Essays on the Equilibrium Valuation of IPOs and Bonds
by
Kehong Wen
B.S.(University of Science and Technology of China) 1987
Ph.D. (The University of Texas at Austin) 1993
A dissertation submitted in partial satisfaction of the
requirements for the degree of
Doctor of Philosophy
in
Business Administration
in the
GRADUATE DIVISION
of the
UNIVERSITY of CALIFORNIA at BERKELEY
Committee in charge:
Professor Mark Rubinstein, Chair
Professor Henry Cao, Co-Chair
Professor Nils Hakansson
Professor Roger Craine
May 2000
UMI Number: 9981117
Copyright 2000 by
Wen, Kehong
All rights reserved
______________________________________________________________
UMI Microform 9981117
Copyright 2000 by Bell & Howell Information and Learning Company.
All rights reserved. This microform edition is protected against
unauthorized copying under Title 17, United States Code.
_______________________________________________________________
Bell & Howell Information and Learning Company

underperformance is consistent with a rational expectations equilibrium. Building on the
dynamic extension, a uni…ed framework is o¤ered in Chapter 3 to address all three IPO
pricing puzzles. Many testable implications are derived and presented in detail to facilitate
future empirical work.
Chapter 4 investigates the general equilibrium implications of introducing new
2
industries into the economy. It …rst establishes that the equilibrium of an N-industry pure-
exchange economy supports an N-factor Vasicek term structure of interest rates. It then
shows that industry characteristics enter as direct determinants of the yield curve, the
term premium, the forward premium, and the stock premium. Depending on the nature
of industry heterogeneity, the term structure of interest rates and the stock premium can
have qualitatively di¤erent dynamics. Depending on how industries interact, the market-
price-of-risk vector may admit di¤erent signs for its components. Consequently, risky assets
representing high impact industries can have negative return premia over bonds. This helps
explain why new industries may appear over-valued at times.
Professor Mark Rubinstein
Dissertation Committee Chair
iii
To my wife, Yunfang Lu,
and my daughter, Yanming Melinda Wen,
the stars in my life.
iv
Contents
List of Figures vi
List of Tables vii
1 A Rational Approach to IPO Underperformance 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Relation to Other Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3 Model Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4 “Creative Destruction” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.6.1 Yield Curve Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.6.2 Term Premium and Stock Premium . . . . . . . . . . . . . . . . . . 107
4.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5 References 112
A Proofs 118
vi
List of Figures
4.1 The solid line plots the quadratic function ± = 1 + "(1 +")´: The dotted line
plots the quadratic function " = ¡±(± ¡ 1)=´ ¡ 1: The Relative volatility is
de…ned as ´ = ¾
2
M
=¾
2
N
: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.2 Extending Figure 4.1 into the full parameter space R
2
: . . . . . . . . . . . . 107
4.3 When relative volatility ´ is increased, the solid line narrows and drop down
further into the third quadrant. The dotted line ‡atten out. . . . . . . . . . 109
4.4 When ´ is decreased, the solid line ‡atten out, while the dotted line narrows
and expands further into the …rst quadrant. . . . . . . . . . . . . . . . . . 110
vii
List of Tables
1.1 Asset payo¤s with di¤erential positive skewness . . . . . . . . . . . . . . . . 30
4.1 Yield curve dynamics in the one-factor case . . . . . . . . . . . . . . . . . . 83
viii
Acknowledgements
I thank …rst of all my committee members for their general guidance for completing the

these puzzling observations. For instance, Shiller (1991) proposes an “impresario” hypoth-
esis, which implies that investors are systematically fooled by investment bankers. Ritter
(1991) interprets some of his results as being consistent with Shiller’s hypothesis. More
recently, Teoh, Welch, and Wong (1998) argue that investors may be systematically fooled
also by earnings management of issuers. They conclude that “ it is unlikely that any
fully rational theory will be able to explain why some rational investors are willing to hold
IPOs in the after-market. Returns for what are likely to be risky and illiquid investments
are simply too low to be explained by known equilibrium models.”
The primary purpose of this chapter is to provide rational equilibrium models that
can explain low (average) after-market IPO returns
2
. Clearly, to develop such models, one
must go beyond the traditional Capital Asset Pricing Model (CAPM) of Sharpe (1964) and
Lintner (1965), since many assumptions underlying that model do not apply to the IPO
market. The approach taken here is to recognize and model two prominent features of the
IPO market that break the CAPM: participation restrictions and investor heterogeneity.
Two types of participation restriction are considered: share-supply restrictions and short-
sale restrictions. It is well known that almost all IPOs have lockup policies by which
insiders agree not to sell their shares until after a certain period of time (typically, 180
2
Chapter 3 studies the inter-relations among all three IPO puzzles, building on a dynamic model developed
in Chapter 2.
3
days or longer) has lapsed. It is also well known that shorting IPOs can be di¢cult, if not
entirely impossible. These restrictions in‡ate IPO after-market prices. Over time, however,
both restrictions are relaxed, since more shares become available when insiders sell more
of their shares or when IPO …rms issue more equities, and short sales become easier as
more shares become available for borrowing. The gradual relaxation of restrictions puts
downward pressures on price – leading to underperformance for IPOs, as compared to other
benchmark securities that have less or no such restrictions. These two e¤ects help explain

(1969)
3
along the aforementioned three dimensions of investor heterogeneity. Lintner (1969)
deals with the equilibrium impact of a no-short-sale constraint, in addition to a rich set of
other issues involving heterogeneous investors. I simplify his model setting to one with two
risky assets and two heterogeneous agents. Generalization to cases with more than two
risky assets and/or more than two agents is straightforward. I allow for di¤erent degrees
of short-sale constraints and derive explicitly the pricing impact by obtaining the shadow
3
I thank Mark Rubinstein for singling out to me this important reference.
5
price for the constraint.
In contrast to most recent IPO models, I retain the simplicity of symmetric infor-
mation in Lintner’s model. This allows me to deal with multiple risky assets fairly easily
and to extend one of the models to a multi-period setting in a straightforward manner.
This is not to deny the existence or importance of asymmetric information. However, for
the problem at hand, the results obtained here suggest that this popular assumption is not
necessary.
More importantly, I extend Lintner’s model to the case with heterogeneous endow-
ments, the case he does not consider in the paper. This case is particularly relevant in the
current study for two reasons. First, it is the most tractable case. The closed-form solution
is found to be strikingly simple and the price impacts of participation restrictions can be
clearly identi…ed with their sources. This greatly facilitates analysis and extension.
Second, an important idea related to Schumpeterian “creative destruction” (Schum-
peter 1942) is introduced in this case. Brie‡y speaking, one class of investors is endowed
with a non-tradeable asset that derives future payo¤ from existing knowledge. This estab-
lished knowledge is challenged by the introduction of new enterprises which frequently are
led by entrepreneurs equipped with innovative technologies. Initial public o¤erings of these
new enterprises provide a unique opportunity for the threatened investors to hedge against
the possible erosion of their future endowments. This hedging demand is a powerful motive

previously been observed by Loughran and Ritter (1995) in their empirical work with data
spanning more than two decades, from the 1970s to the 1990s. At a …rst glance, this severe
underperformance presents an insurmountable hurdle to a rational theory. Indeed, it is
di¢cult to imagine such a result, which implies a negative risk premium, from an equilib-
rium model with homogeneous agents. The models presented in this chapter demonstrate
that, when a su¢cient degree of heterogeneity is allowed, this counter-intuitive result can
nevertheless be consistent with a rational equilibrium. In particular, the hedging demand
driven by the economic force of creative destruction is powerful enough to support such an
equilibrium.
The second of these unanticipated results is related to the well-debated size e¤ect
in the asset pricing literature (Banz 1981, Berk 1995). Within the IPO literature, Brav
and Gompers (1997) …nd that long-run underperformance of IPOs concentrates in small
issues, after controlling for size and book-to-market as two independent pricing factors.
Interpretation of this …nding is not clear, however, mainly because the Fama-French style
three-factor model used in that study is an empirically motivated model (see Fama and
French 1992). Absent a theoretical model in which size enters in a meaningful way, “one is
merely testing whether any patterns that exist are being captured by other known patterns”
(Loughran and Ritter 2000). This paper derives CAPM-like asset pricing relationships in
which size enters in a well-speci…ed way. In view of such relationships, the result found by
Brav and Gompers can be interpreted. As will be shown in Sections 1.4-1.6, the inverse of
the size of the IPO stock appears in the coe¢cients of factors that determine IPO expected
return. Hence, size matters in cross-sectional regressions, but not as a risk factor. And since
8
there is a negative sign in front of the coe¢cients, the smaller the size, the more severe the
underperformance, other things being equal.
The rest of the paper is organized as follows. Section 1.2 discusses the relation
between the explanation o¤ered here and those o¤ered in several published papers. Section
1.3 sets up the basic model structure for the three static models presented in Sections
1.4-1.6. A distinct type of investor heterogeneity is considered in each model. The most
important case is the one with heterogeneous endowments, in which the Schumpeterian

constraint is derived in my models by obtaining its shadow price explicitly. This permits a
clear analysis on comparative statics.
A salient feature of the IPO market emphasized here is that IPOs face more pro-
nounced restrictions when they come to the market and that these restrictions are eventually
relaxed to some “normal” levels. Presumably, these market imperfections are all public in-
formation, and hence their e¤ects should be re‡ected in prices. Contrary to the position
taken in Miller (1977), my models show that explicitly incorporating market frictions tends
5
Wen (1999) contains references and discussions on related empirical facts. The key fact is that most of
the shares are closely held – the public ‡oat is typically only 10-30% of the shares outstanding immediately
after the o¤ering, and the pre-issue shareholders rarely allow thier shares to be borrowed for shorting. Also,
shares held in street name by the managing underwriter are most likely not available for shorting. I thank
Jay Ritter for pointing out this key fact.
10
to support the e¢cient market hypothesis (the semi-strong form), which merely says that
security prices re‡ect all public information. Section 4 shows, when the knowledge of market
frictions is included in the public information set, IPO prices follow a martingale process.
When the knowledge is omitted, IPO prices follow a strict supermartingale process.
Shiller (1990) presents an “impresario” hypothesis for IPOs. He argues that the
IPO market is subject to fads, and that investment bankers exploit these fads opportunis-
tically by underpricing IPOs to create excess demand, just as a manager of musical events
attempts to create an illusion of hot shows by issuing tickets at a sale price. Such temporary
fads must eventually fade away, resulting in long-run underperformance. This hypothesis
implies a signi…cant correlation between the measure of underpricing and the measure of
long-run underperformance. Empirical evidence does not appear to support this impli-
cation
6
. Another implication of Shiller’s hypothesis is that average cumulative abnormal
return, including the initial return, should not go below zero in the long-run. This is not
consistent with the results reported in Ritter (1991).

the exogenous interest rate be zero. The payo¤ from asset 1 at the end of the period is
M, which is normally distributed with mean ¹
M
and variance ¾
2
M
. The payo¤ from asset
2 is aM + N, where a is a small fraction, and, in the case with heterogeneous endowments
12
N is normally distributed with mean ¹
N
and variance ¾
2
N
. In the case with heterogeneous
preferences, N has in addition a non-zero third moment (see Section 3.3). M and N are
independent. Hence, a measures the correlation between these two assets, and N represents
the component of the IPO payo¤ which is not spanned by existing securities, i.e. N is the
residual risk of the IPO
7
. In the case with heterogeneous beliefs, the probability assessment
is agent-speci…c (see Section 3.2). It is natural to assume ¹
M
À ¹
N
; ¾
M
À ¾
N
: I also

also endowed with non-tradeable, uncertain incomes fe
i
g
i2I
that are received at the end of
the period.
Participation Restriction. There is no restriction on investment in asset 1. The
total number of shares of asset 1 is normalized to one. There is a lower bound l 6 0 for
shorting asset 2. It is de…ned as the negative of the ratio of the total number of shares
available for short sale over the total number of shares outstanding. IPO shares available
7
Mauer and Senbet (1992) provide an excellent discussion on why IPOs are best viewed as not being
spanned by existing securities, in a non-trivial sense. They also provide empirical evidence supporting this
view. They focus on the underpricing problem and do not develop a sequential, rational expectations model,
whereas in this paper I focus on long-run, sequential markets.