manual. 9

a. 3.5.5?

.3:

.131;

h....;...n .. i
33".)to. 4 I .23).... . II
:. afiwuwmn.
. . 1 L
. fig»...
é ."ustuSa:
.; an. .39., .
i. fififlfififiwkdw
.2 . .. .
f“flfiufl.§ka« I fighfli:t

I...
(.2

,1 It.
3 .235... .
V .5 . . . .2 5
.:.........m..xxu....z 2...... 2...... :8
. :lflnuur 3...»):
. . . z.
Riflofifidggé
.4. $4.9... “1...-..
u 3.3.6.9... . 4... .511 h
.r: . L .. ...,...n.,......_...
. , .. .. , .98.... . a.
$35-.. 5...... i. .
. r»: .\ 5 3...}..Jt: Qty 1...:
. . 3r... . a .2... $1.1...
I it?
“Hawk?!” . . _..(..H.1b.rr . . .. v
.1. ..........r h...
.5... -3

a
.. ”U.-
»I! .....3: H.535»...
fiffifis
.. inn-4);.
4...?
.
1.5.3.. $1.3
.90).". fidfiflrsfl. I “A .
. . .t:......\).1}7$33!
3...! r0551..." I t .
.2. 1. n3“ . 01‘. :
. ohflhnflu. «fag‘bn.
I a .
it»; h»
.. x A... t .
. P7P. mug—SW. In!!! laws}
. ....-,§:..., .3; . any... .92....
EH”: 9:: 59.5““:
32......

I2...
.253...
.w s... 5....
. .idr ....
.alvxnz . 15‘s
{iiww .495. 40.
In... .I .3. L 9
$1.... 1141......
raga... «$1...
.5 1.x.yllxlcflfllatill

. Harv. 5....

.....n
m.%

.. . 130.89..
. )flI‘J' .4...
3.-..»35. . z :
on 61.30...- .AIUH‘I’ ..

 

lat-ill
33.59355...
1 2519‘.
.593)»an
I. .1:
L:\.5
3'53

((4....1 .
. tingling. 11:39....

(1.11»... .123‘3 511:3...
A5. f. .

. éa£§.i.g
‘13.}...4 3 h|zfiai~zv5ellu
. 1“: 3.. ll": I 4 at. . o.
Vt. 7!! I!
. ‘ \ISA {ya-ark
Hirauubuu.‘ . ,

I II 1‘...
nv ! s... Xxx...»
. I. . s. . .v a
3:6 3...}: S

. .4...

 

 

 

THESIS

goDO

 

”a... .l llllllljflljlilflfllfllmil
Michigan estate
University

 

 

This is to certify that the
dissertation entitled

Essays in Financial Economics

presented by

Ramana Sonti

has been accepted towards fulfillment
of the requirements for

Ph . D . degree in _Finance

._Zyg**£¢v‘ AZZ%LVL4««tI

Major professor

(NA Mew KHAN/v A)
Datejl/N—l/JZOOO

MS U is an Affirmative Action/Equal Opportunity Institution 0-12771

 

 

 

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE

DATE DUE

DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

11/00 c/CIM.p85-p.t4

 

ESSAYS IN FINANCIAL ECONOMICS
By

Ramana Sonti

A DISSERTATION

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

Docron OF PHILOSOPHY

Department of Finance

2000

ABSTRACT
ESSAYS IN FINANCIAL ECONOMICS
By

Ramana Sonti

In the three chapters comprising this dissertation, I explore some issues regarding
financial institutions and financial markets. In the first chapter, I present a model
that examines (institutional) herding in rational financial markets. In this model, I
attribute a resource allocation role to stock prices. When informed investors possess
private information important to a firm’s investment decision, they need to transmit
it to the firm manager. A natural way to achieve this is by trading in a way that
allows the manager to infer their information. However, when their trading patterns
affect firm investments, there is an incentive to generate the pattern the manager
responds to. In most models of rational expectations, such manipulation results
in trading losses and can be supported only by imposing market incompleteness or
restricted participation. However, with a real effect, just giving investors positive
inventory leads to potential herding as investors can recoup their trading loss through
the value increase of their inventory. Also, price manipulation in my model is value
increasing since informed investors generate investment-affecting patterns only when
the resulting investment is desirable.

The second chapter examines institutional investment in firms issuing seasoned

equity (SEO firms). I document that institutional investors significantly increase

their investments in SEO firms compared to those in non-issuing firms with identical
characteristics. Also, SEO firms with the greatest increase in institutional investment
outperformed their benchmark portfolios the most over one-year and two-year hori-
zons after the issue. There is no such relationship for non-issuing firms. I interpret
the results in Chapter 2 as evidence that institutional investors are able to identify
above average SEO firms at the time of equity issuance, and increase their holdings
in these potential outperformers.

In the third chapter, I examine so-called “momentum” strategies that have been
suggested as evidence of predictability in stock returns based upon past returns. I
conjecture that firms in growth industries are harder to value, and thus systematic
misvaluation will more pervasive in such firms; hence, these firms will exhibit greater
momentum. To test this conjecture, I investigate momentum profits for individual
stocks split into quintiles along the dimension of industry growth. I find that indi-
vidual stock momentum varies almost monotonically by industry growth. Firms in
highest industry growth quintile have significantly higher momentum compared to
those in the lowest growth quintile. I also separately investigate momentum profits
for two groups of firms within each industry growth quintile: those with asset growth
above the industry average, and those below the average. I find that the above-
average growth group within each quintile has significantly higher momentum profits
than the below-average group. Further, momentum profits of the highest industry
growth quintile are always higher than those for the universe of firms, suggesting an
economic benefit to stratifying firms based on industry growth and relative company

growth intra-industry, while following a momentum investment strategy.

To Deepthi and Sahithi, for their unqualified love and support

iv

ACKNOWLEDGMENTS

I am deeply indebted to my dissertation committee — Dr. Naveen Khanna (Chair),
Dr. C. Edward Fee, Dr. Charles Hadlock, Dr. Jun-Koo Kang, and Dr. Assem
Safieddine for their insightful comments, helpful guidance, and unflinching support.
In particular, I am indebted to Naveen Khanna, who, first as a teacher and later
as a co—author, taught me much of what I know about corporate finance today. To
him, I owe a huge debt of gratitude for teaching me the importance of careful financial
modeling and for guiding me though all phases of my doctoral program. I am indebted
to Assem Safieddine for his patience in carefully guiding me through the data and
methods of empirical finance. I hope that I have imbibed at least some of his voracious
appetite for research and his tireless capacity for hard work. In addition to being an
excellent teacher and guide, he has been a very good friend. I am grateful to Charlie
Hadlock, for the countless hours he spent with me helping me situate my work within
the broader context of corporate finance. Especially in the latter phase of my doctoral
program, Charlie has been an invaluable resource, taking turns at being tough critic,
sage counsel, and reliable friend. I am also thankful to Prof..leffrey Wooldridge and
Prof. Robert De Jong of the Economics department for helping me clearly understand
the fundamental nature and limitations of econometric methods.

I would like to thank Dr. Richard Simonds, Dr. Kirt Butler and Dr. Geoffrey
Booth for supporting me in every way possible through the entire term of my doc-
toral program. I thank the staff of the finance department for the many things they

do everyday to make this a better place to work at. I thank my fellow graduate

students in the finance department, especially Melinda Newman, Wei-ling Song, and
David North for all their help and support. In particular, I would like to thank two
colleagues, who have become close friends of mine: Mike Cichello, for always pointing
me forward when the going got tough, and Malcolm McLelland, for many insightful
discussions about financial economics and econometrics.

Finally, I would like to place on record my deep appreciation for my family, for
their continued love and encouragement. In particular, I thank my parents, my sister
and her family for being patient cheerleaders from halfway around the world. I am
very grateful to my wife Deepthi and my daughter Sahithi for all the sacrifices they
made of valuable family time in order to facilitate the completion of my doctoral

program.

vi

TABLE OF CONTENTS

LIST OF TABLES 1X

LIST OF FIGURES X

l IRRATIONAL EXUBERANCE OR VALUE CREATION? FEED-

BACK EFFECT OF STOCK PRICES ON FUNDAMENTALS 1
1.1 Introduction ................................ 1
1.2 The Model ................................. 8
1.2.1 Trading Set-up .......................... 8

1.2.2 Security Value and Information Structure ............ 9

1.2.3 Herding Equilibrium ....................... 11

1.3 Herding as Equilibrium Behavior .................... 13
1.3.1 Herding Equilibrium ....................... 13

1.3.2 Robustness of the Herding Equilibrium ............. 15

1.4 A No—Herding Equilibrium ........................ 17
1.5 Multiple Equilibria ............................ 18
1.6 Conclusion ................................. 20
APPENDIX 1 TABLES, FIGURES AND PROOFS FOR CHAPTER 1 22
APPENDIX 1A TABLES FOR CHAPTER 1 23
APPENDIX 1B FIGURES FOR CHAPTER 1 30
APPENDIX 10 PROOFS FOR CHAPTER 1 37
BIBLIOGRAPHY REFERENCES FOR CHAPTER 1 60

2 SMART INVESTMENTS BY SMART MONEY: EVIDENCE FROM

SEASONED EQUITY OFFERINGS 63
2.1 Introduction ................................ 63
2.2 Prior Research and Motivation ...................... 66
2.2.1 Seasoned Equity Offerings .................... 66
2.2.2 Institutional Investment: Growth ................ 67
2.2.3 Institutional Investment: Performance ............. 68
2.2.4 Institutional Investment: Behavior ............... 69
2.3 Data and Methodology .......................... 71
2.3.1 Seasoned Equity Offerings .................... 71
2.3.2 Institutional Holdings ...................... 72

vii

2.3.3 Matching Firms .......................... 73

2.3.4 Methodology ........................... 76
2.4 Empirical Results and Discussion .................... 76
2.4.1 Institutional Holdings around SEOS ............... 76
2.4.2 Mutual PIInd Holdings around SEOS .............. 77
2.4.3 Non-Mutual Fund Holdings around SEOS ............ 78

2.4.4 The Pattern of Institutional Investment around SEOs: A Closer
Look ................................ 80
2.5 Summary and Conclusions ........................ 86
APPENDIX 2 TABLES FOR CHAPTER 2 88
BIBLIOGRAPHY REFERENCES FOR CHAPTER 2 100
3 MOMENTUM AND INDUSTRY GROWTH 103
3.1 Introduction ................................ 103
3.2 Data and Methodology .......................... 109
3.3 Empirical Results ............................. 111
3.4 Conclusion ................................. 116
APPENDIX 3 TABLES FOR CHAPTER 3 117
BIBLIOGRAPHY REFERENCES FOR CHAPTER 3 131

viii

LIST OF TABLES

TABLES FOR CHAPTER 1 23
Table 1.1 Prices under Herding ........................ 24
Table 1.2 Beliefs and Outcomes in the Herding Equilibrium ........ 25
Table 1.3 Prices under No—Herding ...................... 27
Table 1.4 Beliefs and Outcomes in the No—Herding Equilibrium ...... 28
TABLES FOR CHAPTER 2 ............................. 88
Table 2.1 Summary Statistics for the Sample of SEOS ........... 89

Table 2.2 Total Institutional Holdings in SEO Firms and Matching N on-Issuers 90
Table 2.3 Mutual thd Holdings in SEO Firms and Matching Non-Issuers 92
Table 2.4 Non-Mutual Fund Holdings in SEO Firms and Matching Non-Issuers 94

Table 2.5 Relative Stock Market Performance of SEO Firms ........ 96
Table 2.6 Relative Stock Market Performance of Matching Firms ...... 98
TABLES FOR CHAPTER 3 ............................. 117
Table 3.1 Momentum Portfolio Returns .................... 118
Table 3.2.1 Industry Groups: Description and Statistics ............ 120
Table 3.2.2 Industry Momentum ......................... 121
Table 3.3 Industry Adjusted Momentum ................... 123
Table 3.4.1 Industry Growth Quintiles: Summary Statistics .......... 124
Table 3.4.2 Momentum and Industry Growth ................. 125

Table 3.5 Momentum, Industry Growth and Relative Company Growth . . 127

LIST OF FIGURES

FIGURES FOR CHAPTER 1 30
Figure 1.1.1 Minimum inventory bound for herding equilibrium ....... 31
Figure 1.1.2 Minimum inventory bound for herding equilibrium ....... 32
Figure 1.2 Range of inventory for multiple equilibria ............. 33
Figure 1.3.1 Price path {+2,+2,+2} with H realization ............ 34
Figure 1.3.2 Price path {+2,+2,+2} with L realization ............ 34
Figure 1.4 Volatility (time-series stande deviation) of prices ....... 35
Figure 1.5 Unconditional expected security value : Herding vs No—Herding 36
Figure A.1 Comparison of inventory bounds for no—herding ......... 59

Chapter 1

IRRATIONAL EXUBERANCE OR VALUE CREATION?
FEEDBACK EFFECT OF STOCK PRICES ON

FUNDAMENTALS

1.1 Introduction

A basic tenet underlying financial economics is that firm fundamentals drive stock
price. Thus, the price discovery process in almost all models of market micro—structure
starts with the assumption that firm value, though possibly unknown, is fixed and
that trading by the better informed investors results in prices which are unbiased
expectations of this value. The presumption is that, in the presence of frictionless
arbitrage, prices cannot deviate from fundamental values and, thus, at any point in
time, they are the market’s best guess about the present value of a firm’s future cash
flow, given the information available at the time. However, recently many apparently
obstinate deviations of prices from fundamentals have been documented, making the
basic principle of informational efficiency of financial markets appear less than robust.

A strong attack has been made by Shiller (1981), who argues that stock prices
are far more volatile than warranted by the expected future dividend stream. Other

pervasive anomalies are over- and under-reaction to public announcements allowing

for apparently profitable momentum based trading strategies. Studies like Friend,
Blume, and Crockett (1970) and Lakonishok, Shleifer, and Vishny (1992b) have re-
ported that in an apparent attempt to take advantage of momentum profits, large
traders follow similar or “herd-like”. trading strategies: buying when other partic-
ipants are buying, and selling when others are selling. More compelling evidence
comes from studies like Grinblatt, Titman, and Wermers (1995) and Nofsinger and
Sim (1999) that document that funds following momentum based strategies appear
to outperform those that do not.

A number of papers provide potential explanations for why institutional investors
may trade in the same direction. Keynes blamed such behavior on “animal Spirits”
and considered it to be destabilizing to financial markets. More recently, authors
have presented rational reasons why institutional investors may herd in their trades.
In Scharfstein and Stein (1990), fund managers trade similarly because incentive
contracts are based on comparative performance. In Hirshleifer, Subrahmanyam,
and Titman (1994), managers do not know whether they are early-informed or late-
informed and, thus, herd. Finally, in Bikhchandani, Hirshleifer, and Welch (1992),
hereafter referred to as BHW, managers who decide later learn from decisions of
earlier fund managers and thus choose to mimic. However, since none of these papers
explicitly model asset prices, they are not suited to studying either whether herding
can exist in rational financial markets.

Avery and Zemsky (1998) introduce a rational market maker into the BHW frame-
work and show that when the market maker is permitted to establish prices in every
round of trading, herding cannot be supported. The market maker conditions on the

2

possibility of herding and offers price functionals that give negative expected profits
to traders who trade against their information.‘ This result is not unlike Harrison
and Kreps (1978) and Tirole (1982) which showed that rational price deviation from
fundamentals is hard to capture without introducing what the authors themselves
viewed as “unrealistic” restrictions.2

In this chapter, I propose an alternative explanation for herding in financial mar-
kets that is grounded in the rational expectations framework and does not require
exogenously imposed restrictions. I argue, as in Khanna, Slezak, and Bradley (1994),
and Leland (1992), that not only do fundamentals drive prices, but that prices also
affect fundamentals (feedback effect).3 In Khanna, Slezak and Bradley, managers can

have different Signals than outside informed. Thus they infer outsiders’ information

 

1 In a different setting, Khanna (1998) demonstrates that Optimal incentive con-
tracts eliminate herding in managerial decision making even when the order of deci-
sions is not known or contractible. In the event contracts can be conditioned on the
order of decision making, simpler contracts are sufficient to eliminate herding. See

also Slezak and Khanna (1999).
2Tirole identifies the minimal set of restrictions to include traders having different

priors which are imperfectly updated, and the ability to sell over-valued assets. Av-
ery and Zemsky capture herding by assuming multi-dimensional uncertainty which
results in non-monotonic signals. Allen and Gale (1992) captures price manipulation
by assuming a particular pattern of information release, first bad then good. Be-
havioral papers like Daniel, Hirshleifer, and Subrahmanyam (1998), Hong and Stein
(1999) and Barberis, Shleifer, and Vishny (1998) that model deviation of prices from
fundamentals need some of the same restrictions identified by Tirole. The most com-
mon are restrictions on short sales, incomplete participation in markets or wealth
constraints.

3See Subrahmanyam and Titman (1999) for an interesting application of the feed-
back effect of prices on firm value. Unlike in their model, in this model, the market
maker is aware of the manipulator, and the strategies he would play in equilibrium.
Hence, he establishes prices taking the possibility of manipulation into account, en-
suring that the manipulator makes negative trading profits when trading against his
information. Thus, the feedback effect alone does not result in either manipulation
or herding.

from price and take it into account while making the firm’s investment decisions.
Higher equity prices suggest better than expected prospects leading to higher invest-
ment levels.4 In Leland too, firms raise more capital if their issue sells at a higher
price and install more capacity. Higher stock prices indicate higher expected revenues,
justifying adding capacity at increasing marginal cost. It is also well documented that
firms tend to raise more capital when equity prices are high. While the existing view
is that firms try to time the market, it could also be viewed as the market’s attempt
to relax the budget constraint of firms/ industries with good prospects. No matter
what the reason, the result is that firms that see a run-up in their stock price are able
to issue new capital at high prices. The additional resources make it easier for them
to make new investment decisions.5

The feedback effect, though, requires the participation of both the informed
traders and firm managers. TI'aderS need to send managers signals that they can
interpret and then act on. If, for instance, the firm manager is expected to consider a
sequence of price increases as a good signal and increase real investment in response

to it, informed traders have an incentive to provide such a signal in the event their

information supports such an increase.6 Thus, if the first few informed traders get

 

4A current example is the stock price behavior of the Internet companies. Yahoo,
Amazon, etrade, Ebay, Inktomi etc. are all selling at multiples of their IPO prices.
This increase has likely made them more confident about their firms’ prospects and

has affected their investment strategies.
5A number of internet firms like Amazon.com, Inktomi, Lycos, Global Crossing

have raised huge amounts of funds through secondary issues at “high” prices. At
lower prices, similar offers would have brought in much lesser funds, decreasing their
ability to make new investments. Steven Case, CEO of AOL refers to this as the
era of “free money” for internet firms and wonders what will happen to the internet

industry when resources become tighter.
”The reader will wonder whether informed investors may create the trading pattern

good information about a firm’s prospects and increase the price by buying shares,
later informed traders may choose to continue buying and increasing prices even when
they have bad signals, to convince the firm manager to increase investment. If the
firm manager responds as expected, desirable new investment occurs, increasing the
fundamental value of the firm.

However, in a market with a rational market maker, the feedback effect alone is
not enough to get informed investors to herd. The reason is that the market maker
is aware that a particular pattern of trades will generate a value increasing feedback
effect. He is also aware that the presence of the feedback effect generates incentives
to herd. Consequently, he conditions on both the feedback effect and the potential
for herding when setting prices. Thus if, by following a number of buy trades with a
buy, the later trader attempts to keep the price high in the face of a bad signal, he
can do so only by buying at a price which is too high given his own Signal.7 Thus, he
makes negative expected profits on his trade, and in order for him to undertake such
a trade he must make profits elsewhere.8

With a feedback effect, there is a natural assumption which makes this possible.

 

to increase investment even when they have bad information. In this model, such
trading generates expected losses and thus is not supported in equilibrium. In that
sense price manipulation is value increasing in the setup of my model.

7Unlike in Grossman and Stiglitz (1980) the informed trader makes a profit if he
trades in the direction of his Signal. That occurs because of noise traders in these

types of models.
8Other papers have used similar arguments to support rational price manipulation

or price bubbles. Allen and Gorton (1993) model agency problems between investors
and fund managers. Even with an Optimal contract, the bad fund manager rationally
buys overvalued shares. They do not mind making losing trades as it does not ad-
versely affect their compensation. Kumar and Seppi (1992) model a manipulator who
intentionally loses in the Spot market to improve his previously taken position in the
futures market.

The only assumption needed is that the informed traders trade a portion of their
holding in the stock, i.e. they keep a minimum positive inventory in the stock at
all times. Since the feedback effect changes the fundamental value of the firm, with
a positive inventory an informed trader is prepared to lose on his trade in order to
increase the value of his inventory. The larger his inventory and/or the larger the
feedback effect, the more likely he is to herd and manipulate prices. It is worth noting,
however, that because of a positive inventory, an informed trader will herd to induce
the firm manager to increase investment only if it is expected to add value to the
firm.

This theory provides a rational explanation for Shiller’s observation of “excessive”
volatility. If prices are used by markets to affect changes in real firm investment, there
may be little or no relationship between prices and dividends. Stock volatility will
in part be a function of how frequently markets try to impact a firm’s investment
decisions. A number of other, new results emerge. Herding is more likely when the
quality of the informed traders’ information is higher. For higher quality information,
the later informed are more likely to trust the information of those who have already
traded and are more comfortable disregarding their own signal. For the same reason,
the critical level of inventory needed to support herding is negatively related to infor-
mation quality. With higher information quality, the information loss from herding
is less. Thus prices remain close to expected prices with no information loss. Since
trading losses from herding are less, smaller inventory is needed to recover the losses.
Not surprisingly, herding is more likely when the feedback effect is larger. Also the
critical level of inventory needed is negatively related to the feedback effect.

6

It turns out that there is a region in the parameter space of this model where there
are multiple equilibria, i.e. both herding and non-herding equilibria can be supported.
Though one cannot tell which will occur, one is afforded the Opportunity of deriving
some welfare implications. It turns out that the time t=0 price is higher for the
herding equilibrium than for the no-herding equilibrium. The reason is that herding
gets the new project accepted with ’a higher probability, thus increasing expected
fundamental value. However, since some information is lost in herding, the probability
that the outcome will be good given a pattern of trades is reduced, which decreases
fundamental value. In this region, though, the first effect appears to dominate. There
are also some results about conditional volatility of price paths. It turns out that on
the extreme price-paths, the ones with the highest volatility, herding serves to dampen
volatility, thus making price movements less extreme. Since these extreme paths have
“bubble-like” characteristics, herding can be argued to be moderating the harm done
by “bubbles”.

Herding and momentum strategies have been interchangeably used in the lit-
erature, primarily because of the presumption that herding causes prices to move
predictably causing serial correlation in returns. However, in this model the market
maker ensures that the price incorporates all the information he has at that point in
time. Thus prices are martingales, and any period’s price is an unbiased expectation
of all possible future prices. Thus rational herding does not translate into the pres-
ence of momentum based trading profits. However, because of the feedback effect,
herding can be correlated to future asset prices through increase in inventory value.

Thus, while the results herein are inconsistent with momentum in returns, they are

7

consistent with findings in papers like Wermers (1999) that funds that display herd
behavior outperform those that do not. It is also consistent with Falkenstein (1996),
that mutual funds herd in stocks with Specific characteristics, if some of them proxy
for the likelihood of the feedback effect.

The remainder of this chapter is organized as follows. Section 1.2 outlines the basic
structure of the model. Section 1.3 identifies parameter Spaces and conditions under
which herding behavior might be supported in equilibrium. Section 1.4 considers
another plausible equilibrium. In Section 1.5, we compare the two equilibria, and

discuss some implications. Section 1.6 concludes the chapter.

1.2 The Model

1.2.1 Trading Set-up

In the model, I try to capture the feedback effect as parsimoniously as possible. I
assume that a firm has existing assets with state and trade dependent per share
terminal payoff, v. For simplicity, I assume two states 0 = H and 0 = L (for “High”
and “Low” respectively). Prior beliefs regarding the state are P(0 =H) = P(0 =L)=
1/2. There are 3 risk-neutral informed traders: IT 1, 2 and 3, each of whom can
trade :5,- from X E {-1,+1}. Following BHW, each informed trader i is endowed with

a signal s.-, which is an imperfect proxy for the state according to:

 

P(s.~ =H| o) P(s,- =L| o)

 

 

I need q > 1 / 2, so that the Signal is informative. Thus the probability of getting
a High signal if the state is High, P(s, =H| 0=H) = q, is higher than getting a Low
signal. Markets Open for trading three times and, for tractability, only one informed
trader trades each round and each informed can trade only once. The order in which
they trade is randomly determined. At each round of informed traders’ trading, they
are accompanied by one noise trader who randomly chooses between two equally
likely trades u,- E U E {-1,+1}. There is a risk-neutral market maker who observes
aggregate demand y,- = 123' + u,- in each round of trading, and sets the price functional
such that his per-trade expected profits are zero, i.e. he sets a price equal to the
conditional expectation Of the value of the traded security, given the current history
of information at that time. This is a standard assumption in several models of

market-making including Kyle (1985) and Glosten and Milgrom (1985).

1.2.2 Security Value and Information Structure

To capture the feedback effect simply, the state-trade-dependent terminal value of
the security v, is modeled as follows. We assume that the only trading pattern that
results in the firm changing its expected investment strategy is when the informed un-
ambiguously buy one share in each round Of trading. This will occur when the trading
pattern over three rounds is {+2, +2, +2}. For all other patterns of trade the firm’s

9

expected investments remain the same. With unchanged expected investments,

 

9The main conclusions are not affected by which trading pattern Signals better
Opportunities. The effect would be captured by any trading pattern that suggests
that the probability Of the High state is greater.

v = 1 in the H state and v = 0 in the L state. However, with the favorable trading
pattern, the firm’s expected investment set increases and the terminal payoffs are v
= 1+d if state is H and v = -d if the state is L. Given uninformative signals (i.e.
with q =1 / 2), the expected value of the firm remains at 0.5, with or without the new
investment, but the variance of payoffs is higher with the new investment. However,
when signals are informative (i.e. with q>1 / 2), and they indicate a higher probability
of the High state, both expected value and payoff variance are higher. The set Of final

payoffs and beliefs is summarized as follows:10

a. v =1+d, if 0 = H and the trading pattern is {+2,+2,+2} over the three rounds.
This occurs when each informed trader and noise trader buy one share each in
all three rounds of trading.

v = -d, if 0 = L and the trading pattern is {+2,+2,+2} over the three rounds.
v = 1 if 0 = H, and v = 0, if 0 = L, with any other combination Of trades over

the three rounds.

b. All players know the information regarding the terminal price of the security,

and the precise value of d (>0).

The following timeline summarizes the sequence of actions that take place in our

model.

 

10Note that the externality ‘d’ occurs when there are several trades in a similar
direction. Intuitively, I want to capture the feedback effect of prices, where higher
prices lead to a broader opportunity set for the firm. However, as will be clear
shortly, endogenously determined prices in this model move in discrete jumps, and
hence modeling the feedback effect Of prices in a straightforward way is not possible.
Nevertheless, the conclusions from this model with this simple set-up are robust to
alternative ways of modeling this resource allocation role Of prices.

10

0 l 2 3 end

All know Rotund 1 Ro'und 2 Rotund 3 State 0
the values of trading : of trading : of trading : and terminal

 

0f q and d Market Market Market “1119," Of
and the maker maker maker security
distribution Observes observes observes realized
Ofterminal yl=$1+ul y2=z2+u2 y3=$3+u3

payoff V and sets 171 and sets p2 and sets 19"

across states

and paths

1.2.3 Herding Equilibrium

I now search for a herding equilibrium under the current set-up and illustrate the
nature of this model in detail. The equilibrium concept used is Symmetric Nash.
Under this concept, a sequence of trading strategies and a belief system constitute an
equilibrium, if given the belief system and the strategies of other players, no player
has an incentive to deviate from his prescribed strategy. For tractability, following

Khanna (1998), I use the following definition of a herding equilibrium.ll

Definition 1.1 A herding equilibrium is defined as one where every trader follows
his own signal, unless he reduces the probability of his being wrong by going against

his own signal.

With this definition of herding, it is now easy to prove the following proposition.

Proposition 1.1 It does not benefit the first two informed traders to ever herd while
it does benefit the third informed trader to herd when he can conclusively observe that

the first two traders have invested 2:; = +1 .

 

11I later identify conditions that support this restriction on choice of candidate. It
turns out that only the conditions on the third informed trader are binding.

11

Proof : The intuition underlying the proof follows from the fact that herding im-
proves the probability that a trader is right regarding the terminal state, regardless
of his own signal, when both previous signals are identical. Hence, with three players,
only the third player will ever herd. For a formal proof, see PrOposition 1 in Khanna

(1998). Q.E.D.

PIOposition 1.1 suggests a candidate equilibrium that gives rise to herding as we
have defined it. This definition of herding is consistent with naive price-momentum or
trend-chasing strategies as documented in recent literature. However, the suggested
candidate equilibrium needs to survive price-setting by a rational market maker.
Thus, I first derive prices that would be established under a belief system of herding
on part of the market maker as well as all informed traders. Next, I verify whether the
informed traders find it profitable to follow conjectured equilibrium strategies under
the prices established in the first step of analysis.

Table 1.1 presents the prices established under the beliefs Of herding.12 Detailed
derivations of these prices can be found in Appendix 10. See Table 1.2 for all combi-
nations of signals and trades by the informed traders in a herding equilibrium. Given
the derived prices, it remains to check whether the informed traders find it profitable

to adOpt the conjectured equilibrium strategies rather than deviate. The following

 

12In Table 1.1, p;- represents a price in round i Of trading, following history j in
previous rounds. i can take values 1, 2 or 3, while j can take -2, 0 or +2 (aggregate
demand level) for each round of trading. For example, pgf, means that this is a price
established in the second round of trading following an aggregate demand Of 0 in the
first round of trading, and -2 in the second round of trading

12

result can then be established.
Proposition 1.2 For the above model a herding equilibrium does not exist.
Proof: See Appendix 1C.

Proposition 2 is a restatement of the result established by Avery and Zemsky
(1998). In the presence of a rational market maker who sets prices on the basis Of
net order flow and the belief system, uncertainty regarding the state is not enough to
induce herding behavior. In this model as in theirs, the market maker, anticipating
herding behavior on part of the third informed trader, sets prices at a level at which it
is unprofitable (in expectation) for the latter to go against an L Signal, and invest 2:3
= +1. The reason is that the market maker sets the third period price knowing that
the third trader will buy independent of his Signal. Thus he pools over the trader’s
next period’s signal being High or Low with equal probability. If the third informed
gets a Low signal, the price he faces when he buys exceeds his expectation of the
terminal value. If he buys he makes an expected loss and is better Off not herding.
Consequently, herding cannot be supported in equilibrium for any set of parameter

values.

1.3 Herding as Equilibrium Behavior

1.3.1 Herding Equilibrium

I now modify the model and information structure to obtain a herding equilib-
rium that can be supported by prices established in Table 1.1. In addition tO the

13

information in Sections 1.2.1 and 1.2.2, I make the assumption that before he trades,
each informed trader has at least a minimum amount of inventory of I(> 0) units of
the security. While the market maker is aware that the informed trader’s inventory
exceeds some minimum level, he need not know the exact value of 1.13

One can immediately see the potential effect this modification has on herding
behavior. Even though the third informed trader makes a loss on trading if he herds,
he stands to gain on his inventory of securities since the expected terminal value of
the security is higher under herding. In other words, he knows that by herding he
will create an externality and as long as he has a sufficient stake in the externality,

he will choose to do so.” For a sufficiently large inventory, herding will be profitable

for the third informed trader. Indeed, we can establish the following result :

Proposition 1.3 In addition to the model above, if informed traders have invento-

ries I > I‘, where

r = mm - a] + t... - 1]

 

there exists a herding equilibrium Vq E (0.5,1].

Proof: See Appendix 1C.

 

lilMost models Of price manipulation or price bubbles assume no inventories. With-
out a feedback effect, inventory value is independent of the manipulation strategy

and thus does not play a role.
1‘Kumar and Seppi (1992) have a model where also a price manipulator purposely

takes a loss in one trade (the spot market) but by so doing more than makes up on
a previous position in the future’s market.

14

The criticality of the feedback effect of prices in our model is evident from PrOpo-
sition 1.3. In the absence of any externality (i.e. if d is zero), the third informed
trader does not make any gains on his inventory that can offset his trading loss.
Alternatively, this can be seen from the expression for I ‘, the minimum required in-
ventory becomes very large as d goes to zero. Hence, for herding behavior to exist
in a rational expectations framework, this model requires that a) there is a feedback
effect of prices into the underlying value of the security, and b) traders need to make
non-trading gains from this feedback effect; in other words, they must be interested

in “making the externality occur”.

1.3.2 Robustness Of the Herding Equilibrium

A natural question at this stage is whether herding is possible when the signals are
totally uninforrnative. After all, if there are gains to herding (in the form of the
externality that is created), totally uninformed traders might decide to start herding
by trading x, = +1. In terms of this model, is it possible that herding survives as an
equilibrium when q=0.5? Corollary 1.1 provides the answer to this question, along

with simple comparative statics on the minimum inventory bound I ‘.

Corollary 1.1 a. With totally uninformative signals, i. e. at q = 0.5, a herding

equilibrium is not possible.
b. For given (1, I ‘ decreases in q, ‘v’q > 0.5.

c. Vq E (0.5,1],I' decreases in d, Vd > 0

Proof:

a. Substitute q=0.5 into Condition (1.1) in Appendix 1C. Clearly the inequality
is not strictly satisfied. Stated another way, this means that it is not possible
for traders with totally uninformative Signals to start and maintain herding in

equilibrium.

b. This part is illustrated in Fig. 1.1.1. The figure shows that herding is more
likely when the quality Of the informed traders’ information is higher. For higher
quality information, later informed are more likely to trust the information of
those who have already traded and are more comfortable disregarding their own
signal. For the same reason, the critical level of inventory needed to support
herding is negatively related to information quality. With higher information
quality, the information loss from herding is less. Thus prices remain close to
expected prices conditional on no information loss. Since trading losses from

herding are less, smaller inventory is needed tO recover the losses.

c. See Fig. 1.1.2 for an illustration Of this part of the corollary. The intuition
here is that holding q constant, as (1 increases, the potential gains to herding
increase, and hence smaller levels of inventory are sufficient to start herding.

Not surprisingly, herding is more likely when the feedback effect is larger.

16

1.4 A N o-Herding Equilibrium

TO facilitate comparison with the herding case, it is useful to establish conditions un-
der which there exists a no—herding equilibrium. Note that the additional investment
still occurs after a {+2, +2, +2} pattern of trades. However, without herding, the
probability of the additional investment occurring is less as the third informed trades
x3 = +1 only if his signal is H. Recall that with herding, he trades x3 = +1 indepen-
dent of his signal. There is also a counter effect. Since in the no—herding equilibrium
the additional investment occurs conditional on three H signals, the probability of the
terminal state to be High is greater than in the herding equilibrium. Thus, from a
social welfare angle, it is not clear in which equilibrium society is better Off. I attempt

to answer this question next.

Definition 1.2 A no-herding equilibrium is defined as one where every informed

trader follows his own signal.

Table 1.3 presents the prices established under the beliefs of no—herding. ‘5 Detailed
derivations of these expressions can be found in Appendix IC. See Table 1.4 for all
combinations of signals and trades by the traders in a no—herding equilibrium. Once
again, as for the herding case, given the prices, I check whether the informed traders
find it profitable to adOpt the conjectured equilibrium strategies rather than deviate

(and herd). The following result can be established.

 

15In Table 1.3, pg“ represents a price in round i of trading, following history j in
previous rounds. i can take values 1, 2 or 3, while j can take -2, 0, +2 (aggregate
demand level) for each round of trading. The n in the superscript refers to the fact
that these prices are derived under the belief system of nO-herding.

17

Proposition 1.4 For the above model, if informed traders have inventories I < 13,

where

_. 29’ <1" _ __§g_ 03-(1-Q)3 _
I3 _ ld(2¢I-1)I¢1’+(1-9)2] + d(2q—1)lq3+(l-<I)rl 4994) + (24’1l[93+(1‘9)3] 1]

there exists a no-herding equilibrium.
Proof : See Appendix 1C.

Intuitively, Proposition 1.4 says that for each informed trader to follow his own
signal in equilibrium, the informed traders’ inventories should be small enough. If
they are large, then informed traders will be tempted to go against their L signals and
trade in the positive direction in the hope of creating this feedback effect, and making
profits on their inventories. But this deviation on their part causes the equilibrium

to break down.

1.5 Multiple Equilibria

Comparing I ‘ (which is the lower bound on inventory in the herding equilibrium)
and 13 (the upper bound on inventory in the no—herding case), one can see that for
the relevant support Of q that is considered i.e. for q E (0.5,1], I3 is always greater
than 1*. While this is not immediately obvious from the expressions for the inventory
bounds, it can be seen from Fig. 1.2 that there is always an intermediate range of

inventory for which both equilibria are possible. Though it is not possible to tell

18

which equilibrium will occur, these multiple equilibria provide the Opportunity to
derive some welfare implications. It turns out that the time t=0 price is higher for
the herding equilibrium than for the no—herding eqUilibrium. Compare the values of
time 0 price in Tables 1.1 and 1.3 of the text (Also, see Fig. 1.5). The reason is
that herding gets the new project accepted with a higher probability, thus increasing
expected fundamental value. However, Since some information is lost in herding,
the probability that the outcome will be good given a pattern of trades is reduced,
which decreases fundamental value. In this region, though, the first effect appears to
dominate.

The region for which multiple equilibria exist while widest for low q (see Fig. 1.2),
increases fastest for the intermediate q s. The reason is that the information loss from
herding, P(0 = H | 31 = H,sg = H,33 = H) — P(0 = H | 31 = H,32 = 11,33 =
H orL), is greatest at the intermediate quality of information. For low q, information
loss from herding is small because the signal is not particularly informative. For high
q, the marginal contribution Of the third signal is low since there is little noise in
the first two Signals. Thus, the slopes of the lower and upper inventory bounds are
steepest at these values.

There are also some results about conditional volatility Of the price paths. It turns
out that on the extreme price paths, the ones with the highest volatility, herding
serves to dampen volatility, thus making price movements less extreme. See Fig.
1.3.1 and Fig. 1.3.2. The reason lies in the way market makers set prices under the
two equilibria. The figures Show that, not only is p0 higher with herding, but so are p1
and p2. However, p3 is higher without herding. p0 is higher because the probability of

19

the increase in investment is higher with herding. p1 and p2 are higher both because
of the higher probability of investment and because that probability approaches one
faster (after two rounds of trading). p3 is lower because the market maker cannot
infer the third trader’s signal under herding since he buys, independent of his Signal.
So he averages over his expected value of firm with an L and an H signal. The price is
lower than under no-herding which is unambiguously conditioned on three H signals.

Since these extreme paths have “bubble-like” characteristics, herding can be ar-
gued to be moderating the harm done by ‘bubbles’. This pattern is more obvious in
Fig. 1.3.2. Under an unconventional definition of bubbles, that they are due to bad
realizations and not necessarily bad expectations, one can see that when the bubble
bursts, the drop in price is less under herding. From Fig. 1.4 one can Observe that
the conditional volatility of the extreme price path is uniformly less for the herding

equilibrium, independent of the quality of information.

1.6 Conclusion

In this chapter, price manipulation and herding are established in a rational market,
without imposing strong restrictions like incomplete markets or restricted participa-
tion. When price paths influence a firm’s investment decisions, just giving informed
investors positive inventories results in herding and price manipulation. In this envi-
ronment, herding by institutions or funds increases fundamental value and is unlikely
to be destabilizing. Also, volatility of extreme price paths is dampened because ratio-

nal price makers cannot perfectly infer investors’ signals from their trades and thus

20

pool over them. Thus investors are hurt less when bad outcomes occur.

While I am able to generate rational herding, it does not translate into momentum
profits. Like in other rational expectation models, prices in this model have no pre—
dictive power over future prices. The market maker conditions both on the feedback
effect and the possibility of herding when establishing prices. Uncertainty over states
does not cause any predictable bias in prices set by market maker. In the current

form, this model does not generate momentum profits.

21

APPENDIX 1

TABLES, FIGURES AND PROOFS FOR CHAPTER 1

APPENDIX 1A

TABLES FOR CHAPTER 1

Table 1.1

Prices under Herding

 

Price at time i=0

m=i+fl%fl
Round 1 of Trading
p12 = (1 - q)

pi = is

pi» = q + 52-25—11

Round 2 of Trading
_ _ 1— 2

P3 = Pia—2 - aim—3%?
Pi Eliza =Pfi,—2 = (1‘ ‘1)
P: E 1732;) = 173,-2 = 173,0 = i
P: E Pile = Pip = ‘1

2 _ _ d 2 —1
p3 = pg»? — q +(l-q) + 5 a +(1—0)
Round 3 of Trading

3 _ 1-q 3
p.,-2 r Firs-E:

3 _ 1— 2
I’m-2 - Fifi

192-2 = (1 - q)
Pit—2 = %
102-2 = q

1_ 2
102,0 = aim”?! 193.2 = (1 ‘ ‘1)

Pin = (1 — ‘1) P23 = i
p10 = % 172,2 = ‘1

2
P3» = ‘1 P12 = Fifi—T)?

3 = g2 _ 92 d. -1
p8,” 02+(1-9l2 p23 — 412+(1-q)2 + 92+(l-0)’

 

24

Table 1.2
Beliefs and Outcomes in the Herding Equilibrium

 

 

 

 

Valuev in State
31 171 III 32 $2 92 33 $3 93 H L
L -1 -2 L -1 -2 H +1 +2 1 0
H +1 0 1 0
L -1 -2 1 0
L -1 0 1 0
L -1 -2 L -1 0 H +1 +2 1 0
H +1 0 1 0
L -1 -2 1 0
L -1 0 1 0
L -1 -2 H +1 0 H +1 +2 1 0
H +1 0 1 0
L -1 -2 1 0
L -1 0 1 0
L -1 -2 H +1 +2 H +1 +2 1 0
H +1 0 1 0
L -1 -2 I 0
L -1 0 1 0
L(H) -1(+1) 0 L -1 -2 H +1 +2 1 0
H +1 0 1 0
L -1 -2 1 0
L -1 0 1 O
L(H) -1(+1) 0 L -1 0 H +1 +2 1 0
H +1 0 1 0
L -1 -2 I 0
L -1 0 1 0
L(H) -1(+1) 0 H +1 0 H +1 +2 1 0
H +1 0 1 0
L -1 -2 1 0
L -1 0 I 0
L(H) -1(+1) 0 H +1 +2 H +1 +2 1 0
H +1 0 1 0
L -1 -2 1 0
L -l 0 1 0

 

 

 

 

 

25

Table 1.2 (Continued)

 

 

 

Valuev in State
81 $1 yl 82 $2 112 33 $3 313 H L
H+1+2L-1 -2H+1 +2 I 0
H +1 0 1 0
L -1 -2 I 0
L -1 0 1 0
H +1 +2 L -1 0 H +1 +2 1 0
H +1 0 1 0
L -1 -2 1 0
L -l 0 1 0
H+1+2H+10H+1+2 1 0
H +1 0 1 0
L -1 -2 1 0
L -1 0 1 0
H +1 +2 H +1 +2 H +1 +2 1+d -d
H +1 0 1 0
L +1 +2 1+d -d
L +1 0 1 0

 

 

 

 

26

 

 

Table 1.3
Prices under No-Herding

 

Price at time t=0
2"“ = :1; + J—J—Ll“
Round 1 of Trading
p312 = (1 - 4)
p31 = 1
p31 = q + d.lq3-4(l-923I

Round 2 of Trading
02 = 1— 2

= P—2 -2- Flat-1W
P32 5 P521) = P3,—2 = (1 " Q)

5 P222 = P3312 = P3,?) =
P32— =—P3,2= -P2,o- = q

3

= 1922231213732 + 2 3273—332

Round 8 of Trading

NIH

P212=ggfiisz 122$=p£lfi93275 102,32=(1-t1)
1233.2= gram-)7): 1233=(1-4) 23,3=%
p2,“.2=(1-q) piti=i PZ,%=4
pr.2=%.- ps=a 222=W

3 _ n3 _ 2 3 __ d.q3- l— 3
Pit-2 — q 103,0 - q5+(1—q)5 172,2 - PHI-q)5 + film-cl;

 

27

Table 1.4
Beliefs and Outcomes in the No—Herding Equilibrium

 

 

 

 

 

 

 

 

 

Valuev in State
81 $1 111 32 1‘2 21/2 33 $3 313 H L
L -1 -2 L -1 -2 H +1 +2 1 0
H +1 0 1 O
L -1 -2 1 0
L -1 0 1 0
L -1 -2 L -1 0 H +1 +2 1 0
H +1 0 1 0
L -1 -2 I 0
L -I 0 1 0
L -1 -2 H +1 0 H +1 +2 1 0
H +1 0 I 0
L -1 -2 I 0
L -1 O 1 0
L -I -2 H +1 +2 H +1 +2 1 0
H +1 0 1 0
L -1 -2 1 0
L -1 0 1 0
L(H) -1(+1) 0 L -1 -2 H +1 +2 1 0
H +1 0 1 0
L -1 -2 1 0
L -1 0 1 0
L(H) -1(+1) 0 L -1 0 H +1 +2 1 0
H +1 0 1 0
L -1 -2 1 0
L -1 0 1 0
L(H) -1(+1) 0 H +1 0 H +1 +2 1 0
H +1 0 I 0
L -1 -2 1 0
L -1 0 1 0
L(H) -1(+1) 0 H +1 +2 H +1 +2 1 0
H +1 0 I 0
L -1 -2 1 0
L -1 0 1 0

 

28

Table 1.4 (Continued)

 

 

 

Valuev in State
81 331 III 32 $2 112 33 333 113 H L
H+1+2L-1 -2H+1 +2 1 0
H +1 0 1 0
L -1 -2 1 0
L -1 0 1 0
H+1+2L-10H+1+21 O
H +1 0 1 0
L -1 -2 1 0
L -1 0 1 0
H+1+2H+10H+1+21 0
H +1 0 1 0
L -1 -2 1 0
L -1 0 1 0
H +1 +2 H +1 +2 H +1 +2 1+d -d
H +1 0 1 0
L -1 -2 1 O
L -1 0 1 O

 

 

 

 

29

 

 

APPENDIX 1B

FIGURES FOR CHAPTER 1

Fig 1.1.1
Minimum inventory bound for herding equilibrium (d=0.1)

16

 

14~

—3
M
I

._.s
O
r

Minimum Inventory I‘
0') 00

A

M
r

 

 

 

 

g 5 0 6 0 7 0 8 0.9 1
Quality of Information q

I " is the minimum bound on inventory for a herding equilibrium to exist. It can be
seen that holding the value of d constant, as q increases and signals become more
informative, smaller levels Of inventories are needed to start herding.

31

Fig 1.1.2
Minimum inventory bound for herding equilibrium (q=0.7 5)

20 I I l 1 f

 

18-

_L ._l .3
M b O)
I I I

1

Minimum Inventory l'
8

 

 

 

C) M b C) (X)
I r I r
J

 

0 0,5 1 1 .5 2 2.5 3
Extemality d

I ‘ is the minimum bound on inventory for a herding equilibrium to exist. It can be
seen that holding the value of q constant, as (1 increases and the potential gains to
herding increase, smaller levels of inventories are needed to start herding.

32

Fig 1.2
Range Of inventory for multiple equilibria (d=0.1)

25 . fl r

 

N

O
r
1*

Hunting Equibtiui
“We
Eat-Ibis

_.x
()1
I

_s
O
1

Bound on Inventory
to

Ito-Herring Emfliluim

 

 

 

0.5 0.6 0.7 0.8 0.9 1
Quality of Information q

I3 is the maximum bound on inventory for a no—herding equilibrium to exist. I ‘ is
the minimum bound on inventory for a herding equilibrium to exist. It can be seen
from the above figure that over the support of q that is relevant i.e. for q E (0.5, I],
there is always an intermediate range of inventory for which multiple equilibria exist.

33

Fig 1.3.1
Price path along the trade sequence {+2,+2,+2} with H
realization (q=0.75, d=0.4)

l4

 

4.!"
I
I”,
d—r

1.3- /

1.1 ~ Herring

 

 

 

 

Fig 1.3.2
Price path along the trade sequence {+2,+2,+2} with L
realization (q=0.75, d=0.4)

14 f f f

 

12~ Mmfludhg ————a/ \

0.8» x
05» "“‘W \

Pnce

04~ \

02* \

-02- +

 

 

 

-04
0

Tune

34

Fig 1.4
Volatility (time-series standard deviation) of prices along the
price path {Poipiipggipizz} (d=0-4)

0.4

 

0.35 -

Price Volatility
O

O to .0

M 01 (D

O
'_..\
01

 

 

 

 

[0,5 0.6 0.7 08 0.9 1
Probability

35

Fig 1.5
Unconditional expected security value : Herding vs
No—Herding (d=1.0)

057 l T

 

.0 .0 .0 .0 .0
01 01 E 01 01
[\J (A) 01 0')
I l T I l

Unconditional Expected Value

C)

01

A
r

 

 

 

 

0. . J L 1
105 0.6 0.7 0.8 0.9 1
Quality of Information q

The unconditional expected security value is the price that would prevail at time t=0
in each equilibrium

36

APPENDIX 1C

PROOFS FOR CHAPTER 1

Prices under Herding : Expressions in Table 1.1

Price Setting: Round 1 of Trading

 

p12=P(9=H|81=L)=(1-4)
P3=%[P(9=H|31=H)+P(9=H|31=L)l=%
p§=P(32=L&0=H|sl=H)+P(32=H&y2=0&0=H|sl=H)
+(l+d)P(32=H&y2=2&33=H&y3=2&0=H|31=H)
—d.P(32=H&y2=2&33=H&y3=2&0=L|sl=H)
+(1+d)P(32=H&yg=2&s3=L&y3=2&0=H|sl=H)
—d.P(32=H&y2=2&33=L&y3=2&0=L|31=H)
+P(32=H&y2=2&33=H&y3=0&0=HIsl=H)
+P(82=H&y2=2&s3=L&y3=0&0=H|sl=H)
=q+§(2q-1)

From the above three prices, it is easy to derive the price at time 0 that would prevail
in this equilibrium.

P°=Pl_2p(y1=-2)+P3P(y1 =0)+P$P(y1=2)
=%(1-q)+%(%)+%[Q+%(2q-1)]

=%+1%(2q—1)

Price Setting: Round 2 of Trading

 

p32,-2=P(0=H|81=L&S2=L):_é.__)_1-q2

q+(1-9)
p32,o=P(0=Hlsi=L)=(1-q)
p323=P(9=H|31=L&32=H)=%

P3,_2=P(9=H|82=L)=(1-Q)

38

173,0: (9=H)=%

pg’2=P(0=H|32=H)=q
p§,_2=P(0=H|31=H&32=L)=%
P§,o=P(9=H|31=H)=q
p33:(1+d)P(33=H&y3=2&0=H|31=H&32=H)
—d.P(s3=H&y3=2&9=L|sl=H&32=H)
+P(s3=H&y3=0&0=H|sl=H&32=H)
+(1+d)P(33=L&y3=2&0=H|51=H&32=H)
—d.P(s3=L&y3=2&0=L|31=H&32=H)

+P(33=L&y3=0&0=H|31=H&32=H)

_ 9’ . + é_29___-1
_ «PHI-«1)2 2<1’+(1-q)2

Price Setting: Round 3 of Trading

 

P2,—2=P‘:2,—2,—2=P(9=H|31=L&S2=L&S3=L)=359—61327!
P3,0=P32,-2,0=P(9=H|31=L&52=L)=q’2gfiq_%i
P3,2=Pi2,—2,2=P(9=Hl31=L&32=L&;93=H)=(1—Q)
Pg,—2=P3-2,o,—2=P(9=H|31=L&33=L)=;2%(;1q;):—)7
Pg,o=Pi2,o,o=P(9=Hl31=L)=(1-Q)
p2’2=p§2’0’2=P(9=H|31=L&s3=H)=%

Pg,—2 =P32,2,—2 =P3,0,—2 = PW = H I 33 = L) = (1‘9)
Pin =P?-2,2,o =Pg,o,o =P(9 = H) =%
pg,2=p32,2’2=p3,0,2=P(0=HI33=H)=q

121-2 = Pia—2 = viii—2 = P(0 = H I s. = H & 33 = L) = %
p10 =pg,2,o =Pg,o,o = P(9 = H I 31 = H): q

39

2

P3,2=P3,2,2=P3,0,2=P(0=Hl31=H&33=H)=;=:(%_TI

2

p2,o=pg’2,o=P(0=H|sl =H&32=H)= m

p2,2=p3,2’2 = (1 +d)P(0= H I 31 = H & 32 = H & 33 = HorL)
-d.P(0=L|sl=H&32=H&s3=HorL)

= «Ti-(“Ear + did-i5

= —f—v + hit—)—

Under the proposed herding equilibrium, 122:2 = 1233,42 is off the equilbrium path.
Here, I use the intuitive criterion (Cho and Kreps (1987)) to interpret this sequence of
events i.e. the market maker assumes that the third informed trader made a mistake
in moving off-equilibrium by not herding, but that such a mistake is more likely if he
had an L signal rather an H signal.

Therefore, p24 = P(0 = H | 31 = H & 32 = H & 33 = L) = q

This completes the derivation of the prices in Table 1.1.

40

Proofs of Propositions 1.2 and 1.3: A herding equilibrium does not exist

unless I > 1*

Under the prices established above, it has to be verified whether the conjectured be-
havior is indeed Optimal for each of the informed traders. Specifically, I verify the
equilibrium behavior for each informed trader assuming equilibrium behavior on part
of the other two.

Informed Trader 1: IT 1’s expected profits are given by

E[7r1 I 31,:51 = +1] = EIv I 31,251 = +1] —% (Id-Pi] and

El?“ I 31:31 = ‘1]: %[p(13+p1—2]_ El” I 51,221 = ‘1]

We need to develop expressions for EIv I 31,2:1 = +1] and EIv I 31,21 = —1]

EIv I 31,31 = +1] = %[P(0 = H I 31)]

+%{P(32 = L & 0 = H I 31)

+P(32=H&y2=0&9=HI31)

+P[(32=H&y2=2&s3=H&y3=0) and0=HI31I
+P[(32=H&y2=2&s3=L&y3=0)and0=HI31]
+(1+d)P[(sg=H&y2=2&s3=H&y3=2) and9=HIsl]
—d.P[(32=H&y2=2&s3=H&313:2) and0=LIsl]
+(1+d)P[(sg=H&y2=2&s3=L&y3=2) and0=HIsl]
—d.P[(32=H&y2=2&s3=L&y3=2) and0=LIsl]}

So, EIv I 31 = H,:1:1 = +1] = q+ g-(2q— 1) and

EI‘UISl =L,$1=+1I=(1—q)

41

Setting d=0 in the above two expressions, we get the following :
EIv I 31 = H,:r.1= —1I=q
EIv I 31 = L,:r1= —1]=(1—q)

Trading Strategy:

 

E[7r1 I 31 = H,:r1= +1] = q+ 3(2q — 1) — inll) +19%]: and

EIW1I31= 11,321 = “1]=%[P3+P1_2]— q

When 31 = H, :61 = +1 is preferred to $1 = —1 if, and only if

«1+ 3(24- 1)- %lé+q+ 2394-1)] > %I%+(1-q)l -q

4:: q > §

which is true under the assumptions of the model. Thus, 2:1 = +1 is optimal when
31 = H.

EI7r1I31= L,$1= +1] = (1 —q) - .1; (VI-Pi]: and

EIW1I31= [1,331 = ‘1] = iIPcli +P1_2] — (1 - CI)

When 31 = L,:r1 = —1 is preferred to $1 = +1 if, and only if
%[%+(1-q)l-(1-q) > (l-q)-%I%+9+%(2q-1)l

©(2q-1)>§(1-24)

which is true Vq > 5 Thus, when 31 = L, the first informed trader makes a
trading loss if he trades x1 = +1 rather than $1 = —1. Also, he cannot gain
on his existing inventory of securities by choosing 2:, = +1 over $1 = —1, as
EIv I31 = L,:r:1= +1] = EIv I 31 = L,:c1= —1] = (1 —q). Thus, 3:1: —1 is

Optimal when 31 = L.

42

Informed 'Iiafier 2:

Here we have to consider all three cases that might have occurred in the first round
of trading.

Case 1 : p1 =p1_2(=:> 31 = L)

IT 2’s expected trading profits are given by

E[7r2 II’1 = P12232132 = +1I= EI'U I P1 = Pl—za 32,372 = +1] - % 2-2,o +1953]
and

EI7r2 I191: 171—21322-752 = ‘1I=%IP2-2,o +P2—2,—2I " EIU I171: P14232232 = ‘1I
Here we know for sure that there cannot be any externality created by prices.
So, EIv Ip =p_ 2,32: H, :52: +1] = EIvIp1=p’_2,s2 = H,a:2 = —1]
=P(0= HI31=L,=32 H)=%,a nd

EIv Ipl =p1_2,s2 = L,:r2 = +1] = EIvIp1= p1_2,s2 = L,:r2 = —1I
=P(0=HI31=L,32=L)= 31%;)?

Trading Strategy:

 

When 32: H, 1.2: +1 is preferred to :1:2=—1 if, and only if
1 1 1 1—
‘§I(1(1‘4)+§I>5I(1 “WI
(1.222
é g> _Q) + q—+(l —q)

which is true Vq > %. Thus, 232 = +1 is Optimal when 32 = H.

NIH

When 32 = L, $2 —1 is preferred to 2:2: +1 if, and only if

1 Il—gI’ (1- a)” --q 1 1

5 I q) + q+(1-q) I_ q +(1-0) > a +(1-0) —5 I5 + (1 - (1)]

which 1s true Vq >2 - .,Thus when 32: L, the IT 2 makes a trading loss if he trades
$2 = +1 rather than $2 = —1. Also, he cannot gain on his existing inventory of

securities by choosing $2 = +1 over 222 = —1, as EIv I p1 = 1912,32 = L,:r2 = +1] is

43

equal to EIv I p1 = 1912,32 = L,$2 = -1]. Thus, $2 = —1 is Optimal when 32 = L.
Ca862:pl=p},(=>sl=HarL)

IT 2’s expected trading profits are given by

E[7r2 IP1= P31321552 = +1] = EIUIP1=P3232132 = +1] —% 0,0 +1732]

and

EIW2IP1= P32321372 = ~11 = étvfip +P3,-2] - EIv IP‘ = 19352.1» = -1]

Here tOO we know for sure that there cannot be any externality created by prices.
SO, EIv Ipl =p(1,,s2 = H,$2 = +1] = EIv Ip1=p(l,,32 = H,$2 = —1]
=P(0=Hls2=H)=q, and

EIv Ip1=p3,s2 = L,$2 = +1] = E[v Ip1 =p3,s2 = L,$2 = —1]
=P(9=HI32=L)=(1—q)

Trading Strategy:

 

When 32 = H, $2 = +1 is preferred to $2 = —1 if, and only if

4- %[%+41 > %[%+(1-Q)l-q

4:) q > %

which is true under the assumptions of the model. Thus, $2 = +1 is Optimal when
32 = H.

When 32 = L,$2 = -1 is preferred to $2 = +1 if, and only if
%[%+(1-q)]-(1-q)>(1-q)-%[%+q]

¢=>q>

NIF—

which is true under the assumptions Of the model. Thus, when 32 = L, the IT 2
makes a trading loss if he trades $2 = +1 rather than $2 = —1. Also, he cannot
gain on his existing inventory Of securities by choosing $2 = +1 over $2 = —1, as

44

EIv I p1 =p3,s2 = L,$2 = +1] = Eh) I p1 = 133,32 = L,$2 = —1]. Thus, $2 = —1 is
Optimal when 32 = L.

Case 3:};1 =p§(=> 31: H)

IT 2’s expected trading profits are given by

EIM IP1=Pi:32,$2 = +1] = EIU I1?1 =Pi132,$2 = +1] " %[P§,o +P§,2I
and

EI7r2 I191 =Pi1321$2 = ‘1I=%U’§,o +P§,_2I — EI” I191 =Pi:32:$2 = ‘1]
E[v Ip1 =p§,s2,$2 = +1] = %[P(0= H I 31 = H & 32)]
+%{(1+d)P(s3=H&y3=2&0=H|31=H&s2)
—d.P(s3=H&y3=2&6=LI31=H&32)
+(1+d)P(33=L&y3=2&0=HI31=H&s2)
—d.P(s3=L&y3=2&0=LI31=H&s2)
+P(s3=H&y3=0&0=HIsl=H&S2)
+P(s3=L&y3=O&9=HIsl=H&32)}

SO,E[v Ip1=p;,s2 = H,$2 = +1] = 55:51:56? + g, 30:1,”

and, EIv |pl =p;,s2=L,z2=+1]=%

Setting d=0 in the above two expressions, we get the following :

2

EI'U Ipl zp;132 =H,.’E2 = —1I: W
EIv “71:14:32 =L,$2= —1I=%

Trading Strategy:

 

When 32 = H, $2 = +1 is preferred to $2 = —1 if, and only if

2 a —1 1 2 d -1 1 1 _ 2
$fififi+Efi%—T’ik+fifififi+%+mmI>2k+d Pfitw

-¢I)
2

3 1
”Ewmw)>4+3

45

which is true Vq > %. Thus, $2 = +1 is Optimal when 32 = H.

When .92 = L, $2 = —1 is preferred to $2 = +1 if, and only if

%Iq+%I'—%> 217-$-IcI"I—17’T(Sllz-T’-I-gt:+(l--1q) I

slams—g] >%%

which is true Vq > % and d > 0. Thus, when 32 = L, the IT 2 makes a trading
loss if he trades $2 = +1 rather than $2 = —1. Also, he cannot gain on his existing

inventory of securities by choosing $2 = +1 over $2 = —1, as E [v I p1 = p21,,s2 =

L,$2 = +1] = EIv I p1 = p§,s2 = L,$2 = —1]. Thus, $2 = —1 is optimal when

82 = L.
Informal Trflgr 3:

Here five cases need to be considered i.e. all distinct prices that could have been

established in the second round of trading. All the possible cases are listed below:
afi=fi5fik2

b- P2 = P: 5 P329 = P1214

c. p2 = p3 E 192.22 = 173,42 = 193,0
d. p2 = 19,21 5 Pan = 173,2
9- P2 = P: 5 133,2

In Cases 1 through 4 above, IT3’s trade does not impact the value as the externality
in value is likely to be created only in Case 5. It can be verified that in all these
cases, 1T3 trades according tO his own signal i.e. he trades $3 = +1 when 33 = H and
$3 = -1 when 33 = L. I take up the more interesting Case 5 next.

46

Case5:p2=p2= p§2(=>sl=H, 32: H)
IT 3’s expected trading profits are given by

EI7T3 IP2 =Pe33325€3= +1]: EIv Ill?2 =P§a~933$3 = +1] '2 3,0 +1022] and
EIWa I172 = P3331553 = "1I=%IP3,0 +P3,_2I - EIv I1?2 = p3,83,$3 = *1]
E[v Ip2 = p2,83,$3 = +1] = %{(1+ d)P(9 = H I 31 = H, 32 = H, 33)
—d.P(0 = L I 31 = H,$2 = H,s3)] +P(0 -— H I 31 = H,$2 = H,s3)}
SO,EI’U Ip2 =pe,s3= H,$3=+1]=W%EF+%I$§II—:ggl
and E[v Ip2 =p§,s3=L, $3: +1]=q+g —(2q——1)

When 1T3 invests $3 = —1, he knows that the externality d will not be created.

3

SO, EI’U I172 =pz,33 = H,$3 = —1]= «75:31:35

EI’U IP2=P3,33=L,$3=—1]=q

Trading Strategy:

 

When 33 = H, $3 = +1 is preferred to $3 = -1 if, and only if

3 2 d 2—1
>—2 (I 2+_2(q )2+2
20+(1-4) 2a +(1-q) 2

 

 

 

 

203 QIqZ- (1 - (1)3]
2q

(13+(1-QI3 3+(1-q)3

which is true Vq > % and d > 0. Thus, $3 = +1 is Optimal when 33 = H. When

33 = L, $3 = +1 is preferred to $3 = -—1 (i.e. IT 3 herds) if, and only if

 

 

1
3_§q"+(1- a) >§(2q 1)Ir12+(1-q)"’—1I

which fails for q > % and d > 0. Thus, when 33 = L, IT 3 makes a trading loss if he

trades $3= +1 rather than $3: —1(i.e. if he herds). The quantum Of this trading

47

loss is:

 

 

2
gIII"’+(ql -<I)2 _qI +§(2q_1)Iq2+(I-q)2 -II
It is clear that under the information and model structure outlined in Sections LA
and LB of the paper (i.e. in the absence Of inventory), herding is not an equilibrium.
However, when we allow informed traders to have inventories in the security (as in
Section II), IT 3 can gain on his inventory by herding since

d
EI" IP2=P3333=L31=3=+11=<1+ 5(20-1) >E[v IP2=p§,sa=L,xs=—1] =3

Vd>0

By herding, 1T3 can gain an extra d(2q—1)/2 per each security in his inventory. Thus,
for herding tO be supported in equilibrium, we need
(I 2

3 q d 1
15(2q— 1) > 5 Iq2+(1-—q)2 —q]+§(2q—1)[qz_+_(1_q)2 —1] (1.1)

 

 

which reduces to (since q > 3 is assumed)

 

 

.= 3 r12 _ 1 _
I>I—d(2r1-1)III"+(1--q)2 qI+Iq2+(1-q)2 1I

Q.E.D

48

Prices under No-Herding : Expressions in Table 1.3

Price Setting: Round 1 Of Trading

 

P312=P(9=H|31=L)=(1-f1)
P31=1/2IP(9=HI31=H)+P(9=HI31=L)I=%
p31=P(s2=L&0=HI31=H)+P(s2=H&y2=0&9=HI31=H)
+P(s2=H&y2=2&s3=L&0=HI31=H)
+P(s2=H&y2=2&s3=H&y3=0&l9=HIsl=H)
+(1+d)P(s2=H&y2=2&s3=H&y3=2&0=HIsl=H)
—d.P(s2=H&y2=2&33=H&y3=2&9=LI31=H)
=q+%[q’-(1-q)3l

From the above three prices, it is easy to derive the price at time 0 that would prevail
in this equilibrium.

p"° =P’1‘2Piy1 = -2)+p3‘P(yi=0)+P31P(3/1 =2)

= 3(1-q)+%(%)+%[q+%(q3-(1-q)3)l

= %+%Iq3—(l-q)3l

Price Setting: Round 2 Of Trading

 

Prices p22 through p22 can be derived exactly as in the herding case. The interacting
case is 192” = 123,22, which is derived below.
p22=p3§=P(s3=L&0=HI31=H&s2=H)
+P(s3=H&y3=0&0=HI31=H&32=H)

+(1+d)P(S3=H&y3=2&0=HI51=H&32=H)

49

-d.P(S3=H&y3=2&0=LI31=H&32=H)
_ ’ 4103-(1-923I
- «Fm—q)5 + 21 +(1-q) 1

9

Price Setting: Round 3 of Trading

 

Prices 192,34 through 192:2 can be derived exactly like in the herding case. The inter-

esting cases are p2}, and p23, , which are derived below.

_91__
02+(1-q)2

1):},=p3,%’0=P(0=HIsl=H&s2=H&s3=HorL)=
=p"322= (1+d)P(0=HI31=H&s2=H&s3=H)
—d.P(9=LIsl=H&32=H&s3=H)
=73? + d [aid-031

This completes the derivation Of the prices in Table 1.3.

Proof of Proposition 1.4: A no-herding equilibrium exists as long as I < I3

Under the prices established above, we have to verify whether the conjectured be-
havior is indeed Optimal for each Of the informed traders. Specifically, we verify the
equilibrium behavior for each informed trader assuming equilibrium behavior on part
Of the other two.

Informed Trader 1:

IT 1’s expected profits are given by

EI7r1 I81,$1= +1] = E[v I sl,$1 = +1] —% 31 +1931] and

E[1r1 I 31,$1 = —1I= éIp31+p212 — EIv I 31,$1 = —1]

We need tO develop expressions for EIv I sl,$1 = +1] and EIv I 31,$1 = —1]

EIv I31,$1= +1] = %IP(9 = H I 31)]

+%{P(s2 = L & 0 = H I 31)

+P(s2=H&y2=0&6=HIsl)

+P[(s2=H&y2=2&33=H&y3=0) and0=HIsl]
+(1+d)P[(s2=H&y2=2&s3=H&y3=2) and0=HIsl]
-d.P[(s2=H&y2=2&s3=H&y3=2)and9=LIsl]}

SO, EIv I 31 = H,$1= +1] = q+ qu3 — (1 — q)3] and

Eiv l81= m. = +11=(1— q) + £131.12 — 2,3 — 0

Setting d=0 in the above two expressions, we get the following :

EIvI31=H,$1= —1I=q

EIvI31=L1$1=—'1I=(1_Q)

51

Trading Strategy:

 

E[7r1 I31=H:$1=+1I=Q+§IQ3—(1-€I)3I— 0+P21I and

EIF1I31= H3331: —1I=i 31+P'112I‘q

When 31: H,$1= +1 is preferred to $1 = —1 if, and only if
q+%'[rf-(1-q)3]-%Ié+q+%’[03—(1-q)3lI> -%+(1—q)]—q

4:) q > %

which is true under the assumptions of the model. Thus, $1 = +1 is Optimal when
31 = H.

EIW1|81=Lz1=+1I=(1-¢1)+§ -I3q2- 203 -q]- 31+P311,and

EIW1I81= L,$1= ‘1I=% 31+P'112-(1-Q)

When 31 = L,$1 = —1 is preferred to $1 = +1 if, and only if
%I%+(1—q)I-(1—q)>(1—q)+%l302—2q3-q]—[+q+( 1-q)3)]
41>(2q—1)>§(6q2 —4q3 — 4q+ 1)

which is true Vq > % and d > 0. Thus, when 31 = L, trading $1 = —1 instead Of
trading $1 = +1 yields IT 1 an expected profit Of

(20— 1) — 5(602—403 —4q+ 1)

However, trading $1 = +1 rather than $1 = —1 increments the expected value Of
each unit Of inventory by f,‘-[3q2 — 2q3 — q].(This is the difference between E [1) I 31 =
L,$1 = +1] and EIv I 31 = L,$1 = —1]). Thus, we require the inventory Of the first
informed trader to be such that his potential expected value addition to inventory
from deviating from the equilibrium behavior (and trading $1 = +1) is outweighed

by his trading profits from following the equilibrium strategy. i.e. we need that:

52

d d
1§I3q2 - 203 - r1] < (20 - 1) - -,;(6<r2 - 403 - 4q+ 1)

®I<I = 8(2q-1) _(6q2-4q3—4q+1)
1" d(3q"’-2r13-<1) (302-203-0)

 

 

Informed Trader 2:

Here we have tO consider all three cases that might have occurred in the first round
of trading. Cases 1 and 2 where p"1 = 10212 and p"1 = p31 can be dealt with exactly
as in the herding case. I deal with the more interesting case 3 here.

Case 3 : p"1 = p31(=> 31: H)

IT 2’s expected trading profits are given by

E[7r2Ip"1=p31,s2,$2 = +1] = EIv Ip"1= p31,s2,$2 = +1] —% 3’?) +113;

and

EIW2 l P'” = 3931,3332 = -1l = % 52% + 1033.2 - EIv l P'” = 1231,8242 = -1]
EIv I10"1 =p'2‘1,s2,$2 = +1] = %[P(6 = H I 31 = H & 32)]
+%{P(s3=L&9=HIsl=H&32)
+P(s3=H&y3=0&0=HIsl=H&32)
+(1+d)P(33=H&y3=2&0=HI31=H&32)

—d.P(s3=H&y3=2&9=LI31=H&32)}

1 _ 1 _ _ _ g? ales-Il- 23]
301EI'U I?” -P3 :32 " H, 32 - +1] — q +(1-0) + Z 9 +(1'Z)

and, Eh) lpnl =p31,32 = L,$2 = +1] : %+ g(2q — 1)

Setting d=0 in the above two expressions, we get the following :

2

151le"1 =P3‘,82 = H,$2 = ‘1]: 1:3,?

9

EIv Ip"1=p31,32 = L,$2 = —1I=%

53

Trading Strategy:

 

When 32 = H, $2 = +1 is preferred to $2 = —1 if, and only if

 

 

 

 

 

 

q2 éIq3—(1—q)3l_1 (1+ 02 +£[qz-(1-q)3]
02+(1-q)2 4112+(1-q)2 2 (12+(1-0)2 2421-0-11)”
> _ I +1] — ‘12
2 q 2 (12+ (1 -<1)2
4:? ‘12 > +1
2 (12+ (1 —q)2 q 4
which is true ‘v’q >3- Thus, $2: +1 is Optimal when 32: H.
When 32 = L,$2 = —1 is preferred to $2 = +1 if, and only if
1 d <12 9M" - (1 —Q)3I

 

 

1 1 1 1
_ ___ _ _2_1__
2Iq+2I 2>2+8( ‘1 ) 2IQ+02+(1-q)2+2 (12+(1-q)2

 

 

 

 

<12 3 d 2[q3 - (1 - (1)31)
¢¢ — — < — 2 — 1 —
Iq+2[42+(1-0)2I 4 8 (q ) (PHI-(1)2
which is true Vq > 3 and d > 0.
However, trading $2: +1 rather than $2: —1 increments the expected value Of each

unit Of inventory by §(2q -— 1). (This is the difference between E [v I p"1 = 1931,32 =
L,$2 = +1] and EIv I p"1 = 1031,32 = L, $2 = —1]). Thus, we require the inventory
Of the second informed trader to be such that his potential expected value addition
tO inventory from deviating from the equilibrium behavior (and trading $2: +1) is

outweighed by his trading profits from following the equilibrium strategy i.e. we need

 

that :

 

 

 

 

 

d 3 q2 d 2[03 - (1 - (1)31)

I§(2‘I‘1)<(‘I‘ZI‘L2102+(1-0)2]—g (23—1)— 42:10—22]

_ 8,4; 4.,2 2113—0—01) _
““12— d(2q_1)+d(2q—1)[02+(1-q)2] (24-1)I92+(1“I)21 II

Informed Trafder 3:
Here, as with herding, five cases need tO be considered i.e. all distinct prices that

could have been established in the second round of trading. All the possible cases are

listed below:
a- P"? = P22 5 17223—2
b- 11"? = 1032 s P3230 = 193312

112.. n2: n2 _ n2 _ 112
C- P —Pc — P-2,2 —P2,—2 —P0,0

CD

- in"? = P22 3 123,22

Cases 1 through 4 above are identical tO those in the herding equilibrium. In all
these cases, IT 3’s trade does not impact the value as the externality in value can be
created only in Case 5. It can be verified that in all these cases, 1T3 trades according
to his own signal i.e. he trades $3 = +1 when 33 = H and $3 = —1 when 33 = L. I

take up the more interesting Case 5 next.

01
O!

Case 5 : p"2 =pg2 =p3§(=> 31: H, 32 = H)

IT 3’s expected trading profits are given by

E[7r3 I10"2 =p22,33,$3 = +1] = EIv Ip"2 = p22,s3,$3 = +1] --;— 2}, +p252] and
EI713 I19"2 =PZ’2133123 = —1I=% 2,?) +1932] — EIU I1?"2 =PZ‘2133123 = ’1]
EIv Ip"2 =p22,33,$3 = +1] = %P(6 = H I31 2 H, 32 = H, 33)

+%{(1 + d)P(9 = H I 31 = H, 32 = H, 83)

—d.P(0 = L I 31 = H, 32 = H, 33)}

3_1_ 3
301 W I?"2 = 1232,33 = H,$3 = +1] = 55:33—71 + w: +0.31

1-0
and
Eiv no“? =p22,s3 = 1,33 = +11: q+ 1(21 — 1)
Setting d=0 in the above expressions, we get

EIv Ip"2 =p22,s3 = H,$3 = —1]= qTJrIgf—w)?’

EI'v Ip"2 =p22,s3 = L,$3 = —1]= q

Trading Strategy:

 

When 33 = H, $3 = +1 is preferred to $3 = —1 if, and only if

 

 

 

 

 

q3 9(03-(1-q)3l_1[ a” + «13 +qu‘"-(1-q)3]
03+(1-0)3 21134-(1-0)3 2 [(12+(1-q)2] (13+(1--q)3 q3+(1-q)3
1 q2 <13
>2 Q+02+(1-q)2I—q3+(1-0)3

 

3 q3 (12 q
‘2 5 Iq3+<1—q)3I > Iq2+(1-q)2I +5

 

 

which is true Vq > % and d > 0. Thus, $3 = +1 is Optimal when 33 = H.

56

When 33 = L, :53 = —1 is preferred to $3 = +1 if, and only if

 

 

 

 

 

1 a” d 1 q” (13 db“ - (1 - (1)3]
§IQ+02+(1-q)2I-q>q+§(2q-1)—§[42+(1-q)2+q3+(1-c1)3 (13+(1-q)3
q2 (13 _§g g _ _gi_[r13-(1-q)3l
Iq2+(1—q)2+2[q3+(1—q)31 2 >2”" 1) 2q3+(1—q)3

which is true for q > % and d > 0. Therefore, trading $3 = —1 instead of 2:3 = +1

yields IT 3 a profit of:

 

 

 

2 3 3 d d 3_ 1_ 3

2 4 2+ q 3__<1___(2q_1)+_[q ( (1)3]

q+(1-r1) 2[q3+(1-q)l 2 2 243+(1-q)
However, trading $3 = +1 rather than $3 = -1 increments the expected value of

each unit of inventory by §(2q — 1). Thus, we require the inventory of IT 3 to be
such that his potential expected value addition to inventory from deviating from the
equilibrium behavior (and trading 93;; = +1) is outweighed by his trading profit from
following the equilibrium strategy i.e. we need that:

d <12 43 3Q d 9M" - (1 - (1)3]

Ii'(Zq-lk«12+(1-<1)2+2[q3+(1-q)3l—3—§(2q_1)+2 (13+(1-q)3

 

 

 

[03-0-03] _ 1]

= 292 ‘13 _ 3‘1
4:) I < 13 _ d(2q—1)[q7+(l—q)2] + d(2q_1)Iq3+(l—q)3] d(2q-l) + (29-1)[93+(1—q)3]

 

 

Since informed traders have been assumed to be symmetric (with identical invento-
ries), a sufficient condition for a no—herding equilibrium to exist is that I be smaller
than min(11,12,13). It can be verified that 13 is the smallest of II,I2 and I3. This
intuitively makes sense, as the third informed trader, knowing about the two H sig-
nals in the two earlier rounds of trading has the strongest temptation to herd, even
though his own signal is an L signal. Thus, the constraint on his inventory is much

more binding than those on the earlier two traders. It can be seen from Fig. A.l

57

that I 1 — I3 and 12 — 13 are both positive over the support of q that we consider in
this model. Another interesting observation can be made from perusal of Fig. A.1
regarding the shape of 11 — 13, which is sloping upward as q increases. The reason
is that the first informed trader is increasingly more reluctant to start herding by

trading against his own signal, as his signal becomes more informative.

Q.E.D.

58

Fig A.1
Comparison of inventory bounds for no-herding

 

 

 

l1-l3

I243

\

L

 

 

5 0.6 o 7 0T8 _ 0 9 1

Quality of Information q

59

BIBLIOGRAPHY

REFERENCES FOR CHAPTER 1

BIBLIOGRAPHY

Allen, Franklin, and Douglas Gale, 1992, Stock-price manipulation, Review of Finan-
cial Studies 5, 503—529.

Allen, Franklin, and Gary Gorton, 1993, Churning bubbles, Review of Economic
Studies 60, 813-836.

Avery, Christopher, and Peter Zemsky, 1998, Multidimensional uncertainty and herd
behavior in financial markets, American Economic Review 88, 724—748.

Barberis, Nicholas, Andrei Shleifer, and Robert Vishny, 1998, A model of investor
sentiment, Journal of Financial Economics 49, 307—343.

Bikhchandani, Sushil, David Hirshleifer, and Ivo Welch, 1992, A theory of fads, fash-
ions, customs and cultural change as informational cascades, Journal of Political
Economy 100, 992—1026.

Cho, In-Koo, and David M. Kreps, 1987, Signaling games and stable equilibria, Quar-
terly Journal of Economics 102, 179—221.

Daniel, Kent, David Hirshleifer, and Avanidhar Subrahmanyam, 1998, Investor psy-
chology and security market under-and overreaction, Journal of Finance 61, 1839—
1886.

Falkenstein, Eric G., 1996, Preferences for stock characteristics as revealed by mutual
fund portfolio holdings, Journal of Finance 51, 111-135.

Friend, Irwin, Marshall Blume, and Jean Crockett, 1970, Mutual Funds and other
institutional investors (McGraw-Hill: New York, NY).

Glosten, Lawrence, and Paul Milgrom, 1985, Bid, ask and transaction prices in a
specialist market with heterogeneously informed traders, Journal of Financial Eco-
nomics 14, 71—100.

Grinblatt, Mark, Sheridan Titman, and Russ Wermers, 1995, Momentum investment
strategies, portfolio performance and herding : A study of mutual fund behavior,
American Economic Review 85, 1088—1105.

Grossman, Sanford, and Joseph Stiglitz, 1980, On the impossibility of informationally
efficient markets, American Economic Review 71, 393—408.

Harrison, Michael, and David M. Kreps, 1978, Speculative behavior in a stockrnarket
with heterogeneous expectations, Quarterly Journal of Economics 92, 323—336.

61

Hirshleifer, David, Avanidhar Subrahmanyam, and Sheridan Titman, 1994, Security
analysis and trading patterns when some investors receive information before oth-
ers, Journal of Finance 49, 1665—1698.

Hong, Harrison, and Jeremy C. Stein, 1999, A unified theory of underreaction, mo-
mentum trading and overreaction in asset markets, Journal of Finance 54, 2143—-
2184.

Khanna, Naveen, 1998, Optimal contracting with moral hazard and cascading, Review
of Financial Studies 11, 559—596.

-— , Steve L. Slezak, and Michael Bradley, 1994, Insider trading, outside search,
and resource allocation : why firms and society may disagree on insider trading
restrictions, Review of Financial Studies 7, 575—608.

Kumar, Praveen, and Duane Seppi, 1992, Futures manipulation with ”cash settle
ment”, Journal of Finance 47, 1485—1502.

Kyle, Albert S., 1985, Continuous auctions and insider trading, Econometrica 53,
1315—1336.

Lakonishok, Josef, Andrei Shleifer, and Robert Vishny, 1992b, The impact of institu-
tional trading on stock prices, Journal of Financial Economics 32, 23—43.

Leland, Hayne, 1992, Insider trading: should it be prohibited?, Journal of Political
Economy 100, 859—887.

Nofsinger, John R., and Richard W. Sias, 1999, Herding and feedback trading by
institutional and individual investors, Journal of Finance 54, 2263-2295.

Scharfstein, David S., and Jeremy C. Stein, 1990, Herd behavior and investment,
American Economic Review 80, 465—479.

Shiller, Robert, 1981, Do stock prices move too much to be justified by subsequent
changes in dividends?, American Economic Review 71, 421—436.

Slezak, Steve L., and Naveen Khanna, 1999, The effect of organizational form on
information aggregation and project choice : The problem of informational cascades
in teams, forthcoming Journal of Economics, Management and Strategy.

Subrahmanyam, Avanidhar, and Sheridan Titman, 1999, Real effects of financial
market trading : market crises and the going public process, UCLA Working paper.

Tirole, Jean, 1982, On the possibility of speculation under rational expectations,
Econometrica 50, 1163—1181.

Wermers, Russ, 1999, Mutual fund herding and the impact on stock prices, Journal
of Finance 54, 581—622.

62

_ ‘ v.

Chapter 2

SMART INVESTMENTS BY SMART MONEY:

EVIDENCE FROM SEASONED EQUITY OFFERINGS

2.1 Introduction

Recent empirical studies have documented the underperformance in stock market re-
turns of firms conducting Seasoned Equity Offerings (SEOs).l Subsequent research
has shown that the poor post-issue stock market performance of firms issuing seasoned
equity (SEO firms) is accompanied by a decline in several indicators of Operating per-
formance over the medium to long term.2 These empirical results raise the question
of how institutional portfolio managers react to SEOs. Surely “smart” portfolio man-
agers would know that, on the average, SEOs are bad news and adjust their portfolios
accordingly. In other words, we would expect institutional investors to reduce their
investments in the average SEO firm. Of course, not all SEOs are bad news; about
40% of my sample of SEO firms outperformed their matching portfolios based on
size, book-to—market and momentum characteristics. If institutional portfolio man-

agers were better informed or had better selectivity, we would expect them to be able

 

lSee, for example, Loughran and Ritter (1995) and Spiess and Affleck-Graves

( 1995) for evidence of this phenomenon in the United States.
2See Loughran and Ritter (1997) and McLaughlin, Safieddine, and Vasudevan
(1996).

63

to separate potentially outperforming SEO firms from those that are expected to do
worse in the aftermarket. If this were true, we would expect SEO firms in which in—
stitutional holdings increased around the time of the offer to significantly outperform
those in which institutional investors decreased their holdings around the offer date.

In this study, I examine institutional investment behavior towards SEOs to ex-
amine the value added by active portfolio management. In a sample of 2912 SEOs
during the period 1980—1994, I study the investment behavior of institutional in-
vestors towards SEOs in the period surrounding the offer. I then contrast this with
their investment in non-issuers with identical characteristics at the same time. I find
strong evidence that institutional investors, both mutual fund and non-mutual fund,
significantly increase their investments in SEO firms compared to those in a sample
of non-issuing firms with identical characteristics, with non-mutual fund institutions
increasing their investments to a greater extent.

I also examine the relationship between changes in institutional investment, and
post-issue stock market performance of SEO firms relative to their matching portfo-
lios based on size, book-to—market and momentum. I find that SEO firms with the
greatest increase in institutional investment outperformed their matching portfolios
the most over one year and two year horizons after the issue. However, I find no
such pattern among the sample of matching non-issuers. Taken together, the above
results seem to suggest that institutional investors have stock selection ability that
enable them to better identify potential outperforrners from among SEO firms. In
order to investigate whether this is indeed an information effect, I use sell-side ana-
lysts’ forecasts of earnings revisions from the Institutional Brokers Estimate System

64

(I/B/E/S) database as a control variable for revelation and assimilation of public
information. I find that, for SEO firms, the ratio of the number of earnings forecast
upgrades to forecast downgrades at the end of the first and second calendar quarters
following the issue has a monotonic relationship with the increase in investment by
institutional investors i.e. firms in which institutions increased their investment the
most around the issue had the greatest ratio of upgrades to downgrades at the end
of each of the two quarters following the issue. No such trends are apparent for the
sample of matching non-issuers.

This is not, in and of itself, irrefutable evidence that institutional investors have
superior information or stock—selection ability. One might argue that sell-side an-
alysts upgrade earnings forecasts because institutional holdings in these firms have
increased, in the following quarters. However, if this were true, a similar pattern
would be found in the sample of non-issuing firms too. Due to the absence of any
such discernible trend in non-issuing firms, I interpret these results as evidence that
institutional investors are able to ex-ante identify above average SEO firms at the
time of equity issuance, and increase their holdings in these potential outperformers.

The organization of the remainder of this article is as follows. In Section 2.2, I
summarize prior research in this area and motivate the hypotheses underlying this
study. Section 2.3 describes the data used for analysis and my algorithm for con-
struction of the matching sample. Section 2.4 describes the results of my analysis. In

Section 2.5, I offer a summary and conclude the chapter.

2.2 Prior Research and Motivation

2.2.1 Seasoned Equity Offerings

Several empirical studies have examined the stock market underperformance of sea-
soned equity issuers. Loughran and Ritter (1995) in a study of SEOs during the period
1970-1990, document that the average raw return for issuing firms is only 7 percent
per year during the five years after the offering, compared to 15 percent per year for
non-issuing firms of the same market capitalization. Spiess and Affleck-Graves (1995),
in their study of SEOs, find that a strategy of investing in SEO firms at the close
of trading on the day of the offer and holding them for three years would have left
the investor with only 85.4 cents relative to each dollar from investment in industry-
and—size-matched firms that did not publicly issue equity. They also document that
holding this investment for five years would have further eroded the investment, leav-
ing the investor with even less, only 78.6 cents relative to each dollar from investment
in similar non-issuing firms. More recent research in this area by Brav, Geczy, and
Gompers (1995) documents that underperformance in SEO firms’ stocks is concen-
trated only in small firms and those with low book—to—market ratios, indicating that
any investigation into SEO firm performance must take these characteristics into
consideration.

Other, related work has shown that the poor post-issue stock market performance
of SEO firms is accompanied by a decline in several indicators of operating perfor-
mance. McLaughlin, Safieddine, and Vasudevan (1996), using a sample of 1296 SEO

firms during the 1980-91 period, find that firms conducting SEOs experience a sharp,

66

statistically significant decrease in profitability following the SEO in both industry-
adjusted and unadjusted comparisons. Loughran and Ritter (1997 ) document median
Operating performance patterns consistent with those of the results of McLaughlin,
Safieddine, and Vasudevan (1996).

This empirical evidence suggests a course of action for rational portfolio managers
in their behavior towards the average SEO. Indeed, portfolio managers would do well

to heed the warning of Loughran and Ritter (1995):

Investing in firms issuing stock is hazardous to your wealth. Firms issuing
stock during 1970 to 1990, whether an IPO or an SEO, have been poor
long-run investments for investors...The magnitude of underperformance
is large: it implies that 44 percent more money would need to be invested
in the issuers than in the non-issuers to be left with the same wealth five
years later.

I thus begin with the conjecture that institutional portfolio managers who know
that the average SEO is bad news, will sell or take short positions in the stock of such

a firm around the time of the Offer.

2.2.2 Institutional Investment: Growth

The issue of institutional investor behavior towards SEOs assumes greater significance
when we consider the enormous impact that institutional investment has on the US.
capital markets, especially in equities. At the end of 1997, mutual funds in the US.
had combined assets of $4.468 trillion, making them second only to commercial banks
(total assets: $5.179 trillion) in asset size. Other major financial assets were private
pension funds with total assets of $3.578 trillion, life insurance companies with total

assets of $2.581 trillion and finally, state and local government pension plans with an

67

"v‘

asset size of $ 2.1 trillion.3 Clearly, institutional assets represent a large prOportion
of US. capital market asset holdings.

The composition of institutional holdings has also undergone a dramatic change
during the 1990s. More than ever, equity instruments constitute a higher proportion
of institutional assets. For example, at the end of 1990, stock funds comprised 23% of
all mutual fund assets. By the end of 1997, stock funds accounted for $2.368 trillion
or about 53% of all mutual fund assets. During the same period the prOportion of
bond funds fell from 27% of all mutual fund assets to 16%. These figures outline
the general trend of higher ownership and greater participation of institutions in the

equity markets.4

2.2.3 Institutional Investment: Performance

In spite of the obvious growth in funds managed by institutional portfolio managers,
the evidence on value added by active portfolio management remains a subject of
debate. If one were to interpret the market efficiency hypothesis in its purest form,
it would follow that security prices fully reflect all available information (see Fama
(1991)), which in turn would mean that security analysis is an uncompensated ex-
ercise. Under this interpretation, active institutional investors who trade based on
research cannot hOpe to consistently earn returns above the market average.

Other models of informational efficiency imply a more positive role for active

 

3Source: Investment Company Institute.

‘Schwartz and Shapiro (1992) report that institutional investors held about 50%
of the equities listed on major US. stock exchanges and generated over 70% of the
daily trading volume in 1989.

68

portfolio management. The “noisy rational expectations” model of Grossman and
Stiglitz (1980), for example, predicts that investors who engage in costly information
production are compensated when security prices adjust to reflect the information.
Then, institutional portfolio managers who have superior information or stock selec-
tion ability may be able to capture the rents from their ability in the form of higher
fees and fund expenses. Thus, one can examine the value-adding nature of insti-
tutional portfolio managers by measuring gross returns of institutional investment
that do not have transaction costs, fees, and other expenses subtracted from them.
Empirical studies following such interpretations have documented evidence of some
value added by active portfolio management. For instance, Grinblatt and Titman
(1989) using a sample of mutual fund holdings during the period 1975-1984 provide
empirical evidence that growth and aggressive growth mutual funds exhibit higher
gross returns, and interpret these results as being at least partly generated by active

portfolio management strategies.

2.2.4 Institutional Investment: Behavior

More recent work in the area of mutual funds examines the behavior rather than
the performance of institutional investment. For instance, Gibson, Safieddine, and
Titman (1998), using all NYSE, Amex and Nasdaq stocks during the 1980-94 pe-
riod, examine the extent of superior information that institutional investors possess.
They find that, for all but small capitalization stocks, stocks experiencing the great-

est increase in institutional ownership outperform those that experience the greatest

69

decrease by an average of 7.2% per quarter over 1980-94. Further, to distinguish
between naive momentum strategies that could have caused this strong correlation
between increases in institutional investment and stock returns, and trades based on
active information production, the authors utilize sell-side analyst earnings forecasts
as a control for revelation of new information. They find that institutions trade ahead
of sell-side analysts over the entire sample period, with the effect growing stronger
towards the latter years. This is consistent with institutions trading on privately pro-
duced information. Such research lends credence to the argument that active portfolio
managers add value.

The behavior of institutions other than mutual funds has also been studied, al-
beit to a lesser extent. For instance, Lakonishok, Shleifer, and Vishny (1992a) and
Lakonishok, Shleifer, and Vishny (1992b) study the performance and behavior of large
institutional investors. In particular, Lakonishok, Shleifer, and Vishny (1992a) study
a sample of 769 all-equity pension funds over the period 1983 to 1989, and conclude
that active management by the portfolio managers of these funds did not yield any
excess returns above a simple buy-and -hold strategy.

In this study, I examine the value-adding nature of active money management,
using the well-known phenomenon of negative post-issue drift in stock prices as a
framework. The analysis in this study is related to work carried out by Field (1995),
who examines a sample of 2,973 conducting Initial Public Offerings (IPOs) in the
US. during 1979-1989. She studies the relationship between institutional ownership
changes and the long-run performance of IPO firms, and documents that firms with

larger institutional shareholdings within one quarter of the IPO date tend to perform

70

better over a three-year period than those with little or no institutional shareholdings
at the end of the first quarter. Further, in her research, this effect persists even after
controlling for factors such as size and age of the firm, that have been found to

influence IPO firm returns.

2.3 Data and Methodology

2.3.1 Seasoned Equity Offerings

The final sample of 2912 SEOs conducted over the period 1980-1994 used in this
study was obtained as follows. I start with an original sample of 3848 primary SEOs
spanning the period 1980-1994, obtained from the Securities Data Corporation (SDC).
I choose 1980 as the starting point for the sample, as the institutional holdings data
begins in 1979; so I have holdings data for at least one quarter before the earliest
SEO date within the sample. Of the original sample, I lost 255 observations due to
missing data in the Center for Research into Security Prices (CRSP) database, and
a further 673 due to missing characteristic-based ranks 5, which will be described
as part of my matching methodology. As will soon be clear, this rank data is vital
to my matching procedure. My matching algorithm, to be described shortly, does

not find matches for 8 sample firms, which are eliminated leaving the final sample of

 

5I am grateful to Kent Daniel for providing this database of characteristic based
rankings. Details of criteria for inclusion in the rankings database are provided in
Daniel, Grinblatt, Titman, and Wermers (1997). They require, among other things,
that COMPUSTAT data be available for at least two years prior to the inclusion of
a firm in their database. Since these data are not available for many firms in several
years, I find that 673 firms in my sample have missing ranks in the database.

71

2912 SEOs. I present in Table 2.1 summary details of the SEO sample. A glance at
the sample will confirm that trends in overall seasoned equity issuance in the US,

familiar to researchers in this area, are mirrored in my sample.6

2.3.2 Institutional Holdings

Institutional investor holdings data for 60 quarters from the first quarter of 1980 to
the fourth quarter of 1994 are obtained from the Spectrum database compiled by CDA
Investment Technologies. Spectrum contains quarterly information on institutional
ownership of NYSE, Amex, and NASDAQ listed stocks extracted from 13(f) reports
filed with the SEC. The 1975 revision to the Securities Exchange Acts requires all
institutional investment managers with $100 million or more in exchange-traded or
NASDAQ-quoted equity securities under management to file 13(f) reports within 45
days of the end of each calendar quarter. Institutions are required to report all equity
positions greater than either 10,000 shares or $200,000 in market value.

For each firm and each quarter, Spectrum reports each institution’s holdings.
Spectrum also classifies each institution as one of five “types” according to Stan-
dard and Poor’s definition of the institution’s primary line of business. Type 1 is
made up of large bank holding companies. Type 2 comprises insurance companies.
Type 3, investment companies and their advisors, consists of mutual funds. Type

4, independent investment advisors, includes investment banks or other financial

 

6For classification of “hot” and “cold” periods in seasoned equity markets, please
refer to Bayless and Chaplinsky (1996), and compare the observations therein to
Table 2.1 of this chapter.

72

institutions, but explicitly excludes commercial banks whose primary business is mu-
tual fund management. Type 5 encompasses foundations, ESOPs, and individuals
who invest others’ money who are not otherwise categorized.

For this study, I have used Type 3 to represent mutual funds, the sum of Types
2, 4 and 5 for non-mutual fund institutions and the sum of all Types 1 through 5 to

represent total institutions.

2.3.3 Matching Firms

My aim is to match each SEO firm observation with a non-issuing firm that has
similar book-to-market, size and momentum at the time of the offer. I choose these
three characteristics since empirical financial economists have identified them as best
explaining the cross-sectional variation in stock returns. Matching or performance
measurement with characteristic-based benchmarks is usually accomplished using
the Daniel, Grinblatt, Titman and Wermers (hereafter, DGTW) characteristic-sorted
benchmark portfolios database. This database provides yearly rankings (updated ev-
ery July) for each firm listed on the NYSE, AMEX and Nasdaq based on the above
three characteristics.7 These rankings are from a yearly triple sort on the universe
of firms, on each of the three characteristics. In this study, however, I cannot di-
rectly use these yearly rankings to match non-issuers to issuers. The reason can be

illustrated by a simple example. Consider a sample SEO firm with issue date in May

 

7For details of the exact definitions of Book-to-Market, Size and Momentum used in
the characteristic rankings database, please refer to the appendix in Daniel, Grinblatt,
Titman, and Wermers (1997).

73

n

1991. Matching using the DGTW database will result in a matching firm with similar
size, book-to-market and momentum as at the end of July 1990, which is ten months
prior to the event date. This use of “stale” (ten-month old, in this example) rankings
for matching leads to incorrect matching on two counts. For one, the most recent
momentum is not accounted for during matching. Second, due to the fact that SEO
firms typically have a higher stock price run-up immediately prior to the issue, they
will tend to be matched with smaller market capitalization firms.

In order that I find matching firms similar to SEO firms in the sample without
encountering these problems, I implement the following procedure. I replicate the
DGTW methodology of portfolio formation in all respects except that the frequency
of sorting is quarterly in my case. Benchmarking based on quarterly portfolio rankings
ensures that rankings are not “stale” and subject to the problems discussed above. I
sort the universe of firms listed on the NYSE, Amex and N asdaq (with available data
on CRSP) every quarter beginning March 1979 to December 1994 based on market
equity (size) and six-month momentum. At each date, the universe of stocks is first
sorted into quintiles based on each firm’s market equity just prior to the formation
date. Following DGTW, the break points for this sort are based on NYSE firms
only. Then the firms in each size quintile are further sorted into quintiles based on
the preceding six-month return, giving us a total of 25 portfolios. The preceding
six-month return is calculated through the end of the month before quarter end. For
instance, every second quarter sort is based on six-month returns ending May, while

every third quarter sort is based on corresponding six-month returns ending August,

74

and so on.8 This is in order to avoid problems associated with market micro-structure
effects (see Jegadeesh (1990). For sorting on six-month momentum, I require that
each firm have at least three monthly returns (out of the preceding six) available on
CRSP. Finally, the firms in each of the above 25 size/six—month momentum portfolios
are sorted based on their book-to-market rankings from the DGTW database. In
other words, I do not specifically sort on B / M ratios of individual firms, but retain
the yearly rankings from the DGTW database. For the limited purpose of matching
firms, I believe that this is adequate, as book-to-market rankings are not as variable
as say, momentum rankings. This procedure yields 125 size, book-to-market and
six-month momentum sorted portfolios in each quarter.

For each SEO sample firm, I look up its characteristic rankings in the issue quarter.
Next, I identify a matching firm i.e. a firm with identical characteristics in that
quarter. There are two restrictions I impose on the matching firm: first, it should
not have been a seasoned equity issuer in the five years preceding the SEO sample
firm’s issue date — this is to make sure I draw a clear separation between issuers and
non-issuers during the sample period; second, it should not have been selected as a
matching firm for any other SEO sample firm in any year. This restriction is to make
sure that I avoid the same matching firm for more than one SEO sample firm. This
ensures that my matching non-issuer sample is large enough to facilitate meaningful

statistical inference.

 

8In unreported analysis, I sort the firms in each size quintile based on the preceding
twelve-month return. This leads to a smaller sample size, since I impose more strin-
gent data restrictions on each firm; the results, however, are qualitatively identical to
the ones presented here with six-month momentum sorting.

75

2.3.4 Methodology

I am interested in the nature of institutional holdings in firms conducting SEOs. Thus,
I measure institutional holdings in SEO firms and matching firms at the end of the
quarter of the offer. Institutional holdings are measured for mutual funds, non-mutual
fund institutions and total institutions. I measure for each category of institutions, the
change in percentage holdings in each sample firm and the corresponding matching
firm. These changes are measured over each quarter from the offer quarter until the

end of the fourth quarter following the offer.

2.4 Empirical Results and Discussion

2.4.1 Institutional Holdings around SEOs

I present in Table 2.2 statistics regarding total institutional holdings in the SEO and
the matching samples at the end of each quarter, beginning two quarters before the
offer quarter, and ending four quarters afterwards. Panel A shows levels of holdings
of all institutions in SEO firms, and matching non-issuers.9 It can be seen that at
the end of each quarter, mean and median institutional holding levels in SEO firms

are significantly higher than those in matching non-issuers. For example, at the end

 

9In Panel A of Table 2.2, the sample size drOps from 2582 at the end of the issue
quarter to 2546 at the end of the fourth quarter after the issue. This decline of about
1.40% might seem small given that close to 5% of listed firms disappeared each year
in the 19805 and 19905 in the US. However, of the entire sample of 2912 firms, only
1.48% delisted during the year after the issue. Therefore, this is a feature of my data,
and occurs because I require institutional holdings data for each SEO firm in the
sample.

76

of the offer quarter, mean (median) institutional holdings in SEO firms are 36.68%
(35.65%) of outstanding shares. These figures are significantly higher than the 22.48%
(15.29%) holdings for non-issuing firms.

Panel B reports the mean change in institutional holding over each quarter sur-
rounding the offer by SEO firms. It can be seen that (a) institutional holdings in SEO
firms increased over every quarter around the offer. (b) the same is true of non-issuing
firms. Both these observations are consistent with the overall trend of an increase in
the flow of funds into the equity market. (c) increases in holdings of SEO firms are
significantly higher than increases in holdings of matching non-issuers. In the offer
quarter, institutions increased their holdings in SEO firms by 6.67% of outstanding
shares; in non-issuing firms with identical characteristics, their holdings increased by
0.54%. ((1) Among SEO firms, much of the increase in institutional holding is realized
in the offer quarter, with very small increases in surrounding quarters. For instance,
compared to the 6.67% increase in SEO firms in the offer quarter, increases of 1.69%
in the previous quarter, and those in the two subsequent quarters of 0.17% and 0.84%

are small.

2.4.2 Mutual Fund Holdings around SEOs

Table 2.3 reports information on mutual fund holdings in the SEO and the matching
sample at the end of each quarter beginning one quarter before the offer quarter, and
ending four quarters following the offer quarter. In Panel A, I report levels of holdings

of mutual fund institutions in SEO firms, and matching non-issuers. I Observe that at

77

the end of each quarter, mean and median mutual funds’ holding levels in SEO firms
are higher than those in matching non-issuers. For example, at the end of the offer
quarter, mean (median) holdings of mutual funds in SEO firms are 4.64% (3.20%)
of outstanding shares. These figures are significantly higher than the 2.29% (0.08%)
holdings for non-issuing firms.

Panel B reports the mean change in mutual funds’ percentage holdings over each
quarter surrounding the offer by SEO firms. It can be seen that mutual fund holdings
in SEO firms increased almost every quarter around the offer, and the same trend is
true of non-issuing firms. Also, increases in holdings of SEO firms in the offer quarter
are significantly higher than increases in holdings of matching non-issuers. In this
quarter, mutual funds increased their holdings in SEO firms by 1.18% of outstanding
shares; in non-issuing firms with identical characteristics, the holdings increased by
0.08%. Finally, among SEO firms, much of the mutual fund holding increase occurs
in the Offer quarter, with very little increases in surrounding quarters. Compared
to the 1.18% increase in SEO firms in the offer quarter, an increase of 0.36% in the
previous quarter, a decrease of 0.04% in the first subsequent quarter, and the increase

of 0.07% in the next quarter are small.

2.4.3 Non-Mutual Fund Holdings around SEOs

In Table 2.4, I report information on non-mutual fund institutional holdings in the
SEO and matching sample firms at the same points of time as before. In Panel A, I

report levels of holdings of non-mutual fund institutions in SEO firms, and matching

78

non-issuers. In contrast to the numbers in Panel A of Table 2.3, we observe that non-
mutual fund institutions hold a much higher proportion of the average firm, whether
SEO or non-issuing, compared to mutual funds. It can be seen that at the end of
each quarter, mean and median holding levels of non-mutual fund institutions in SEO
firms are higher than those in matching non-issuers. For example, at the end of the
offer quarter, mean (median) holdings of such institutions in SEO firms are 23.86%
(22.24%) of outstanding shares. These figures are significantly higher than the 14.96%
(9.24%) holdings for non-issuing firms.

Panel B reports the mean change in percentage holdings of non—mutual fund in-
stitutions over each quarter surrounding the offer by SEO firms. It can be seen
that (a) holdings in SEO firms increased over every quarter around the offer (b) the
same trend is present in non-issuing firms (c) increases in SEO firm holdings are
significantly higher than increases in holdings of matching non-issuers. In the offer
quarter, non-mutual fund institutions increased their holdings in SEO firms by 4.74%
of outstanding shares; in non-issuing firms with identical characteristics, the holdings
increased by 0.36% (d) among SEO firms, much of the holding increase occurs in
the offer quarter, with very little increases in subsequent quarters. Compared to the
4.74% increase in SEO firms in the offer quarter, increases in the previous quarter of
1.06%, and those in the two subsequent quarters of 0.17% and 0.55% are small (e)
the magnitude of holding increases of non-mutual fund institutions is much higher
compared to those of mutual funds. In contrast to the 4.74% increase in SEO firm
holdings of non-mutual fund institutions in the offer quarter, the comparable figure

for mutual funds (from Table 2.3, Panel B) is a significantly smaller 1.18%.

79

There are three principal facts that emerge from the analysis so far. First, in-
stitutions have held a greater proportion of equity in SEO firms than they did in
non-issuing firms. Second, institutional investors seem to increase their prOportional
holdings in SEO firms more than in matching non-issuers around the period of the
offer. Third, non-mutual fund investors increase their relative holdings in SEO firms
by a greater extent compared to mutual fund institutions. Prima facie, these results
seem to indicate that institutional investors, especially non-mutual fund investors
have not come to appreciate the underperformance of SEO firms compared to their
non-issuing counterparts, and are investing in a value-decreasing activity by increasing
their holdings in issuing firms around SEOs. However, one can draw this conclusion
only if one also assumes that institutional investors do not have any stock selection
capability. In other words, before we can cast doubt on the portfolio decision making
of institutional investors based on the above analysis, we need to examine if they were
able to separate the above-average SEO firms from the truly underperforrning ones.

It is to this analysis that I turn next.

2.4.4 The Pattern of Institutional Investment around SEOS:

A Closer Look

I now examine more closely the pattern Of institutional investment in SEO firms
surrounding an offer. First, I sort the sample of SEO firms into quintiles based on the
increase in institutional holdings around the offer. Next, for each quintile so formed,

I measure mean pre-issue stock market returns during months -12 and -2 relative

80

to the offer date, and oneyear and two-year post-issue stock market returns from
the date of the offer.10 All returns (in Tables 2.5 and 2.6) are measured relative to
a DGTW matching portfolio based on size, book-to-market and momentum.11 The
numbers in the second column of Table 2.5 show the mean change in holdings of
each SEO firm quintile between quarters -1 and +1 relative to the offer quarter. i.e.
from the end of the quarter immediately preceding the offer quarter to the end of the
one immediately succeeding it.12 Columns 3 through 5 contain details of pre— and
post-issue stock market performance of each quintile.

In Panel A, results are shown for quintiles formed based on changes of holdings
by all institutional investors. First, we see that even though institutions increase
their holdings of SEOs relative to non-issuers in the offer quarter on average, there
is a wide dispersion in the changes. Institutions as a whole decreased their holdings
during quarters -1 through +1 in firms in the bottom quintile (Quintile 1) by a mean
amount of 4.60%. By comparison, in the tOp quintile (Quintile 5), they increased their

holdings by 21.03% during the same period. The third column of Panel A reports

 

loIn unreported analysis, I also replicate the analysis with post-issue returns mea-
sured not from the issue date, but from the end of the issue quarter. This coincides
with the date at which the change in institutional holdings is measured. The results

are qualitatively identical to those presented here.
11I measure all returns relative to a portfolio based on a triple-sort on size, book-

to-market and momentum i.e. using a DGTW benchmark. As described earlier, the
DGTW database provides monthly value-weighted returns for each of 125 portfolios.
I extract monthly returns for sample firms from CRSP. Then I compute the bench—
mark adjusted one-year (two-year) returns for each sample stock by subtracting the
compounded one-year (two-year) return on the matched portfolio from the sample

stock return over the same time period.
12In an unreported robustness check, I conduct a similar analysis sorting the sample

of SEO firms into quintiles based on institutional change in holdings between quarters
-1 and 0 relative to the offer quarter i.e. during the offer quarter, and obtain results
that are qualitatively identical to the results presented here.

81

that SEO firms had benchmark-adjusted returns ranging from 30% (for quintile 1) to
54% (for quintile 5) in the months preceding the offer. This reflects the sharp run-up
in stock market performance of firms conducting SEOs, and is consistent with earlier
research on this subject.13 Similar trends are apparent from the first three columns
of Panels B and C.

Most interesting however, is the information on post-issue benchmark-adjusted re-
turns of SEO firms. We see in Panel A that SEO firms that had the greatest increases
in institutional holdings significantly outperformed their benchmark portfolios, com-
pared to those SEO firms that has lesser increases or decreases in institutional hold4
ings around the offer. In the oneyear period following the offer, SEO firms in quintile
5 (in which firms institutions had increased their holdings the most) outperformed
their benchmark portfolios by 7.66%, compared to those in quintile 1 (in which firms
institutions decreased their holdings the most) who underperformed their benchmark
portfolios by 6.88%. The difference in adjusted performance between these two ex-
treme SEO firm quintiles is highly statistically significant (at the 1% level). Over a
two-year period following the offer, the top quintile outperformed their benchmark
portfolios by 4.68%, compared to the bottom quintile that underperformed by 1 1.54%.
Again, the difference in performance between the two quintiles is highly statistically
significant.14 In Panel B, I present results of a similar analysis for mutual fund hold-

ings only. We observe that SEO firms in which mutual funds increased their holdings

 

13See, for example, Loughran and Bitter (1995) and Spiess and Affleck-Graves
(1995).

1“Three-year post-issue returns follow the same trend as one-year and two—year
returns, but are omitted from the table due to their marginal statistical significance.

82

the most significantly outperformed their matching portfolios compared to those SEO
firms in which funds had lesser increases (or decreases) in holdings around the offer.
In the year following the offer for instance, quintile 5 (in which firms mutual funds in-
creased their holdings the most) outperformed their benchmark portfolios by 4.30%,
while quintile 1 (in which firms mutual funds decreased their holdings the most) un-
derperformed by 6.15%. The difference in adjusted performance between the top and
bottom quintiles of SEO firms is statistically significant at the 1% level. Further, we
find that those quintiles of SEO firms in which mutual fund holdings decreased the
most (quintiles 1 and 2) are exactly those that underperformed in terms of adjusted
returns. Apparently, mutual fund managers are able to separate those SEO firms that
potentially have above-average benchmark-adjusted returns in the post-issue period.
Over a two-year period following the ofler, the tOp quintile outperformed their bench-
mark portfolios by 5.12%, compared to the bottom quintile that underperformed by
11.29%. Again, the difference in performance between the two quintiles is highly
statistically significant.

Panel C reports results for non-mutual fund institutions. Once again, we see that
SEO firms in which these institutions increased their holdings the most significantly
outperformed their benchmark portfolios, compared to those SEO firms in which
they affected lesser increases (or decreases) in holdings around the offer. In the
year following the offer, quintile 5 firms (in which firms non—mutual fund institutions
had increased their holdings the most) outperformed their benchmark portfolios by
5.54%, compared to quintile 1 firms (in which firms these institutions decreased their

holdings the most) who underperformed their benchmark portfolios by 7.95%. Once

83

again, the difference in adjusted performance between the tOp and bottom quintiles
of SEO firms is highly statistically significant (at the 1% level). Results for two year
post-issue returns also tell the same story in a statistically significant manner.

Rssults of a similar analysis for the sample of matching non-issuers are presented
in Table 2.6. I form quintiles of matching firms based on changes in institutional
investment in them, between quarters -1 and +1 relative to the offer quarter of the
corresponding SEO firm. It can be seen that, for all categories of institutions, there
is no clearly discernible relationship between institutional investment and pre- and
post-issue stock market performance across quintiles of matching firms. Further,
the difference in post-issue stock market performance between the top and bottom
quintiles over one— and two-year horizons is not statistically significant at conven-
tional levels. Together, the results on post-issue performance in Tables 2.5 and 2.6
suggest that stocks of SEO firms experiencing increases in institutional investment
have greater benchmark-adjusted returns than those that experience decreases in in-
stitutional investment. This result is consistent with ongoing research by Gibson,
Safieddine, and T itman (1998).

Looking at Table 2.5, we observe that across all categories of institutional invest-
ment, there is a substantial degree of correlation between pre-issue adjusted returns
between months -12 and -2 relative to the offer and post-offer one-year returns. These
results lead one to suspect if these results are simply a manifestation of institutional
portfolio managers buying the biggest winners in the recent past around the offer
date. In other words, I want to admit the possibility that these results are not

a result of informed portfolio managers, but rather the outcome of an uninformed

84

momentum strategy. 15 In unreported analysis, I sorted the sample of SEO firms into
quintiles based on pre—issue benchmark returns, and examined the post-issue one-
year, tweyear and three-year benchmark-adjusted returns for each of these quintiles.
I find that there is no significant correlation between the pre—and post-issue adjusted
returns. i.e. the significant outperformance of those SEO firms in which institutional
holdings increased around the offer, which I document, cannot be interpreted as a
naive momentum strategy.

To investigate this point further, and examine if the above results are indeed due
to an information effect, I make use of sell-side analysts’ earnings forecasts. For each
quintile of SEO firms formed earlier, I calculate an IBES Revision Ratio at the end
Of the first and second quarters following the offer quarter. This ratio is calculated as
follows: every quarter, I count within each quintile, the number of firms that whose
forecasts have been upgraded and those that have been downgraded. The IBES
Revision Ratio is simply the number of upgraded stocks within each quintile divided
by the number of downgraded stocks, at the end of the required quarter. Thus a higher
IBES Revision Ratio for a quintile of firms indicates a more positive outlook regarding
the firms in that quintile. I present in Columns 6 and 7 Of Table 2.5, IBES Revision
Ratios calculated for various quintiles of SEO firms. Corresponding columns in Table
2.6 show these ratios for non-issuing matching firms. Among SEO firms, across all
categories of institutional investment, there is a near-monotonic relationship between

institutional changes in ownership and the IBES revision ratio. That is, sell-side

 

”Recently, momentum strategies have been extensively studied in the finance liter-
ature. See Chan, Jegadeesh, and Lakonishok (1996), Jegadeesh and Titman (1993),
and more recently Wermers (1997) on this subject.

85

analysts forecast a positive outlook three to six months after the offer, for precisely
those SEO firms in which institutional investors invested around the Offer. As can be
seen from Table 2.6, this pattern is absent among the sample of matching non-issuers.

The above results indicate that although institutional investors increased their
proportional investments in SEO firms relative to comparable non-issuers, these in-
creases are apparently not due to ignorance of the fact that the average SEO is bad
news. It seems that institutional investors have increased their investment in those
81303 that are likely to outperform their benchmark portfolios in the years following
the offer, by significantly more than the ones that are likely to underperform their
benchmarks, notwithstanding the empirical observation that the average SEO is a
bad investment in the medium to long term. This evidence is consistent with ear-
lier literature that attributes some stock selection ability to institutional investors,

especially mutual funds (e.g., Daniel, Grinblatt, Titman, and Wermers (1997)).

2.5 Summary and Conclusions

Extant empirical research has examined the value added by active institutional port-
folio management by using a variety of measures, either by comparing institutional
portfolio returns with pre-defined benchmarks or by using holdings data for these
institutions, and a battery of measures deveIOped to detect aboveaverage results.

In this article, I examine the value-adding nature of institutional portfolio manage-
ment by studying the behavior rather than the performance of institutional portfolio

management. I deveIOp a simple test to understand if institutional managers indeed,

86

possess some superior stock selection ability. I base this test against a well-known fact
in empirical corporate finance: the negative drift in both stock market and operating
performance of seasoned equity issuers.

Using a sample of SEOs conducted during the period 1980-1995, I find that in-
stitutional investors increase their investment in SEO firms significantly more than
that in a matched sample of non-issuers. This is counterintuitive investment strategy,
in light of the fact that on average, SEOs are bad news. However, upon imposing a
foresight bias on institutional investors, I find that the greatest increases in their SEO
firm holdings were in those firms that were the best outperfomers in the sample, and
that the smallest increases in SEO firm holdings were in the worst outperformers. I
find that this difference is consistent, and is statistically significant, across all classes
of institutions. I interpret these results as evidence of superior stock selection ability
of institutional portfolio managers. This interpretation is consistent with earlier work

regarding portfolio performance measurement, especially in mutual funds.

87

APPENDIX 2

TABLES FOR CHAPTER 2

Table 2.1
Summary Statistics for the Sample of SEOs

Key statistics are provided below regarding the sample of Seasoned equity offerings.
For each year, the number of issues in each quarter is presented. The percentage of
each year’s observations of the total sample is also reported.

 

Year Quarter
1 2 3 4 Total %age

1980 29 29 38 76 172 5.91
1981 52 59 27 59 197 6.77
1982 36 42 47 76 201 6.90
1983 115 139 119 57 430 14.77
1984 34 33 23 33 123 4.22
1985 29 60 43 46 178 6.11
1986 60 80 53 26 219 7.52
1987 34 57 38 11 140 4.81
1988 7 19 21 15 62 2.13
1989 10 25 38 41 114 3.91
1990 30 35 23 15 103 3.54
1991 44 96 73 66 279 9.58
1992 78 86 51 41 256 8.79
1993 65 79 61 66 271 9.31
1994 48 46 26 47 167 5.73
Total 671 885 681 675 2912 100

 

 

 

 

89

 

88 u z 38 u z 38 n z 28 n z 2.3 n z 88 u z 88 n z
GE: 8.8V 8%: Es: $3: ass: 83: 288-8:
3.3.. 8.8 8.8 8.8 $8 8.8 8.8 8238

2.8 n z :8 n z 88 n z 88 u z 88 n z 88 u z 38 u z
338 833 82.3 Sosa $33 38.5 833

 

 

 

wows 3.2.. was” «Eon 8.3 3.8 Ram 885 Cam
v m n 8 c H- a- “828:0
awnmEo—m m0 896‘— “4 8.8%
EEBE
:82

888888 8 08.88: 88 88880 .88 8 88:87:08 8888 88 m8£ OMm 0.: 80382
@820; 8 8888 05 8 8088u€ 8: m0 00805890. 0.: 88 3 82978 .m 885 E .85 :08 m0 888 88680880 m0
“83.80.88 0 8 “88988 88 amaze—om .8888 8&0 8: 3 838—8 8888 88 H0 88 0.: 8m 08 30.02 0888.8 80.0 amaze—0m

.8830; 18032888 1308 80888
3 m @808: H 88$. :0 m0 8% 8: 08m: 88: 83 285m 85 8h 8888880 023880 80: 88 88 8:08 .8050 838
0:3 £86888 88 mQOmm $805888 88.38088 m 0931 88883.88 8.8 83:8 8 88883 >888 8.8085 88.3
8888800 80288 b80288 85 .805358 .8885 .850 8 385 888838 88:08 80838 888802: 8208888
.v 33. 8.83 83:8 m0 88800 88:60 :8: 88 8288800 888882: 6 88¢. 88.8800 088.888 *0 88800 a 08G.
883800 maze—0: 0:82 “88— wo a: 288 mm H 881C. @8885 .8 8:: .3088 9:052:88 8: m0 80588.0 mason— 88 @88me
3 858000.» :88»? 95 m0 080 8 805359: wane—0: :08 88580—0 88885 .883 85 m0 .302 808 85 8 8:8 3 88
0888s 8: 8030 2885 .8808 .88: G<Qm<z 88 88< @954 “0 828830 28035888 :0 8.8.8830 E8888 8:3
-800 8380.5 8080—08808 £88802: <00 ,3 8:888 8.388 88.885 8: 80¢ 88030 88 8820; 8805358—

muosmmméoz 885302 88 088mm Om—m 8 88303 1805358: _maofi
N.N 058B .

90

 

830.8 83.3 38.3 325.8 283$ 283$ 82.8-3
So- 8.? So and. 8.8 8.8 88588
wt.“ n z 88 u z 83 u z 83 n z 88 n z 88 n 2 288-8:
and 28 one 36 3.0 was 85632
38 n z 88 n z 88 u z 23 n z 83 u z 58 n z
«3 86 Ed :5 $0 8.8 8:8 08m

 

«8» no; mo: ~80 00:- 79;. 9:0 8258
mwamgo: E owamsU 8832 "m 3st

688.88 3 «38.

91

 

wgm M Z mmwm M Z :mwm M Z mam N Z ovum N Z mam M Z mwvm N Z

 

 

 

:83 8.3 88.8 $0.8 30.8 3.8 3.8 888-8:
:8 8.8 83.. 8.8 8.8 8.“ 8.8 82382
2.8 n z :8 u z 88 n z 88 u z 88 u z 88 n z 38 n z

68.: $3: :83 38: 88: 80.8 :8:
a: m: 8.8. 8.8. 8:. 8.8 8.8 8:: 08

v m a : 0 T a- 88:0

mwsmgom :0 2861: u< 8.8m
:56sz
802

8885.88: 8 :88an 0.8 8:880 :08 8 8.808780: 8:088 :88 88:: 0mm 0:: .8038:
880—0: 8 888:0 8:: 8 8088::% 8:: :0 80805.88 8:: :8: 0: 828?: .m .08: 8: .88: :08 :0 88:8 $588880 :0
888808: 8 8 88808 08 8820: 888:0 80:0 8:: 0: 0388: 8:880 :08 :0 88 8:: :0: 08 30.8: 88888 88: 8820::

.8820: 88: 83:8 88888 0: 8820: m 89¢. :88 88: 83 88:8 8:: :0 885.8880 8:38:80 :08 08 88 8:08 .8050
:88: 0:3 £88238: 88 mmOmm 68058880: 8838008 m 89? 8888888 88: .8308 m: 8888:: 888:8: 88:3 88:
8888800 88:08 3:0:on .8: 88053588 .8088: 8::0 :0 88: 888888: 88:08 .8858 808882: 88:08:08:
.v 8%. .888: .8088 :0 888800 80838 88:: 88 8888800 888888: 5 89¢. 8888800 00888: :0 88800 a 093.
8888800 8:20: :8: 88. :0 a: 288 m: : 095. 8888: :0 88— :88:: $805388 8:: :0 80588: 8.8005: 88 @8885
0: $580008 289$: 83: :0 8:0 8 805388 8:20: :08 8:888 8:50am .88: 8:: :0 300: 888 0:: 8 880: 8: 88
88:88.0 0:: 80:8 £889 8:008 :88: 0:592: 88 88< .mm>z :0 8:88:30 88053588 :0 8:80:30 38:88 88:
-800 88:00am 880—08088 8:08:88: <00 m: 8.8800 88:88: 80.5085 8:: 80:: 888:0 88 8820: 8803358:

8888-807: 9:50.82 88 88.5.: Oflm a: mafia—0m: :55 833):
ad 2:85

92

 

 

8.2.8 :88 888.8 888.8 :88de 38.38 @2978
8.8 8.8 3.0 NS- 2: 8o 88380
ER n z a: n 2 ER n z 8% n z 88 n z 88 n 2 858-8:
2; n; 8.9 86 mod 28 852“:
88 u z 8.8 u z 8.8 u 2 88 n z 88 n z 38 u z
8.8 86 So :3. w: 8o 255 0mm

 

v3» 83a «0: :30 00:- TEN- 25 H.858
8880mm 8 mum—8:0 882 “m 388nm

82.8.80: :8 2:8.

93

 

88 n z 88 n z 38 u z 88 n z .88 n z 8.8 n z 88 u z
.388. E88. .83 .58 .83 .88 .83 888-8:
8.8 8.8 8.8 8.8 8.8 8.8 8.: 8888

8.8 n z :3 u z 88 n z 88 n z 8.8 u z 88 u z 38 n z
8.8 .88 .38 .88. .88 :8: £8:

 

 

 

vwém no.8 36m Sdm wwdm wvd. $8. 88:. 0mm
8. m. a 8 o 8- a. 888:0
88.6.0... .0 £95.. "< .ouan.
.888.
883.

888.8888. 8. .8888. 88 8.88 8.88 8 888.80: .8888 .88 m8... Cam 8.. 8838..
88.88. 8. 8888.8 8.. 8 8888...... 8.. .0 8888.86 8.. .8. 3 88.87.. .m .m88n. 8. .8... 8.88 .8 88.... 8:88.38 .8
888.888. 8 8 88888 88 88.83. .8888 8.8 8... 3 8.8.2 .8888 :88 .o .88 8.. 8. m8 30.8. 88888. 88.. 88.80..

.m .88 v .m 88...... .o 88 8.. 8
88:28. M85358: .88.. 8388-87. 88.8.. 28.. a? $.88 8... 8.”. 88.8880 8.38:8 8: 88.8 .88 888 .828 .82:
8.3 28.83.88. .88 mmOmm. £888.88. 888.888 m 8.8.. 88888888 .88. .8388 w. 888.88. 888.8. 88.3 8.88:
8.08888 8.8.88 8.88.8.8 88. £85358: 8.888.. 88.8 8 9.88. 888.82: 8.8.8: 883.8 888.82: 8888.88.
.v “8.88 8.88. .8588 .0 £8.88 £8.38 :8... .88 8.88.888 888.82: 6 2.8.. 8.88.88 8888: .0 $888 w 8......
88.88.88 8:28. :8: 88. .o a: 0.88 m. . 8...... 88:88. .8 8:. 888.8. 98.8888. 8.. .o 8.5.8.8.. 8.80m .88 .Emvafim
8 8:888 .89.... 8.. .8 88 8 8.8538: 8:28. 88 8:683 838me .888. 8.. .o 8.88. :88 8.. 8 .885. 8. 88
88.88.. 8.. .888 £88.. 858,. 8.88 .88.. G<Qm<z .88 88< £5er .0 88.8830 88.85.88: 8 8.8.8826 8.8888
8.888 888.885 88088.88 888.88. <90 .3 8.8.88 88.88.. 8.5885 8.. 88.. 8:830 88 88.88. 88.85.88.

muwsmmuuaoz 8.8.083. .88 88:... Oflm a. 85.83. .885 .8883...ch
«in 058$

94

 

:83 E83 825.8 page cooodvv :25de “SEA:
:5. v3- mg :6- as $5 85893
EN n z 3% n z 33 u 2 mg n z 28 u 2 %fi u 2 $8578:
and one and and and 23 $53.22
88 n z 88 n 2 83 u 2 $3 n 2 mg n z 3% n 2
2d :5 moo :.o v? 84 3% 0mm

 

v 3 m m 3 N N 3 a a 3 o o 3 H- fl- 3 a- 950 nomBumm
mwamgom E wmaaaU gum—2 um _maam

€85.88 "an 2an

95

 

 

Nmém MNQN :34. secs 333$ no.8 800083 0000mm: m
Eu? 3.: 25 EN odmv mg: 0
02: and“ 3.5. mod- 3.3 00...“ m
8.2 8.2 EN- who- afiwN 3: N
$32 .553 $5.2- 05%...- 058.8 .83.- A388... .8330 _
N- 00 NT
N .50 g .50 0.80% N .80.» w 05:02 09:30 0:830
035m 00mmm>0m mm—mu 0=mmmémom 0000???“ 000—2

 

28:332. 038. J. 380

8&0 0.: 8:50:00 0000800 0.5 00.5 05 80 fl
0305 30D 0000300 m\m\m\_ 05 080... 005030 08 3000080 HEN—00¢. 000.800 00.: E 0:880 0000 02:3 00—0000 000008300
08.050-03.080 8 000.08: 0.: 00 0x030 000080: 0883008880 .8 000080 0.: 8 0:00 05 00 0080080 0_ $008.00 N 000:
0500 006300 mam: 0.; amigo: 8005350.: 008 8088-000 E 000085 00 $580 .3 .0088.“ 005500 80 300 0:: 03000
O 300% .09:an 003 8308 E 00.0085 00 $580 .3 00880 005080 8.“ 300 0:: 03000 m .050.“ .0388: 8853508
.080 E 000080. 00 @580 .3 0088.. 00—5500 80 .200 0:: 03000 < 60.3 00:038.“ 35088 :05 00 0.50.0“ .0000 8&0 05
08¢ 008000 :00? 080000000 0008 00003000 80.5003..— 000 0.3 .000 000 .080 8&0 05 00 8€0 N- 5008 00 NT .3008 08¢
00800.. 000038 ”$38.80 0.: 080008 03 .0088“ 00 main 0mm 00 0:880 00.00 8h 0:880 0000 .8.“ $0.20: 0m 038:0 00
80008 05 000008 03 .N 88.00 E 000800 00.:0 0.: 00 0300—00 H+ 000 H- 800800 000.500 @5203 3.853305 5 00008.:
.8 000008 0.3 .3 00—3500 005 00080 0. 0005 Cam .8 0.0800 0.; 0880082 000 00:82-00300m .006 00 @0000 00:000.:
0:03.80 0 00 0200—00 08.6 Cam 8 0000880000 00x88 #030 00003000 wEvBmE .300 80008 03 .053 988:8 0.: :—

mEhm 0mm .8 00.858000m 000—82 800m 0200—0m
m.N 030E

96

.3358.“me 053 28 aka 55H 3 mmmeE Ammfimzo; 623: H 255:0 E 82:
Sea 32¢ch baawofiamfi 98 $382: mev—on 623:: m 355:0 E 938:: m5 ”:2: 8365 u was arm Entomaasm "m2

 

3.3 83 em? %3 63.3. 8.2 30.855 32%;: m.
H2: 2.: 8.” one 8.2. as v
8.3 8.8 3.? 3o- 3.8 cm.” m
86 3.2 So. 23. 8Q 84 m

$3.: $32 058.3- 0&3- 053.3 058.”- Homaeuqimgfi:
£83332: 3:5 33395.2 "O 728%

 

 

 

2.8 8.8 :2...“ a? .88 £4». 38205 $235 w
8.2 2.5 8.? a.“ 8.8 o: v
£2 8.2 «E. a.” 3.3.. as m

H2. 36 $4... $3... 8.3" mod- N
$5: $5.2 $3.3. $2.9 053.8 $3.“- 39885 ”.83qu fl

a- 3 2-
N .50 g .50 989a N .89» a mane—2 awn—BU man—£90
owe—«m .3333“ mam: mammmémom mammméum :82

 

mag—rm 33:2 um 3an

325588 3 same

97

 

 

8.: 8.: 8:- 2.3- 8.8 E: 3822: 82:80 m.
8.2 8.: 8:- 8:- 8.8 8.: v
8.: 8.: 8.: 8:- 8.8 2.: m
8.: 8.: 2.: 8.: 8.: 8:- m
82.2 83.: 83:- 82.3- 08:: 88:- $828: 82.6: :
n- o... 2-
N :30 a :30 :82» N :38 n 23:02 0w:::~0 335:0
03:3 :03?va mam: w:mm~-3mom 282.3% 532

 

28:332.: :38. “< 3.8:

 

.330 23 w:_30__0: 838:: 03: 3:3
23 :03 2 850:: :::Q 0333:: m\m_\m\_ 23 803 38:30 2: 333:8 392:5: 338:: :23 :_ 238:: 3:: 8:33 300::
3:38:30: 8:833..:w:_:::: :0 338:: 23 0: 830:: 338:: 038323853 :0 338:: 23 .30 03:: 23 m: 38:80: 2
8:828 m 3:: 03:: :223: mmm: 23. .3820: 3803338 0:3 _::::8-:0: 8 83:08 :0 w:3:0: 3 38:0: 338:: :0:
3:: 2:3 950:: 0 33m .3820: 3:: _::::8 8 83:08 :0 w:3:0m .3 38:0,: 338:: :0: 3:: 2:3 @503 m _:::n_ .3820:
8:03:38: .30: 8 83:08 :0 m:3:0m 3 38:0: 338:: :03 3:: 2:3 290:: < 33: 82—038: 853:8 :23 0: 23:3:
03:: 330 23 80:: 883: 030:: 33:83: :38 383:0: 82:32.3 3: 03: 0:0 3: 63:: 3.30 23 0: :03: m- 3:08 0:
«T 3:08 80:: 8:33: 3:835 ” 330:0: 23 83:08 :3 .388: 0: 28:3 333:8 .30 238:: 3:: Sb 238:: 3:0 :03
3830: 8 3:23 .30 8:08: 23 333:: :3 .m :8:_0O :_ .:0::::0 330 23 0: 33:3: :+ 3: H- 828:: 3:33: @830:
3803338 8 33:08 :0 8:08: 23 :3 3.38:: 03:: 33:0: 2 338:: 858:8 2E. 833802 0:: 323:2-Sioom 08m
:0 338:: 0mm 23 0: 333:8 :85 :0 0088830: :23:8 030:: 032-30: w:_:::m0: 3:: 333:: 03 63:: 3:30:03 23 :—

mEhm 2:503:33 .30 8:28:03?“ 30:82 xooum 233—03
9N 033E

98

80830280: R03 0:: .05.: 55: :: 0::0:08 A8803: 3:030: H 0.38:0 8 0:23
808 3:08.80 388088: 0:: 08808 880—0: 3:235 m 238:0 8 2008:: 23 :23 8:808 0 0:: 0.: 20308086 “mi

 

$0.: mag-Z 5.2- 2.:- 36: has 02088 3:28;: m
mwd 006 90.0 09.0- 8.5 0m; 0
we.” 38 Fwd- $.07 wwd: mod n
mug». En: no.0- 2.0:- 3.3 92o- m

88: 88.: 83.: 8:;- 888 8:2.- 0882:3833:
88555::— 0::.m 8:88:02 "0 08$

 

 

 

:3: 6:: 8:. 8.:- 38 3: 0:88: 32:80 :
:3: 2.: 2.2 8.: 8.: a: v
:0: :20 8: 9.:- 3: 8.: m
:2 :2: 8::- 8.:- :8 8:- m
8:: 88.: 88.2- 0:82:- 83: 0:8,:- 09855 $0330 :
a- 3 n:-
N .50 a .50 :82: n .80.: g 25:02 08880 838:0
853m :88>0m mam: 08:85:?” 0:::_-0:nm 8:02

 

:25: 3382 um .28.:

 

8:58.800 :0: 058.

99

BIBLIOGRAPHY

REFERENCES FOR CHAPTER 2

BIBLIOGRAPHY

Bayless, Mark, and Susan Chaplinsky, 1996, Is there a ’window of Opportunity’ for
seasoned equity issuance?, Journal of Finance 51, 253—278.

Brav, Alon, ChristOpher Geczy, and Paul A. Gompers, 1995, The long-run underper—
formance of seasoned equity offerings revisited, forthcoming Journal of Financial
Economics.

Chan, Louis K.C., Narasimhan Jegadeesh, and Josef Lakonishok, 1996, Momentum
strategies, Journal of Finance 51, 1681-1714.

Daniel, Kent, Mark Grinblatt, Sheridan Titman, and Russ Wermers, 1997, Measuring
mutual fund performance with characteristic based benchmarks, Journal of Finance
52, 1035—1058.

Fama, Eugene F., 1991, Efficient capital markets ii, Journal of Finance 46, 1575-1617.

Field, Laura C., 1995, Is institutional investment in initial public offerings related to
long-run performance of these firms?, UCLA Working paper.

Gibson, Scott, Assem Safieddine, and Sheridan Titman, 1998, Institutional ownership
changes, analyst earnings forecast revisions and stock returns: Implications for
market efficiency, Michigan State University Working paper.

Grinblatt, Mark, and Sheridan T itman, 1989, Mutual fund performance: An analysis
of quarterly portfolio holdings, Journal of Business 62, 393—416.

Grossman, Sanford, and Joseph Stiglitz, 1980, On the impossibility of informationally
efficient markets, American Economic Review 71, 393—408.

Jegadeesh, Narasimhan, 1990, Evidence of predictable behavior in security prices,
Journal of Finance 45, 881—898.

 

, and Sheridan Titman, 1993, Returns to buying winners and selling losers:
Implications for stock market efficiency, Journal of Finance 48, 65—92.

Lakonishok, Josef, Andrei Shleifer, and Robert Vishny, 1992a, The structure and
performance of the money management industry, Brooking Papers: Microeconomics
pp. 339—391.

 

, 1992b, The impact of institutional trading on stock prices, Journal of Fi-
nancial Economics 32, 23—43.

Loughran, Tim, and Jay R. Ritter, 1995, The new issues puzzle, Journal of Finance
50, 23-51.

101

 

, 1997, The operating performance of firms conducting seasoned equity offer-
ings, Journal of Finance 52, 1823—1850.

McLaughlin, Robyn, Assem Safieddine, and Gopala Vasudevan, 1996, The operating
performance of firms conducting seasoned equity offerings, Financial Management
25,41—53.

Schwartz, Robert, and James Shapiro, 1992, The challenge of institutionalization for
the equity market, New York University Working paper.

Spiess, D. Katherine, and John Affieck-Graves, 1995, Underperformance in long-run
stock returns following seasoned equity offerings, Journal of Financial Economics
38, 243—267.

Wermers, Russ, 1997 , Momentum investment strategies of mutual funds, performance
persistence, and survivorship bias, University of Colorado Working paper.

102

 

Chapter 3

MOMENTUM AND INDUSTRY GROWTH

3. 1 Introduction

There has been a substantial body of recent literature documenting that the cross-
section of stock returns is predictable based on past returns. DeBondt and Thaler
(1985) and DeBondt and Thaler (1987) find that long-term past losers outperform
long-term past winners over the subsequent three to five years. Jegadeesh and Titman
(1993) show that, over intermediate horizons of three to twelve months, a portfolio
that purchases past winners and sells past losers has a positive abnormal return.
This evidence that simple trading strategies based on past returns can be used to
achieve abnormal returns has received a great deal of attention. Such “momentum”
strategies have been found to yield abnormal returns not only in US. markets, but
also internationally. Rouwenhorst (1998), using a sample of stocks from twelve Eu-
ropean countries, finds that a portfolio that is long in medium-term winners and
short in medium-term losers earns approximately 1 percent per month. In addition
to academia, practitioners such as stock analysts and portfolio managers have come
to subscribe to the view that momentum strategies are one way to “beat the market”,

so much so that today, momentum investing constitutes a distinct style of investment

103

 

in the United States and elsewhere.

While the existence of momentum per se has been well documented, there is
little agreement on the sources of profits of such strategies. There have been several
explanations proposed for this apparently anomalous behavior in stock returns. The

proposed explanations typically fall into one of the following three categories.

a. those that argue that these results provide strong evidence of market ineffi-

ciency: The original conjecture of Jegadeesh and Titman (1993) was that the

 

market systematically underreacts to firm—specific information regarding their
short-term prospects. Alternatively, it is possible that transactions by investors
who buy past winners and sell past losers temporarily move prices away from
their long-run values, thereby causing prices to overreact. This is consistent
with arguments put forth by DeLong, Shleifer, Summers, and Waldmann (1990)
that such overreaction is caused by rational speculators who indulge in positive
feedback trading. Most recently, there have been prOposed some “behavioral”
models that suggest that momentum profits arise due to inherent biases in the
way investors interpret information. Papers representative of this genre are
Daniel, Hirshleifer, and Subrahmanyam (1998), Barberis, Shleifer, and Vishny
(1998), and Hong and Stein (1999). While all three are “behavioral” models,
momentum in the first model is an outcome of overreaction, while the last two
models posit that momentum occurs due to underreaction — prices adjusting

too slowly to news.

b. those that argue that the returns to these strategies are compensation for risk:

104

Conrad and Kaul (1998) argue that the profitability of momentum strategies
can be entirely explained by the cross-sectional variation in mean returns of
individual securities, rather than appealing to time-series predictability. More
recently, Ahn, Conrad, and Dittmar (1999) utilize the stochastic discount factor
methodology to study momentum trading strategies and conclude that momen-
tum profits are not abnormal when judged against a non-parametric bench-
mark. These studies suggest that momentum profits are simply a manifestation

of compensation for systematic risk factors that have yet to be included in ex-

 

tant asset pricing models. However, the preponderance of empirical evidence

weighs heavily against a risk-based explanation.l

c. those that argue that these results are a product of data mining: PrOponents
of this argument maintain that momentum and other anomalies are simply the
outcome of an elaborate data mining process. After all, return reversals and
continuation are only two of the many patterns that empirical researchers have
uncovered using the same stock price data. This suggests that once the momen-
tum anomaly has been “discovered” and well documented, market participants
will act in a way so as to make it disappear in later years. However, Jegadeesh
and Titman (1999) shows that in the time period since 1990 (their 1993 paper
analyzed stock return data upto 1989) momentum profits continue to be prof-

itable and past winners continue to outperform past losers by about the same

 

1Fama and French (1996) note that momentum effects cannot be explained by
their three-factor model. Jegadeesh and T itman (1999) take issue with Conrad and
Kaul’s methodology and argue against momentum being a manifestation of the cross-
sectional variation in mean returns.

105

magnitude as in the earlier period. Together with the Rouwenhorst (1998) in-
ternational evidence, one may conclude that it is unlikely that the momentum
phenomenon is due to mere chance. Fama (1998) argues that, consistent with
the market efficiency hypothesis that most anomalies are chance results, ap-
parent overreaction in financial markets is about as common as underreaction.
However, in the same paper, he (cautiously) notes that the return continuation

over the medium-term (momentum) seems to be an anomaly “above suspicion”.

The empirical literature documents that momentum has been a consistently prof-
itable trading strategy, and continues to be so, at least before transaction costs are
taken into account. It is a fairly robust phenomenon that has presented itself in vari-
ous markets around the world. It is not surprising, therefore, that financial economists
have devoted some attention in recent research to refining and improving the basic
momentum strategy prOposed by Jegadeesh and Titman in their 1993 paper. One
such paper is Moskowitz and Grinblatt (1999) which documents that momentum
is primarily an industry phenomenon. Using data on a sample of NYSE, AMEX
and Nasdaq firms during the period July 1963 through July 1995, they form indus-
try portfolios of stocks based on 2-digit Standard Industry Classification (SIC) codes.
They find that these industry portfolios exhibit significant momentum even after con-
trolling for size, book-to-market equity (BE/ME), individual stock momentum, the
cross-sectional dispersion in mean returns, and potential microstructure influences.
In their paper, once returns are adjusted for industry effects, individual stock momen-

tum profits are significantly weaker, and for the most part, statistically insignificant.

106

Further, industry momentum strategies are more profitable than individual momen-
tum strategies.2

In this chapter, I provide an extension to Moskowitz and Grinblatt’s work, with
a focus on the relationship between industry growth and momentum. Absent a vi-
able risk-based explanation, momentum in individual stocks is currently understood
as a result of apparently systematic errors in valuation by the market; the actual
mechanism at work might be underreaction or overreaction or both. Whatever be
the underlying mechanism, if one firm in an industry is likely to be misvalued sys-
tematically, it is more than likely that other firms in the same industry are misvalued
too. More generally, there might exist entire classes of industries in which firms are
systematically more misvalued than in other classes of industries. This implies that
momentum profits should vary along this dimension of classification. I posit that
one variable that could prove useful in classifying stocks is industry growth. It is
well known that firms in growth industries are characterized by greater uncertainty
and faster reversals of fortune than those in stable, mature industries. Thus, firms
in growth industries are presumably harder to value accurately compared to firms
more mature industries. If systematic misvaluation is indeed the underlying cause of
momentum profits, then such systematic misvaluation is likely to be more pervasive

within higher growth industries compared to those with lower growth rates. Thus,

 

2There are other studies which are tangentially related to this onezChan, J egadeesh,
and Lakonishok (1996) find that the medium-term return continuation can be ex—
plained in part by underreaction to earnings information, but price momentum is not
subsumed by such earnings momentum;Lee and Swaminathan (2000) investigate the
relationship between trading volume and momentum; Hong, Lim, and Stein (1999)
investigate size, analyst coverage and momentum.

107

this study can be characterized as an attempt to refine the basic momentum strategy
of buying winners and selling losers among the universe of firms, and identify a class
of stocks in which momentum profits are more prevalent and larger in magnitude.3
To preview, using two samples of firms for roughly the same time period, one
including Nasdaq firms and the other including only NYSE/AMEX firms, I investi-
gate momentum profits for individual stocks split into quintiles by industry growth.
I define industry growth as growth in total industry assets in the two years preceding
portfolio formation. I find that individual stock momentum varies almost monotoni-
cally by industry growth. Firms in highest industry growth quintile have significantly
higher momentum compared to those in the lowest industry growth quintile. I also
separately investigate momentum profits for two groups of firms within each industry
growth quintile: those with asset growth above the industry average, and those below
the industry average. I find that the above-average growth group within each quin-
tile has significantly higher momentum profits than the below-average group. The
monotonicity of momentum profits by industry growth is preserved among the higher
relative growth firms. Further, the momentum profits of the highest industry growth
quintile are always higher than those for the universe of firms, suggesting an economic
benefit to stratifying firms based on industry growth and relative company growth

intra—industry, while following a momentum investment strategy.

 

3This study is closely related to recent work by Daniel and Titman (1999) who find
that the lowest BE/ ME stocks are the ones with the highest momentum. Daniel and
Titman argue that momentum is a result of pervasive overconfidence among investors,
and that their overconfidence leads to the greatest misvaluations in those stocks that
have a large growth component. In this study, I implicitly assume momentum is a
result of misvaluations in firm-specific components, but this occurs in an entire class
of firms viz. all those that are in the same industry growth category.

108

The remainder of this chapter is organized as follows. In Section 3.2, I describe
the data and methodology employed in this study. In Section 3.3, I discuss the main

empirical results, while Section 3.4 concludes the chapter.

3.2 Data and Methodology

I consider for analysis two samples which are labeled the JT and the GM samples
respectively. The JT sample includes all NYSE and AMEX stocks during the period
1965:01-1997 :12. The GM sample, on the other hand, includes all NYSE, AMEX, and
Nasdaq firms and covers the period 1963:08 through 1995:06. The principal reason
for analyzing these two different samples spanning roughly the same time period is to
observe if the inclusion or otherwise of N asdaq firms makes any significant difference
to momentum strategy profits. The JT and the GM samples have been chosen with
a view to comparing the results herein to previous work by Jegadeesh and Titman
(1999) and Moskowitz and Grinblatt (1999) respectively. For both samples, I exclude
all stocks priced below $5 at the beginning of the holding period. This is to ensure
that results are not driven by the extreme movements in these low priced stocks.
Stock returns used in the analysis are obtained from the Center for Research in
Securities Prices (CRSP) monthly return files. Data on total assets used in the firm
and industry growth calculations are from the COMPUSTAT database.

I follow the same technique as in Jegadeesh and T itman (1993) to avoid test
statistics that need to correct for overlapping returns. Each momentum strateg is

executed as follows. At the beginning of each month t, all securities in the sample are

109

 

ranked on the basis of their returns in the past 6 months. Based on these rankings,
portfolios of “winners” and “losers” are formed, according to the momentum strategy
being followed. The four momentum strategies considered will be described shortly.
In each month t, the strategy buys the winner portfolio and sells the loser portfolio,
holding this position for 6 months. In addition the strategy closes out the position
initiated in month t-6. Hence under this strategy, each month’s holding return is an
average of returns under six ranking strategies. For example, a January 1992 mo-
mentum strategy return is determined 1/ 6 by winners-losers from July 1991 through
December 1991, 1/6 from May 1991 through November 1991 and so on.

I consider four momentum strategies in my analysis. The differences among these
strategies are the classification of “winners” and “losers”, and the weighting scheme

employed. The four strategies are as follows:

0 JTE: The sample of stocks is ranked in descending order based on past 6—month
returns into deciles following Jegadeesh and Titman (1993). The top decile is

designated as “winners” and the bottom decile is designated as “losers”.

0 JT V: Here too, securities are ranked in descending order based on their past 6-
month returns into deciles. Then, the stocks within the top and bottom deciles
are value-weighted, with the top decile designated as “winners” and the bottom

decile designated as “losers”.

e GME: In this strategy, securities are ranked in descending order based on their
past 6-month returns. However, instead of deciles, I determine “winners” and
“losers” based on 30 percent break-points following Moskowitz and Grinblatt

110

(1999). These authors argue that value-weighting and 30 percent break points
help reduce noise and avoid the momentum portfolio returns being dominated
by small size firms. The top 30 percent is designated as “winners” and the

bottom 30 percent is designated as “losers”.

e GMV: Again, I employ 30 percent break-points to determine “winners” and
“losers”. Then, I value—weight the stocks in the top 30 percent, designated as

“winners” and those in the bottom 30 percent designated as “losers”.

3.3 Empirical Results

In Table 3.1, I present the results of implementing the four aforementioned strategies
for both the JT and the GM samples. It can be seen from Panel A that results for the
JT sample are a close match to the results in Jegadeesh and Titman (1999). In their
paper, over the 1965—1997 period, the JT E strategy yields a profit of about 1.09%
per month, this number being highly statistically significant. I obtain a comparable
profit of 1.05% for the same strategy, also highly statistically significant. Using the
GM sample, I obtain a monthly momentum profit of 1.26%, with greater significance
than for the JT sample. Hence, including N asdaq firms actually increases momentum
profits of this strategy. Results for the other strategies follow a similar pattern as can
be seen from the remaining panels of Table 2.1. Panel B shows that the JTV strategy
earns about 0.74% a month for the JT sample, and about 0.99% per month for the GM
sample, both these results being statistically significant. This is not surprising since

value-weighting assigns a lower weight to small firm stocks than equal-weighting, and

111

it is known that small firm stocks have higher momentum than large stocks.4 It can be
seen from Panel C that the GME strategy yields 0.53% per month for the JT sample,
and 0.69% for the GM sample, again with a high level of statistical significance.
The value of momentum profits from this strategy is lower, as we are now choosing
“winners” and “losers” as the mp 30% and the bottom 30% respectively instead as
deciles in the above strategies. Finally, Panel D shows that the GMV strategy for the
JT sample yields momentum profits that are statistically indistinguishable from zero.
The same strategy for the GM sample yields 0.36% per month, this number being
(somewhat) statistically significant. These results are in sharp contrast to those
obtained by Moskowitz and Grinblatt ( 1999) for an identical time period. These
authors, using a sample of NYSE, AMEX and Nasdaq during 1963-1995, find that
the GMV strategy yields a profit of 0.43% with a t-statistic of 4.65. One reason for
this divergence could be that the criteria used for sample selection by Moskowitz and
Grinblatt are different from mine. For example, they exclude all stocks that do not
have available book-to—market data on the COMPUSTAT database. They need this
filter because they go on to adjust the returns of these stocks by portfolios based
on size and book-to-market characteristics. Since I do not need their filter, I use a
simple filter of prices below $5 to screen out “penny” stocks which may experience
huge variations that may potentially impact the (average) profitability of momentum
strategies.

Tables 3.2.1 and 3.2.2 present results on “industry momentum”. Each month,

 

‘See Hong, Lim, and Stein (1999) for evidence that once one moves past the very
smallest stocks, the profitability of momentum strategies declines sharply with firm
size.

112

 

I slot all stocks in my sample into 20 industry groups. I utilize the CRSP time
series of 2-digit SIC codes for the purpose of this classification, following Moskowitz
and Grinblatt. Details of the industry groups and summary statistics regarding the
number of firms in each group are provided in Table 3.2.1.

Table 3.2.2 presents results of the industry momentum strategy for both the JT
and the GM samples. To implement this strategy, all the industries are ranked in
descending order each month, based on their past 6—month returns. Monthly returns
for each industry are calculated as value-weighted averages of the firm returns consti-
tuting that industry. The industry momentum strategy is to form a portfolio that is
long the tOp i industries and short the bottom i industries. Results in the table show
four strategies: TOp 1 —Bottom 1 through Top 4 - Bottom 4. It can be seen that none
of these strategies, except the TOp 4 - Bottom 4 strategy for the GM sample, results
in any statistically significant profits. These results are in contrast to Moskowitz and
Grinblatt’s results, where they find that the Top 3 - Bottom 3 strategy yields 0.43%
per month with a t-statistic of 4.24. None of the strategies in my analysis yields such
strong and statistically significant industry momentum profits, as can be seen from
Panels A through D of Table 3.2.2. One possibility for this sharp divergence in results
could be the differing criteria for data filtration discussed earlier.

In Table 3.3, I present results of industry-adjusted momentum. Here, I rank
stocks based on their previous 6-month raw returns, but the holding period returns
are industry-adjusted by subtracting the corresponding industry return from the in-
dividual stock’s return. I have presented results for the JTV strategy only. This
strategy yields a profit of 0.61% per month for the JT sample, and 0.82% for the GM

113

sample. Both these numbers are highly statistically significant. Comparing them
to the unadjusted JTV strategy results (Table 3.1, Panel B) we see that profits are
slightly lower than the 0.74% and 0.99% respectively, obtained earlier. However, in-
dustry adjustment does not wipe out the profits of the momentum strategy as can be
seen from the high statistical significance of these profits. From the results in Tables
3.2.2 and 3.3, one can only conclude that for the samples of stocks that I consider, and
with the data filtration criteria that I employ, momentum is not an industry-driven
phenomenon, but is very much an individual firm phenomenon.

Having established that individual level momentum matters, I now seek to refine
the basic momentum strategy. In Tables 3.4.1 and 3.4.2, I present results of mo-
mentum strategies implemented in each industry growth category. At the beginning
of each month in each sample, I split the sample of stocks under consideration into
quintiles based on the growth in total assets of the corresponding industry in the two
years prior to the portfolio formation. It can be seen from Table 3.4.1 that the average
sizes of firm quintiles in the JT sample are higher than those in the GM sample. This
is not surprising considering the inclusion of Nasdaq firms in the former sample.

Within each quintile, I implement the four momentum strategies. Each Panel
of Table 3.4.2 presents the mean return on the “winner”-“loser” portfolios for all
quintiles, for one of the four momentum strategies considered. 1 also test whether
the difference between the momentum profits in the highest and the lowest quintiles
is statistically significant by means of a t-test for difference in means. It can be seen
from Panels A and B that, for both samples, the strongest results are for the JTE

and JTV strategies. There is a monotonic relationship between industry growth and

114

momentum profits, this effect being strongest for the JTE strategy and somewhat
muted for the JTV and the GMV strategies (Panel D). The t-tests for significance of
difference between the tOp and bottom growth quintiles are significant at the 10% level
for the JT sample, and at the 5% level for the GM sample. It can be seen that these
results are not merely due to a size effect; there is no clear monotonicity in size across
the quintiles in either sample. The results in this table are indicative of the fact that
industry growth is definitely one factor affecting momentum profits, as hypothesized
earlier. Also, a stratification of firms based on industry growth can be used to make
higher momentum profits than a generic momentum strategy implemented with the
universe of firms. For instance, the JTE strategy within the highest growth quintile
implemented for the JT (GM) sample (see Panel A) yields a profit of 1.17% (1.48%)
compared to a JTE strategy for the entire sample of firms (see Table 3.1, Panel A)
that yields 1.05% (1.26%) per month.

In Table 3.5, I Split each industry growth quintile into two groups, those firms
with higher asset growth than their corresponding industry, and those that have
lower growth compared to their industry average. Once again, results for all four
momentum strategies are presented here, one in each panel. Across all panels, the
strongest result that emerges from this table is that above average growth firms
have higher momentum profits than the below average growth firms. This result
holds across all quintiles in these strategies. For instance, under the JTE strategy
using the JT sample (see Panel A), momentum in the above average growth firms in
Quintile 1 is 1.36% while that for the below average growth firms in the same quintile

is 0.60%. Comparable numbers for the GM sample are 1.73% and 0.71%. Also,

115

 

the earlier recorded pattern of monotonicity in momentum profits across quintiles is
clearly evident for the higher relative growth firms, the statistical significance of the
difference between the profits of the tOp and bottom quintiles being very high in the

GM sample.

3.4 Conclusion

In this study, I use two samples for analysis: one including only NYSE/AMEX firms,
and the other including NYSE/AMEX and Nasdaq firms, and investigate momen-
tum profits for individual stocks split into quintiles by industry growth. I find that
individual stock momentum varies almost monotonically by industry growth. Firms
in highest industry growth quintile have significantly higher momentum compared to
those in the lowest industry growth quintile. I also separately investigate momentum
profits for two groups of firms within each industry growth quintile: those with asset
growth above the industry average, and those below the industry average. I find
that the above-average growth group within each quintile has significantly higher
momentum profits than the below-average group. The monotonicity of momentum
profits by industry growth is preserved among the higher relative growth firms. Fur-
ther, the momentum profits of the highest industry growth quintile are always higher
than those for the universe of firms, suggesting an economic benefit to stratifying
firms based on industry growth and relative company growth intra-industry, while

following a momentum investment strategy.

116

 

APPENDIX 3

TABLES FOR CHAPTER 3

Table 3.1
Momentum Portfolio Returns

This table presents monthly returns of the JTE and JTV momentum portfolios. Re

sults for the JT sample refer to strategies implemented for all NYSE/AMEX stocks
during 1965201 through 1997 :12 (T=396 months), while results for the GM sample re-
fer to momentum strategies implemented for all NYSE / AMEX/ Nasdaq stocks during
1963:08 through 1995:06 (T 2383 months). All stocks with prices less than $5 at the
time of portfolio formation are excluded from the sample. The momentum deciles are
formed based on 6-month lagged returns and held for six months. For the JTE (J TV)
strateg, P1 is the equal (value)-weighted portfolio of ten percent of stocks with the
highest six-month lagged returns, and P10 is the equal (value)-weighted portfolio of
the ten percent of stocks With the lowest six-month lagged returns.

 

Panel A: JTE Momentum Strategy
JT sample GM sample

 

 

 

P1(Past Winners) 1.67 1.71
P2 1.44 1.47
P3 1.35 1.37
P4 1.28 1.27
P5 1.27 1.25
P6 1.22 1.17
P7 1.20 1.13
P8 1.16 1.08
P9 1.08 0.95
P10 (Past Losers) 0.62 0.46
P1-P10 1.05 1.26
t-stat 5.26 6.34

 

 

Panel B: JTV Momentum Strategy
JT sample GM sample

 

 

 

P1(Past Winners) 1.43 1.50
P2 1.25 1.24
P3 1.14 1.14
P4 1.06 1.08
P5 1.02 0.93
P6 0.09 0.89
P7 1.00 0.95
P8 1.02 0.95
P9 0.99 0.90
P10 (Past Losers) 0.69 0.51
P1-P10 0.74 0.99
t-stat 3.17 4.14

 

118

Table 3.1 (Continued)

This table presents monthly returns of the GME and GMV momentum portfolios.
Results for the JT sample refer to strategies implemented for all N YSE / AMEX stocks
during 1965:01 through 1997:12 (T =396 months), while results for the GM sample
refer to momentum strategies implemented for all NY SE / AMEX / N asdaq stocks dur-
ing 1963:08 through 1995:06 (T =383 months). All stocks with prices less than $5
at the time of portfolio formation are excluded from the sample. GME refers to the
equal-weighted strategy with 30% breakpoints for “winners” and “losers”, GMV is
the same as GME strategy except that the “winner” and “loser” portfolios are value-
weighted.

 

Panel C: GME Momentum Strategy
JT sample GM sample

 

 

 

 

P1(Past Winners) 1.49 1.51
P2 1.24 1.20
P3 (Past Losers) 0.95 0.83
P1-P3 0.53 0.69
t-statistic 3.72 4.84

 

 

Panel D: GMV Momentum Strategy
JT sample GM sample

 

 

 

P1(Past Winners) 1.23 1.22
P2 0.99 0.96
P3 (Past Losers) 0.94 0.86
P1-P3 0.29 0.36
t-statistic 1.81 2.22

 

119

Table 3.2.1
Industry Groups: Description and Statistics

Details of the industry group classification are presented below. These industries are
formed monthly for both the samples considered. In case of the JT sample, these
are formed from January 1965 to December 1997 using the CRSP time series of SIC
codes for all the stocks on NYSE and AMEX. In case of the GM sample, these are
formed from August 1963 to June 1995 using the CRSP time series of SIC codes for
all the stocks on NYSE/AMEX and Nasdaq.- All stocks with prices less than $5 at
the time of classification are excluded from these industries.

 

 

 

Industry SIC Codes Avg. No. stocks
JT sample GM sample
1. Mining 10—14 121.32 160.68
2. Food 20 77.96 106.75
3. Apparel 22-23 69.05 86.65
4. Paper 26 37.80 47.90
5. Chemical 28 116.36 167.66
6. Petroleum 29 32.04 35.96
7. Construction 32 38.41 49.04
8. Prim. Metals 33 62.33 74.57
9. Fab. Metals 34 72.89 95.42
10. Machinery 35 126.92 209.26
11. Electrical Eq. 36 134.03 218.92
12. Tiansport Eq. 37 71.26 86.75
13. Manufacturing 3839 85.09 156.99
14. Railroads 40 15.22 18.49
15. Other Transport 41-47 44.76 70.79
16. Utilities 49 152.10 180.91
17. Dept. Stores 53 35.28 48.54
18. Retail 50—52,54—59 160.38 277.79
19. Financial 60-69 434.01 780.97
20. Other other 318.25 535.15

 

120

 

Table 3.2.2
Industry Momentum

This table presents results on momentum in the 20 industry portfolios formed with
both the JT and the GM samples, for a variety of strategies. The J T sample covers all
NYSE/AMEX stocks during 1965:01 through 1997:12, while the GM sample covers
all NYSE/AMEX and Nasdaq stocks during 1963:08 through 1995:06. In the table,
TOp i - Bottom i means that the i industry groups (of 20) with the highest 6-month
lagged return are designated as “winners” and the i industry groups with the lowest
6—month lagged return are termed “losers”. Returns and t-statistics are shown for a
portfolio that is long “winners” and short “losers” so defined.

 

Panel A: Top 1 - Bottom 1 Strategy
JT sample GM sample
Mean t-statistic Mean t-statistic
P1(Past Winners) 1.26 4.61 1.35 4.86

 

 

 

 

P2 1.03 4.50 0.99 4.28
P3 (Past Losers) 0.96 3.54 0.87 3.27
P1-P3 0.30 1.24 0.48 2.01

 

 

Panel B: 'Ibp 2 - Bottom 2 Strategy
JT sample GM sample

Mean t-statistic Mean t-statistic
P1(Past Winners) 1.23 4.82 1.28 4.94

 

 

 

 

P2 1.03 4.48 0.98 4.24
P3 (Past Losers) 0.95 3.68 0.90 3.54
P1-P3 0.28 1.45 0.37 1.92

 

121

Table 3.2.2 (Continued)

 

Panel C: Top 3 - Bottom 3 Strategy

 

JT sample GM sample

 

Mean t-statistic Mean t-statistic

 

P1 (Past Winners) 1.22 4.96 1.23 4.94

 

P2 1.03 4.47 0.98 4.24
P3 (Past Losers) 0.92 3.70 0.87 3.49
P1-P3 0.30 1.81 0.36 2.15

 

 

Panel D: Top 4 - Bottom 4 Strategy

 

JT sample GM sample

 

Mean t-statistic Mean t-statistic

 

P1(Past Winners) 1.21 5.01 1.22 5.01

 

P2 1.04 4.51 0.98 4.24
P3 (Past Losers) 0.89 3.61 0.84 3.43
P1-P3 0.32 2.17. 0.38 2.59

 

122

Table 3.3
Industry Adjusted Momentum

This table presents industry-adjusted momentum for both the JT sample and the
GM sample. The JT sample covers all NYSE /AMEX stocks during 1965:01 through
1997:12, while the GM sample covers all NYSE/AMEX and Nasdaq stocks during
1963:08 through 1995:06. All stocks with prices less than $5 at the time of portfolio
formation are excluded from the sample. Momentum deciles are formed based on
6-month lagged (raw) returns and held for six months. Holding period returns are
industry-adjusted i.e. the return of the corresponding industry group is subtracted
from each raw stock return. P1 is the value-weighted portfolio of ten percent of stocks
with the highest six-month lagged returns, and P10 is the value—weighted portfolio of
the ten percent of stocks with the lowest six-month lagged returns.

 

Momentum Strategy: JTV
JT sample GM sample

 

 

 

P1(Past Winners) 0.33 0.43
P2 0.16 0.18
P3 0.09 0.11
P4 0.05 0.07
P5 0.02 -0.01
P6 —0.04 -0.03
P7 0.00 0.00
P8 0.00 —0.01
P9 -0.03 -0.05
P10 (Past Losers) -0.28 -0.39
P1-P10 0.61 0.82
t-statistic 3.40 4.33

 

123

Table 3.4.1
Industry Growth Quintiles: Summary Statistics

At the beginning of each month, stocks are ranked into quintiles based on the two-
year growth in total assets of their corresponding industry. All stocks with prices
less than $5 at the time of portfolio formation are excluded from the sample. This
table presents summary statistics for the quintiles so formed for both the JT sample
and the GM sample. The JT sample covers all NYSE/AMEX stocks during 1965:01
through 1997 :12, while the GM sample covers all NYSE/AMEX and N asdaq stocks
during 1963:08 through 1995:06. The panels below present average size and average
growth for each growth quintile within each sample.

 

Panel A: Growth (70)
Growth Quintile JT Sample GM Sample

 

 

1 (Highest) 43.55 63.09
2 27.66 27.91
3 22.14 22.34
4 16.92 17.30
5 (Lowest) 8.97 9.91

 

 

Panel B: Size ($ mn)
Growth Quintile JT Sample GM Sample

 

 

1 (Highest) 893 481
2 989 525
3 867 511
4 1027 561
5 (Lowest) 1002 623

 

124

Table 3.4.2
Momentum and Industry Growth

This table presents individual stock momentum by industry growth for both the JT
sample and the GM sample. The JT sample covers all NYSE /AMEX stocks during
1965:01 through 1997 :12, while the GM sample covers all NYSE/AMEX and Nasdaq
stocks during 1963:08 through 1995:06. At the beginning of each month, stocks are
ranked into quintiles based on the two-year growth in total assets of their correspond-
ing industry. All stocks with prices less than $5 at the time of portfolio formation are
excluded from the sample. Mean returns shown are the returns on “winner”-“loser”
portfolios for each of the four strategies implemented, within each quintile.

 

Panel A: J TE Momentum Strategy

 

 

 

 

JT sample GM sample
Growth Quintile Mean Return t-statistic Mean Return t-statistic
1 (Highest) 1.17 5.00 1.48 4.96
2 1.15 5.22 1.22 5.15
3 0.86 4.03 0.92 3.78
4 0.86 4.01 0.88 3.78
5 (Lowest) 0.57 2.88 0.63 2.62
t—statistic 1.95 2.12
p-value (0.0515) (0.0347)

 

 

Panel B: J TV Momentum Strategy

 

 

 

 

JT sample GM sample
Growth Quintile Mean Return t-statistic Mean Return t-statistic
1 (Highest) 0.76 2.82 1.00 3.20
2 1.01 3.84 1.14 4.35
3 0.92 3.55 1.01 3.80
4 0.79 2.90 0.85 2.69
5 (Lowest) 0.11 0.48 0.18 0.80
t-statistic 1.84 1.95
p-value (0.0659) (0.0516)

 

125

Table 3.4.2 (Continued)

 

Panel C: GME Momentum Strategy

 

 

 

 

JT sample GM sample
Growth Quintile Mean Return t-statistic Mean Return t-statistic
1 (Highest) 0.55 3.42 0.80 3.36
2 0.61 4.15 0.72 4.03
3 0.41 2.80 0.50 2.66
4 0.50 3.31 0.59 3.17
5 (Lowest) 0.33 2.64 0.46 2.23
t-statistic 1.07 1.29
p—value (0.2841) (0.1976)

 

 

Panel D: GMV Momentum Strategy

 

 

 

 

JT sample GM sample
Growth Quintile Mean Return t-statistic Mean Return t-statistic
1 (Highest) 0.34 1.80 0.49 1.88
2 0.51 2.86 0.54 3.06
3 0.31 1.69 0.35 1.83
4 0.38 2.13 0.41 2.04
5 (Lowest) -0.07 -0.45 0.03 0.17
t-statistic 1.68 1.58
p-value (0.0937) (0.1153)

 

126

 

 

 

 

 

 

 

 

822: 85.8 8.2a

m2 a.“ 9833

£2... 3: a? a3 a...” £5 :83qu 1..
$82 an m3 3.: m3 2: v
88.: and man :5 m3 ”2 m
3:3 9% 8.” 8.: 8.... on; a
58.9 t.“ 3.” :5 as «.5 :sgwé s
$36 a; «3. a; as...» a: 5..

vacuum EU

$3.98 22:3 833

mg 8; 8:383

new; 9.2 was ”no we” was :83qu m.
5:3 ".2 2s 3.: as 2:. v
3.8.; new a: on... was a: m
38.: 8s 3.” 2:. as as a
$85 2.“ v3 8.; c3 e3 9853 H
:85 new 3.» %s as 53 E.
2:979 cams—3m-“ £33.33 53% .822 0:33?“ 538m 582 235:0 5390

8:98me mafia omcuo>< ape—om SEE omauo>< m>on<
935m a...

 

Amen—53m 53.8532 mun—L. ”< Back

 

%mech wt: 2: no.“ mom—organ ..8mo_..-..8q53.. no
2:38 2: 8w .223 an: E 53% £552 :32 .oonmmmm awn—85 momma? waist 933m cacmmz can Xm2<\mm>z =w E38

9388 2O 2: 253 .332 5.5:: 882 mass 9.8%. xmz<\mm>z =.w 228 mass .5. 2a. 83.59 20 2: is t.
2: flop H8 255:0 532m remix: :38 35:5 532m 3388 25ch 13 83.882: #906 :32sz $585 2&3 at;

539—0 %RQEOO gued—om can 53ch about:— .Egnofioz
m.» 03mm.

127

 

 

 

 

 

 

 

53.8 8:38 :32:

:3 8.: 3:533

m:::.: :3 3.: 5.: :5 :m: 2833: m
8%.: 3.: 2.: 3.: 8.: ::.: v
:3:.: :2 3.: 3.: 3.: :2 :
2.8.: 8.: 3.: 3.: vs: :3 :
38.: :3 3.: 3.: :3 :2 ragga :
$8.: :3 3.: 3.: :3 3.: 3

2.58m 20

3:32 53:: 59-:

:3 :3 05:32

:3: ::.: ::.:- 8:- «:4 S: 9833: :
::::.: 2.: 3.: 8.: 8.: ::.: v
22.: :5 :2 ::.: 3.: 8.: :
A2%.: 8.: :3 8.: 3.: 3: :
$8.: :2 :3 :v: 8.: 3: 383m: _
:23: x: E: :m: R: 3: 3:
05—97:“ US$033; umummadamua Hun—50¢ so: omammedawnu asué so: 355:0 8.39:0

 

8:20me

3:3 «@294 32mm

85m omauo>< 269:.

 

Sana—am En.

 

amen—3am 53.3562 >BH ”m 3.3m

 

62.5280: 9: 2%,:

128

 

 

 

 

 

 

sane 8:3: 2.33

85 B.“ 33:33

33.: m2 2: 5o 23 :3 :83qu m
$53 a; Sn :3 a; 3.: v
2.8.: 3% c2 2.: 3v «3 m
38.: a.“ 2: 3.: m3 2; a
£85 a: a: 23 ea... 2: 9835 _
3.86 we.” a.“ m2 m3 :3 =<

295m 20

83.98 85:: 233

3.: m2 0:333

£25 23 m2 8.: we.“ :8 :83qu m
2&3 «3 c3 3.: E.” a; v
5:; an.“ :3 2:. 5.” S... m
585 3.“ 2: a... «.2 E. N
£85 a: 2.“ «2 3.” E... 2835 _
$26 2.» 8a 23 a: Rs =<
03.97““ Umummumumua umummaflemua nausea so: umawmadamuu nuns—QM 502 23590 5.30.20

 

8.83.99

SEE ammum>< 3075

SEE owwuo>< m>on<

 

«Baum H...

 

39.935 83.5502 "520 "D .055

 

€859.88 m.» 2an

129

 

 

 

 

 

 

 

83mg 3.39.8 0295

:2 3.: 5:583

92:: 2:- 2...: 5.: ::.: ::.: 38%: n
8%.: 2.: :3 8.: ::.: a: v
82.: :3 z: E: 2...: 2.: :
25:: 2.: :3 a: 5.: 8.: :
33:: :2 :3 ::.: ::.: E: 3835 :
:35: :3 :3 2.: :3:- ::.: E.-

oasam :5

8:38 35:3 3.2-:

2.: 2.: 26:83

:8: 8:- ::.:- 3:- ::.:- 8:- 3833: m
:8: ::: :3 8: :2 2.: .-
23: a: S: S: :5 5.: m
:8: :3 :2 ::.: 8.: 8.: :
ES: :3 8.: ::.: 3.: S: smegma: :
8%.: :3 :9: 2.: ::.: 2:: E.-
oEgd 03:33:-» 05:53:: 550m .832 03:53:: Egg :82 25:30 530:6

ooamuoma nah-m mum-8:3:- Bo_mm max-m $825. 963:.

 

vacuum Ba

 

.3335 53.3502 >20 “G 3.3%

 

£85280: .3 2%.:-

130

BIBLIOGRAPHY

REFERENCES FOR CHAPTER 3

BIBLIOGRAPHY

Ahn, Dong-Hyun, Jennifer S. Conrad, and Robert F. Dittmar, 1999, Risk adjustment
and trading strategies, University of North Carolina working paper.

Barberis, Nicholas, Andrei Shleifer, and Robert Vishny, 1998, A model of investor
sentiment, Journal of Financial Economics 49, 307—343.

Chan, Louis K.C., Narasimhan Jegadeesh, and Josef Lakonishok, 1996, Momentum
strategies, Journal of Finance 51, 1681—1714.

Conrad, Jennifer S., and Gautam Kaul, 1998, An anatomy of trading strategies,
Review of Financial Studies 11, 489—519.

Daniel, Kent, David Hirshleifer, and Avanidhar Subrahmanyam, 1998, Investor psy-
chology and security market under-and overreaction, Journal of Finance 61, 1839—
1886.

Daniel, Kent, and Sheridan Titman, 1999, Market efficiency in an irrational world,
Northwestern University working paper.

DeBondt, Werner F.M., and Richard H. Thaler, 1985, Does the stock market overre-
act?, Journal of Finance 40, 793—805.

 

, 1987, Further evidence on investor overreaction and stock market seasonality,
Journal of Finance 42, 557-581.

DeLong, J. Bradford, Andrei Shleifer, Lawrence H. Summers, and Robert J. Wald-
mann, 1990, Positive feedback investment strategies and destabilizing rational spec-
ulation, Journal of Finance 45, 379—395.

Fama, Eugene F., 1998, Market efficiency, long-term returns, and behavioral finance,
Journal of Financial Economics 49, 283—306.

 

, and Kenneth R. French, 1996, Multifactor explanations of asset pricing
anomalies, Journal of Finance 51, 55—84.

Hong, Harrison, Terence Lim, and Jeremy C. Stein, 1999, Bad news travels slowly:
Size, analyst coverage, and the profitability of momentum strategies, forthcoming
Journal of Finance.

Hong, Harrison, and Jeremy C. Stein, 1999, A unified theory of underreaction, mo-
mentum trading and overreaction in asset markets, Journal of Finance 54, 2143—
2184.

132

 

Jegadeesh, Narasimhan, and Sheridan Titman, 1993, Returns to buying winners and
selling losers: Implications for stock market efficiency, Journal of Finance 48, 65-
92.

 

, 1999, Profitability of momentum strategies: An evaluation of alternative
explanations, N BER working paper 7159.

Lee, Charles M.C., and Bhaskaran Swaminathan, 2000, Price momentum and trading
volume, forthcoming Journal of Finance.

Moskowitz, Tobias J ., and Mark Grinblatt, 1999, Do industries explain momentum?,
Journal of Finance 54, 1249—1290.

Rouwenhorst, Geert K., 1998, International momentum strategies, Journal of Finance
53, 267—284.

133

HICHIGQN STATE UN V.

I|I3I|II1IIIII2IIIIISIIIIIIIIIIIIIIIII III |II8ILIII|III|I8IIIIIII|ES