HOT MARKETS, INVESTOR SENTIMENT, AND IPO PRICING
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Forthcoming, Journal of Business
Preprint typeset using LATEX style emulateapj v. 6/21/04
HOT MARKETS, INVESTOR SENTIMENT, AND IPO PRICING
Alexander Ljungqvist
Stern School of Business, NYU and CEPR
Vikram Nanda
University of Michigan Business School
and
Rajdeep Singh
Carlson School of Management, University of Minnesota
Forthcoming, Journal of Business
ABSTRACT
We model an IPO company’s optimal response to the presence of sentiment investors and short-sale
constraints. Given regulatory constraints on price discrimination, the optimal mechanism involves the
issuer allocating stock to ‘regular’ institutional investors for subsequent resale to sentiment investors,
at prices the regulars maintain by restricting supply. Because the hot market can end prematurely,
carrying IPO stock in inventory is risky, so to break even in expectation regulars require the stock
to be underpriced – even in the absence of asymmetric information. However, the offer price still
exceeds fundamental value, as it capitalizes the regulars’ expected gain from trading with the senti-
ment investors. This resolves the apparent paradox that issuers, while shrewdly timing their IPOs
to take advantage of optimistic valuations, appear not to price their stock very aggressively. The
model generates a number of new and refutable empirical predictions regarding the extent of long-run
underperformance, offer size, flipping, and lock-ups.
Subject headings: Behavioral corporate finance; initial public offerings; investor sentiment; long-run
underperformance.
1. INTRODUCTION little light on the long-run performance of IPOs.2 Work
There are several anomalous aspects to the process by on long-run performance is primarily empirical and em-
which firms go public [Ritter and Welch (2002)]. Initial phasizes the role of investor sentiment and bounded ra-
public offerings (IPOs) exhibit positive first-day returns tionality in explaining the price behavior of IPO stocks.
on average and so seem to be ‘underpriced’. The initial The impact of investor sentiment is regarded as partic-
price run-up appears to be undone in subsequent months ularly acute in hot markets. Over time, investor exu-
as IPO stocks underperform the market.1 Hence, from berance fades, resulting in long-run underperformance.
the vantage of a longer horizon, IPOs can arguably be re- Loughran, Ritter, and Rydqvist (1994) go further in
garded as ‘overpriced’ in the after-market. The strength claiming that issuers ‘time’ their IPOs to coincide with
of these patterns varies over time, with both the ini- periods of excessive optimism, consistent with the finding
tial price run-up and subsequent underperformance more in Lee, Shleifer, and Thaler (1991) that more companies
dramatic in ‘hot’ periods of high IPO volume [Ritter go public when investor sentiment is high. Such patterns
(1984, 1991)]. Firms may even be able to ‘time’ their IPO can persist if rational investors are dissuaded by the cost
to coincide with periods of excessive valuations [Baker of implementing arbitrage strategies [Shleifer and Vishny
and Wurgler (2002)]. (1997), Lamont and Thaler (2003)].
What is one to make of these patterns? The litera- The behavioral story sketched above has some obvi-
ture offers no consensus. There are numerous models of ous appeal, but it raises an apparent paradox: if issuers
IPO underpricing, typically based on investor rationality are regarded as rational and shrewd enough to choose
in incomplete information settings, but these have shed a hot market in which to go public, why are they less
than aggressive in setting the offer price? After all, it
Electronic address: aljungqv@stern.nyu.edu (Ljungqvist), seems plausible that the presence of sentiment investors
vnanda@umich.edu (Nanda) and rajsingh@umn.edu (Singh). could lead to higher offer prices and a lower level of un-
1 There is a debate in the literature as to whether IPOs really
derpricing as rational issuers take advantage of them.
do underperform. Ritter (1991) shows that they underperform
the index, while Brav and Gompers (1997) and Brav, Geczy, and Reconciling the simultaneous existence of underpricing
Gompers (2000) show that they are not alone in doing so: small and long-run underperformance thus requires additional
and high-growth companies also underperform the index. Once structure on the behavioral assumptions and the nature
that is taken into account, IPO firms appear to perform no worse of the economic environment.
than similar firms (i.e. small and high-growth companies). The
evidence in these later papers is consistent with the possibility that The task we set ourselves in the paper is, therefore,
investors get optimistic about small and high-growth firm stocks,
2 Among these are explanations based on the ‘winner’s curse’
not just IPO stocks, and firms choose to go public at that time.
Our model takes this as a given and derives pricing implications [Rock (1986)], signaling [Allen and Faulhaber (1989), Welch
from issuers’ optimizing behavior. (1989)], cascades [Welch (1992)], and investor incentives to reveal
information truthfully [Benveniste and Spindt (1989)].2 Ljungqvist, Nanda and Singh
to develop a model of IPO pricing in hot issue mar- is an attempt to capture the equilibrium response of is-
kets that elucidates the connection between underpricing suers and underwriters in the face of divergence of opin-
and long-run underperformance. We ask, what should a ion among investors. It is thus related to an empirical
profit-maximizing issuer do in the presence of exuberant literature in which firms act strategically to take advan-
investor demand and short-sale constraints? We argue tage of the market’s mispricing or mis-perceptions.4
that the issuer should seek to capture as much as pos- We do not attempt to rationalize the existence or be-
sible of the surplus under the exuberant investors’ de- havior of exuberant investors. Biases that might lead
mand curve, in a setting where demand may build over to such behavior have been studied by psychologists for
time. We derive an optimal mechanism (which we argue some time and financial economists have recently intro-
is consistent with institutional reality) that achieves the duced them into formal models. See Daniel, Hirshleifer,
issuer’s first-best outcome. and Subrahmanyam (1998) for a discussion of the litera-
The model starts with the premise that some investors ture.
may, on occasion, be ‘irrationally exuberant’ about the Testing a model that relies on investor sentiment re-
prospects of IPOs from, say, a particular industry. As- quires unique and refutable empirical predictions. Our
suming short-sale constraints, this is consistent with model generates a number of novel predictions:
long-run underperformance.3 More interestingly, the
model suggests possible connections between IPO under- • Companies going public in a hot market underper-
performance and the initial price run-up. We show that form, both relative to the first-day price and the
value to an issuer is maximized if underwriters allocate offer price. Underperformance relative to the first-
IPO shares to their regular (institutional) investors for day price is not a surprising prediction; it follows
gradual sale to sentiment investors who arrive in the mar- from the twin assumptions of sentiment investors
ket over time. Regulars maintain stock prices – thereby and limits to arbitrage. Underperformance relative
extracting surplus from sentiment investors – by holding to the offer price is a stronger (and novel) predic-
IPO stock in inventory and restricting the availability of tion. It follows because the offer price will exceed
shares. Underpricing emerges as fair compensation to fundamental value by an amount equal to the is-
the regulars for expected inventory losses arising from suer’s share in the surplus extracted from the sen-
the possibility that sentiment demand may cease. In re- timent investors. Cross-sectionally, we predict that
turn, the expropriation of value from sentiment investors the extent of underperformance relative to the of-
is capitalized into a higher offer price than would other- fer price increases in the issuing firm’s bargaining
wise be the case. power vis-à-vis the underwriter.
For the inventory holding strategy to be implemented, • As investor sentiment grows, IPO offer size in-
there must either be a dominant investor or, when there creases and lower-quality companies are taken pub-
are many investors, it must be incentive compatible for lic, resulting in a decrease in average issuer quality.
regular investors not to deviate by selling their IPO al-
locations prematurely. To deter cheating, it may be nec- • Underwriters penalize investors who engage in ex-
essary for the underwriter to punish deviations from the cessive flipping. Importantly, they do so even in
equilibrium strategy. We show that the degree of the IPOs that do not receive price support. Such penal-
underwriter’s ability to impose penalties determines the ties are targeted primarily at retail and infrequent
optimal size of an offer, the extent of underpricing, and investors.
subsequent long-run performance.
It is worth emphasizing that when there is a dominant • Corporate insiders are released early from their
investor or when the underwriter can impose sufficient lock-up provisions, if after-market demand from
costs to ensure cooperation among regular investors, the sentiment investors is unexpectedly strong, once
full benefits are passed on to the issuer in the form of regular investors have unloaded their excess inven-
a higher offer price. In the economic environment we tory, or if the hot market has come to an end.
model, issuers cannot do better by the use of alternative Our model also addresses two hitherto puzzling empir-
ways to sell equity. For instance, if the issuer were to ical findings:
engage in a quick succession of equity offerings (an IPO
followed by seasoned offerings), the value obtained would • Ritter (1991) documents that underpricing and
not exceed the value from the inventory holding process long-run performance are negatively related, while
we model. In any case, issuing stock repeatedly over a Krigman, Shaw, and Womack (1999) find a posi-
short period is implausible, given significant economies tive relation. Our model shows that the relation is
of scale in issuing costs and the necessity to satisfy reg- not necessarily monotonic. In particular, we show
istration and disclosure requirements repeatedly. that the relation is negative only if the probability
Our paper has a focus quite different from much of of the hot market ending is small.
the existing work in behavioral finance. The behavioral
• The empirical evidence on the relation between
finance literature has tended to focus on asset pricing
underwriter prestige and underpricing is mixed.
anomalies, such as the predictability of returns, the eq-
Consistent with evidence from the 1990s [Beatty
uity premium puzzle, and under- and over-reactions [for
and Welch (1996)], we predict that underpricing
an exhaustive survey, see Hirshleifer (2001)]. Our model
increases in underwriter prestige, but that this re-
3 In a different setting Miller (1977) shows that a divergence lation depends on the state of the IPO market.
of beliefs – similar to the notion that some investors are more
4 For example, see D’Mello and Shroff (2000) and Dittmar (2000)
optimistic than others – can lead to long-run underperformance.
on firms’ strategic use of share repurchases.Hot Markets, Investor Sentiment, and IPOs 3
Two recent papers that test some of the main predic- by the presence of optimistic investors.5 Pessimistic in-
tions of our model, and that provide empirical support vestors, if present, are prevented from expressing their
for it in the context of the recent ‘dot-com mania’, are demands by short-sale constraints, which are pervasive
Ofek and Richardson (2003) and Dorn (2002). Ofek and in IPOs.6 As will become clear later, short-sale con-
Richardson show that high initial returns occur when in- straints arise naturally in our model. Though they hold
stitutions sell IPO shares to retail investors on the first excessively optimistic beliefs about the prospects of firms
day, and that such high initial returns are followed by going public, s-type investors still act rationally given
sizeable reversals to the end of 2000, when the bubble their beliefs, in ways we will make more precise shortly.
had burst. This is precisely the pattern we predict, and The second investor type holds beliefs that correspond
it highlights the importance of heterogeneous beliefs and to an unbiased estimate of the issuing firm’s future
short-sale constraints in explaining both the initial IPO prospects. It may be reasonable, for instance, to regard
price run-up and longer-term performance. Using Ger- institutional investors as belonging to this category. For
man data on IPO trading by 5,000 retail customers of an expositional ease, we will label these investors ‘rational’.
online broker, Dorn documents that retail investors over- All other market participants (issuers, underwriters) are
pay for IPOs following periods of high underpricing in re- taken to be rational and value-maximizing as well. There
cent IPOs, and for IPOs that are in the news. Consistent is no private or asymmetric information in the model,
with our model, he also shows that hot IPOs pass from and the nature and characteristics of the market partic-
institutional into retail hands. Over time, high initial ipants and their beliefs are common knowledge. Hence,
returns are reversed as net purchases by retail investors sentiment and rational investors know each others’ be-
subside, eventually resulting in underperformance over liefs, but still ‘agree to disagree’ on the valuation of the
the first six to 12 months after the IPO. IPO shares.7 For simplicity, everyone is taken to be risk-
The paper proceeds as follows. The basic model is neutral.
developed in Section 2. In Section 3, we analyze the is- The model has four relevant dates: t = 0, 1, 2, and T .
suer’s optimal unconstrained strategy for extracting sur- At t = 0, the period prior to the offering, the pricing
plus from the exuberant investors. Since this strategy and size of the IPO are determined. Date t = 1 is the
would violate regulatory rules, we derive in Section 4 initial day of trading in the IPO shares. Once trading
an alternative mechanism that implements the optimal has begun, the market may continue to be hot – that is,
strategy, which involves inventory-holding by a regular it may continue to be characterized by the presence of
investor. We solve for the optimal issue size and offer optimistic investors – but sooner or later the hot market
price, and derive the patterns of prices in the short- and will come to an end. This captures the notion that there
long-run. We also analyze the comparative statics of the will eventually be incontrovertible evidence of the IPO
price patterns with respect to the strength of sentiment shares being overpriced, or that the cost of shorting IPO
demand and the probability of the hot market coming stock will fall to the point where prices are no longer set
to an end. Section 5 considers three extensions to the by optimistic investors.8 For now, we model this by in-
model: multi-period sentiment demand, multiple regular troducing a subsequent trading date t = 2 at which the
investors, and multiple pre-IPO owners. In Section 6, IPO market may or may not still be hot. In Section 5.1,
we discuss empirical support for various aspects of the we will explicitly extend the model to a setting with mul-
model and offer new testable implications. Concluding tiple periods of trading in the after-market. Finally, T is
remarks are in Section 7. All detailed proofs are collected the terminal date by which the hot market is definitely
in the Appendix. over and there is no more disagreement about firm value.
We denote by γ the (exogenous) probability of the hot
market ending at t = 2. In addition to disagreeing about
value, investors disagree about γ. Rational investors un-
2. THE MODEL derstand that the hot market may end before T with
We model a firm that is going public in a ‘hot’ IPO probability γ > 0, in which case the marginal investor
market, to be defined shortly. The firm’s equity is sold will be someone holding unbiased beliefs. Sentiment in-
via a standard firm-commitment IPO in which an under- vestors, on the other hand, dismiss this possibility: in
writer assumes responsibility for distributing the issuer’s their mind, the hot market will continue for sure.
shares to investors. The offer price is finalized at the end Let VT denote the terminal payoff of the security at
of bookbuilding, just prior to the start of trading, and T . There are no distributions (e.g. dividends) and the
is subject to a uniform-pricing rule such that neither the discount rate is zero. At t = 1, the ‘fundamental’ or
issuer nor the underwriter can price-discriminate among long-term expected value of an IPO share – the value
investors [see also Benveniste and Wilhelm (1990)]. The from the perspective of rational investors – is denoted by
offer size Q and price P0 will be chosen so as to maximize
5 This mirrors Miller’s (1977) divergence-of-opinion model. Our
the owner-manager’s wealth.
sentiment investors hold beliefs that are in the right tail of the
The demand side of the IPO market consists of two distribution of beliefs.
types of investors. The first type are small, unsophisti- 6 Geczy, Musto, and Reed (2002) show that borrowing IPO stock
cated investors who are prone to episodes of optimistic in the early after-market is extremely expensive in general, the
or pessimistic ‘sentiment’ about the stock market, es- more so, the higher was the initial day return.
7 The notion of investors ‘agreeing to disagree’ is commonly em-
pecially IPOs, where sentiment denotes incorrect beliefs ployed in models with a diversity of opinions among market par-
about the fundamental value of an asset arising from ticipants, a good example being Harris and Raviv (1993).
treating noise as relevant information [Black (1986)]. We 8 Ofek and Richardson (2003) show that the bursting of the
will label these investors sentiment or ‘s-type’ investors. dot-com bubble in March/April 2002 coincided with a substantial
In our set-up, a ‘hot’ IPO market is one characterized increase in the availability of stock to borrow.4 Ljungqvist, Nanda and Singh
VR = E(VT ). Absent sentiment investors and additional will be given by the demand curve in equation (1). We
information, VR would be the market price of the IPO assume here that the quantity of shares sold is such that
shares at t = 1. As we will see, the presence of senti- Q < Q. This, as we will show later, is consistent with an
ment investors can affect pricing and trading patterns, optimal choice for Q. For a given quantity of shares Q
and thus the institutional arrangements that result. issued at t = 0, rational investors’ valuation is E R (P2 ) =
The value sentiment investors place on the IPO shares γVR + (1 − γ)E s (P2 ). Note that this exceeds their long-
is not uniform. Specifically, we assume that sentiment run valuation VR , since they expect to be able to sell
investors are budget-constrained and that their aggregate the security to s-types at t = 2 with probability (1 − γ).
demand curve for IPO shares can be represented as Sentiment investors value the shares at E s (P2 ) = VR +
a − λQ.
Vs = VR + a − λQ (1)
To summarize, we model a ‘hot’ market that is char-
where Q is the total number of IPO shares held by sen- acterized by the presence of optimistic investors. Not all
timent investors.9 Define Q = λa . For all Q < Q, s-types optimistic investors are present at t = 1 and, if the hot
(if they are present) place a value higher than VR on the market persists, more are expected to show up at t = 2.
IPO shares. Sentiment investors know the demand curve Rational investors expect the terminal value of the IPO
and the value put on the shares by rational investors.10 shares to be VR . Unlike the optimists, they recognize
To model the dynamics of a hot market that may come that the hot market may come to an early end at t = 2,
to a premature end, we allow for the possibility that not with probability γ > 0. In the longer run, by the termi-
all sentiment investors are present in the market at t = 1. nal date T , the hot market will end with certainty. All
If the hot market continues at t = 2, additional sentiment investors, rational or otherwise, act in a manner consis-
investors may arrive in the market.11 Thus, sentiment tent with their beliefs.
demand can evolve over the two periods (or, in Section
3. SELLING IPO SHARES
5.1, over multiple periods). The fact that sentiment de-
mand can build over time affects the interpretation of We consider the optimal procedure for selling IPO
demand in equation (1). Acting rationally, the sentiment shares so as to maximize issuer wealth in the presence
investors present in the market at t = 1 would never be of optimistic valuations. For now we maintain the as-
willing to pay a price at t = 1 that is greater than the ex- sumption that the offer quantity Q is given exogenously.
pected price conditional on their beliefs at t = 2. Thus, The unconstrained optimum involves selling IPO shares
they properly anticipate the prices of the security in the at both t = 1 and t = 2. This is, of course, contrary to
short run, by forecasting what demand will be at t = 2. the market practice of selling the shares in a single shot
Conditional on the (mistaken) belief that the hot market and the requirement that investors be sold IPO shares at
will continue at t = 2 for certain, s-type investors expect a uniform price. As we will see, such discretion will have
demand at t = 2 to be the aggregate demands of s-types no impact if sentiment demand at t = 1 is large enough
arriving at t = 1 and t = 2. It is this ‘longer-term’ de- to absorb the full offering.
mand (and not just the t = 1 sentiment demand alone) Let q1 be the number of IPO shares sold at t = 1,
that affects the value Vs they put on the IPO shares in while q2 is sold at t = 2. The expected proceeds, Ψ, to
equation (1). the issuer are
We can now determine the price of the IPO shares at
t = 2 and, thereby, the offer and trading prices at t = 0 Ψ = q1 P1 + q2 (E s (P2 ) (1 − γ) + VR γ).
and 1. If the hot market has ended, the price at t = 2 Given their beliefs, sentiment investors expect the price
will be set by the expectations of the rational investors at t = 2 to be E s (P2 ) = VR + a − λ(q1 + q2 ). Hence, so
such that P2 = VR . If the hot market persists, the price long as the sentiment investors hold all the IPO shares
9 The linear form of the demand curve is chosen to simplify the
issued at t = 1, the marginal investor is a sentiment
presentation and does not affect our results materially. investor and the price at t = 1 will be E s (P2 ). Let Q1 ≤
10 Our results do not depend on any particular reason why senti- Q denote the total optimistic demand present at t = 1.
ment investors are willing to pay more than fundamental value VR If q1 > Q1 , the marginal investor is a rational investor
for the shares at t = 1. For example, rather than holding optimistic
beliefs about VR , sentiment investors may hold optimistic beliefs and the price at t = 1 will be E R (P2 ). Thus we have:
about their ability to sell out to other sentiment investors in the ½
future. Our results go through as long as i) there exist a limited VR + a − λ(q1 + q2 ) if q1 ≤ Q1
number of sentiment investors with a downward sloping demand P1 =
curve at t = 1 who value the shares above fundamental value; ii)
γVR + (1 − γ)(VR + a − λ(q1 + q2 )) if q1 > Q1
more such investors may arrive in the market at t = 2; and iii) the (2)
sentiment investors may disappear at t = 2. Assuming the firm does not need to raise a particular
11 The fact that not all sentiment investors are present in the
level of financing, the owner-manager’s objective is sim-
market at t = 1 may be the result of the time required for in-
formation to disseminate among the less informed investors; for ply to maximize the ‘profit’ from selling IPO shares, that
enthusiasm about the IPO to build while the market stays hot; or is, the excess value Π of the proceeds over his own val-
the additional time needed for some sentiment investors to raise uation VR Q. The optimal (q1∗ , q2∗ ) can, therefore, be re-
resources and bid for IPO shares, especially when many ‘hot’ IPOs garded as the solution to the following constrained opti-
come to market around the same time. It is also possible that senti-
ment investors may have noisy information about their value func- mization problem:
tions and about the existence of other sentiment investors. High
underpricing at t = 1, caused by investors with positive signals, max Π ≡ Ψ − VR Q
q1 ,q2
may lead even those with negative signals to join the crowd [e.g.
Welch (1992)] at t = 2. We hope future work will provide insights s.t. q1 + q2 = Q
into the relation between the existence of sentiment investors and
their propensity to form rational cascades. Its solution is given in the following proposition.Hot Markets, Investor Sentiment, and IPOs 5
Proposition 1 For a given number of shares to be is- are given by q1∗ and q2∗ , respectively. The staggered sale
sued, Q, the optimal choice of q1∗ and q2∗ is such that strategy requires the regular investor to hold q2∗ shares
½ in inventory from t = 1 to t = 2, when the quantity to
(Q, 0) ¢ if Q ≤ Q1 . be sold is such that Q > Q1 . Given our assumption of
(q1 , q2 ) = ¡
∗ ∗
(3)
Q1 , Q − Q1 if Q > Q1 a monopolist profit-maximizing regular investor, there is
no incentive to deviate by selling the shares early.
Proposition 1 shows that the issuer may do better by Increases in the supply of stock in the market under-
staggering the sale of equity over two time periods in- mine the inventory-holding strategy, creating an incen-
stead of one. By restricting the initial supply of shares, tive to limit short sales. In practice, short sellers must
the issuer ensures that the marginal investor at t = 1 borrow stock from investors who are long, which at t = 1
is a sentiment investor. If, however, the total quantity in our model means the owner-manager or the regular in-
Q to be sold is less than the demand by sentiment in- vestor. The owner-manager almost invariably is ‘locked
vestors at t = 1, then the issuer optimally chooses to set up’ and the regular has no incentive to lend stock. Thus
q2∗ equal to zero. The intuition is straightforward. In our there will be no short sales until the regular begins to
set-up there is no price advantage from delaying the sale trade out of the security, and the short-sale constraint
of equity if it can be sold to sentiment investors at t = 1. relaxes over time.13
Delay exposes the issuer to the risk of the market crash-
ing at t = 2. Hence, the issuer is strictly better off selling 4.1. Optimizing Offer Size and Price
to the sentiment investors at t = 1 and thus taking ad- In equilibrium, a regular investor will invest in IPOs
vantage of their mistaken belief that the hot market will only if he does not expect to lose as a consequence. If
persist at t = 2. As we will discuss later, a similar result an IPO share is bought at an offer price P0 , the regular
holds when the model is extended to consider the arrival investor’s participation constraint is
of sentiment investors over a larger number of periods.
Proposition 1 indicates that it may be optimal to sell −QP0 + q1∗ P1 + q2∗ [(1 − γ)E s (P2 ) + γVR ] ≥ 0 (4)
an offering in stages. However, as mentioned, laws and where q1∗ and q2∗ are as given in (3). The first term is
regulations effectively prevent issuers and their under- the cost of purchasing all the shares in the IPO. The
writers from conducting firm commitment offerings in a second and third terms represent the cash flows received
staggered fashion. In the U.S., for instance, NASD rule from selling at t = 1 and t = 2. The bracketed part of
IM-2110-1 on “Free-riding and Withholding” prevents the third term is the price at which the regular investor
an underwriter who holds IPO shares in inventory from expects to be able to sell IPO shares at t = 2.
selling them in the after-market above the offer price.12 Assuming, as before, that the issuer does not need to
Thus, there is considerable downside risk without upside raise a particular level of financing, the objective remains
potential. We now consider an alternative arrangement to maximize the excess value, Π, of offered shares over
by which an underwriter can achieve the same ends with- their ‘true’ (long-term) value, subject to the participa-
out directly selling the IPO in stages. tion constraint defined in (4). Thus, the issuer solves
4. INVENTORY HOLDING BY INSTITUTIONAL max Π ≡ Q (P0 − VR )
INVESTORS P0 ,Q
Given constraints on the underwriter’s ability to (di- s.t. −QP0 + q1∗ P1 + q2∗ [(1 − γ)E s (P2 ) + γVR ] ≥ 0
rectly) stagger the sale, we suggest that institutional (or
other ‘regular’) investors can be delegated the task of Lemma 1 The participation constraint will always be
holding inventory in the after-market for resale to sen- binding.
timent investors. Specifically, we assume (for now) that
there exists a monopolist regular investor who purchases Proof. Suppose not. That is, the optimal P0 and Q
Q shares at the offer price P0 and then sells q1 shares are such that the constraint has slack. Then the issuer
at t = 1 and the remainder q2 at t = 2, when the full can increase P0 and so increase his profits, which contra-
demand by s-type investors is established (so long as the dicts the optimality of P0 and Q.
hot market persists). The assumption of a single (or Using the lemma, Π = [q1∗ P1 + q2∗ E s (P2 ) (1 − γ) +
dominant) regular investor simplifies the exposition and q2 VR γ] − QVR , where q1∗ and q2∗ are given by (3). The
∗
abstracts from concerns about free-riding among regular bracketed term is the maximum amount a regular in-
investors. The case with a multitude of regular investors vestor is willing to pay for the IPO shares, from the par-
is discussed later, with the threat of punishment dissuad- ticipation constraint in (4). From Proposition 1, we know
ing regulars from engaging in free-riding behavior. q1∗ ≤ Q1 . Thus, P1 is determined by s-type investors, on
Once the shares have been allocated, the regular in- the basis of their expectation regarding P2 . Substituting
vestor’s problem is no different from that of the issuer. for P1 = E s (P2 ) = VR + a − λQ in Π and simplifying,
Thus, the regular investor will find it optimal to follow the issuer’s objective function can be written as
the staggered sale strategy, where the aggregate quan-
tities sold in the secondary market at t = 1 and t = 2 max [q1∗ (Q) + (1 − γ) q2∗ (Q)] [a − λ (q1∗ (Q) + q2∗ (Q))] ,
Q
12 Countries where staggered sales are possible include Germany. 13 In practice, not all IPO shares are allocated to the regular;
Though rare and usually confined to small companies, such offer- some are allocated to retail investors. Retail investors could in
ings proceed as follows. Rather than allocating stock to investors principle lend stock to short sellers. Interestingly, the most un-
at t = 0, the issuer announces a quantity Q it intends to sell via derpriced IPOs are associated with the smallest retail allocations
the stock exchange, in one or more trading sessions, at the market- (Aggarwal, Prabhala, and Puri (2002)) and the least amount of
clearing price. This closely resembles our mechanism. short selling (Geczy, Musto, and Reed (2002)).6 Ljungqvist, Nanda and Singh
where we explicitly recognize the dependence of q1∗ and Fig. 1.— Issuer Surplus
q2∗ on Q. We can now derive the issuer’s optimal offer
size.
The figure illustrates two different selling mechanisms when
Proposition 2 With a single regular investor, the is- the optimal quantity chosen (Q∗ ) is strictly greater than the
suer’s optimal choice of quantity Q∗ = q1∗ + q2∗ , where sentiment demand at t = 1 (Q1 ). First, suppose the issuer
(³ ³ ´´ can sell in stages directly to the investors (as modeled in
a γ a(1−γ) Section 3). The s-type investors present at t = 1 rationally
Q , − Q 1 + if Q1 < λ(2−γ)
(q1∗ , q2∗ ) = ¡ 1 2λ ¢ 1 2(1−γ) anticipate demand at t = 2 and price the security at P1 . At
a
2λ , 0 otherwise t = 2, the hot market persists with probability (1 − γ), in
which case the issuer sells quantity (Q∗ − Q1 ) at price P2 =
Proof. We obtain the above expressions from first- P1 . If the hot market ends, he is forced to sell the shares at
their fundamental value VR . The rectangle GHIJ represents
order conditions obtained by taking the derivative of the the expected surplus obtained at t = 2, which is equal to
firm’s objective function with respect to q2 . It can be (1 − γ)(P1 − VR )(Q∗ − Q1 ). The issuer’s total surplus is given
shown that there is a unique maximum because the sec- by the area in the two rectangles ABJK and GHIJ. Second,
ond order condition with respect to q2 is negative. if the issuer is prevented from directly selling in stages, but
We now turn to pricing. The issuer needs the regular he can obtain the cooperation of a regular investor, we have
the case modeled in Section 4. The issuer sells Q∗ shares to
investor to hold inventory if Q1 is small (relative to to- the regular investor at price P0 . At t = 1, the regular investor
a(1−γ) obtains a profit equal to the rectangle ABEF and at t = 2
tal sentiment demand), i.e. less than λ(2−γ) . So long
suffers an expected loss equal to the rectangle DEGH. The
as the hot market persists, the regular investor sells his zero profit condition on the investor ensures that the gain at
inventory to newly-arriving sentiment investors at t = 2. t = 1 is equal to the expected loss at t = 2, leaving the issuer
If the hot market ends, he is left with shares priced at with the same profits as in the earlier case. Underpricing
arises because the regular investor needs to be compensated
VR . For a regular investor to accept this negative-valued for the expected inventory loss, and so P0 < P1 . Long-term
gamble, the initial offer price needs to be set at a discount underperformance arises because the issuer always extracts
relative to the price at which the shares are expected to some surplus from the sentiment investors, and so P0 > VR .
trade initially, so that P0 < E s (P2 ) = P1 . In our model,
the share price will eventually drift to VR , where VR < P0
from the binding participation constraint of the investor.
Price
Thus, with a regular investor holding inventory that he
disposes of over time, both an initial price run-up (un- VR + a
− λQ
derpricing) and long-run underperformance will be ob-
A
served. These patterns can be viewed as arrangements P1
B
C
that have, in effect, evolved as a means to maximize value
extraction from s-type investors.
If Q1 is large (relative to total sentiment investor P0
F
E
D
demand), there are no benefits from having a regular
G
investor hold inventory and the offering being under- H
priced.14 Thus, the presence of sentiment investors is
a necessary but not sufficient condition for the first-day
return. The long-run return (VR − P1 ) /P1 , on the other VR
K J I
hand, is always negative in our set-up. It results from
the overly optimistic valuation of sentiment investors and
represents market inefficiency – sustained by the diffi-
culty and cost of establishing short positions in the stock. Q1 Q∗ Quantity
By implication, we do not expect a monotonic relation
between underpricing and the long-run price drift.
Proposition 3 summarizes the above discussion regard-
ing the predicted price patterns. Figure 1 illustrates.
Though optimistic about the issuer’s stock, sentiment
Proposition 3 With a single regular investor, investors, in our model, are still acting rationally given
their beliefs: they correctly anticipate the arrival of more
1. if Q1 is small enough such that q2∗ > 0, then sentiment investors at t = 2 (albeit with the wrong prob-
the IPO shares will exhibit an initial price run-up: ability) and price the stock accordingly. If the sentiment
P0 < P1 ; investors were not forward-looking in this sense, then the
price at t = 1 would be determined by the marginal sen-
2. if Q1 is large, then the shares will not exhibit an timent investor present at t = 1. In that case, the price
initial price run-up: P0 = P1 ; run-up would, in fact, be even higher than that predicted
by our existing set-up.
3. ∀ Q1 the long-run return will be negative: VR < P1 . We can make a more precise prediction regarding the
relative magnitudes of underpricing and long-run perfor-
14 It is important to note that our model does not predict that
mance:
underpricing increases with offer size. Underpricing is required
only if the optimal offer size derived in Proposition 2 exceeds the
sentiment demand that is available in the market at that time, Proposition 4 With a single regular investor, the ini-
which could be true for either ‘large’ or ‘small’ IPOs. tial price run-up [P1 − P0 ] and long-run price driftHot Markets, Investor Sentiment, and IPOs 7
[P1 − VR ] will be related as follows: a reduction in the quantity issued increases the price at
γq2 t = 1, thus worsening long-run performance.
P1 − P0 = (P1 − VR ). An increase in γ has two opposing effects on the first-
Q day return. First, it increases the regular investor’s re-
quired compensation due to the direct effect of an in-
For expositional ease, we will refer to the ratio of the crease in the probability of a crash. Second, the indirect
initial price run-up and the long-run price drift as the effect of a reduction in the quantity issued is to reduce
‘price reversal ratio’. From Proposition 4, the price re- the inventory the regular investor holds. Proposition 5
versal ratio is proportional to the inventory carried by shows that the first effect dominates for low γ as the per-
the regular investor as a fraction of offer size. Thus, centage change in q2∗ for low γ is small. For high enough
P1 − P0 q2 γ, q2∗ goes to zero and so the first-day return disappears.
Price Reversal Ratio ≡ =γ . For intermediate levels of γ, the change in the first-day
P 1 − VR Q
return is ambiguous. Similar characteristics are inherited
4.2. Comparative Statics by the price reversal ratio.
We now study the properties of the first-day return, 4.3. Discussion
long-run performance, and the price reversal ratio. We
In this section, we have developed an alternative to
focus on two parameters of interest: the intercept of the
the direct-sale mechanism described in Section 3. Our
sentiment investors’ demand function (a) and the prob-
alternative mechanism requires the regular investor to
ability of the hot market coming to an end (γ). In the
carry inventory for sale in the secondary market. It is
context of the model, both parameters are exogenous and
important to understand that both mechanisms give the
affect the nature of the hot market.
issuer exactly the same expected proceeds, even though
the delegated-inventory mechanism involves underpric-
Proposition 5 With a single regular investor,
ing. This simply follows from the zero-profit condition
in Lemma 1. In words, in the delegated-inventory mech-
1. the number of shares issued, the first-day return,
anism, the issuer underprices the stock to compensate
and the price reversal ratio are all increasing, while
the regular investor for bearing the risk of sentiment de-
long-run performance is decreasing, in investor
mand evaporating too soon. Thus, underpricing is not a
sentiment (a);
value transfer from the issuer to the regular investor; it
2. long-run performance and the number of shares is- is a fair payment for the regular’s expected loss. In the
sued is decreasing in γ; and direct-sale mechanism, the issuer bears the exact same
risk himself. Noting that everyone is risk-neutral, it is
3. the first-day return and the price reversal ratio are straightforward to show that the expected proceeds from
increasing in γ for low γ. the two mechanisms are equivalent. Figure 1 illustrates.
In some sense, the direct-sale mechanism described in
An increase in the intercept of the demand function, a, Section 3 resembles an IPO followed – if the sentiment
can be interpreted as an increase in sentiment investors’ demand survives – by an SEO. Couldn’t the issuer im-
optimism. As one might expect, issuers in our model re- prove on the delegated-inventory mechanism by conduct-
spond by increasing the size of the offering. The predic- ing an SEO shortly after the IPO? The answer is no: the
tion on the first-day return, however, is not obvious. It expected proceeds are at best the same (ignoring trans-
may seem anomalous that a more bullish market does not action costs for the SEO) or, more realistically, strictly
translate into a smaller first-day return: why don’t is- lower (net of transaction costs). Leaving aside trans-
suers take advantage of the bullishness of the market and action costs, if sentiment demand develops over several
increase the offer price, resulting in a smaller first-day re- periods (perhaps stirred by the buzz of the IPO), it is
turn? The reason why the first-day return increases with clearly impractical for the issuer to take advantage of it
market sentiment is that underpricing is a way of com- via a sequence of possibly small SEOs. The regular in-
pensating the regular investor for taking on the risk of vestor, on the other hand, faces no constraints on the
the hot market crashing at t = 2. As offer size increases, frequency or size of after-market sales, and so can opti-
the fraction of the offering carried over to t = 2 also mally take advantage of sentiment investors as and when
increases. Consequently, the regular investor needs to they arrive in the market. Thus, while we do not rule
be compensated more (on a per share basis) for taking out an SEO soon (within a few weeks) after the IPO, we
on the risk of carrying this inventory. Thus we predict argue the issuer can better take advantage of developing
that companies going public in a ‘hot’ market are more sentiment demand by obtaining the regular investor’s co-
underpriced.15 operation than by planning to do multiple SEOs.
An increase in γ, the probability of market sentiment 5. EXTENSIONS
turning sour, reduces the expected gain from holding in-
ventory until t = 2. As a consequence, the issuer is bet- We now outline three extensions to the model. In the
ter off reducing the quantity of shares issued. However, previous section we analyzed a very tractable model to
understand the properties of the initial price run-up when
15 Note also that IPO volume tends to increase in hot markets. issuers optimally take advantage of the sequential arrival
Thus, in hot markets, multiple issuers compete for a resource that is of sentiment investors. In Section 5.1, we generalize the
in short supply in the short-run, namely sentiment investors. So as
more companies go public in a hot market, the need to underprice
model to show that similar results obtain if sentiment
increases unless the supply of s-types grows faster than the supply investors arrive over many periods. In Section 5.2, we
of IPO shares. examine the strategy of underwriters who have to pay8 Ljungqvist, Nanda and Singh
rents to induce cooperative behavior among multiple reg- From these expressions it is easy to see that our results
ular investors. In Section 5.3, we relax the assumption of on the existence of an initial price run-up and long-run
a single owner-manager and link the pre-IPO ownership underperformance will go through in a multiple-period
structure to the magnitude of underpricing and long-run setting. The following proposition summarizes without
underperformance. proof.
5.1. Multi-Period Sentiment Demand Proposition 6 If sentiment demand evolves over mul-
We now extend the model to incorporate sentiment tiple periods and the underwriter has access to a single
demand that arises over several periods, say weeks or regular investor, then
months. The set-up captures the notion that as poten-
tial sentiment investors hear the ‘buzz’, some are likely 1. if Q1 is sufficiently small such that S ∗ > 1, then
to invest in the stock. The arrival of future sentiment the IPO shares will exhibit an initial price run-up:
investors, though likely, is still uncertain. This will be P0 < P 1 ;
reflected in the setting of the offer price. 2. ∀ Q1 the long-run return will be negative: VR < P1 .
We assume that new sentiment investors may arrive
every period after the IPO. The demand, however, decays Obtaining the comparative statics in closed-form is not
over time at rate α. Specifically, we assume feasible in general. Given that the multi-period model is
Qt = αQt−1 , α < 1. not as tractable as the two-period model analyzed ear-
lier, we resort to providing numerical solutions for se-
As in the two-period model analyzed earlier, if the senti- lected parameter values. We solve the problem for the
ment demand has survived up to period t then with prob- following parameter values: the long-term value VR is 5;
ability γ it will disappear in that period. We maintain the probability of the hot market ending in any period,
all other assumptions of the two-period model developed γ, is 10%, which is roughly equivalent to a 10-period ex-
earlier. Thus, the marginal sentiment investor’s reserva- pected length of the hot market; sentiment demand is
tion value is given by VR + a − λQ, sentiment investors assumed to decay at rate α = 10%; the initial demand
account for the arrival of future sentiment investors, and Q1 is normalized to 1 unit; and the slope of the demand
they do not share the regular investor’s belief about the curve λ is 0.5. Given the above parameter values we nu-
possibility of the hot market ending. We assume that merically solve for the optimal S and plot the predicted
the number of shares issued is sufficient to satisfy sen- price patterns as a function of the level of optimism (a).
timent demand for up to S periods. Note that we are Figure 2 shows that the first-day return and the price
characterizing the optimal quantity to be sold in terms reversal ratio are both increasing in a. Long-run perfor-
of the number of periods. The reason we can do this is mance is always negative and decreasing in the level of
that, for a given quantity to be sold, the optimal selling optimism. The intuition is similar to the one provided
strategy (as in Proposition 1) is to sell whatever can be earlier. An increase in optimism among sentiment in-
absorbed by sentiment investors each period till the hot vestors makes it optimal for the issuer to increase issue
market ends or else the allocation is fully sold. size, which implies that the regular investor has to carry
Thus, the number of shares issued, Q, is given by more inventory and bear a greater expected loss if the
hot market ends.
1 − αS The multi-period model developed in this section can
Q = Q1 + αQ1 + α2 Q1 + . . . + αS−1 Q1 = Q1 (5) also be used to study the relation between the first-day
1−α return and the expected length of the hot market. In
A single regular investor, who is allocated Q shares at our
P∞ model, then−1 expected length of the hot market is
price P0 , sells Q1 shares at t = 1, if the hot market n=1 n (1 − γ) γ n = γ1 . In Figure 3, we plot the first-
persists αQ1 shares at t = 2, and so on. The break-even day return as a function of the expected length of the hot
condition implies market for the same parameter values as in Figure 2. In
(P0 − VR ) Q = Q1 (P1 − VR ) + (1 − γ) αQ1 (P1 − VR ) addition, we assume that the intercept of the sentiment
S−1
demand curve (a) is 5. The first-day return is initially
+ . . . (1 − γ) αS−1 Q1 (P1 − VR ) increasing and then decreasing in the expected length of
the hot market. This result is consistent with the pre-
Substituting for (P1 − VR ) = a − λQ and using (5), we
diction in Proposition 5. A decrease in γ increases the
obtain
expected length of the hot market, which has two oppos-
S µ ¶
1 − (1 − γ) αS 1 − αS ing effects. First, it decreases the risk that the hot mar-
(P0 − VR ) Q = a−λ Q1 Q1 . ket will end with the regular investor holding inventory,
1 − (1 − γ) α 1−α
(6) which implies less underpricing is required to compen-
Thus, the issuer’s problem is to maximize the right-hand sate the regular investor. Second, the issuer will choose
side of (6) by the choice of S. We denote the optimal S to increase the quantity issued, which increases the regu-
by S ∗ . At the optimum, lar investor’s inventory risk. As in the two-period model,
for low values of γ (i.e. high expected length of the hot
∗
1 − αS market) the first-day return decreases as the expected
Q∗ ≡ Q (S ∗ ) = Q1 length of the hot market increases.
1−α
S∗ ∗ µ ¶ Figures 2 and 3 suggest, therefore, that the qualitative
1 − (1 − γ) αS 1−α nature of our results is unaffected by an extension to
P 0 = VR + (a − λQ∗ )
1 − (1 − γ) α 1 − αS ∗ many periods. We also believe that the multiple periodHot Markets, Investor Sentiment, and IPOs 9
Fig. 2.— Plot of first-day return, long-term performance and 5.2. Limited Ability to Obtain Cooperation from
price reversal ratio Institutional Investors
In this figure we plot the first-day return [ P1P−P0 ], the long-term We have so far considered the case of a monopolist reg-
0
ular investor. Being a monopolist, the investor has an
performance [ VRP−P1 ], and the price reversal ratio [ PP1−V
−P0
]. We
1 1 R incentive to cooperate with the underwriter, by holding
solve for the optimal S and calculate P1 and P0 at the optimal
S for the following parameter values: the long term value (VR ) is
inventory and delaying the sale of part of his IPO allo-
5; the probability of the hot market ending in any period, γ, is cation. However, if there are many regular investors, say
10%, which is equivalent to a 10-period expected length of the hot N , they face a free-rider problem. Collectively, regular
market; the demand is assumed to decay at a rate (α) of 10%; the investors are better off holding on to their inventory until
initial demand (Q1 ) is normalized to 1 unit; and the slope of the t = 2. However, individually each can benefit by unload-
demand curve (λ) is 0.5.
ing his entire allocation at t = 1. Hence, an underwriter’s
ability to induce cooperative behavior is determined by
0.4 the extent to which he can offer inducements or threaten
P1 −P0 punishment. A likely form of punishment is the threat
0.3 P1 −VR
0.2 of exclusion of regular investors from future IPOs (or
0.1 P1 −P0 other desirable deals). Such an exclusion will impose a
0 P0 cost on the regular investors only if they obtain non-zero
-0.1 rents from IPO allocations. Given the clamor to obtain
-0.2 IPO allocations witnessed in the late 1990s, it seems rea-
-0.3 VR −P1 sonable that regular investors do obtain rents. In this
-0.4 P1 section, we generalize the analysis to explicitly allow for
-0.5 such rents. For analytical tractability, we use the two-
-0.6 period model of Section 4 rather than the multi-period
-0.7 model introduced in Section 5.1.
2 4 6 8 10 We assume the underwriter can extract some rents on
Sentiment demand intercept (a)
behalf of his regular investors. These rents can be viewed
as the outcome of a bargaining game between the issuer
and the underwriter and in general would depend on the
Fig. 3.— Plot of first-day return level of competition in the IPO market. We denote the
per share rent by r. Given these rents, an underwriter
In this figure we plot the first-day return [ P1P−P0 ] as a function of can impose penalties on regular investors by excluding
0
the expected length of the hot market, which is given by γ1 . Thus, them from future allocations of IPO shares – thereby
expected length equal to 2 corresponds to a 50% probability of the deterring deviation from the inventory holding strategy.
hot market ending in every period and expected length equal to 5 The extent of punishment depends on the magnitude of
periods corresponds to an 20% probability. We solve for the opti- r and the anticipated frequency of future IPO alloca-
mal S and calculate P1 and P0 at the optimal S for the following tions. Specifically, we assume regular investors’ valua-
parameter values: the long term value (VR ) is 5; the demand is
assumed to decay at a rate (α) of 10%; the initial demand (Q1 ) is
tion of such future benefits is rπ, where π is the multiple
normalized to 1 unit; the slope of the demand curve (λ) is 0.5; and that accounts for the probability and timing of future
the sentiment demand intercept (a) is 5. IPOs. One would expect an investment bank with a big-
ger market share to have a higher π. Similarly, if the
market believes the hot market to continue for some time,
one would expect π to be high. Conversely, if the near-
0.18 term outlook for the IPO market is bleak, or if the un-
0.17 derwriter’s market share is small, exclusion from future
0.16 IPOs will provide only limited incentives for inventory
0.15
holding.
Let P̂0 be the offer price that incorporates the rent r.
0.14 P1 −P0
P0
Thus, P̂0 = P0 − r, where P0 , as defined in Section 3, is
0.13 the offer price for r = 0. On the margin, regulars can
0.12 choose to sell a share at price P1 at t = 1, or sell at
0.11 t = 2 and expect to get E R (P2 ) = γVR + (1 − γ)E s (P2 ).
The potential loss from future exclusion from the IPO
0.1
process, rπ, must be large enough to deter deviation from
0.09 the inventory holding strategy. Therefore, we need
1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
q2 ¡ ¢
Expected Length of Hot Market ( γ1 ) rπ ≥ P1 − E R (P2 )
N
where qN2 represents the inventory each investor carries
to t = 2. Denoting R ≡ rπN we can express the above
constraint as
R ≥ q2 (P1 − γVR − (1 − γ)E s (P2 )) . (7)
extension better captures the notion that the disposal of Substituting for P1 from (2) in (7) the constraint reduces
shares by the regular investor is gradual, taking place to
over a number of periods. R ≥ γq2 (a − λ(q1 + q2 )). (8)10 Ljungqvist, Nanda and Singh
The analysis presented in Section 4 corresponds, there- The next proposition analyzes the impact of R on the
fore, to the case where the above constraint has slack. IPO price patterns when the inventory holding constraint
We now consider the situation in which the constraint is is binding.
binding, i.e. in which (8) is violated at the optimal q1∗
and q2∗ . The next proposition shows that the constraint is Proposition 9 If the number of shares issued Q is such
more likely to be violated when market sentiment is more that regular investors’ inventory holding constraint is
exuberant or when the market has a higher probability binding, then the first-day return (P1 − P̂0 )/P̂0 , long-run
of crashing. performance (P1 − VR ) /P1 , and the price reversal ratio
(P1 − P̂0 )/ (P1 − VR ) are all increasing in R.
Proposition 7 The expected gain to regular investors
of deviating from the inventory holding strategy and sell- The positive relation between the first-day return and
ing shares at t = 1, R predicted in Proposition 9 may seem surprising, for it
γq2∗ (a, γ)[a − λ(q1∗ (a, γ) + q2∗ (a, γ))] implies that IPOs lead-managed by more active or more
prestigious underwriters are more underpriced.16 Recall
is increasing in a and γ. Thus, if constraint (8) is vio- that underpricing serves as a form of compensation to
lated at (q1∗ , q2∗ ) for some a = â and γ = γ̂, then it will the regulars for carrying inventory. An underwriter with
be violated for all a > â and γ > γ̂. a lower R can induce only a relatively small amount of
inventory holding q2c , as shown in Proposition 8. The less
The gain from deviating from the inventory holding
inventory is carried, the less need there is for the offering
strategy depends on the product of q2 and (P1 − VR ).
to be underpriced.
An increase in a increases both (Proposition 5), increas-
That lower R offerings are associated with worse long-
ing the incentive to deviate as indicated in Proposition
run performance is immediate, since the decrease in q2
7. Similarly, an increase in the probability of a crash γ
(and thus in Q) increases the P1 = VR + a − λQ that
increases the incentive of regular investors to deviate by
sentiment investors are willing to pay. This prediction
selling their entire allocation of IPO shares at t = 1.
is generally consistent with the empirical evidence that
The issuer’s constrained problem is to solve the follow-
IPOs done by larger, more established underwriters tend
ing:
to exhibit better long-term performance.
max (q1 + (1 − γ) q2 ) (a − λ (q1 + q2 ))
q1 ,q2
5.3. Ownership structure and bargaining power
s.t. R ≥ γq2 (a − λ(q1 + q2 )). So far, we have implicitly assumed that the owner-
Let the solution to the above programming problem be manager has all the bargaining power relative to the un-
(q1c , q2c ). The next proposition characterizes the quanti- derwriter and the regular investor, so that the surplus
ties chosen by the issuer. extracted from sentiment investors is fully incorporated
into the offer price. In this section, we study the impact
Proposition 8 If the optimal (q1∗ , q2∗ ) defined in Propo- of bargaining power on the first-day return and long-run
sition 2 are such that (8) is violated, then the optimal performance.
choice of shares issued (q1c , q2c ) is given by We assume that the issuing firm’s ownership structure
is such that β of the extracted surplus is captured by the
q1c = Q1 issuing firm and 1−β is captured by a combination of the
³ q ´
q2c = 2λ
1 2
(a − q1 λ) − (a − q1 λ) − 4Rλ
. (9) regular investor and the investment bank. For a firm with
γ
highly concentrated ownership, we believe β will be close
to 1, reflecting the high incentive to bargain hard over
The optimal quantity sold in the secondary market at
the surplus, while for a firm with dispersed ownership
t = 1 is the same as that in the earlier unconstrained
or other agency problems β will be significantly smaller
case. This is because if more than Q1 were sold at t = 1,
than 1. From the issuer’s perspective, the key choice
the marginal investor would no longer be a sentiment
variables are the quantity to be issued Q∗ and the offer
investor but instead a rational investor. However, con-
price P0 . Figure 1 shows that the total amount of surplus
straint (8) does decrease the quantity sold at t = 2, and
extracted, which equals the sentiment investors’ expected
consequently the total issue size. This distortion in q2 is
loss, is a function of Q∗ :
highest for underwriters with a small R: with a smaller ¡ ¢
amount of potential rent at stake, incentive compatibil- (P1 − VR ) Q1 + (1 − γ) Q∗ − Q1 (P1 − VR ) (10)
ity requires regular investors to carry fewer IPO shares
in inventory. Thus, banks with small R have less IPO Even when the issuer captures only a fraction of the sur-
placing capacity and so do smaller deals. plus, it is still in his best interest to maximize the total
The positive relation between R and q2 in equation surplus. Therefore, Q∗ is independent of β and, conse-
(9) has one further implication. If periods of high IPO quently, P1 is also independent of β. The issuing firm
volume imply increases in R, the size of the IPOs will chooses P0 such that its surplus (P0 − VR ) Q∗ is β times
also be larger, ceteris paribus. Similarly, underwriters the total surplus given in (10). Thus,
who gain (or are expected to gain) larger market shares ¡ ¢
Q + (1 − γ) Q∗ − Q1
can impose bigger penalties, i.e. they have larger R. All P0 − VR = β (P1 − VR ) 1
else equal, this allows them to increase the size of their Q∗
offerings. Thus, growth will beget more growth and a hot 16 As we will discuss later, recent empirical evidence tends to
market will get hotter. This suggests that a hot market support this prediction. However, certification arguments imply
can have a certain self-fulfilling logic. the opposite relation.You can also read
