant at the
10% level for high-volume portfolios but are not significant for low-volume portfolios.
The results are in line with our conjectures, but the statistical significance of

substitutability risk is not as high as for the other systematic risk factors.

33

What is l
differenCt

The resul

The differ
or the bu:l
is, markc

portfolios

Hypothes
and low-x
negative I
that have

cannot ex]

The differ

 

 

for the ori
Volume pC
The SubSI

31014.0

 

 

What is more crucial here is that substitutability risk may explain the return premium
difference between the portfolios that experienced positive and negative volume shocks.

The results for the six hypotheses are presented in Table 1.6.1.23

The difference in market betas is not statistically significant for either the original sample
or the buy/sell pressure control sample. Therefore, hypothesis 1 cannot be rejected, that
is, market risk may not explain the return differential between high- and low-volume

portfolios.

Hypothesis 4 also cannot be rejected. The momentum factor difference between high-
and low-volume portfolios is zero before the eighth day, but it becomes significant and
negative thereafter. In other words, in the short run, return premium is higher for stocks
that have performed relatively poorly during the reference period. Therefore, momentum

cannot explain the return differential between hi gh- and low-volume stocks.24

The difference in the skewness of prior distributions is not statistically significant either
for the original or the buy/sell sample. Therefore, hypothesis 5 cannot be rejected, that is,
difference of opinion may not account for the return differential between high- and low-

volume portfolios.

The substitutability risk coefficients reveal interesting patterns. The arbitrage risk
difference is statistically significant at the 1% level for the cumulative returns from days

3 to 14. Comparison of the substitutability risk coefficient differential in part A and B of

 

23 We also estimated the same system by using all possible combinations or explanatory
variables. The results and conclusions are unaffected. The results presented in Tables 1.6
to 1.8 include all the variables we considered.

24 GKM (2001) reach the same conclusion by using both daily and weekly returns.

34

Table 1-‘
Furtherm
substitute
portfolio:

zero in al

lnterestin
significar
differertec

concave a
1.4.7 R.

Hmothes:
the aboyc
Volume P
equations

POHfolios

 

 

 

 

Table 1.6.2 shows that temporary buy/sell pressures cannot account for this result.25
Furthermore, all significant beta differentials are positive, which indicates that
substitutability risk is more likely to be priced in high-volume portfolios than low-volume
portfolios. The substitutability risk coefficient difference is significant and greater than

zero in all cases from days 3 to 14, so hypothesis 6 is rejected.26

Interestingly, the p-values of the arbitrage risk coefficient difference reveal a U-shaped
significance. During the test period, the standard deviation of arbitrage risk coefficient
difference is fairly constant, which suggests that the pattern is indeed caused by a

concave arbitrage risk coefficient difference. We will address to this issue later.
1.4.7 Relationship between Size and Substitutability Risk

Hypothesis 2 cannot be rejected on the basis of the overall sample. In order to understand
the above pattern of the substitutability risk difference, we separate high- and low-
volurne portfolios according to the company size and test the following systems of
equations using seemingly unrelated regression for portfolios of large companies and

portfolios of medium and small companies separately.27
H m H
Ru 2 IBHC + IBHMRrr + 161155“an + flHHHmit + flHOMZSOr +

[BHSKSKtH + IBHAATH + gtH

 

25 High volume premium documented by GKM (2001) is becomes insignificant around
the 15th day.

26 We tested our hypothesis by using different measures for substitutability risk with
different estimation periods and confirm the above results in each case with minor
differences.

27 We combined medium and small size companies to increase the number of stocks in
portfolios in order to create a better substitute for the market portfolio.

3S

\then the
size high-
until the
which int

1.7.1 and

For medii
volume p
«’10 not aft

Table 1.8

These tm
by the (
hWOIhesi
SOoner th
c0mpanie
base. Bet

arbitrageu

. Lame
l1“ estOrs

 

RitL = flLC + flLM Ram + flLsSMBu + flLHHMit + flLOMZSOtL +

flISKSKIL + flLAALt + 81L

When the same tests are applied to the substitutability risk coefficient differential of large
size high- and low-volume portfolios, the differences remain significant at the 5% level
until the eleventh day. Most of these effects disappear in the buy/sell control sample,

which indicates that immediate returns are more significant for large companies (Table

1.7.1 and Table 1.7.2).

For medium and small companies, the arbitrage risk differential between high- and low-
volume portfolios is significant after day three. Furthermore, possible buy/sell pressures
do not affect the significance of he high-volume premium for this group (Table 1.8.1 and

Table 1.8.2).

These two observations suggest that the pattern observed for the whole sample is created
by the combination of arbitrage and company size. This supports the visibility
hypothesis: An arbitrage opportunity in large companies is more likely to be identified
sooner than an opportunity in stocks of small and medium companies, because large
companies are followed by more analysts and a larger investor (presumably arbitrageur)
base. Because small size firms are less visible to a large number of competitive

arbitrageurs in a short period, price corrections takes longer time.28 Substitutability of the

 

28 Large size can be interpreted as a proxy for less information asymmetry between
investors and the companies. In this sense, variables that measures transparency, such as
index membership and wide coverage by analysts, are all by-products of size.

36

stocks

which
1.4.8

Value

respect
altemzit
arbitrag
which 5
We reje.
between
strategic
that fact
Parts of

Premium

1.5 Eco
Hed;

If it is z

 

TECeiVed

 

11115336”

7

 

thaf fill] Li

 

stocks of large companies increases arbitrageurs’ interest and trading volume (visibility),

which will reduce the possibility and duration of mispricing.
1.4.8 Explanatory Power of the B/M Ratio

Value investors tend to buy high B/M stocks when they become relatively cheap with
respect to their fundamental values. Therefore, a high B/M ratio can be viewed as an
alternative arbitrage risk measure. Interestingly, the correlation between HML and
arbitrage risk is quite small (0.07 for the original sample, 0.11 for the buy/sell sample),
which suggests that they capture different aspects of mispricing. For the original sample,
we reject the hypothesis 3 after day nine and find that the short-term return difference
between high- and low-volume portfolios may also be associated with value investing
strategies due to higher factor loadings on the HML factor. Although the significance of
that factor is not as strong as the substitutability risk factor, it shows effects in the latter
parts of the test period. Therefore, HML may be a viable explanation for high-volume

premium puzzle but its significance is not as strong as the substitutability risk.

1.5 Economic Significance of Arbitrageur’s Profits and High-Volume Investing as a

Hedge Fund Strategy

If it is assumed that the possibility of getting positive or negative information on a
particular asset is equally likely in the long run, then the returns due to information
received during abnormal trading period should eventually be canceled (diversification of

unsystematic risk).

Yet, returns obtained from deviations from fundamentals exhibit an asymmetry. Assume

that fundamental prices of two perfect substitutes (A and B) are $100. For some reason,

37

 

asset A is
long 105»
Mien ass

arbitraget

Now com
10% and i
Once the
by 9.090 i.
yield a re
with abno
Symmetrid
observed
and skewt
The strate
StockS, an
merflbre
to be trad
described
Shows the
the magni

If it is as

 

mart—en u

ParameIEr

 

 

 

asset A is underpriced by 10% and sold at $90. In this case, the arbitrageur’s strategy is to
long 10/9 shares of asset A and short 1 share of asset B (zero investment), and wait.
When asset A reverts to its true price ($100), its price will increase by 11.11%, and the

arbitrageur makes $11.11.

Now consider another pair of substitutes (C and D) and assume asset C is overpriced by
10% and sold at $110. The arbitrageur shorts 10/11 shares of asset C and longs 1 asset D.
Once the prices converge to $100, arbitrageur makes $9.09, and the price of C declines
by 9.09%. For an equally weighted portfolio of A, B, C and D, longing all of them will
yield a return of 0.505%. This represents the return on the portfolio that contains assets
with abnormally high trading activities. Although deviations from fimdamental values is
symmetric (i.e., a security can be under priced or overpriced equal likelihood), the
observed return on an equally weighted portfolio of mispriced securities is asymmetric

and skewed to positive values, as presented above.

The strategy of arbitrageurs includes selling overpriced stocks and/or buying underpriced
stocks, and presumably their trading activities are signaled as increased trading volumes.
Therefore, their profit depends on the price movements of the stocks that are more likely
to be traded in high-volume portfolio. We should reemphasize that the situation that is
described above does not distinguish which stocks are overpriced or underpriced, but it
shows the relationship between average mispricing in an equally weighted portfolio and

the magnitude of mispricing.

If it is assumed that high-volume portfolios include all the mispriced securities in the
market, then the level of correction for mispricing can be estimated. Based on the

parameter estimates obtained for the risk factors for lS-day cumulative returns

38

(BHC=0-0031: BHM =1.0295, 0H5 =0.3828, and BHH =0.3707) given in Table 1.5 and the
val ues of the average of observations (RH=1.2%, RM = 0.45%, HML= 0.54%, and
S MB=0.03%), the return captured by the substitutability risk is 0.23%. In a market where
shor‘t selling is not constrained, this premium corresponds to a mispricing of 6.75%. As
the selling constraints become binding, however, the return from substitutability risk
drops down to 0.23% per 15 days.29 Therefore, as a hedge fund strategy, identification of
mi 8 pricing via “positive” volume shocks may produce positive returns, depending on the

lev e] of short-selling constraints.
1 -6 Conclusion

In this paper, we provide new insights to the visibility hypothesis of Miller (1977), who
at gues that increased attention to a given stock (such as heavy trading) should attract and
Convince more investors to buy the stock. Therefore, abnormal trading activities should
Signal price increases in a market where short selling is restricted. Miller’s argument can
explain the relationship between abnormal trading activity and subsequent price
increases, but it falls short to explain why particular stocks experience high trading
volume in the first place. We argue that stocks with low substitutability risk are more
likely to experience abnormal trading activity when their price deviates from
fundamentals and we postulate that the abnormal trading activities may signal the
intentions of the traders, presumably arbitrageurs. Thus, in an economy where short sales

are restricted, stocks with substitutes are more likely to be “visible” when they are

underpriced. We have presented empirical evidence that substitutability risk can explain

 

29 Conrad, Gultekin, and Kaul (1997) estimate that one-week return of less than 1 percent
on zero investment portfolios would be wiped out by one-way transaction costs of 0.2
percent.

39

the premium between high- and low-volume stocks (Gervais, Kaniel, and Mingelgrin

(2001 )).

The arbitrage interpretation of the visibility hypothesis complements Chan and
Lakonishok (1993), who suggest that investors typically only consider the assets they
hold when making their sell decisions and all assets in the market when making buy
decisions. They postulate that the decision about which asset to buy conveys more
information to the market than the decision to sell, because sell orders usually are
interpreted as liquidity motivated. We maintain that the information effect on trading
volume is only one side of the story. In the model presented here, the trading strategies of
investors who have access to all assets in a segmented market may not be driven only by
information. Investors, who provide the liquidity to other investors with limited
investment opportunity sets and who profit from any price discrepancy between markets
segments, care about the availability of perfect substitutes (substitutability risk). Their
demand for such assets increases the visibility of those assets and forces other investors
to consider them. When assets with low substitutability risk are underpriced, increased

visibility causes prices to appreciate and expected returns to depreciate.

Finally, our approach relates extreme trading volume to the most fundamental motive of
trading: arbitrage and its limits and it may shed light to trading activities that cannot be

explained by announcement affects, difference of opinion, or liquidity.

4O

APPENDIX 1

TABLES AND FIGURES FOR CHAPTER 1

41

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67

 

 

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Speculative Markets, Econometrica 51, 485-505.

72

Wang, J ., 1993, A Model of Intertemporal Asset Prices under Asymmetric Information,
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Wang, J ., 1994, A Model of Competitive Stock Trading Volume, Journal of Political
Economy 102, 127-168.

Wurgler, J ., and E. Zhuravskaya, 2002, Does arbitrage flatten demand curves for stocks?,
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73

Chapter 2

2 Tests of Competing Theories of Momentum: Market Intelligence and
Statistical Arbitrage

2.1 Introduction

The simple investing strategy of buying prior winners and selling prior losers, now
dubbed momentum, appears significantly profitable both statistically and economically in
both US (Jegadeesh and Titman (1993)) and other major markets (Rouwenhorst (1998,
1999) and Griffin, Ji, and Martin (2003)). As an example, in the US, from 1965 to 2000,
stocks in the t0p six-month return decile beat stocks in the bottom decile by 5.59% (p-
value = 0.00), on average, during the subsequent six months. This finding is interesting

because it suggests that prices are not weak form efficient.

In general, we can summarize the momentum literature in terms of their interpretation of
the sorting procedure that is employed in the empirical setup. Let us assume that realized
returns can be decomposed into a sum of unconditional expected return and unexpected

return,
rm '"" nut + gin.

Explanations based on rational expectations (such as Conrad and Kaul (1998) and
Johnson (2002)) argue that the sorting procedure classifies securities with respect to their
expected returns (pi); Therefore momentum profits reflect the risk that is inherit in

expected returns. On the other hand, explanations based on behavioral explanations argue

74

that sorting on realized return is mainly dominated by the effect of unexpected return (8"),
hence firm specific risk should be the driving factor behind momentum profits (Jegadeesh
and Titman(1993), Barberis, Shleifer and Vishny (1998)). Although many studies
empirically compare the relative explanatory power of these two explanations, none test

these two competing hypothesis using out-of-sample data.

In this study, we fill this void in the literature. Our first hypothesis is that, if momentum
profits are due to the idiosyncratic risk of securities, as argued by behavioral models of
momentum such as Hong and Stein (1999) and Daniel, Hirshleifer, and Subrahmanyam
(1998), then countries that have high asset price comovements should not exhibit
momentum profits. In our tests, we show evidence consistent with this hypothesis,
suggesting that momentum strategies rely on firm-specific rather than well-known
systematic risks. This evidence is also consistent with other studies such as Liew and
Vassalou (2002), who show that the growth rate of GDP cannot be captured by
momentum strategy profitability, and Griffin, Ji, and Martin (2003), who show that
macroeconomic risk cannot capture the difference between momentum profitability in an

international context.

Exploiting the relation between asset price comovements and country-specific factors, we
develop empirical tests to study determinants of momentum profitability. We present
three novel findings. First, momentum is more pronounced in countries that have severe
earnings management practices, suggesting that momentum is not due to market
underreaction that is related to eamings-related information. This finding is not consistent
with Chan, Jegadeesh, and Lakonishok (1996) who show that, in the US, past return and

earnings surprise predict large drifts in future returns after controlling one another.

75

Moreover, in some countries where momentum strategies are more profitable, winners
and losers subsequently experience reversals in their stock prices, which suggests that
profitability of momentum strategies may be due to overreaction induced positive
feedback strategies of the sort discussed by DeLong, Shleifer, Summer, and Waldman

(1990). However, this pattern is not common to all markets analyzed in this study.

Second, momentum strategies appear to be profitable in countries that have more
SOphisticated investors. Findings indicate that in sophisticated markets, firm-specific
information can be used to infer more informative prices; hence investors make better
decisions. This is consistent with Roll (l988)’s predictions: higher firm-specific return
variation as a fraction of total variation signals more information-laden stock prices. High
stock price synchronicity represents a failure to incorporate firm-specific information into
market prices, as discussed in Morck, Yeung and Yu (2000) and Durnev, Morck, Yeung,
and Zarowin (2003), and momentum profits are more pervasive in markets where firm-

specific information can be incorporated into prices.

Third, after decomposing momentum profits into two parts as suggested by Hogan,
Jarrow, Teo, and Warachka (2004), trading profit per unit of time and the growth rate of a
trading strategy’s volatility (exploitability risk), we document that investor sophistication
is positively related to exploitability risk, suggesting that momentum strategies are riskier
in markets dominated by sophisticated investors. In other words, exploitability risk is the

price of momentum profits.

Thus, we conclude that momentum explanations based on rational expectations are

capable of explaining differences in momentum profitability across countries. Our results

76

indicate that a combination of earnings management and investor sophistication explain
about 40% of the cross-sectional differences of momentum profitability in 31 countries.
Findings are robust after controlling for country-specific factors including investor

protection, market size, and industry concentration.

The rest of the paper is organized in four sections. In the following section, we briefly
review the related literature in momentum and asset price comovements. In the third
section, we present a simple economy where momentum profits are generated with the
idiosyncratic risks of individual stocks. In the fourth section, we describe our data and
tests, and report the results of the hypotheses in three parts: (1) momentum profits and
asset price comovement, (2) determinants of momentum profitability, and (3) risk of
momentum strategy arbitrage and investor sophistication. The fifth section offers

conclusions and directions for future research.
2.2 Related Literature

Our study is related to two different streams of finance literature: asset price
synchronicity and momentum. Morck, Yeung, and Yu (2000) show that two factor model
R2 (with US. and local market factors) and other measures of stock market synchronicity
are higher in countries with relatively low per-capita GDP and less-developed financial
systems. These results imply that the stocks markets in emerging economies may be less
useful in terms of processing information and guiding capital towards its best economic
use. Moreover, they imply that stocks markets in underdeveloped countries act as ‘side
shows’ in the sense that stock market performance does not influence managers’

investment decisions (Morck, Shleifer and Vishny (1990)).

77

Durnev, Morck, Yeung and Zarowin (2003) and Campbell, Lettau, Malkiel, and Xu
(2001) document a radical decline in the R25 in the US over the last century, which
indicates that we may be able to learn about profitability of certain trading strategies not
only from the level of stock prices but also from second or higher moments of stock
returns. Jin and Myers (2004) argue that these findings are mainly driven by the risk-
bearing division between inside managers and outside investors. Our study distinguishes
itself from this strand of literature by showing the relationship between investor
sophistication and asset price comovement. In other words, we focus on the effects of the
investment environment on exploitability of momentum strategies, rather than
investigating the reasons why particular countries end up with current investment

environment.

Most studies agree on the existence of momentum profits. An exception is Lesmond,
Schill, and Zhou (2004), who present evidence that profits from momentum strategies
may not be large enough to cover transaction costs. Despite the near unanimity with
regard to the existence of momentum profits, there are diverging opinions on why it

exists.

Some argue that momentum profits can be attributed to firm-specific returns. For
instance, Lo and MacKinlay (1990) show that momentum could be caused by
autocorrelation in returns, lead-lag relations among stocks (cross-serial correlation), or

cross-sectional dispersion in unconditional means.1 Jegadeesh and Titman (1993) show

 

' lntuitively a stock that outperformed other stocks in the past might continue to do so for
three reasons: (1) the stock return is positively autocorrelated, so its own past return
predicts high future returns; (2) the stock return is negatively correlated with the lagged

78

that momentum is not driven by market risk. Fama and French (1996) demonstrate that
Fama and French (1992) unconditional three-factor model cannot explain momentum.
Conrad and Kaul (1998) argue that cross-sectional differences in expected returns explain
the profitability of momentum returns, whereas Grundy and Martin (2001) measure
conditional exposure to three-factor risk and show that neither industry effects nor cross-
sectional differences in expected returns are the primary cause of the momentum.
Jegadeesh and Titman (2002) argue that cross-sectional differences in expected retums
explain very little, if any, of the momentum profits. Johnson (2002) shows that a highly
persistent shock to the dividend growth rate can produce momentum patterns in a rational
expectations setting. His model predicts momentum profits which can decline rapidly (as

observed empirically), but remain positive at longer horizons.

Berk, Green and Naik (1999) offer a model based on economic risk factors that affect
firm investment life cycles and growth rates. In their model, a firm’s value depends on
interest rates as well as the number and systematic risk of its existing projects. Slow
turnover in the firrn’s project portfolio leads to persistence in both the firm’s asset base
and its systematic risk, all of which makes expected returns positively correlated with
lagged expected returns. Simulations results of this model produce momentum profits

that are roughly equal to the magnitude observed in the US. at slightly longer horizons.

Behavioral approaches such as Barberis, Shleifer, and Vishny (1998), Daniel, Hirshleifer,
and Subrahmanyam (1998), and Hong and Stein (1999) argue that imperfect formation

and revisions of investor expectations in response to new information causes momentum

 

returns on other stocks, so their poor performance predicts high future returns; and (3) the
stock simply has a high unconditional mean relative to other stocks.

79

patterns in stock data. Chordia and Shivakumar (2002) investigate the one-step-ahead
forecasts obtained by projecting momentum profits onto lagged macroeconomic variables
and conclude that US. momentum profits are completely explainable using these

forecasts.

Momentum profits are also associated with several characteristics not typically associated
with priced risk in standard models of expected returns. For example, Chan, Jegadeesh,
and Lakonishok (1996) show that return momentum coexists with earnings momentum.
Lee and Swaminathan (2000) document that momentum is more prevalent in stocks with
high turnover. Hong, Lim, and Stein (2000) show that small firms with low analyst
coverage have more momentum. Moskowitz and Grinblatt (1999) demonstrate that
industry momentum is large. Grinblatt and Moskowitz (2004) present evidence that
momentum is more prevalent for small firms with few institutional owners, growth firms,
and firms with high volume. Jegadeesh and Titman (2001) show that US. momentum
returns quickly dissipate after the investment period, a finding difficult to reconcile with
standard notions of priced financial risk. Lewellen (2002) shows that behavioral models
based on firm-specific returns cannot explain a significant component of momentum.
Momentum shows up in stocks and many types of portfolios, suggesting that momentum
cannot be attributed solely to firm-specific returns. He suggests that a coherent story
should explain why momentum shows up in, say, individual stocks and size quintiles, but
vanishes at the market level. Griffin, Ji, and Martin (2003) study the relation between
stock returns and macro-economic risk through the use of the unconditional approach of
Chen, Roll, and Ross (1986) and examine if the conditional macroeconomic risk

argument of Chordia and Shivakumar (2002) is robust. Their evidence shows that

80

 

international momentum profits extinguish slowly, as predicted by many risk-based
explanations, or reverse sign completely, consistent with several behavioral explanations.
In this sense, our study confirms and complements the findings of Griffin, Ji, and Martin
(2003). They argue that macroeconomic risks cannot explain momentum profits whereas
we demonstrate that firm-specific risk mainly drives the profitability of momentum
strategies. Moreover, we show that exploitability of momentum profits depends on
certain market characteristics such as investor sophistication and earnings management.

These factors need to be related to factors controlled in Griffin, Ji, and Martin (2003).

2.3 Model

In this section, we present a simple model that shows the relation between the
idiosyncratic risk of individual stocks and momentum profitability. We choose to focus
on the effect of idiosyncratic risk on momentum profitability because of the previous
empirical evidence that suggests macroeconomic risk cannot account for momentum
profitability. Similar models have been offered by Lo and MacKinlay (1990), Jegadeesh

and Titman (1993, 2002) and Chen and Hong (2002).

Our main objective in this setup is to demonstrate that in a simple economy where
systematic risk cannot account for the expected returns by design, idiosyncratic risk can

drive momentum profitability.

Consider a one-factor world in which the only source of momentum is investor under-
reaction to shocks. Assume there are N stocks each with the following one-factor

SITUCIUI'CI

81

ft = ,0]; +613:

rig : tut + fli/t + air (1)

where e, is a mean-zero, serially uncorrelated shock to the factor f, and 81)! is a mean-zero,

positively serially correlated idiosyncratic shock with variance 0”, and E[8,-,,, 8,3,4] =

2
08.

The unconditional varlance of factor f, 18 0' f. The parameter p 15 the serial correlation of

the factor. All other correlations are assumed to be zero. Also, for simplicity, assume that

every asset has the same mean and beta, [1,- : ,u and fli=fl=1. The only source of

momentum in this setting is the positive serial autocorrelation of the idiosyncratic shock,
which one can think of as due to some under reaction mechanism along the lines of recent
behavioral models. The momentum strategy relies on buying stocks based on their returns
in period t-l and holds it in period t. With this strategy, the portfolio weight assigned to

stock i is

1

Wit : —(rit—1_rt—1)
N (2)

where

82

1N
n=— r-

i,t
N=i 1

is the equally weighted index return. Note that if a return is less than the equally weighted

return, then its weight will be a negative number indicating a short position.
The time t profit of this momentum strategy at time t is
N
7ft : 2 jWiJriJ .
t=l

Given the one-factor structure in equation (1), the momentum strategy in equation (2) is

given by the weights of each asset of

N—l l N
Wl,l = N2 8i,t-I ——N—2.Zgj9t-l , (3)
13¢]

Therefore, the momentum profit in equation (3) is simply
N N —1 8 1 N
7: = z __ ...—2.9. r.
t 2 i, ,_1 2 , t—l 1,:
1:1 N N j¢i

The expected momentum profit is

Em.) = 1,510:

There are two properties of these results. First, by construction, expected momentum
profits only depend on the positive autocovariance of the idiosyncratic shocks since the
unconditional means and stock betas are assumed to be identical. Second, as idiosyncratic
shocks increase, expected momentum profits increase. In the following section, we focus

on this relationship between expected momentum returns and idiosyncratic risk.
2.4 Empirical Setup
2.4.1 Data

In this section, we describe our sample selection procedure and calculations. We used
data from 31 countries. US. monthly stock return data include common shares of all
NYSE, Amex and NASDAQ listed firms available from CRSP between January 1965
and December 2000.2 In order to mitigate from possible microstructure effects, we

eliminated observations if stock price is less than $5.

For non-US. data, we follow Griffin, Ji, and Martin (2003) and select countries from
TSF Datastream International which have at least 50 stocks after Janauary 1982. This

yielded an additional 30 countries. 3

Table 2.1 displays sample starting dates for each country and some market statistics. The
sample of non-US data ends in December 2003. We also eliminated real estate trusts and

investment companies from our international sample. We did not employ any price-

 

2 ADRs, SBIs, certificates, REITs, closed-end funds, companies incorporated outside the
US, and Americus Trust Components are excluded from the sample to maintain
consistency with the existing momentum literature.

3 Some countries (Egypt, Argentina, Brazil, Peru, China, Taiwan, Thailand) are excluded
from our sample due to lack of data on reliable risk free rate note.

84

 

related filtering for non-US data.4 Table 2.1 also reports the number of firms available at
the beginning of 1982 (or the first available month for countries when they are included
in the sample). Our sample contains all of the major markets (US, UK, Canada, France,
Germany and Japan) and some of the emerging markets that have enough data to

calculate momentum profits.
2.4.2 Variables
Returns to the momentum strategy

In order to calculate the returns to the momentum strategy, we employed the procedure
used in previous studies. Any momentum strategy consists of a ranking period over
which winners and losers are determined, and an investment period over which winners
are held and losers sold short. We use an N-month ranking and investment period
(N=3,6,9 and 12) and created portfolios with equal weights. This investment rule is

followed every month.

Our international strategies examine the top (winner) and bottom (loser) 20 percent of
stock returns as some countries do not have enough stocks to allow for use of the more
common top and bottom decil‘e classification. For the US, we use the top and bottom 10
percent of stock returns.5 To avoid microstructure distortions, we skip a month between

portfolio ranking and investment periods. Thus, for each month t, the portfolio (Winner

 

4 Ince and Porter (2004) discuss the reliability of Thomson Datastream individual equity
return data. In this study, we followed their suggestions about data cleaning procedures.
We also excluded monthly returns above 500% and less than -99% since such
observations are unlikely unless there is a recording error. Our results are not sensitive to
such filtering procedures.

5 Using the top and bottom 20% in the US. does not materially alter the results.

85

minus Loser (WML)) held during the investment period months t to t+(N-1), is
determined by performance over the ranking period, months t—(N+ I) to t - 2. We denote
such a strategy by “N/l/N”. Table 2.2 presents the sample statistics of cumulative

momentum profits for the corresponding investment period in 31 countries.‘5

A close inspection of Table 2.2 reveals two important patterns that we exploit in later
parts of the study. First of all, momentum strategies are profitable in most of the major
markets, such as Australia, Belgium, Canada, Demnark, Finland, France, Spain, Sweden,
Germany, UK and US, whereas it is rarely profitable in emerging countries. Second,
3/1/3 and 6/1/6 strategies seem to produce the highest cumulative profits in some
countries. However, this pattern disappears as we increase the ranking and investment
periods. These reversals in winners and losers suggest that the profitability of momentum
strategies may be due to overreaction induced positive feedback strategies of DeLong,
Shleifer, Summer, and Waldman (1990). It is important to note that some countries (such
as Japan, Korea, Philippines, Portugal, and Turkey) never present momentum

profitability in any ranking or investment periods.

In order to test our hypotheses, measures for asset price comovement, investor
sophistication, earnings management severeness, and the risk of statistical arbitrage need

to be defined.

 

6 We should note that these statistics represent the profitability of zero investment
portfolios, therefore they do not represent returns. Hence, the cumulative profitability of a
certain strategy may be less than -100% in extreme cases. Of course, such positions may
not be attainable in financial markets due to constraints against short selling. We
replicated the study after excluding such cases, the results are essentially the same, if not
stronger. We choose to report the results with all the cases in order to mitigate from
survival bias arguments.

86

 

Asset price comovement measure

We follow the procedure used in Morck, Yeung and Yu (2000) to calculate a measure
that captures the asset price comovement in a given market. In their study, Morck, Yeung

and Yu (2000) follow French and Roll (1986) and Roll (1988), and suggest using st of

regressions of the below specification to measure asset price comovement:

’33: : at + 16,-,trm,1't+ I82, i[rUS,t +efl]+8it. (4)

where i is a firm index,j is a country index, I is a two-week time period index, rm, is a
domestic market index, rug, is the US. market return, and e}, is the rate of change in the
exchange rate per US. dollar. They include the US. stock market return in equation 4
because most economies are partially open to foreign capital. The expression rug, + e},
translates US. stock market returns into local currency units. In order to overcome thin
trading problems, biweekly returns are used. Returns are compounded from daily total
returns. For stock markets in the Far East, US. market returns are lagged by one day to
account for time zone differences. Therefore, if the biweekly stock return in Japan used
data from June 7, 1995 to June 21, 1995, the contemporaneous US. market return uses
data from June 6, 1995 to June 20, 1995. When equation 4 is used for US. data, [32,,- is set
to zero. A high R2 indicates a high level of asset price comovement. Morck, Yeung, and
Yu (2000) show that this measure has high correlations with other comovement

measures.7 R2 is shown in Table 2.3 for each country.

 

7 We also used other measures that are suggested in Morck, Yeung and Yu (2000), such
as “% of stock moving in the same direction” and obtained similar results.

87

Investor sophistication measure

For investor sophistication, we used four proxies. The first measure, education enrollment
rate, shows the total enrollment in tertiary education regardless of age, expressed as a
percentage of the population in the five-year age group following on from the secondary-
school leaving age. The second measure, education life, shows the average education
level of population, which is proxied by school life expectancy, in each country from
1988 through 1996. The other two measures we use are the number of domestic firms per

capita and education expense per capita. All investor sophistication data are summarized

in Table 2.3-2.8

Earnings management severeness measure

For earnings management severeness, we use the aggregate earnings management
severeness index of Leuz, Nanda, and Wysocki (2004) who show that firms in countries
with developed equity markets, dispersed ownership structures, strong investor rights,
and legal enforcement engage in less earnings management. Their aggregate earnings
management measure relies on four different aspects of earnings management: (1)
smoothing reported operating earnings using accruals, (2) the correlation between

changes in accounting accruals and operating cash flows, (3) the magnitude of accruals,

 

8 The existing literature on investor sophistication generally uses institutional ownership
as a measure (e.g., Hand (1990), Walther (1997) and El-Gazzer (1998) and Bartov,
Radhakrishnan, and Krinsky (2000)). Due to a lack of international data on this measure,
we are unfortunately not able to use this measure. Some critics argue that institutional
ownership data is a noisy measure of investor sophistication as institutions tend to be
more passive (index) investors.

88

 

and (4) small loss avoidance.9 They rank countries with respect to each of these four
earnings management measures, and calculate an aggregate earnings management score
by averaging the country rankings. A high value in the ranking represents severeness of
earnings management. A detailed discussion of this measure is provided in Table 2.9.
Table 2.3 reports the rankings of counties with respect to the aggregate earnings

management severeness index.
Risk of momentum strategies.“ Statistical arbitrage approach

To calculate the risk of momentum strategies, we followed the methodology developed in
Hogan, Jarrow, Teo, and Warachka (2004) who introduce the concept of statistical
arbitrage, a long horizon trading opportunity that generates a riskless profit and is
designed to exploit persistent anomalies. Following their methodology, which is briefly
summarized in Table 2.10, we decompose momentum profits of 31 countries into two
parts: momentum profit per month (1.1) and the grth rate of volatility of momentum
profits (It), and classify countries with respect to these two measures. The idea of this
decomposition is similar to that of the intercept (or) test of classical asset pricing models,
except decomposition of the intercept term (WML profits in our case) allows us to study
its time series behavior. In this framework, momentum profit per month (11) represents the
true risk free profit, provided that the volatility of the trading strategy declines fast. The

decline is governed by the second parameter (k), which is the growth rate of volatility.

 

9 We used the first three components of the aggregate earnings management sevemess
index separately and found essentially similar results.

89

Of these two measures, we focus on the second one (it), volatility growth rate of a given
zero investment trading strategy, since it defines the exploitability of a given momentum
strategy. A lower (higher) volatility growth rate (3.) means that the momentum portfolio’s
profit is less (more) likely to be wiped out by the fluctuations in the long and short parts
of the portfolio. In our sample, most 7t estimates are below 0, indicating that risks

associated with particular momentum strategies are declining over time. '0

With the use of momentum profit per month (H) and exploitability risk of momentum
profits (is), we can also test whether a particular momentum strategy presents any
statistical arbitrage opportunity in a given country. For statistical arbitrage opportunities
to be present, momentum profits per month should be greater than zero (11>0) and growth
rate of volatility should be less than zero ()1<0).ll Results of the momentum strategy

statistical arbitrage tests are summarized in Table 2.4 and Figure 2.2.

In Figure 2.2, the third quadrants (11>0 , lt<0) show the countries that presented statistical
arbitrage opportunities. For the 6/1/6 strategy, 15 countries allow statistical arbitrage.
However, it and 7t estimates are statistically significant at a 10% level only for 8 countries
(US, UK, Denmark, Finland, India, Italy, New Zealand and Spain). Other countries do

not seem to present any statistical arbitrage opportunities.

Two things should be noted. First, even though some countries present momentum

profitability with respect to simple t-tests on the mean of the WML profits, they do not

 

'0 The link between exploitability risk (71) and momentum profits depends on the
specification of incremental momentum profits. Please see Table 2.10 for the
specification we employed in this study.

H Table 2.10 describes the estimation procedure for u and 71.

90

 

necessarily offer statistical arbitrage (e.g., Belgium, Switzerland). Second, as we increase
the ranking and investment horizons (fi'om Figure 2.2.1 to Figure 2.2.4), the patterns
change slightly, but not dramatically. What is important for our study is, the volatility
growth rate of the zero investment portfolios determines most of these patterns.
Therefore, the determinants of this factor may give us insights about the riskiness of

momentum strategies.
Other variables

Risk-sharing and hedging opportunities offered by markets may be different because of
many reasons. First of all, some markets may be dominated by few industries; therefore
an industry related shock may force asset prices to comove more frequently than it does
in other markets. Second, in order to maintain a viable market, the volume of trade must
be large enough to ensure sufficient market depth and liquidity to avoid excessive price
volatility. In this sense, indirect and direct transactions costs also may affect the
profitability of trading strategies. In this paper, we use several measures to control for
liquidity-related transactions costs. Third, uncertainty about how the legal system will
treat the introduction of new securities may be a barrier for risk arbitrageurs (Allen and
Gale(2001)). Consequently, issues that are linked to the legal system, such as corruption
and investor protection, may matter in the exploitability of certain momentum strategies

(La Porta, Lopez-de-Silanes, Shleifer, and Vishny (1997, 1998, 1999, 2000, 2002)).

In order to control for such effects, we employed industry concentration, the size of the
market, legal origin, a corruption perception index, the relative size of the equity markets

(CAP/GDP(%)), ratio of value traded to GDP (Trading), and an index of state owned

91

enterprises in the economy as our control variables. Descriptions of each of these
measures and their data sources are reported in Table 2.9 and summarized in Table 2.3.

Correlations between these variables are disclosed in Table 2.5.
2.4.3 Hypotheses , Tests, and Results:
(1) Momentum profits and asset price comovement

Our first hypothesis is that, if momentum profits are due to asset price comovement, then
momentum profits should decrease in asset price comovement. Formally, we test the

following specification:
MOM = p, + p118

where MOM is the momentum profits with x month ranking and investment period, and

R2 is the measure of asset price comovement.

Hypothesis (Ho) 1: If momentum profits are due to the idiosyncratic risk of securities,
then there should not be a negative relationship between asset price comovement and

momentum profits; that is Br 2 0.

We should note that the independent variable, R2, can be represented as a function of
various country specific factors, including investor protection (Morck, Yeung and Yu
(2000)), industry concentration, choice of organization (conglomerate vs. focused firms)
(Campbell, Lettau, Malkiel, and Xu (2001), Gertner, Scharfstein, and Stein (1994)), and
power of outside investors (Jin and Myers (2004)). We break up R2 into such factors in

the next section.

92

 

The results in Table 2.6 show that hypothesis 1 is rejected at 5% level (one sided test) for
3/1/3 and 6/1/6 strategies. The coefficient signs for 9/1/9 and 12/1/12 are also negative as
predicted; however, the coefficient estimates are statistically significant at a 10% level.12
The momentum literature mostly reports significant profits for medium term (3-6

months), therefore the decrease in the significance of the p-values for longer periods is

consistent with existing research.

This evidence complements the findings of Liew and Vassalou (2002) and Griffin, Ji, and
Martin (2004). In their study, these authors show that momentum is not a compensation
for macroeconomic risk. Consistent with the predictions of the simple model presented in
Section 3 and some behavioral models in the literature (Hong and Stein (1999) and Chen
and Hong (2002)), the results show a positive relation with idiosyncratic risk. Our
findings also support the conjectures of Hong, Lim and Stein (1998), who find that
momentum profitability declines with firm size and analyst coverage. In other words,
they argue that firm-specific information, especially negative information, diffuses
gradually across investing public, and small firms and low analyst coverage are the

factors capture the information dissemination process.

The consistency of our results and the behavioral models should not be overemphasized.
Because, as we will demonstrate, if asset prices are more informative when idiosyncratic
risk is higher, then momentum profits may have rational components that can be

explained by risk measures based on idiosyncratic risk. Using these results, at this stage

 

‘2 We employed both Newey-West and White heteroscedasticity robust standard errors to
test our hypothesis. Results are essentially the same. The tables report White
heteroscedasticity robust p-values.

93

 

we can only conjecture that R2 captures some of these factors. In the next section, we
disentangle the comovement measure to test for the determinants of momentum
profitability (or lack of thereof) and get a deeper look at the validity of such behavioral

models’ predictions.
(2) Determinants of momentum profitability

If momentum profits present systematic differences across countries with respect to
idiosyncratic risk, then we may find the determinants of momentum profits by
investigating the attributes of economies that lead to idiosyncratic risk. In this section, we
test two different but related hypotheses. The intent of these two hypotheses is to assess
the effectiveness of the information flow from companies to the investment audience. In a
perfect market, managers reveal firm-specific information to the market instantaneously,
and the investors instantaneously capitalize this information in stock prices. Any
distortion of this process affects the informativeness of stock prices and trading
strategies. We break up distortions to information flow into two parts: (1) distortions due
to the ability of the investment audience to comprehend the value of firm-specific
information and, (2) information flow distortions due to managers’ activities, such as
earnings management practices. Obviously, these two types of distortions need not be

independent of each other.13 However, the combined effects of these two factors define

 

‘3 For instance, proponents of earnings management argue that information distortion via
earnings smoothing helps investors evaluate companies in a less volatile environment.
This does not necessarily imply that investors base their decisions on wrong information,
but less informative earnings, provided that they know that managers are allowed to
engage in such activities. In fact, investors in certain markets, such as Germany, know
that companies smooth their earnings legally. In short, the market for firm-specific
information is determined by suppliers of information (managers) and the demand of
information users (investors) under several frictions. In this paper, we are only concerned

94

the efficiency of information flow from companies to investors, and therefore determine a
given market’s information (intelligence) environment. Nevertheless, the important issue
for our case is that any distortion to information flow can influence on the profitability of

momentum strategies.

First, we investigate the effect of investor sophistication. Our hypothesis is that in
economies that are dominated by sophisticated investors, firm-specific information can
be incorporated into asset prices easily and quickly and such economies should present
less asset price comovement. Therefore, there should be a positive relation between
momentum profits and investor sophistication. The foundation of this idea goes back to
Grossman (1980), who argues that the existence of informed traders (sophisticated
investors) ensures correctly priced securities, so that firm-specific information is more

likely to be incorporated into prices in such economies.

Roll (1988) also has similar predictions, that higher firm-specific return variation as a
fraction of total variation signals more informed stock prices. Because high stock price
synchronicity represents a failure to incorporate firm-specific information into market
prices, as discussed in Morck, Yeung and Yu (2000) and Durnev, Morck, Yeung, and
Zarowin (2003), momentum profits should be more pronounced in markets where firm-

specific information can be incorporated into prices.

On the other hand, if firm-specific information drives momentum profitability and this

information diffuses gradually across the investing public as in Hong, Lim and Stein

 

with certain attributes of markets that may help us evaluate the effectiveness of
information flow, namely investor sophistication and earnings management.

95

 

(1998) and Hong and Stein (1999), then there should be a positive medium-term
autocorrelation in stock returns that are owned by less sophisticated investor groups. This
type of “underreaction” based behavioral model assumes that prices adjust slowly to
news. Therefore, momentum profits should be decreasing in investor sophistication. The
key underlying assumption of this competing hypothesis is that, in economies dominated
by sophisticated investors, information is disseminated immediately rather than

gradually.

Second, we test if earnings management, information flow distortions due to managers’
activities, is related to the profitability of momentum strategies. A number of studies in
the momentum literature argue that profitability of momentum strategies should be due to
the component of medium-horizon returns that is related to earnings-relevant news;
therefore, momentum strategies should not be profitable after accounting for past
innovations in earnings and earnings forecasts (Bernard and Thomas (1990), Chan,
Jegadeesh, and Lakonishok (1996)). Use of international data gives us an opportunity to
test the validity of such arguments. If momentum is due to market underreaction due to
earnings related information, then countries that have severe earnings management
practices should not present momentum profitability because investors can easily forecast

the future direction of returns by using past earnings.

We summarize the above conjectures in the following specification and hypotheses:

MOM = ,60 + ,BllnvestorSophistication + ,BzEarningMan ,

where MOM represents the profits to the WML portfolio for x month ranking and

investment period, InvestorSophistication represents one of the four proxies we described

96

in Section 2.4.2, and EarningMan represents the severeness of earnings management

practices as described in Table 2.9.

Hypothesis (Ho) 2: Assume that momentum profits are more pronounced in markets
with low asset price comovement. Firm specific information cannot be incorporated into
asset prices easily and quickly in economics that are not dominated by sophisticated
investors; therefore such markets allow more asset price comovement. Consequently,
there should not be a positive relation between momentum profits and investor

sophistication (i.e., Br S 0).

Hypothesis (Ho) 3: Assume that earnings surprises are less likely to occur in markets
with severe earnings management practices. In that case, if momentum profits are caused
by under-reaction to earnings related information (earnings surprises), then there should
not be a positive relationship between momentum profits and earnings management

severeness (i.e., Bz S. 0).'4

As discussed before, markets may portray different characteristics and these

characteristics may affect the results. For example, some countries are more concentrated

 

‘4 We should note that hypothesis 3 is based on the assumption that earnings surprises are
less likely to occur in markets with a severe earnings management environment. We are
not aware of any study that contradicts this assumption. Of course, the validity of this
assumption is based on the continuation of earnings management; if companies are likely
to smooth their earnings indefinitely, which means truth will never reach the market and
earnings surprises are less likely to occur, then investors may be reluctant to take
positions by using the difference between their expected earnings and realized smoothed
earnings.

97

in certain industries than others; therefore a shock to these industries may comove the

asset prices. We use the Herfindahl index to control for industry concentration.

Market size, transactions costs and liquidity also effect the execution of momentum
strategies. We use three proxies to capture such effects: (1) the relative size of the equity
market (CAP/GDP), (2) the ratio of value traded to GDP (Trading), (3) the per capita

number of domestic firms listed in an exchange (Domestic).

Factors such as an economy’s legal origin and corruption index capture certain market
characteristics related to investor protection, and information dissemination process of
firms is closely related to investor protection (Jin and Myers (2004)). In order to isolate
the effects of investor protection, we use origin of law (LAW), corruption, and an index
for state-owned enterprises (SEO). Table 2.9 and Table 2.3 discloses a detailed

description and values of these variables.ls

After controlling for these factors, we formally test the below specification:

MOM = ,60 + ,6, LA W + flzCorruption + ,B3Herfindahl + ,B4CAP / GDP

+fl5Trading + ,BéEarningMan + ,6,SOE + flsEduEn + ,B9Edusze + ,BmDomestic

 

’5 We assume that the variables we use to control for investor protection implicitly
control for outside shareholder rights. Recent research shows that better legal protection
of outside shareholders is associated with more valuable stock markets (La Porta, Lopez-
de-Silanes, Shleifer, and Vishny (1997)), a higher number of listed firms (La Porta,
Lopez-de-Silanes, Shleifer, and Vishny (1997), larger listed firms in terms of their sales
or assets (Kumar, Rajan, and Zingales (1999)), higher valuation of listed fmns relative to
their assets (La Porta, Lopez-de-Silanes, Shleifer, and Vishny (2002)), greater dividend
payouts (La Porta, Lopez-de-Silanes, Shleifer, and Vishny (2000)) and lower
concentration of ownership and control (La Porta, Lopez-de-Silanes, Shleifer, and Vishny
(1999)).

98

In this specification, we are interested in the coefficients of EduEn ([33), EduLife ([39),
Domestic ([310) and EarningsMan (136). In Table 2.7.1 to Table 2.7.4, we examine the

cross-sectional determinants of various momentum strategies.

Hypothesis 3 is rejected at a 5% level for the 3/1/3, 6/1/6 and 9/1/9 strategies, suggesting
that the profitability of momentum strategies is not due to the component of medium-

horizon returns that is related to earnings-related news.

This finding is not consistent with the findings of Chan, Jegadeesh, and Lakonishok
(1996)), who show that, in the US, past return and earnings surprise predict large drifts in
future returns after controlling one another. In other words, momentum is not created by
market underreaction due to earnings-related information. Had it been related to earnings
surprises, countries with severe earnings management practices would not have presented
momentum profitability. One possible explanation for this finding is that, in countries
that have severe earnings management practices, investors’ can predict the future returns
better because earnings smoothing will help stock returns to present positive

autocorrelations.

Overall, the results in Table 2.7 suggest that hypothesis 2 is rejected at 1% in medium-
term momentum strategies, i.e., 3/1/3 and 6/1/6 WMLs. However, the effect of investor
sophistication is positive but statistically insignificant for longer ranking and investment

periods. ‘6

 

‘6 The results are robust to all proxies used for investor sophistication and earnings
management severeness index constituents. For instance, in Table 7-5, we used “principal
component of private enforcement and anti-director rights” measure of La Porta, Lopez-
de-Silanes, Shleifer, and Vishny (1999) as a control variable in the 6/1/6 WML

99

 

These findings support the notion that when sophisticated investors’ trades incorporate
firm-specific information into stock prices, asset prices comove less. Therefore,
momentum strategies become profitable. However, predictions of “prices adjust too
slowly to news” type behavioral models, such as Hong and Stein (1999) and Daniel,
Hirshleifer, and Subrahmanyan (1998), are not supported by these results. Moreover, the
dependence of momentum profitability on investment horizon indicates that firm-specific
information is more likely to be incorporated in short- to medium-term rather than longer
horizons. If positive feedback traders are less likely to exist in markets with more
sophisticated investors, then this finding is also inconsistent with the positive feedback
trader model of DeLong, Shleifer, Summers, and Waldman (1990). In their study, authors
argue that prices initially overreact to news about fundamentals, than overreact further for

a period of time.

Finally, although the correlation between earnings management severeness and investor
sophistication is strongly negative (045), their combined effect on momentum profits is
positive for all momentum strategies. Furthermore, a combination of these two factors
explains about 40% of the cross-sectional variation in momentum profitability across

countries.

We believe that these findings are thought-provoking for three reasons. First, we know

that momentum is not related to systematic risk or the risk factors of Fama and French

 

regression. The correlation between earnings management and investor protection is
negative (-0.50); therefore, when we test the relationship between earnings management
and momentum strategies, we excluded the “investor protection” variable in order to
mitigate possible multicollinearity problems.

100

(1993) (see also Liew and Vassalou (2002), Griffin, Ji, and Martin (2004), and F ama and
French (1996)). Second, we established that idiosyncratic risk is positively related to
momentum profitability in hypothesis 1, a finding that is compatible with predictions of
some behavioral models of momentum mentioned above. Third, neither “underreaction to
news” nor “continuing overreaction to news” types of behavioral models explain the
relationship between momentum profitability and investor sophistication. In sum,
existing behavioral models fall short in explaining the three observations we summarized
above. On the other hand, our second hypothesis posits a link between a relationship
between momentum profits and firm specific risk based on immediate information
incorporation, and is capable to explain the crossectional differences of momentum
profits across countries. Up to this point, we only analyzed the returns to momentum
strategies and have not commented on the riskiness of such strategies. In the next section,
we will revisit this issue and investigate the relation between the risk of momentum

strategies and investor sophistication.
(3 ) Risk of momentum strategies

Rational expectation models of momentum argue that momentum profits have a risk-
based explanation. Examples of this approach include Conrad and Kaul (1998) and
Johnson (2002). Since we have already established a positive link between investor
sophistication and momentum profitability, that is inconsistent with some behavioral
models, the next logical step is to test the relation between the risk of momentum

strategies and investor sophistication.

101

In contrast to previous studies of rational momentum effects, our main focus is the
exploitability of momentum strategies, rather than cross-sectional differences in the
expected returns as in Conrad and Kaul (1998) or growth rate risk as in Johnson (2002).
Our argument is as follows. Competitive momentum traders accumulate firm-specific
information until the marginal cost of gathering an additional unit of information exceeds
its risk-adjusted marginal return. In such an environment, the exploitability of such
strategies constitutes the major risk of momentum strategies. Therefore, assuming that
investor sophistication is a proxy for the intensity of competitive risk arbitrage activities,
momentum strategies should be less likely to be exploitable in markets dominated by
sophisticated investors. In other words, exploitability risk is the price of momentum
profitability. It is important to emphasize that we built on the notion that the greater the
number of the sophisticated investors, the more they influence the stock price, because
they are expected to quickly correct the mispricing that arises from the trades of

unsophisticated investors.

We employ the statistical arbitrage framework of Hogan, Jarrow, Teo, and Warachka
(2004) to estimate the exploitability risk of momentum strategies. As discussed in Section
4.2, we decompose momentum profits of the 31 counties into two parts: momentum
profit per month (u) and growth rate of volatility of momentum profits . (it), i.e.,
exploitability risk of momentum strategies. A high volatility growth rate (X) means that a
given WML’s profit is more likely to be wiped out because of the increases in volatility;

therefore the exploitability risk of such a strategy is high. On the contrary, a low volatility

102

 

growth rate (It) means that a given WML’s profit is less likely to be wiped out; hence

exploitabi lity risk of such strategy is low.17

To isolate the effects of country-specific characteristics, we control for industry
concentration, size, liquidity, origin of law (LAW) and corruption. Motivations for these

COHtI‘OI variables were explained in the previous section.'8

Form ally, we test the below specification:

”1.1/0M = :80 + ,6, LA W + ,BZCorruption + ,83Herfina'ahl

+fl4CAP / GDP + ,BSTrading + flGDomestic + ,67EduEn

Where )1 represents the growth rate of volatility, i.e. exploitability risk, which is estimated
by using the methodology described in Table 2.10 and reported in Table 4. We state the

above arguments in the following hypothesis:

Hypothesis (Ho) 4: If momentum profits are not explained by the exploitability risk, then
there should not be a positive relationship between investor sophistication and the

exploitability risk of momentum strategies, i.e., B75 0.

Results are reported in Table 2.8. Consistent with the risk explanation based momentum

models, coefficient of investor sophistication is positive, i.e., hypothesis 4 is rejected, and

 

'7 One can think of exploitability risk along the lines of Shleifer and Vishny (1997) limits
of arbitrage framework. In this sense, exploitability risk is a measure of limits to arbitrage
that captures the risk of a zero investment portfolio.

'8 Results are not sensitive to various proxies of investor sophistication, liquidity, and
investor protection.

103

statistically significant mostly at a 1% level for all momentum strategies. The coefficients

of all control variables are not statistically significant for 3/1/3, 6/1/6 and 9/1/9 strategies.

Combined with the results of the hypothesis 2, these results suggest that, markets with
SOPhiSticated investors may offer momentum profits, however the exploitability of these

DIOfitS increases in investor sophistication. In other words, exploitability risk can explain

the momentum profits.

Can We reconcile these findings with the prediction of behavioral models? One finding
that is prevalent in US markets is that small stocks and stocks with few analysts present
mOre momentum profits, consistent with the predictions of the “prices adjust too slowly
to news” behavioral models of Hong and Stein (1999) and Daniel, Hirshleifer, and
Subrahmanyan (1998). If exploitability risk is indeed the price of momentum profit as the
international evidence suggests, then we should also argue that small stocks and stocks
followed by few analysts should be owned by more sophisticated investors. Clearly, this
argument is not warranted. However, investor sophistication is only one of the
determinants of the exploitability risk that explains the cross-sectional differences of
momentum profitability across countries. Other measures of limits to arbitrage, such as
substitutability risk or transactions cost, a factor that comes up insignificant in our tests,
may be significant in certain segments of the market.19 In this sense, our findings are

compatible with evidence provided in Lesmond, Schill, and Zhou (2004), who show that

 

'9 Transactions costs involve direct costs (such as brokerage fees, etc.) and indirect costs

(such as liquidity cost). In this sense, our “trading” and “size” variables partly control for
transactions costs.

104

momentum profits are not exploitable because of high transactions costs required to

implement momentum strategies for small size companies in US.

2.5 C onclusion

We Sth that momentum strategies are less profitable in markets where stock price
SYnCl‘lI‘Qnicity is higher. Empirical evidence suggests that momentum profits are largely
due to firm-specific risks, consistent with behavioral models of momentum. However,
aftfil‘ controlling for investor protection, market size, liquidity and high industry
COncentration, we find that factors that proxy the information flow process from

COmpanies to investors (i.e., investor sophistication and earnings management) explain

about 40% of the cross-sectional difference in momentum profitability.

Our results suggest that the profitability of momentum strategies is not due to the
Component of medium-horizon returns that is related to earnings-related news, which
means that momentum is not created by market under-reaction due to earnings-related
information. We conclude that in countries that have severe earnings management

practices, investors can predict future returns better because earnings smoothing forces

stock returns to exhibit positive autocorrelations.

We also document a positive and statistically significant relation between the profitability
of momentum strategies and investor sophistication. Furthermore, the relation between
investor sophistication and exploitability risk is also positive, suggesting that
exploitability risk is the price of momentum profitability. Overall, we conclude that our

evidence is more consistent with risk-based rational expectation models than behavioral

105

models of momentum. In this sense, our results complement the findings of Lesmond,

Schill, and Zhou (2004).

Our findings provide new research directions. First of all, what are the other determinants
0f exploitability risk other than competition between arbitrageurs (sophisticated
inVCStO rs)? The relation between other limits of arbitrage (such as substitutability risk and
trans actions cost) and exploitability risk also may provide additional insight to the cross-
sectional differences of momentum profitability across countries. Second, can we use
map} Oitability risk as a measure of “limits to arbitrage” to provide rational expectations
explanations for other persistent anomalies? And finally, and more importantly, we only
POint out the explanatory power of exploitability risk without any theoretical model that

Shows that exploitability risk is the price of momentum strategies. Such a model should

answer why exploitability risk, probably a function of idiosyncratic risk, is systematic.

Future research needs to be done in this area.

106

APPENDIX 2

TABLES AND FIGURES FOR CHAPTER 2

107

 

 

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Table 2.9
Data description and sources
0 Investor sophistication variables
Education Enrollment:
This measure shows the total enrolment in tertiary education regardless of age, expressed
as a percentage of the population in the five-year age group following on from the

secondary-school leaving age. Source: UNESCO Institute for statistics:

 

http://www.uis.unesco.org

Education Life

This measure summarizes the average education level of investors, which is proxied by
school life expectancy, in each country from 1988 through 1996. Source: UNESCO

Institute for statistics: http://wwwuisunescoorg

 

Domestic

Logarithm of the average ratio of the number of domestic firms listed in a given country
to its population (in millions) for the period 1996-2000. Source: La Porta, Lopez-de-
Silanes, and Shleifer, (2002)

Per capita education expense

This measure reports the ratio of education expense allocated in GDP to total population
in 2000. Source: UNESCO Institute for statistics: http://wwwuisunescoorg

0 Earnings management index

Leuz, Nanda, and Wysocki (2004)’s aggregate earnings management measure relies on
four different aspects of earnings management: (1) smoothing reported operating earnings

using accruals, (2) correlation between changes in accounting accruals and operating cash

I46

flows, (3) the magnitude of accruals, and (4) small loss avoidance. Countries with respect
to each of these four earnings management measures, and an aggregate earnings
management score is calculated by averaging the country rankings. A high value in the
ranking represents severeness of earnings management. The details of this measure is
discussed in Leuz, Nanda, and Wysocki (2004, p.509);

Smoothing reported operating earnings using accruals

Insiders can conceal changes in their firm’s economic performance using

both real operating decisions and financial reporting choices. Focusing on

insiders’ reporting choices, this measure captures the degree to which

insiders “smooth”, i.e., reduce the variability of reported earnings by

altering the accounting component of earnings, namely accruals. The

measure is a country’s median ratio of the firm-level standard deviation of

operating earnings divided by the firm-level standard deviation of cash

flow from operations. Scaling by the cash flow from operations controls

for differences in the variability of economic performance across firms.

Low values of this measure indicate that, ceteris paribus, insiders exercise

accounting discretion to smooth reported earnings.

Smoothing and the correlation between changes in accounting accruals

and operating cash flows

Insiders can also use their accounting discretion to conceal economic

shocks to the firm’s operating cash flow. For example, they may

accelerate the reporting of future revenues or delay the reporting of current

costs to hide poor current performance. Conversely, insiders underreport

147

strong current performance to create reserves for the future. In either case,
accounting accruals buffer cash flow shocks and result in a negative
correlation between changes in accruals and operating cash flows. A
negative correlation is a natural result of accrual accounting (Dechow
(1994)). However, larger magnitudes of this correlation indicate, ceteris
paribus, smoothing of reported earnings that does not reflect a firm’s
underlying economic performance. Consequently, the contemporaneous
correlation between changes in accounting accruals and changes in
operating cash flows is the second measure of earnings smoothing.
Discretion in reported earnings: The magnitude of accruals

Apart from dampening fluctuations in firm performance, insiders can use
their reporting discretion to misstate their firm‘s economic performance.
For instance, insiders can overstate reported earnings to achieve certain
earnings targets or report extraordinary performance in specific instances,
such as an equity issuance (Dechow and Skinner(2000)). Accordingly, this
earnings management measure uses the magnitude of accruals as a proxy
for the extent to which insiders exercise discretion in reporting earnings. It
is computed as a country’s median of the absolute value of firms’ accruals
scaled by the absolute value of firms’ cash flow from operations. The
scaling controls for differences in firm size and performance.

Discretion in reported earnings: Small loss avoidance

Small losses are more likely to lie within the bounds of insiders’ reporting

discretion. Thus, in each country, the ratio of small reported profits to

148

small reported losses reflects the extent to which insiders manage earnings
to avoid reporting losses. Following Burgstahler and Dichev (1997), the
ratio of “small profits” to “small losses” is computed, for each country,
using after-tax earnings scaled by total assets. Small losses are defined to
be in the range |'_0.0l, 0.00) and small profits are defined to be in the
range [0.00, 0.01].
0 Origin of Law
UK__LAW: 1 if English legal origin.
FR__LAW: 1 if French legal origin.
SC_LAW: 1 if Scandinavian legal origin.
GE_LAW: 1 if German legal origin.
0 Corruption
Corruption Perception Index. Source: Transparency International (2000).
o Investor Protection:
Principal component of private enforcement and anti-director rights. Scale from O to 10.
Source: La Porta, Lopez-de-Silanes, Shleifer, Vishny (1999).
0 Industry Concentration: (Herfindahl)
Time-series mean of weekly industry concentration in each market. The industry
concentration of each market is measured by a Herfindahl variable. For each week,

Herfindahl industry concentration measure is calculated as

2

,- MVYNDi.
[Na-:2 CAR 1 ,

1:1

 

149

where INDi is the industry concentration measure for country i, MVINDjj is the market
value of industry j in country i, and CAPi is country i’s total market capitalization. The
yearly market industry concentration is then approximated by the mean of weekly
industry concentration values in a year. Source: Xing (2004).
o CAP/GDP ("/o)
The Relative Size of the Equity Market - the time-series mean of the yearly relative size
of the equity market in each country from 1988 to 1997. The relative market size in a
year is computed by dividing the the total market capitalization of all listed firms in a
market (CAP) to the gross domestic production (GDP) of that particular country. Both
CAP and GDP are from the World Development Indicator database of the World. Source:
Xing (2004).
0 Trading
Ratio of value traded to GDP in 1995. Source: Beck, Levine, and Loayza (2000)
0 State owned enterprises in the economy (SOE)
Index of State owned enterprises in the economy. Scale from O to 10. Higher values
given to countries with fewer government-owned enterprises. Source: La Porta, Lopez-
de-Silanes, Shleifer, (2002).
0 Descriptive aggregate statistics on countries

Stock market capitalization to GDP: Value of listed shares to GDP in 2001.

Stock market total value traded to GDP: Total shares traded on the stock market

exchange to GDP in 2001.

Stock market turnover ratio: Ratio of the value of total shares traded to market

capitalization in 2001.

150

Source: World Bank’s Financial Structure and Economic Development Database

(http://www.worldbank.org/research/proiects/finstructure/database.htrn)

151

Table 2.10

Statistical Arbitrage

In this table, we summarize the methodology developed in Hogan, Jarrow, Teo and
Warachka (2003) that tests the existence of statistical arbitrage for a given zero
investment trading strategy (such as long 18 worth of the top decile of BM stocks and

short 18 worth of bottom decile of B/M).
To test for statistical arbitrage, a time series of dollar denominated discounted cumulative

trading profits V01), V02), . . . , Van) generated by a trading strategy are

analyzed.
For a given trading strategy, let AVi : V(ti) - V(ti-1) denote increments of the
discounted cumulative trading profit measured at equidistant time points ti - in 2A
with ti = l A.
Let the discounted incremental trading profits satisfy

it

Avi=ui9+oizi

For i=1,2,. . .,n where z, are i.i.d. N(O,1) random variables.

In this case discounted cumulative trading profits generated by the trading strategy are

v(tn) = :Avi ~N(,u:i6,0'2:i”)
i=1 i=1 i=1

and the log likelihood function for the increments is

152

 

1 n
2

LogL(,u,0'2,/1,6l|Av) = —%Zlog(0'2i“) — 2 272170812, — ,uig )2
i=1 0' i=1 1

The parameters to be estimated are u, 02, it are 0. We primarily focus on the estimates of

u, and it since a statistical arbitrage by definition of Hogan, Jarrow, Teo, and Warachka

(2004) should have
(i) Initial investment is zero
(ii) Positive payoff (u)
(iii) Time averaged variance converging to zero (it)

A trading strategy generates a statistical arbitrage with l-a percent confidence if the

following conditions are satisfied:
H1: u > 0

H2 k<0

H3: 0>max(7&—‘/2,-l)

In Table 2.4 and Figure l, we summarize the estimates of u, 02' for 31 countries for
momentum strategies with N-month ranking and investment horizon. We employed
unconditional mean estimates, i.e. 0:0, in order to compare our results with that of
Hogan, Jarrow, Teo, and Warachka (2004). We obtained monthly risk free rate data from

Global Finance Database (wwwglobalfindatacom).

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157

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158

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