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The approach taken here is to recognize and model two prominent features of theIPO market that break the CAPM: participation restrictions and investor heterogeneity.Two types of particip

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

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.

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Bell & Howell Information and Learning Company

300 North Zeeb Road P.O Box 1346 Ann Arbor, MI 48106-1346

Copyright May 2000

by Kehong Wen

Essays on the Equilibrium Valuation of IPOs and Bonds

by

Kehong Wen Doctor of Philosophy in Business Administration

University of California at Berkeley

Professor Mark Rubinstein, Chair

Chapter 1 of this dissertation provides rational explanations for the IPO underperformancepuzzle IPO underperformance is shown to arise in three equilibrium models with investorheterogeneity and participation restrictions The models also help explain why IPO under-performance is concentrated in small stocks and why the average IPO return can be belowthe risk-free rate In these models, IPO residual risk acts as a source of systematic risk.Schumpeterian creative destruction plays a key role in one of the models This model isextended into a dynamic setting in Chapter 2 to demonstrate that persistent after-marketunderperformance is consistent with a rational expectations equilibrium Building on thedynamic extension, a uni…ed framework is o¤ered in Chapter 3 to address all three IPOpricing puzzles Many testable implications are derived and presented in detail to facilitatefuture empirical work

Chapter 4 investigates the general equilibrium implications of introducing new

industries into the economy It …rst establishes that the equilibrium of an N-industry exchange economy supports an N-factor Vasicek term structure of interest rates It thenshows that industry characteristics enter as direct determinants of the yield curve, theterm premium, the forward premium, and the stock premium Depending on the nature

pure-of industry heterogeneity, the term structure pure-of interest rates and the stock premium canhave 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 assetsrepresenting high impact industries can have negative return premia over bonds This helpsexplain why new industries may appear over-valued at times

Professor Mark RubinsteinDissertation Committee Chair

To my wife, Yunfang Lu,

and my daughter, Yanming Melinda Wen,

the stars in my life.

1.1 Introduction 1

1.2 Relation to Other Work 8

1.3 Model Setup 11

1.4 “Creative Destruction” 13

1.5 Heterogeneous Belief 24

1.6 Preference for Skewness 28

1.7 Long-run Underperformance: Benchmarks and Sources 33

2 A Dynamic After-market Model 36 2.1 Model Setup 36

2.2 Equilibrium 39

2.3 Testable Implications 44

2.4 Conclusion 46

3 A Uni…ed Approach to the Three IPO Puzzles 48 3.1 Introduction 48

3.2 Underpricing and Hot-issue Market 52

3.3 Testable Implications 60

3.4 Relation to Other Work 62

3.4.1 Underpricing Literature 62

3.4.2 Hot-issue Market 66

3.4.3 Relation between Underperformance and Underpricing 68

3.5 Conclusion 69

4 Equilibrium Valuation in a Vasicek Economy with Heterogeneous Indus-tries 70 4.1 Introduction 70

4.2 The Model 76

4.3 The One-factor Vasicek Model 79

4.4 The Multi-factor Vasicek Term Structure 85

4.4.1 The Two-factor Case 85

4.4.2 Equilibrium Security Prices 88

4.4.3 Properties of the Two-factor Term Structure 90

4.4.4 The N-factor Case 96

4.5 Stock-fund Valuation 97

4.6 Comparative Dynamics 105

4.6.1 Yield Curve Dynamics 106

4.6.2 Term Premium and Stock Premium 107

4.7 Conclusion 110

List of Figures

4.1 The solid line plots the quadratic function ± = 1 + "(1 + ")´: The dotted lineplots the quadratic function " = ¡±(± ¡ 1)=´ ¡ 1: The Relative volatility isde…ned as ´ = ¾2

M=¾2

N: 944.2 Extending Figure 4.1 into the full parameter space R2: 1074.3 When relative volatility ´ is increased, the solid line narrows and drop downfurther into the third quadrant The dotted line ‡atten out 1094.4 When ´ is decreased, the solid line ‡atten out, while the dotted line narrowsand expands further into the …rst quadrant 110

List of Tables

1.1 Asset payo¤s with di¤erential positive skewness 304.1 Yield curve dynamics in the one-factor case 83

I thank …rst of all my committee members for their general guidance for completing thework presented in this dissertation I thank Jonathan Berk, Henry Cao, Sanjiv Das, Pe-ter DeMarzo, Greg Du¢e, Dwight Ja¤ee, Matthew Spiegel, Brett Trueman, Hal Varian,Miguel Villas-Boas, Ivo Welch, and especially Mark Rubinstein, for helpful discussions andcomments Jay Ritter provided very detailed comments on the work presented in Chapter

1 I also thank my fellow Ph.D students at the Haas School of Business, especially Yuan

Ma, Mark Taranto, Zane Williams, Nick Wonder, and Hong Yan for helpful discussions

as-Current research in this area focuses on econometric issues and model speci…cation

1 See Ibbotson (1975) for the …rst systematic study on underpricing, and Ibbotson and Ja¤e (1975) for their early work on hot-issue markets Ibbotson and Ritter (1995) provide an extensive survey of the IPO literature.

issues that are di¢cult to disentangle for long-window event studies (Brav and Gompers

1997, Barber and Lyon 1997, Brav 1998, Fama 1998, Loughran and Ritter 1998) Little oretical work has been done, however, to o¤er insights into IPO long-run underperformanceand its relation to underpricing Investor naivete appears to be a popular explanation forthese 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 Morerecently, Teoh, Welch, and Wong (1998) argue that investors may be systematically fooledalso by earnings management of issuers They conclude that “ it is unlikely that anyfully rational theory will be able to explain why some rational investors are willing to holdIPOs in the after-market Returns for what are likely to be risky and illiquid investmentsare simply too low to be explained by known equilibrium models.”

the-The primary purpose of this chapter is to provide rational equilibrium models thatcan explain low (average) after-market IPO returns2 Clearly, to develop such models, onemust go beyond the traditional Capital Asset Pricing Model (CAPM) of Sharpe (1964) andLintner (1965), since many assumptions underlying that model do not apply to the IPOmarket The approach taken here is to recognize and model two prominent features of theIPO 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 whichinsiders 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.

days or longer) has lapsed It is also well known that shorting IPOs can be di¢cult, if notentirely 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 asmore shares become available for borrowing The gradual relaxation of restrictions putsdownward pressures on price – leading to underperformance for IPOs, as compared to otherbenchmark securities that have less or no such restrictions These two e¤ects help explainIPO underperformance, but they are not the only source of underperformance

Investor heterogeneity contributes, in a more essential way, towards IPO formance The fact that IPO investors are heterogeneous is evidenced by the unusually largetrading volume on the …rst public trading day of most IPOs (Miller and Reilly 1987, Hegdeand Miller 1989) The existence of large trading volumes in securities markets is one of theimportant reasons for moving from the representative-agent model to explicit modeling ofinvestor heterogeneity (Varian 1989, Wang 1994) In developing a set of static models, Iallow, separately, for di¤erent endowments, di¤erent probability beliefs, and di¤erent pref-erences These models demonstrate that a certain degree of investor heterogeneity alonecan be su¢cient to generate IPO underperformance Compounding on these heterogeneitye¤ects are the e¤ects due to the short-sale cons

underper-t wiunderper-th a raunderper-tional equilibrium, some invesunderper-tors musunderper-t have special reasons underper-towant to hold IPO stocks These investors want the shares so much that they are willing topay high prices Three such special reasons are considered explicitly One, some investors

hold IPO stocks in order to hedge their human capital risks Two, some investors havemore favorable probability beliefs for IPO stocks than other investors do The short-saleconstraint prevents these other investors from driving down the after-market price Three,some investors exhibit preference for skewness, and IPO stocks are known to have positivelyskewed distributions (see e.g Ibbotson 1975, Barber and Lyon 1997).

Another key intuition is that investors in the IPO market are looking for somethingspecial, something that they cannot get by holding seasoned securities More precisely, someinvestors are particularly interested in the residual risk (the risk which is not spanned byexisting securities) of IPOs IPO residual risk acts as a source of systematic risk and is priced

in equilibrium From the point of view that innovation is the source of sustained economicgrowth and economic development (Schumpeter 1934, 1942), new enterprises represent thefuture of the economic system Therefore, the risk associated with the emergence of newindustries becomes part of the economy-wide systematic risks

This paper shows how these intuitions work by constructing and solving threecompletely speci…ed models The set of static models are mostly extensions of Lintner(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 ofother issues involving heterogeneous investors I simplify his model setting to one with tworisky assets and two heterogeneous agents Generalization to cases with more than tworisky 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.

price for the constraint.

In contrast to most recent IPO models, I retain the simplicity of symmetric mation in Lintner’s model This allows me to deal with multiple risky assets fairly easilyand 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, forthe problem at hand, the results obtained here suggest that this popular assumption is notnecessary

infor-More importantly, I extend Lintner’s model to the case with heterogeneous ments, the case he does not consider in the paper This case is particularly relevant in thecurrent study for two reasons First, it is the most tractable case The closed-form solution

endow-is found to be strikingly simple and the price impacts of participation restrictions can beclearly identi…ed with their sources This greatly facilitates analysis and extension

Second, an important idea related to Schumpeterian “creative destruction” peter 1942) is introduced in this case Brie‡y speaking, one class of investors is endowedwith 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 areled by entrepreneurs equipped with innovative technologies Initial public o¤erings of thesenew enterprises provide a unique opportunity for the threatened investors to hedge againstthe possible erosion of their future endowments This hedging demand is a powerful motivefor these investors to hold IPOs in the after-market As a result, this hedging-demand e¤ectalone is su¢cient to explain the low expected return of IPOs

(Schum-Rational investors are willing to hold IPOs and receive low expected returns are

also obtained in the case that investors di¤er in their probability assessments and in thecase that some investors exhibit preference for skewness These results help strengthen theconclusion that rational models can produce the kind of IPO underperformance observedfrom data I also …nd that in these two cases, while share-supply restriction always has ane¤ect, a short-sale restriction may or may not have an e¤ect.

I then develop in Chapter 2 a dynamic extension of the static model with neous endowments, so that the intertemporal aspect of IPO after-market performance underthe environment of changing participation restrictions can be analyzed I obtain closed-formsolution for the dynamic rational-expectations equilibrium The equilibrium concept used

heteroge-is the Radner (1972) equilibrium of plans, prices, and price expectations Using the modelsolution, it is readily shown that, regardless of the number of periods, a similar underper-formance result is obtained in the dynamic context as well The most important messageregarding long-run performance that comes out of this exercise is two-fold On one hand,there are legitimate reasons to expect persistent IPO underperformance over the long run,supporting the still controversial empirical …nding of Ritter (1991) On the other hand,attributing such …nding to things such as persistent investor overoptimism is premature.The dynamic extension also paves the way for linking long-run performance of IPOs to theirinitial pricing mechanism4

This paper also produces some unanticipated results, the …rst of which has to dowith the degree of underperformance It is shown that under a mild condition, the expectedrate of return from IPOs can in fact be below risk-free rate Such a surprising result has

4 This subject is taken up in Chapter 3.

previously been observed by Loughran and Ritter (1995) in their empirical work with dataspanning more than two decades, from the 1970s to the 1990s At a …rst glance, this severeunderperformance presents an insurmountable hurdle to a rational theory Indeed, it isdi¢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 demonstratethat, when a su¢cient degree of heterogeneity is allowed, this counter-intuitive result cannevertheless be consistent with a rational equilibrium In particular, the hedging demanddriven by the economic force of creative destruction is powerful enough to support such anequilibrium.

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, Bravand Gompers (1997) …nd that long-run underperformance of IPOs concentrates in smallissues, 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 stylethree-factor model used in that study is an empirically motivated model (see Fama andFrench 1992) Absent a theoretical model in which size enters in a meaningful way, “one ismerely 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 inwhich size enters in a well-speci…ed way In view of such relationships, the result found byBrav and Gompers can be interpreted As will be shown in Sections 1.4-1.6, the inverse ofthe size of the IPO stock appears in the coe¢cients of factors that determine IPO expectedreturn Hence, size matters in cross-sectional regressions, but not as a risk factor And since

there is a negative sign in front of the coe¢cients, the smaller the size, the more severe theunderperformance, other things being equal.

The rest of the paper is organized as follows Section 1.2 discusses the relationbetween the explanation o¤ered here and those o¤ered in several published papers Section1.3 sets up the basic model structure for the three static models presented in Sections1.4-1.6 A distinct type of investor heterogeneity is considered in each model The mostimportant case is the one with heterogeneous endowments, in which the Schumpeteriancreative destruction process is formalized This model is further developed into a multi-period rational expectations model in Sections 2.1-2.2 Section 2.3 presents a number oftestable implications to facilitate future empirical work Section 2.4 concludes and discusseslimitations and possible future extensions of the static and dynamic models developed inChapter 1 and Chapter 2 All formal proofs are collected in the Appendix

1.2 Relation to Other Work

Miller (1977) provides an intuitive explanation for IPO underperformance based ondivergence of investor opinions, under the condition of no short sales The partial equilib-rium analysis is recently formalized by Morris (1996), who shows that heterogeneity of priorbeliefs and a binding short-sale constraint can support a …nitely lived price bubble Morrisargues that this speculative bubble explains why IPOs appear over-valued immediately afterissuance, relative to their long-run values

The explanation o¤ered by Miller or Morris relies on the hypothesis that divergence

of opinions would narrow over time after the IPO The logic is that as the …rm grows older,

the value of assets in place will grow relative to di¢cult-to-value growth options Whether

or not that does happen systematically is a di¢cult empirical issue This paper does notrely on heterogeneous beliefs as the sole source of IPO underperformance Other forms ofinvestor heterogeneity are also important, and their implications are easier to test than theimplications derived from divergence of opinions

Both Miller and Morris assume that short sales are not permitted for any stock.However, substantial short interests exist for seasoned equities IPOs, on the other hand,are much more di¢cult to short at the beginning5 This paper allows di¤erent stocks to bedi¤erentially short-sale constrained More importantly, the constraint on IPOs is allowed

to change over time

Allowing di¤erential short-sale constraints also distinguishes my models from mostequilibrium models with multiple securities and short-sale constraints in the literature (seee.g Lintner 1969, Jarrow 1980, Sharpe 1992) Explicit pricing impact of the short-saleconstraint is derived in my models by obtaining its shadow price explicitly This permits aclear analysis on comparative statics

A salient feature of the IPO market emphasized here is that IPOs face more nounced restrictions when they come to the market and that these restrictions are eventuallyrelaxed 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 positiontaken in Miller (1977), my models show that explicitly incorporating market frictions tends

pro-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.

to support the e¢cient market hypothesis (the semi-strong form), which merely says thatsecurity prices re‡ect all public information Section 4 shows, when the knowledge of marketfrictions 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 theIPO 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 eventsattempts to create an illusion of hot shows by issuing tickets at a sale price Such temporaryfads must eventually fade away, resulting in long-run underperformance This hypothesisimplies a signi…cant correlation between the measure of underpricing and the measure oflong-run underperformance Empirical evidence does not appear to support this impli-cation6 Another implication of Shiller’s hypothesis is that average cumulative abnormalreturn, including the initial return, should not go below zero in the long-run This is notconsistent with the results reported in Ritter (1991)

Similar to Shiller(1990), Ritter (1991) and Loughran and Ritter (1995) argue thatthere is a “window of opportunity” in which investors are over-optimistic about new …rms’prospects Issuing …rms, instead of their bankers, take advantage of these swings of investorsentiment by timing their IPOs Firms that go public successfully within these windowswill then underperform relative to a market benchmark While there is clear evidence oftiming in the IPO market (Lerner 1994), there is no clear reason why such a window opens

6 Ritter (1991) attempts to identify a relationship between underpricing and underperformance He cludes underpricing as a right-hand-side determinant in his OLS regression for long-run returns, and …nds that underpricing is the only regressor having insigni…cant in‡uence A similar result is found in Hanley’s (1993) regression.

in-from time to time.

Teoh, Welch, and Wong (1998) …nd evidence suggesting that investors may be tematically fooled by issuing …rms’ earnings management They …nd …rms that aggressivelymanage their earnings when going public tend to underperform various benchmarks in theafter-market It is reasonable to argue that if the earnings management e¤ect exists system-atically, short sellers should be able to take advantage of it The reason they cannot do socould be because of the existence of short-sales constraints If the short sale e¤ect is takeninto consideration, I conjecture that the earnings management e¤ect will be weakened

sys-In contrast to the above three explanations, which in one form or another rely oninvestor naivete, the explanation o¤ered in this chapter is based on investor rationality

1.3 Model Setup

This section develops three one-period models, focusing on the equilibrium pricingimpacts of the short-sale constraint and limited share supply when investors di¤er in theirendowments, beliefs, and preferences The basic setup for these models is outlined as follows

Asset and Distribution Consider a competitive, pure exchange economy in whichthere are only two risky assets: asset 1 stands for the “market” (excluding IPO stocks) andasset 2 for an IPO stock (or a portfolio of IPO stocks) Let J ´ f1; 2g There is also arisk-free asset, with zero net supply, available for trading Without loss of generality, letthe exogenous interest rate be zero The payo¤ from asset 1 at the end of the period is

M, which is normally distributed with mean ¹M and variance ¾2

M The payo¤ from asset

2 is aM + N, where a is a small fraction, and, in the case with heterogeneous endowments

N is normally distributed with mean ¹N and variance ¾2

N In the case with heterogeneouspreferences, N has in addition a non-zero third moment (see Section 3.3) M and N areindependent Hence, a measures the correlation between these two assets, and N representsthe component of the IPO payo¤ which is not spanned by existing securities, i.e N is theresidual risk of the IPO7 In the case with heterogeneous beliefs, the probability assessment

is agent-speci…c (see Section 3.2) It is natural to assume ¹M À ¹N; ¾M À ¾N: I alsoassume a2¾2

M ¿ a¾2

M ¿ ¾2

N to re‡ect the fact that the residual component N is a muchriskier component All parameters are positive

Investor Preference For simplicity, I consider only two classes of investors, A and

B Let I ´ fA; Bg Each investor maximizes expected utility over end-of-period wealth:

Ei[Ui(Wi)], i2 I The utility function for each agent is further specialized to the constantabsolute risk aversion (CARA) class in the …rst two cases In the third case, preference forskewness is introduced

Endowment Agents are endowed with initial …nancial wealth fWi

0gi2I They arealso endowed with non-tradeable, uncertain incomes feigi 2I that are received at the end ofthe period

Participation Restriction There is no restriction on investment in asset 1 Thetotal number of shares of asset 1 is normalized to one There is a lower bound l 6 0 forshorting asset 2 It is de…ned as the negative of the ratio of the total number of sharesavailable 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.

for trading is », which is de…ned as the ratio of the ‡oat8 over the shares outstanding Forsimplicity, share supply » is taken to be exogenous to the market.

1.4 “Creative Destruction”

Joseph Schumpeter, in one of his classics (Schumpeter 1942), characterizes talism by its incessant “Creative Destruction” process, driven by entrepreneurial creativityand technological innovation “The fundamental impulse that sets and keeps the capitalistengine in motion comes from the new consumers’ goods, the new methods of production ortransportation, the new markets, the new forms of industrial organization that capitalist en-terprise creates.” The competition thus created is “competition which commands a decisivecost or quality advantage and which strikes not at the margins of the pro…ts and the outputs

capi-of the existing …rms but at their very foundations and their very lives.”

Recently, Schumpeter’s vision of capitalism has received revived interest amongeconomic growth theorists (Romer 1986, 1990, Lucas 1988, Aghion and Howitt 1992, 1994).According to the New Growth Theory, it is the endogenous production of new knowledgethat holds the key to sustained economic growth However, as Fischer Black (1995, pp.107-110) observes, new knowledge damages the value of old knowledge since new knowledge

“steals the market” from old knowledge and reduces its productivity Black’s observation isforeshadowed by Schumpeter’s view that the process of creative destruction is “the essentialfact about capitalism.”

This vision of capitalism is perhaps nowhere more apparent than in the dynamic

8 The ‡oat is the number of shares that are actively tradable in the market, excluding shares subject to lockup restrictions.

IPO market, where new …rms enter the public capital market for the …rst time Thesenew …rms are very often led by entrepreneurs who use and develop new technologies Thecompetitive threat they impose on old …rms points most directly to old technologies andexisting knowledge9 This process of creative destruction has important rami…cations inthe asset market To construct a stock market model that re‡ects this e¤ect of creativedestruction, it is natural to consider the link between the income derived from old knowledgeand the payo¤ from the new stock The following assumption formalizes this link:

Assumption In addition to …nancial asset WA

0 , investor A is also endowed with ´ units of

a non-tradeable asset, which is interpreted as labor income derived from old knowledge.Each unit pays o¤

Y = bM¡ N,

where b is assumed to be a small fraction

Remark 1 Therefore, A’s future endowment eA= ´Y = ´(bM¡N); where ¡N representsthe destruction e¤ect from the new enterprise (IPO …rm), in the following sense Inthe event that new knowledge prevails, old knowledge su¤ers Moreover, the higher the

9 The creative destruction e¤ect is dramatically illustrated by some internet IPOs in 1990s Netscape, a pioneer of the World Wide Web browser, threatened to topple the domination of Microsoft in the software market for personal computers and network computers Amazon.com, the pioneer of online retailing, imposed intense competitive pressure on traditional “bricks-and-mortar” business models, with its enormous cost advantage and superior customer service, both enabled by the proliferation of the internet E*Trade, a pioneer of online brokerage, has not only helped spawn a whole new industry, but also challenged the very relevance of traditional brokers In all these examples, it is not so much that new businesses are replacing old businesses, since they in fact help to expand the markets, but rather that old practices are forced to change Hence, Microsoft started to embrace the internet; Barnes and Noble had to learn online book-selling; and Merrill-Lynch has to walk a …ne line between going online and keeping the privilege of its army of traditional brokers What had been working well has become vulnerable Knowledge and skills accumulated through years of experience and training are becoming less relevant and less productive and hence are commanding less rewards.

expected payo¤ for the new stock generated from taking on the residual risk (i.e higherthe ¹N), the more expected damage for A’s endowment Hence, successful creation

of a high-potential new …rm or a new industry means serious destruction of existinghuman capital It is important to note that the creative destruction process going

on between the new enterprise (aM + N) and the existing human capital (bM ¡ N)

is through the state variable N: This state variable is associated with the emergence

of the new enterprise The process happens only in one direction: from the newenterprise to existing knowledge This captures the spirit of Schumpeter’s discussionquoted above The correlation, which can be any number between ¡1 and +1, betweenpayo¤s aM +N and bM ¡N, is determined by the coe¢cients a and b: The magnitude

of ´ measures the degree of erosion of old knowledge

Remark 2 This assumption and the assumption about the IPO payo¤ (aM + N) ognize the crucial role of residual risk in a new enterprise Here, residual risk isnon-diversi…able, since, as Schumpeter envisioned, these new competitors are forcingtheir way into the mainstream In other words, residual risk is becoming part of thesystematic risk The “creative destruction” process makes certain investors particu-larly interested in the IPO residual risk Consequently, the residual risk is priced inequilibrium

rec-Remark 3 The idea embodied in the above formulation is similar in spirit to Aghion andHowitt (1994) in the sense that new technology may cause unemployment in businessesusing old technology

It is reasonable to think that the creative destruction process must be happening

also in the product market, as in Aghion and Howitt (1992), and hence it may bedesirable to consider a similar relation between the payo¤ of the new stock and thepayo¤s of some existing stocks However, this kind of relation is not considered here,for it does not matter for the purpose of this paper More speci…cally, the a¤ected oldstocks are tradeable assets, which will not cause IPO underperformance in the currentmodel.

I assume eB = 0, to emphasize that these two agents have entirely di¤erent futureendowments B represents professional investors For simplicity, both investors are assumed

to have the same CARA utility function with parameter ½ Each solves the followingoptimization problem

max

® i ; µ i j

De…nition The equilibrium of this pure exchange …nancial market economy is a set ofportfolio holdings and security prices f®i; µij; Pjgi 2I;j2J such that: (a) f®i; µijg solvesthe optimization problem (1.1) for each agent, and (b) security markets clear, i.e

®A+ ®B = 0; µA1 + µB1 = 1; µA2 + µB2 = »:

In order to solve for the equilibrium, let us consider …rst the benchmark case in

which the short-sale constraint is absent, i.e l = ¡1: The equilibrium for the benchmarkcase is characterized by the following proposition.

Proposition 1 (Unrestricted Short Sale) If l = ¡1; the equilibrium asset prices andthe optimal portfolio holdings are:

Do people actually behave this way when facing the competitive threat from anemerging new industry? This is an important empirical question that lies outside thescope of this paper There is no question that within this model it is optimal for A tohedge by purchasing the IPO stock In reality, though, people may have other ways

to deal with the problem when facing possible erosion of human capital They maydecide to invest more in themselves to pick up new skills However, we must realizethat human capital accumulation is a slow and time-consuming process For thosewho have been successful and have already passed their best learning age, the only

viable choice is probably to invest in new enterprises through the capital market It isentirely reasonable to believe that people may be behaving this way, since those whoface the competitive threat the most are in the best position to recognize it early andhedge accordingly Technological leaders such as Microsoft and Intel certainly behavethis way They are known for their strategic investments in promising start-up …rms.Remark 2 Rearranging, P2 can be decomposed into four distinct components:

P2 = a¹M + ¹N (expected payo¤)

2½(a

2¾2M + ¾2N)(1¡ ») (share-supply e¤ect)+1

2½(¾

2

N ¡ ab¾2M)´ (hedging-demand e¤ect)

The …rst two terms are familiar The last two e¤ects are especially important in theIPO market The thinner the ‡oat, the higher the share-supply e¤ect When the

‡oat is equal to the number of shares outstanding, 1 ¡ » = 0, the share-supply e¤ectvanishes This e¤ect can be exploited to arti…cially support the IPO price Indeed,typically within a week after an IPO, underwriters selectively buy back shares forissues that have fallen below their corresponding o¤er prices (Hanley et al 1993,Schultz and Zaman 1994, Prabhala and Puri 1998, Aggarwal 2000) By doing so,underwriters extract shares out of the ‡oat, thereby decreasing » A direct implicationfrom the result above is that the higher the total volatility of the IPO stock ( a2¾2M+

¾2

N), the more e¤ective the price support

The hedging-demand e¤ect comes from the fact that in order to hedge against

the possible erosion of future labor income, A is willing to pay an extra price for theIPO If there is no endowment di¤erence, i.e ´ = 0; A and B simply divide up theshares of the IPO The di¤erence of the optimal holdings of asset 2 between A and

B is exactly ´, the di¤erence in units of endowment between the two agents Thehedging demand term can be regarded as a measure of the “impactness” of the IPO.The higher the impact this new business has, the higher the price it can command.Since the a¤ected labor income can be very substantial, this hedging-demand e¤ectcan be quite signi…cant

Using …nancial assets to hedge labor income risk is a theme that has receivedincreasingly sophisticated mathematical treatment in the recent …nance literature (see,e.g Dybvig 1990, He and Pagés 1993, Cuoco 1997, Du¢e et al 1997) However,this literature is mainly concerned with portfolio problems and o¤ers little help foranalyzing the speci…c pricing impact of the hedging demand For that, one needs anequilibrium approach in which asset prices are solved for10 The model presented hereprovides an extremely simple way to characterize this impact

Corollary 1 is immediate and will be needed to establish Theorem 1

Corollary 1 (Short Sale Condition) Investor B will short the IPO stock if and only if

2 below establishes the condition under which the expected rate of return from the IPOstock can be below the risk-free rate.

Corollary 2 The expected rate of return from the IPO stock is below the risk-free rate, ifand only if

N Hence the condition is approximately equivalent to

´ > », the same as the short sale condition stated in Corollary 1

Remark Corollary 2 shows that even without considering the short-sale constraint e¤ect, it

is possible to rationalize the empirical observation that average IPO return can times be below the T-bill rate (see Loughran and Ritter 1995 for empirical evidence).Corollary 3 The traditional CAPM does not hold in this economy Instead, the followingCAPM-like relations hold:

¾2

M¾2 N

(1 + a)2¾2

M + ¾2 N

; j 2 J:

Remark 1 The relation shown in (1.2) can be thought of as a three-factor model with a

“‡oat” factor and an “endowment impact” factor, in addition to the market factor

In contrast to the usual sense of a factor being a risk factor, here, (1 ¡ ») and ´ areboth certain Nevertheless, this result has a clear cross-sectional implication for IPOs:expected return is lower if the ‡oat is lower, or if the “destruction impact” is higher,

or both These two additional factors contribute to IPO underperformance, making

it possible to have E(R2)¡ ¯2E(RS) below zero

The result in Corollary 3 is related to the two-beta CAPM derived in ers (1972) Similar to the result obtained by Mayers, this result shows that non-marketable assets can have a non-trivial impact on asset pricing

May-Remark 2 The residual risk of IPOs is essential for the asset pricing relationship derivedhere There is a clear cross-sectional implication following from the market completionfunction of IPOs: IPOs of traditional …rms like UPS, Goldman Sachs, and restaurantsshould have higher expected returns than IPOs of more innovative …rms such as theinternet companies This implication is generally consistent with the broad feature ofIPO underperformance reported in the literature (see e.g Ritter 1991, 1998)

Remark 3 It is interesting to note that coe¢cient Áj is inversely related to market ization Pj This implies that underperformance is especially pronounced for small-sizestocks, holding constant other parameters, especially the residual variance ¾2

capital-N This

is consistent with the empirical …nding that IPO long-run underperformance tends toconcentrate in small IPO stocks, as reported in Ritter (1991, Table IV) and Brav andGompers (1997) However, it is important to note that even though size is important

in explaining expected IPO returns, it is not a risk factor.

Now we are ready to consider the case with short sales restrictions on the IPO

We have the following main result of this subsection

Theorem 1 (Restricted Short Sale) Let ¡1 6 l 6 0; the equilibrium asset prices aregiven by

P1 = ¹M ¡1

2½(1 + a» + b´)¾

2

M;

P2 = a¹M + ¹N (expected payo¤)

¡12a(1 + a)½¾2M ¡12½¾2N (risk-aversion e¤ect)+1

2½(a

2¾2M+ ¾2N)(1¡ ») (share-supply e¤ect)+1

2½(¾

2

N ¡ ab¾2M)´ (hedging-demand e¤ect)+½¾2Nmax[l¡ 1

2(»¡ ´); 0] (short-sale constraint e¤ect)

The optimal portfolio holdings are:

Comparing the results in Theorem 1 to those in Proposition 1, we see that the price

of asset 1 is not a¤ected by the short-sale constraint on asset 2, although each investor’sportfolio holdings are a¤ected by the constraint The new e¤ect on IPO price is simplyanother separate term added to the previous four terms This new term has an “option-like” feature: it is positive if and only if the short-sale constraint is binding for B Moreover,given » and ´, it is linearly increasing in l in the interval [1

2(»¡ ´); 0]

Among the three price supporting factors, the short-sale constraint is most likelythe only one over which investment bankers can exert substantial control in the long run.This result shows that tightening the short-sale restriction can be very e¤ective in main-taining high after-market valuations for IPOs, especially for those IPOs of high residualvariance.

Clearly, Corollary 2 of Proposition 1 holds through when short-sale constraint

is binding, since now E(R2) is even lower Hence the conclusion that it is possible forrational investors to demand low returns from IPOs is reinforced by limited short sales.The following corollary extends Corollary 3 above

Corollary There are four factors determining expected asset returns:

E(R1) = ¯1E(RS) + Á1(1¡ ») + Á1(1 + a + b)´

+2Á1(1 + a)[l¡1

2(»¡ ´)]+;E(R2) = ¯2E(RS)¡ Á2(1¡ ») ¡ Á2(1 + a + b)´

¡2Á2(1 + a)[l¡1

where, all parameters are the same as in Corollary 3 of Proposition 1

Remark (Cause of Long-run Underperformance) In light of this corollary, there are

at least three sources that may lead to the long-run underperformance of IPOs as

…rst documented in Ritter (1991) They are a thin ‡oat, a hedging demand due tocreative destruction, and a binding short-sale constraint Compared to a referencestock that has 100% ‡oat (i.e 1 ¡ » = 0), that does not impose a competitive threat

to the established human capital (´ = 0), and that faces no short-sale constraint

(l = ¡1), an IPO stock commands an expected return which is lowered by an amount

Á2f(1 ¡ ») + (1 + a + b)´ + 2(1 + a)[l ¡ 12(» ¡ ´)]+g: These three factors work inthe same direction, and all of them become less signi…cant as time goes by, sinceinsiders will be selling (increasing »), competition will catch up (decreasing ´), andshort sales will become easier (decreasing l) When using the traditional CAPM tomeasure performance of individual IPO stocks, there are the same three sources ofunderperformance

The result has a cross-sectional implication based on comparative statics Over thesame time period, other things being equal, the larger the increase in ‡oat, the more severethe underperformance; the higher the impact on existing human capital at the beginning, themore severe the underperformance; the larger the decrease of a binding short-sale restriction,the more severe the underperformance

1.5 Heterogeneous Belief

In this subsection, the Lintner (1969) model is extended in the direction of erogeneous probability beliefs, incorporating the e¤ect of a short-sale constraint Lintner(1969) has already investigated extensively the equilibrium impact of heterogeneous beliefswhen no short sales are allowed The distinction here is that I focus on the di¤erentialshort-sale constraint, and work out its equilibrium pricing impact explicitly

het-The case of heterogeneous beliefs with short-sale constraints is important, for tworeasons First, the IPO market is one of the most speculative segments of the capital market:short operation history and lack of …nancial transparency may lead to a great degree of

divergence of beliefs or opinions among investors Second, the di¢culty in shorting IPOsmay arti…cially in‡ate their prices, since pessimists cannot express their opinions freely andconsequently the optimists are the ones determining the equilibrium price This is the viewexpressed in Miller (1977) and in Morris (1996) in a single stock context.

However, as Jarrow (1980) shows, in a multiple securities context, a substitutione¤ect may undo the price in‡ation caused by a no-short-sale constraint Hence it is im-portant to study the short-sale constraint e¤ect in a model with multiple stocks Thissubsection works out a fully speci…ed model showing that Miller’s intuition is correct whenthe IPO stock is short-sale constrained but the “market” (excluding the IPO stock) is not.For our purpose, a setting with di¤erential short-sale constraints is more reasonable thanthe setting used in Jarrow (1980), since new stocks and old stocks face di¤erent constraints

Consider again a market consisting of the two risky assets, 1 and 2 They arejointly normally distributed The two risk-averse investors A and B are identical exceptthat they have di¤erent beliefs about the mean and variance-covariance matrix of the assetdistribution For investor i; asset 1 is Normal (¹i

Following a similar procedure as in the last subsection, we have a sequence ofresults

Proposition 2 If l = ¡1 (i.e there is no short-sale constraint), then the equilibrium

prices and asset holdings are:

P1 = ¹M ¡ ½(1 + a»)¾2M;

P2 = a[¹M ¡ ½(1 + a»)¾2M] + ¹N ¡ ½»¾2N;

µA1 = ¡aµ¹;N ¡ a»µB¾;N + µ¹;M + (1 + a»)µB¾;M;

µB1 = aµ¹;N ¡ a»µA¾;N ¡ µ¹;M + (1 + a»)µA¾;M;

µA2 = µ¹;N + »µB¾;N; µB2 =¡µ¹;N + »µA¾;N;

where, ¹j ´ ¹Aj § B

j § A j

Corollary (Short Sale Condition) B will choose to short the IPO if and only if ¹A

It is interesting to note that the short sale condition does not involve short-seller’sbelief of ¾2

N; nor anyone’s belief on asset 1’s distribution

There are no counterparts of Corollary 2 and Corollary 3 of Proposition 1 rem 2 in the following is the counterpart of Theorem 1

Theo-Theorem 2 (Restricted Short Sale) Assume ¹A

N ¡ ¹B

N > ½»§AN and ¡1 6 l 6 0; theequilibrium prices are

P1 = ¹M ¡ ½(1 + a»)¾2M;

P2 = a¹M+ ¹N (expected payo¤)

¡12a(1 + a)½¾2M ¡12½¾2N (risk-aversion e¤ect)+1

2½(a

2¾2M + ¾2N)(1¡ ») (share-supply e¤ect)+½(§AN)(l¡ lB2)+ (short-sale constraint e¤ect),

and the optimal portfolio holdings are

Remark 1 Compared to the results in Proposition 2, the price of asset 1 here is not a¤ected

by a short-sale constraint on asset 2 The net result of imposing a short-sale constraint

on the IPO stock is to increase the IPO price whenever the constraint is binding This