Leaders and Followers in Hot IPO Markets∗
Shantanu Banerjee†
İsmail Ufuk Güçbilmez‡
Grzegorz Pawlina†
March 9, 2012
Abstract
We model IPO timing decisions of firms. Our model’s outcome suggests that
firms with better growth opportunities can signal their quality by leading hot
markets and underpricing their issues. Data supports this outcome such that
mean (median) underpricing is about 30% (13%) at the start of hot markets, but
it falls sharply down to less than 15% (6%) after the second quarter of hot markets.
Moreover, we find that investors value the growth opportunities of leaders more,
and highly-underpriced leaders experience significantly stronger post-IPO growth.
Overall, our theoretical and empirical findings have broad implications for the
literature on hot IPO markets.
JEL classification: C72; D82; E32; G30; G32
Keywords: hot IPO markets; underpricing; adverse selection; signaling
∗
The authors thank Gönül Çolak, Bart Lambrecht, Ronald Masulis, Bill Rees, Jay Ritter, Armin
Schwienbacher, and participants of the Annual International Conference on Real Options (Rome),
Financial Management Association Meeting (New York) and the 9th Corporate Finance Day (SKEMA
Business School, Lille) for helpful comments and suggestions. All remaining errors are ours.
†
Department of Accounting and Finance, Lancaster University Management School, Lancaster LA1
4YX, UK.
‡
Corresponding author. Accounting and Finance Group, University of Edinburgh Business
School, 29 Buccleuch Place, Edinburgh EH8 9JS, UK. Tel: +44 (0)131 650 30 16. Email:
u.gucbilmez@ed.ac.uk.
1
1
Introduction
The literature on initial public offerings (IPO) documents that IPO volume and underpricing vary substantially over time. Moreover, periods of high IPO volume tend to
overlap with periods of high IPO underpricing causing “hot” markets to emerge.1
There is a large number of papers that compare IPOs that take place in hot versus
cold markets. For instance, Alti (2006) argues that hot markets are temporary windows
of opportunities during which the cost of equity is low. He shows that IPO firms raise
significantly more equity in hot markets. Another example is Helwege and Liang (2004),
who compare hot and cold IPOs in terms of operating characteristics. They find that,
consistent with the market timing explanation, the differences are not significant.
This type of papers has a limitation in that they ignore the possibility of variation
in IPO market conditions within a hot market. Hot markets can easily last more than
a year. Therefore, there is no reason to believe that firms that went public in the first
few months of a hot market have the same incentives and/or characteristics as those
that conducted an IPO much later in that market. There is now a nascent literature
on IPO timing decisions of firms within a hot market (see Chemmanur and He (2011)
and Çolak and Günay (2010)).
In this paper we model IPO timing decisions of private firms within a hot market. We assume that some firms have more valuable growth opportunities than others.
Our model’s outcome suggests that these firms can signal their quality to uninformed
investors by leading hot markets and underpricing their issues. This outcome has various empirical implications. The three most significant ones are: (1) IPO underpricing
should rise at the start of a hot market and fall sharply later on within the same hot
market, (2) investors should rationally value the growth opportunities of firms that led
IPO waves more, (3) the post-IPO growth of highly-underpriced leaders should be in
1
See Ibbotson and Jaffe (1975) and Ritter (1984) for early research on hot markets. For more recent
research on IPO cycles see Lowry and Schwert (2002), Lowry (2003), Pastor and Veronesi (2005) and
Yung, Çolak, and Wang (2008).
2
line with the rational expectations of investors.2
We test these three implications and other related ones on a large sample of US
IPOs. We find that mean (median) underpricing is about 30% (13%) at the start of hot
markets, but it falls sharply down to less than 15% (6%) after the second quarter of hot
markets. Moreover, we find that highly-underpriced leaders have much higher market
to book ratios in their IPO years and that their assets, sales and capital expenditures
grow significantly more up to 5 years following their IPOs compared to their pre-IPO
levels. We also provide evidence that highly-underpriced leaders grow more ex post not
because they seize better growth opportunities by leading hot markets, but because they
already have them.
Our paper contributes to the literature on hot IPO markets. It shows that the
average underpricing is not necessarily uniform during the course of a hot market. It
can be much higher initially, and then fall quite sharply. It also shows that investors
value the growth opportunities of highly-underpriced leaders more and that these firms
indeed grow faster ex post. All of these findings are consistent with our IPO timing
model, which provides a rational explanation for IPO timing and underpricing within
a hot market. Overall, our paper’s central message is that future research should
take into account the systematic differences between early and late IPOs in a hot
market. Our model and empirical evidence suggest that early IPOs can be underpriced
significantly more and such IPOs would be conducted by firms that have better growth
opportunities.
The recent work by Chemmanur and He (2011) and Çolak and Günay (2010) have
also implications about IPO timing within a hot market. Our results complement those
by Chemmanur and He (2011), who find that firms that lead IPO waves have higher
productivity and post-IPO profitability. Çolak and Günay (2010)’s model suggests
that some high-quality firms may strategically delay their IPOs. They find that firms
2
Throughout the paper we use the terms “hot (IPO) market” and “IPO wave” interchangeably.
3
in the highest-quality decile wait longer before going public. However, their main
quality measure is long-run abnormal returns. They do not investigate IPO firms’
growth opportunities at the time of going public and their ex-post growth, which are
central to our model and tests. Moreover, neither of these two papers focuses on IPO
underpricing, which is a hallmark of hot markets. Therefore, our paper adds to the
literature by treating IPO timing and underpricing as two sides of the same coin.
Our paper is also related to the strand of literature that views underpricing as a
“money-burning” signal by high-quality issuers. In traditional signaling models, issuers
recoup the cost of underpricing in the secondary market, whereas in our model they
reap benefits of signaling in the primary market. We discuss this strand of literature
and our paper’s relevance to it in Section 2.
Finally, the lead-lag relationship between average underpricing and volume, which
is documented by Lowry and Schwert (2002), is consistent with our model. According
to our model, the driving factor behind the time variation in average underpricing and
volume is the changes in market conditions. We show that once we control for this
factor, the lead-lag relationship disappears. Pastor and Veronesi (2005) also argue that
changes in market conditions is one of the main drivers of IPO waves. However, they
do not investigate the relationship between underpricing and volume.
The remainder of our paper is organized as follows. First, we discuss the related
literature in Section 2. Then, we present our IPO timing model in Section 3. We
develop hypotheses based on our model in Section 4 and test them in Section 5. Section
6 concludes.
2
IPO underpricing and timing as signaling mechanisms
There has long been a view in the literature that IPO underpricing can serve as a
signaling mechanism (see Allen and Faulhaber (1989), Grinblatt and Hwang (1989),
Welch (1989) and Welch (1996)). The premise of this view is that high-quality issuers
4
recoup the cost of underpricing in the secondary market, for instance when they conduct
seasoned equity offerings (SEO).
A new view that is emerging in the literature argues that IPO timing can also be
used as a signaling tool. Grenadier and Malenko (2011) and Morellec and Schürhoff
(2011) study the impact of signaling incentives on investment timing. In particular, the
latter finds that good firms accelerate investment inefficiently to separate themselves
from bad ones. This result is echoed by Bustamante (2012), who also shows that joint
decisions of underpricing and timing can signal quality.
In our model, high-quality issuers tend to lead hot markets by going public early
when there is still uncertainty about the future state of economy. Even though this
action is inefficient due to the value of waiting, it is necessary for high-quality issuers
to signal their quality. However, leading hot markets is usually not sufficient to signal
quality as low-quality issuers might be able to mimic this action. Therefore, highquality issuers have to couple it with issuing underpriced issues to deter low-quality
issuers from mimicking them.
The key point is that, although going public early and issuing underpriced shares
are costly actions for high-quality issuers, they benefit from these actions by receiving a
higher valuation than the one they would have got in a pooling equilibrium. Therefore,
unlike in early models of signaling via underpricing, in our model issuers reap the
benefits of signaling in the primary market, such that they receive a higher offer price.
In other words, our model shows that underpricing can be used as a tool for signaling,
even if high-quality IPO firms do not plan to conduct any SEOs in the near future. This
is relevant to the literature, since the evidence on the link between IPO underpricing
and subsequent SEO activity is not strong (see Jegadeesh, Weinstein, and Welch (1993),
Michaely and Shaw (1994) and Kennedy, Sivakumar, and Vetzal (2006)).3
3
Recently, Francis, Hasan, Lothian, and Sun (2010) have shown that there is a link between foreign
IPOs and subsequent SEO activity abroad for firms “domiciled in countries with segmented markets”.
5
3
Model
We consider an economy with two dates: t ∈ {0, 1}. There is uncertainty about the
state of economy at t = 1, such that it can be good with probability q or bad with
probability 1 − q. At t = 0, private firms have growth opportunities that pay off V
if the economy turns out be good at t = 1, and zero otherwise. A private firm is
of high quality with probability p or of low quality with probability 1 − p, such that
high-quality firms have more valuable growth opportunities Vg > Vb .4 All projects
require an irreversible investment of I and firms can finance this investment by selling
a fraction of their equity to investors during their IPOs. After going public, firms retain
fraction α of their equity. The cost of going public is c. The IPO market is competitive
and investors are uninformed, such that they cannot distinguish high- and low-quality
firms. For simplicity, the discount rate for payoffs at t = 1 is assumed to be zero.
The economic uncertainty gives firms an incentive to wait. If a firm invests at t = 0
and the economy turns out to be bad at t = 1, the payoffs are −c and −I for the firm
and investors respectively. On the other hand, the parties can avoid sinking the issuing
and investment costs, if the firm waits at t = 0 and goes public at t = 1 only if the
economy is good. In other words, in our model, firms have a real option to go public,
which can be kept alive at t = 0 and exercised at t = 1 depending on the state of the
economy. This might give the impression that our model’s outcome is obvious, such
that all firms would choose to wait at t = 0. However, such an impression is false, since
(as we show next) the asymmetric information about firm quality gives high-quality
firms an incentive to move at t = 0.
4
From this point we refer to “private firms” simply as “firms”, with the understanding they are
private unless otherwise stated.
6
3.1
Outcome
Our model can lead to three different types of equilibrium: (1) pooling equilibrium:
all firms go public at the same date, (2) separating equilibrium without underpricing:
high- and low-quality firms go public at different dates, (3) separating equilibrium with
underpricing: high- and low-quality firms go public at different dates, and high-quality
ones send a costly signal to investors by underpricing their issues.
All firms have an incentive to wait due to the economic uncertainty. On the other
hand, high-quality firms have an incentive to move to distinguish themselves from lowquality firms. Interestingly, high-quality firms’ incentive to move can give low-quality
firms an incentive to move as well, since they can benefit from mimicking high-quality
firms. Thus, the type of IPO market equilibrium depends on the tradeoff between
firms’ incentives to wait and to move.
Before moving on to our propositions, we define the average firm value at t = 1
when the economy is good, since this variable helps simplify the notation:
V ≡ pVg + (1 − p)Vb
Proposition 1 For 0 ≤ q ≤ q, the IPO market is in a pooling equilibrium, such that
all firms wait at t = 0 and go public at t = 1 only if the economy is good, where:
q=
I +c
(Vg /V )I + c
(1)
The equity stake firms retain after their IPOs is:
αp = 1 −
I
V
(2)
Proof. See Appendix A
If the economy is likely to be bad, no firm would want to move at t = 0, even if
7
they would be valued as high-quality firms by investors. Consequently, all firms wait
at t = 0 and go public at t = 1 only if the economy is good. αp reflects the average
firm value, such that the IPOs are fairly priced on average at t = 1. When q exceeds q,
the pooling equilibrium breaks down, since it becomes optimal for high-quality firms
to deviate from this equilibrium.
Proposition 2 For q < q ≤ q ∗ , the IPO market is in a separating equilibrium without
underpricing, such that high-quality firms move at t = 0, while low-quality ones wait at
t = 0 and go public at t = 1 only if the economy is good, where:
q∗ =
(Vb /Vg )I + c
I +c
(3)
I
> αp
qVg
(4)
I
Vb
(5)
At t = 0, high-quality firms retain:
αg = 1 −
and at t = 1, bad firms retain:
αb = 1 −
Proof. See Appendix A
When q < q ≤ q ∗ , q is sufficiently high for high-quality firms to move, but not high
enough for low-quality firms to mimic high-quality ones. Consequently, high-quality
firms lead and low-quality ones follow if the economy turns out to be good. αg and αb
reflect the true values of high- and low-quality firms, such that each IPO is fairly priced.
Note that high-quality firms enjoy a better valuation, since αg > αp . This is precisely
the reason why they move, despite the uncertainty about the value of their growth
opportunities. As soon as q exceeds q ∗ , however, it becomes optimal for low-quality
firms to mimic high-quality ones, and the separating equilibrium without underpricing
breaks down.
8
Proposition 3 For q ∗ < q ≤ q, the IPO market is in a separating equilibrium with
underpricing, such that high-quality firms move at t = 0 and underprice their issues,
while low-quality ones wait at t = 0 and go public at t = 1 only if the economy is good,
where:
q=
c
(pVg /V )I + c
(6)
At t = 0, high-quality firms retain:
αu = αb +
(1 − q)c
< αg
qVb
(7)
and at t = 1, low-quality firms retain αb .
Proof. See Appendix A
When q ∗ < q ≤ q, high-quality firms still move at t = 0, but they now have to underprice their issues just enough in order to deter low-quality firms from mimicking them.
Consequently, unlike in separating equilibrium without underpricing, high-quality firms
no longer receive a fair valuation (i.e., αu < αg ). But, even though their issues are underpriced, their valuation is still sufficiently better than the valuation they would have
got in pooling equilibrium (i.e., αu > αp ). The problem is that ∂αu /∂q < 0. That is,
as q increases, high-quality firms have to underprice their issues more. Consequently,
when q exceeds q, the separating equilibrium with underpricing becomes unsustainable.
Above this threshold, high-quality firms prefer pooling with low-quality firms rather
than underpricing their issues heavily.
Proposition 4 For q < q ≤ 1, the IPO market is back in a pooling equilibrium, such
that all firms wait at t = 0. All firms retain fraction αp of their equities after their
IPOs.
Proof. See Appendix A
If the economy is likely to be good, high-quality firms no longer have an incentive
9
to move at t = 0. This is because, they know that low-quality firms have a strong
incentive to mimic them if they move, and they could deter low-quality firms only by
underpricing their issues heavily, which turns out to be a worse option than pooling
with low-quality firms at t = 1. Consequently, all firms wait at t = 0 and go public
at t = 1 only if the economy is good. αp reflects the average firm value, such that the
IPOs are fairly priced on average.
3.2
Discussion
We illustrate our model’s outcome in Figure 1. For 0 ≤ q ≤ q and q ≤ q ≤ 1, the
IPO market is in a pooling equilibrium (the white regions). For q < q ≤ q ∗ , it is in a
separating equilibrium without underpricing (the black region), and for q ∗ < q ≤ q, it
is in a separating equilibrium with underpricing (the gray region). Several points are
worth noting about our model’s outcome:
1. In a separating equilibrium without underpricing, high-quality firms can signal
their quality solely by taking the risk of going public before the economic uncertainty
is resolved. They do not have to underprice their issues in addition to taking this
risk. However, for reasonable sets of parameter values, this type of equilibrium exists
in a very narrow region (see Figure 1). This implies that, empirically, the IPO market
should be far more likely to be either in a separating equilibrium with underpricing or
in a pooling equilibrium.
2. For the IPO market to be in a separating equilibrium with underpricing, the
following conditions should hold: (1) the number of high-quality firms should be low
relative to the number of low-quality ones (i.e., p should be low) and the quality wedge
between the two types of firms should be sufficiently large (i.e., Vg /Vb should be large),
(2) the future state of economy should be uncertain (i.e., q should be neither too low
nor too high). The reason why these two conditions are necessary is as follows. Highquality firms receive a particularly poor valuation in pooling equilibrium when the first
10
condition holds. This gives them a strong incentive to signal their quality. However, the
first condition is not sufficient for a separating equilibrium with underpricing. Highquality firms would not lead hot markets if the economy is highly likely to be bad.
Interestingly, they would not lead them if the economy is highly likely to be good
either, since this would require heavy underpricing to deter low-quality firms from
mimicking. Therefore, economic uncertainty is essential for this type of equilibrium
to exist. These two conditions imply that, empirically, the IPO market is most likely
to be in a separating equilibrium with underpricing when a small proportion of the
private firms waiting to go public has much better growth opportunities than the rest,
and when there is significant uncertainty about the future state of economy.
3. Finally, the most important point about our model’s outcome is the following. In
a pooling equilibrium the average IPO is fairly priced; and in a separating equilibrium
without underpricing, which is empirically unlikely, each IPO is fairly priced. On the
other hand, in a separating equilibrium with underpricing, IPOs of high-quality firms
are underpriced, whereas those of low-quality firms are fairly priced. Therefore, the
pooling equilibrium and the separating equilibrium without underpricing fail to explain
the periods during which average underpricing is quite high empirically. The separating
equilibrium with underpricing offers an explanation for the existence of such periods
based on the high-quality firms’ desire to signal their type. High-quality firms reap
the benefits of their costly signal when they go public (not later on in the secondary
market) by receiving a better valuation compared to the one they would get in pooling
equilibrium. Our model also implies that, when the IPO market is in a separating
equilibrium with underpricing, average underpricing should fall sharply when highquality firms are followed by low-quality ones.
11
3.3
A numerical example of separating equilibrium with underpricing
Suppose that the IPO market is in a separating equilibrium with underpricing and
consider a high-quality firm that goes public at t = 0. The high-quality firm retains
fraction αu of its equity in a separating equilibrium with underpricing, while it would
retain αg of its equity in a separating equilibrium without underpricing. The crucial
point is that αu < αg . That is, in a separating equilibrium with underpricing, the
high-quality firm accepts to retain a less-than-fair fraction of its equity in order to
signal its quality. In other words, it relinquishes too much equity to investors (i.e.,
1 − αu > 1 − αg ) in return for obtaining I. Then, the issue’s underpricing in percentage
points is:
1 − αu
− 1 × 100
1 − αg
Plugging in the definitions of αg and αu from Equations (4) and (7) yields:
Vg
c
(q − (1 − q) ) − 1 × 100
Vb
I
where q ∗ < q ≤ q
(8)
This suggests that underpricing is linearly increasing in q. This is no surprise, since as
q increases low-quality firms become more willing to mimic high-quality ones, so highquality firms have to underprice more to deter low-quality firms from pooling with
them. Apart from q, underpricing depends on Vg /Vb and c/I.
In order to provide a numerical example of separating equilibrium with underpricing, we need to choose parameter values for Vg /Vb , c/I, and p. Welch (1996) estimates
that high-quality firms are 2 to 3 times more valuable than low-quality firms. Therefore,
the parameter values we try for Vg /Vb are 2, 2.5, and 3. Lee, Lochhead, Ritter, and
Quanshui (1996) report that the direct issuance costs are about 11% of the proceeds
on average. We should also take into account other costs of going public, such as the
entrepreneur’s loss of private benefits (Benninga, Helmantel, and Sarig (2005)) and the
opportunity cost of the management’s time spent on preparing the firm for an IPO.
12
Consequently, for c/I, we try 10%, 15%, and 20%. For p, we have to try small values,
since separating equilibrium with underpricing exists when the number of high-quality
firms is low relative to the number of low-quality firms (see Section 3.2). Consequently,
we try 2.5%, 5%, and 7.5%.
Table 1 shows the range of q values in which the IPO market is in a separating
equilibrium with underpricing and the range of underpricing figures high-quality firms
have to bear in order to signal their quality, given the parameter values above. As an
example, for the middle scenario (p = 5%, Vg /Vb = 2.5, and c/I = 15%), the IPO
market is in a separating equilibrium with underpricing when q ∈ (0.48, 0.56). In this
scenario, the magnitude of underpricing high-quality firms have to bear ranges between
0% (when q = 0.48) and 24.45% (when q = 0.56).
The figures in Table 1 makes it clear that the IPO market is unlikely to be in a
separating equilibrium with underpricing when p is not low. In Panel C, even when p
is only 7.5%, the range of feasible q values is quite narrow and in some cases the IPO
market is never in a separating equilibrium with underpricing.
Overall, this numerical example indicates that given realistic values of Vg /Vb and
c/I, and low values of p, the IPO market is in a separating equilibrium with underpricing when the economic uncertainty is high (i.e., q is not close to 0 or 1).
4
Testable Hypotheses
According to our model, the IPO market is in either pooling or separating equilibrium.
It is likely to be in a separating equilibrium with underpricing when the economic
uncertainty is high, the number of high-quality firms relative to the number of lowquality ones is low, and the quality gap between high- and low-quality firms is wide.
At other other times, it is likely to be in a pooling equilibrium. In general, the IPO
market is unlikely to be in a separating equilibrium without underpricing (see Section
3.2).
13
If a hot market is in a pooling equilibrium, average underpricing should stay uniformly low throughout the course of the hot market, since high- and low-quality firms
go public at the same time and as such IPOs are fairly priced on average.5 On the
other hand, if the hot market is in a separating equilibrium with underpricing, then
average underpricing should be high in the beginning of the hot market and it should
fall sharply later on in the same market. Overall, in a pooled cross-sectional sample
of hot markets, even if only one hot market was in a separating equilibrium with underpricing, we should observe that average underpricing was higher at the start of hot
markets. This leads us to our first hypothesis (tested in Sections 5.2 and 5.4):
H1: Average underpricing is higher at the start of hot markets and the
IPOs of firms that lead hot markets are underpriced more after controlling
for pre-IPO characteristics.
In a separating equilibrium, firms’ IPO timing and underpricing decisions reveal
their type to investors. Consequently, the growth opportunities of leaders should be
valued more by investors. Our second hypothesis (also tested in Sections 5.2 and 5.4)
is related to the market to book ratios of firms in their IPO year. The idea is that
a firm’s market to book ratio in its IPO year is a proxy for the value of its growth
opportunities as assessed by investors at that time.
H2: Average market to book ratio of IPO firms is higher at the start of hot
markets and the market to book ratio of a leader in its IPO year is higher
after controlling for pre-IPO characteristics.
If investors could distinguish high-quality firms from low-quality ones using preIPO public information, the former type of firms would not need to lead hot markets
5
Theoretically speaking, average underpricing should be zero. Empirically, we expect to observe a
base level of underpricing. The base level suggests that firms might have to issue underpriced shares
due to various reasons (see e.g. Ljungqvist (2007)) other than signaling their quality to investors as
well.
14
and underprice their issues to signal their superior quality. Therefore, our model’s
assumption that the quality of private firms is unobservable is valid if the following
hypothesis (tested in Section 5.3) holds:
H3: Leaders and followers cannot be differentiated reliably on the basis of
pre-IPO firm and issue characteristics.
On the other hand, even though leaders should not look too different than followers
ex ante, especially those that underprice their shares should grow significantly more ex
post. This is because, IPO timing and underpricing are signaling mechanisms for firms
with better growth opportunities. Therefore, our fourth hypothesis (tested in Section
5.5) is related to post-IPO growth:
H4: Highly underpriced leaders experience a significantly stronger post-IPO
growth in assets, sales and capital expenditures.
Our model also has testable implications about the time series behavior of IPO
underpricing and volume. To understand these implications let’s assume that q, the
probability that the economy is good at t = 1, is a function of time: q(t). In Section 3.2,
we argued that when q is low, the IPO market is in a pooling equilibrium such that all
firms wait at t = 0. In this case, a hot market is unlikely to emerge, since the economy
is likely to be bad at t = 1. But, as q rises over time hot markets become more likely to
emerge. Furthermore, when q ∗ < q ≤ q, high-quality firms take the risk of going public
at t = 0 and underprice their shares to prevent low-quality firms from imitating them.
At t = 1, low-quality firms follow if the economy is good. This implies that following
improvements in market conditions (i.e., increases in q) there would be periods of high
underpricing in which high-quality firms go public and these periods would tend to
be followed by periods of high volume in which low-quality firms conduct their IPOs.6
6
Note that the separating equilibrium with underpricing requires the number of low-quality firms
to be large relative to the number of high-quality ones (see Section 3.2).
15
This lead-lag relationship between average underpricing and volume is documented by
Lowry and Schwert (2002). However, it is not the increase in average underpricing
per se that leads to a subsequent increase in volume. According to our model, the
evolutions of these two time series are governed by changes in market conditions. As
market conditions improve such that q(t) rises to a level between q ∗ and q, high-quality
firms go public creating a period of high average underpricing, which is followed by
a period of high volume if market conditions continue to improve, in which case lowquality firms follow. This suggests that the positive correlation between current average
underpricing and future IPO volume can be accounted by market conditions. We proxy
changes in market conditions by returns on a stock market index and state our final
hypothesis (tested in Section 5.6) as follows:
H5: The relationship between monthly IPO volume and average underpricing in previous months is driven by the lagged market returns.
5
Tests
Our empirical tests are conducted in IPO time (see e.g., Alti (2006)). We define a
firm’s IPO year as the fiscal year during which the firm went public. We set the IPO
year as y = 0. The fiscal year that precedes (succeeds) the IPO year is set as y = −1
(y = 1), and so on.
We use a method similar to the one employed by Yung, Çolak, and Wang (2008) to
identify the hot markets that took place within our sample period. In particular, for
each quarter, we compare the 3-quarter moving average IPO volume ma(3) with the
historical average in all previous quarters.7 Then, we classify a quarter as “hot” (“cold”)
7
In order to alleviate concerns about a potential nonstationarity of quarterly IPO volume (see
Lowry (2003)), we deflate the number of IPOs in each quarter by the total number of public firms
in the previous quarter before calculating the ma(3). Public firms are defined as those that have a
sharecode of 10 or 11 in CRSP (see Pastor and Veronesi (2005)). The augmented Dickey-Fuller test
rejects the null hypothesis that the deflated quarterly IPO volume time series contains a unit root at
1% significance level.
16
if its ma(3) exceeds (falls short of) the historical average by 50%. The remaining
quarters are classified as “warm”. Hot markets are defined as sequences of hot quarters.
The hot markets we identify empirically are periods during which IPO volume is
high. They correspond to the cases in our model when the economy turns out to be good
at t = 1, such that low-quality firms go public and a hot market emerges. Moreover,
the hot markets we identify can be one of the two types. The first type is in separating
equilibrium with underpricing, such that average firm quality and underpricing are
higher at the start of this type of hot markets. The second one is in pooling equilibrium,
such that average firm quality and underpricing are uniform throughout this type of
hot markets. In our tests we work with a pooled cross-sectional sample of hot markets,
which is likely to contain both types of hot markets, such that average firm quality and
underpricing would be higher at the start of the pooled cross section of hot markets, due
to the presence of hot markets in separating equilibrium with underpricing. In other
words, as long as at least one of the hot markets we identify is in separating equilibrium
with underpricing, we should observe changes in firm quality and underpricing during
the course of the pooled cross section of hot markets.
Figure 2 illustrates the hot markets we identify between 1975 and 2010. The data
on aggregate IPO volume is obtained from Jay Ritter’s website.8 We use the “net”
count variable that excludes penny stocks, units, closed-end funds, REITs acquisition companies, ADRs, limited partnerships, banks and S&Ls, and IPOs not listed on
CRSP.9
After identifying the hot markets in our sample period, we define the position of a
firm within a hot market as Q, where Q = q if the firm went public in the qth quarter
8
http://bear.warrington.ufl.edu/ritter/ipoisr.htm
The net count variable is available only from 1975, whereas a “gross” count variable is available
from 1960. Since we need to use a historical average figure to classify each quarter as hot, cold, or
warm, we regress net count on gross count between 1975 and 2010 (we suppress the intercept so that
when gross count is zero net count is also zero) and use the regression line (the R2 is 90.29%) to predict
net count prior to 1975. By this way we make sure that we have at least 15 years of history when
classifying each quarter.
9
17
of a hot market. For instance, Q = 2 for all firms that went public in the 2nd quarter of
a hot market. Moreover, we set Q = 0 for all firms that went public in a warm quarter
that immediately precedes the first quarter of a hot market.
Figure 3 depicts average underpricing in cold, warm and hot quarters. The data
on average underpricing is obtained from Jay Ritter’s website as well. We exclude the
Nasdaq Bubble quarters (the last quarter of 1999 and the first quarter of 2000) in this
figure to make sure that the level of average underpricing is not driven by the IPOs that
took place during these two outlying quarters.10 Note that we group warm quarters
that immediately precede a hot quarter (the quarters in which an IPO firm’s position
is Q = 0) with the first two quarters of hot markets (i.e., Q = {1, 2}) rather than
with the other warm quarters. This is because the firms going public in those quarters
might already be high-quality firms going public early to signal their type. Thus, for
the rest of the paper, we consider warm quarters that immediately precede hot markets
as parts of hot markets and exclude them from the sample of warm quarters.
Figure 3 shows that average underpricing is below 15% in both cold and warm
quarters and also in the late quarters of hot markets. On the other hand, in early
quarters of hot markets and in warm quarters that immediately precede hot markets,
average underpricing is more than twice higher, such that its value is above 30%.
This pattern in average underpricing is consistent with a separating equilibrium
with underpricing in which underpricing rises during the early part of a hot market
when high-quality firms go public, and it falls sharply in the later part of the same hot
market when low-quality firms follow. Consequently, in our empirical tests, we classify
a firm that conducts an IPO in Q = {0, 1, 2} as a “leader” and a firm that goes public
in a later quarter of a hot market Q > 2 as a “follower”. More specifically, we define a
10
The average level of underpricing was 96.8% during these two quarters.
18
dummy variable L as follows:
L=


 1 0≤Q≤2
(9)

 0 Q>2
5.1
Data
We obtain our IPO data from Securities Data Company (SDC), financial data from
Compustat, and price data from Center for Research in Securities Prices (CRSP).11
Finally, we get the data on firm foundation years from the Field-Ritter dataset.12 SDC
contains 11,136 U.S. common stock IPOs between January 1st, 1975 and December
31st, 2010.13 We employ the sample selection criteria of Helwege and Liang (2004) and
construct our initial sample by dropping IPOs by financial firms (2,605 observations),
reverse leveraged buyouts (337 observations), spinoffs (574 observations), IPOs with
an offer price less than $1 (145 observations), IPOs that have duplicate CUSIP codes
(24 observations), and unit offers (957 observations). Consequently, our initial sample
contains 6,494 IPOs. Then, we merge this initial sample with CRSP and drop 196
IPOs either because the issuer does not exist in CRSP, or the trading date according
to CRSP is 2 days earlier or 10 days later than the IPO date according to SDC (see
Helwege and Liang (2004)).14 As a result, there are 6,298 IPOs in our final sample.
The main variables that are used in our empirical analysis are defined as follows.
IniR, our underpricing measure, is the initial percentage return between the offer price
11
Although SDC is the industry standard database for IPO data, it contains errors. We correct those
identified by Jay Ritter (http://bear.warrington.ufl.edu/ritter/SDC corrections122811.pdf). Furthermore, we find that CUSIP codes of 60 issuers are wrong and manually correct them as well.
12
http://bear.warrington.ufl.edu/ritter/FoundingDates.htm
13
Even though IPO data is available in SDC from 1970, we choose 1975 as the starting point of our
sample period. There are several reasons why we make this choice: (1) The pre-1973 IPO data in SDC
is incomplete (Gompers and Lerner (2003)); (2) The majority of pre-1975 IPOs have missing financial
data in Compustat (Helwege and Liang (2004)); (3) The pre-1973 price data for NASDAQ-listed IPOs
is unavailable in CRSP (Lowry (2003)); (4) the data on net IPO volume, which we use to identify hot
markets is available from 1975 in Jay Ritter’s website; and (5) the data on foundation years, which we
use to calculate firm age is also available from 1975 in Jay Ritter’s website.
14
It is worth noting that Helwege and Liang (2004) drop 1,245 IPOs when they apply a similar filter
between 1975 and 2000, whereas we drop only 196 IPOs between 1975 and 2010.
19
and the first trading day closing price. T P ro is the total proceeds as a percentage of
total assets in y = −1. SecS is the number of secondary shares offered as a percentage
of total shares offered. V Cap is a dummy variable equal to 1 if the IPO is backed by
a venture capital firm. Age is the difference between the firm’s IPO and foundation
years. M toB0 is the firm’s market to book ratio in y = 0. It is calculated as the
ratio of market value of equity (the number of shares outstanding times the share
price) plus debt (long-term debt and debt in current liabilities) to book value of equity
(common/ordinary equity) plus debt in y = 0. Salesi and Assetsi are net sales and
total assets measured in millions of 2010 dollars in y = i respectively. CapXi is capital
expenditures, P rofi is EBITDA, Debti is long-term debt in y = i as a percentage of
total assets in y = i. Finally, Bubble is a dummy variable equal to 1 for the firms that
went public during the last quarter of 1999 and the first quarter of 2000.
5.2
Descriptive statistics
In our final sample of 6,298 IPOs, 364 IPOs take place in cold quarters, 1,550 in warm
quarters, 1,232 in Q = {0, 1, 2}, 1,542 in Q = {3, 4, 5} and 1,610 in Q > 5. This means
that there are 1,232 leaders (L = 1) and 3,152 followers (L = 0) in our sample. Among
followers, there are 227 IPOs that took place during the NASDAQ Bubble period.
Table 2 provides descriptive statistics for the variables we use. We report mean
and median values separately for cold quarters, warm quarters, leaders in hot markets
(L = 1), followers in hot markets (L = 0 except the bubble quarters), and bubble
quarters.
The mean values of IniR in Table 2 concord with the average levels of underpricing
depicted in Figure 3.15 In particular, the mean value of IniR is below 15% in both
cold and warm quarters and also in the late quarters of hot markets, whereas it almost
15
The mean values of IniR in Table 2 are calculated from firm-level observations using the data from
SDC and CRSP, whereas average levels of underpricing in Figure 3 are calculated from market-level
monthly observations using the data from Jay Ritter’s website.
20
reaches 30% in early quarters of hot markets and in warm quarters that immediately
precede hot markets. The median values of IniR follow an identical pattern. Median
underpricing soars to 13% at the start of hot markets, while its value is around 6% otherwise. The Mann-Whitney U-test statistic is -10.758. Thus, the null hypothesis that
the underpricing distribution is the same across leaders and followers is comfortably
rejected at 1% significance level.
The market to book ratios in the IPO year M toB0 follow the same pattern as
underpricing. The mean and median values of M toB0 are substantially higher for
leaders. This is consistent with our model. Leaders, which tend to be firms with
better growth opportunities, signal their quality to investors via underpricing, such
that investors who become informed after receiving the signal attach higher market to
book ratios (a proxy for the value of growth opportunities) to leaders following their
IPOs. The Mann-Whitney U-test statistic is -6.304 in this case. The null hypothesis
is again comfortably rejected at 1% significance level.
The descriptive statistics of the remaining variables show that leaders are younger,
smaller, less profitable, less levered, and more likely to receive venture capital backing
compared to followers. These observations strengthen the view that leaders fit the
profile of a firm with high-growth potential better than followers. However, as we
show in Section 5.3, investors cannot reliably distinguish leaders from followers on the
basis of pre-IPO variables such as Age, Sales−1 , etc. Therefore, it is still necessary
for high-quality firms to lead IPO waves and issue underpriced shares to signal their
quality.
Finally, Table 2 reveals that the firms which went public during the bubble period
are markedly different from other IPO firms in our sample. Therefore, in our subsequent
empirical analysis we use the dummy variable Bubble to control for the outlying nature
of these firms.
To summarize, the descriptive statistics of our variables provide strong evidence that
21
average underpricing and average market to book ratio of IPO firms are much higher
at the start of hot markets. These findings lend support to our first two hypotheses H1
and H2 (see Section 4).
5.3
Can investors distinguish leaders from followers?
If issue and firm characteristics that are observable at the time of a firm’s IPO could
reveal the firm’s quality to investors, high-quality firms would not need to signal their
type as investors could readily infer it from the distinct characteristics of high-quality
firms.
In order to investigate whether leaders have distinct characteristics or not, we run
logistic regression models. The dependent variable in these regressions is L (see Equation (9)), and independent variables are issue and firm characteristics observable at the
time when firms go public. The results are presented in Table 3. Model (1) uses issue
characteristics only, (2) uses firm characteristics only, (3) uses both, and (4) also uses
both and excludes the bubble period IPOs.
The R2 values are quite low across the models. Moreover, the odds ratio estimates
are very close to 1 for all explanatory variables except V Cap. This suggests that
changes in ceteris paribus changes in explanatory variables have almost no influence on
the odds ratio of being a leader in a hot market. The odds ratio estimates of models (3)
and (4) show that results are not influenced by the bubble-period IPOs. Furthermore,
the AUC figures are not much higher than 0.5, which indicates that the models do a
poor job in discriminating leaders from followers.16
Our model assumes that there are high- and low-quality firms and that investors
cannot observe quality. Therefore, a necessary condition for the validity of this assumption is that leaders should not be significantly different from followers in terms of
pre-IPO observable characteristics. The results presented in Table 3 provide evidence
16
AUC is the area under the ROC curve and its value varies between 0.5 and 1. The model has no
(full) discriminating power when AUC is equal to 0.5 (1).
22
that this condition is satisfied. However, the fulfilment of this condition is not sufficient
to validate our assumption. It is possible the reason why the observable characteristics
of leaders and followers do not differ is simply because they have similar quality. We
address this issue in Section 5.5, where we show that leaders grow significantly more
than followers ex post. This supports the idea that there is a significant quality difference between leaders and followers that is unobservable at the time of their IPOs, but
that becomes observable through the difference in their post-IPO growth performance.
5.4
Do leaders underprice more and do investors value the growth
opportunities of leaders more?
The main implication of our model is that in a separating equilibrium with underpricing,
average underpricing is much higher at the start of a hot market. This is because,
high-quality firms lead hot markets and underprice their issues to signal their superior
growth opportunities.
If this is the case, after controlling for factors that are known to explain underpricing, being a leader in a hot market should still have marginal explanatory power on
underpricing. Consequently, we regress underpricing IniR of hot market IPOs on our
dummy variable for leaders L and a set of control variables. The results are reported
in Table 4. The coefficient estimate for L shows that, all else equal, the IPO of a leader
is underpriced 14.12% more. Note that this figure is quite close to the difference in
average underpricing of leaders and followers: 29.31%-13.72%=15.59% (see panel A
in Table 2). This suggests that being a leader has an impact on underpricing that is
nearly orthogonal to the controlling factors known to explain underpricing.
We also use a more strict leader dummy Ls to check whether the impact on underpricing is robust to the way we define leaders. Ls classifies only firms that went
public in the first quarter of a hot market (i.e., Q = 1) as leaders. It classifies firms
that went public in later quarters (i.e., Q > 1) as followers. Even with this more strict
23
definition, the IPO of a leader is expected to be underpriced 11.11% more than the
IPO of a follower.
High-quality firms would lead hot markets and underprice their issues only if these
actions reveal their quality to investors. Then, investors who become informed should
attach higher market to book ratios to leaders once they go public. The idea is that
market to book ratio is a proxy for the market’s assessment of the value of a firm’s
growth opportunities. We test whether this is the case by regressing firms’ market to
book ratios in the year they go public M toB0 on a leader dummy (L or Ls ) and the
control variables we used in the underpricing regressions. The results reported in the
final two columns of Table 4 indicate that market to book ratios of leaders in their IPO
year exceed those of followers significantly. For instance, when our main leader dummy
L is used, being a leader increases the market to book ratio almost by 2. As was the
case in underpricing, this difference is nearly orthogonal to the controlling factors.
In Section 5.2, we provided evidence that average underpricing and average market
to book ratio of IPO firms are high at the start of hot markets. In this section we
control for pre-IPO observable characteristics and find: (1) leaders underprice their
issues significantly more, and (2) they have significantly higher market to book ratios
in their IPO year.
5.5
Do highly-underpriced leaders grow more ex-post?
Our model suggests that in a separating equilibrium with underpricing, high-quality
firms lead IPO waves and underprice their issues in order to signal their superior growth
opportunities. In the previous section, we showed that underpricing is indeed much
higher at the start of hot markets. We also showed that investors attach higher marketto-book ratios to leaders following their IPOs, which is consistent with the argument
that investors value firms that send a signal by underpricing their issues and leading
IPO waves as those with better growth opportunities.
24
In this section we investigate whether highly-underpriced leaders in fact grow more
ex post. We define highly-underpriced leaders as the leaders that are in the top quartile
of the full sample’s underpricing distribution. In our analysis, we use a dummy variable
Lhu , which is equal to 1 if the issuer is a highly-underpriced leader. Lhu is equal to 0 if
the issuer is either a follower or leader with low underpricing. We calculate industryadjusted growth rates of total assets, net sales, and capital expenditures. For instance,
∆Assetsi is the growth in total assets of a firm between one year before its IPO (y = −1)
and the ith year after it (y = i). It is adjusted by subtracting the contemporaneous
median growth rate within the firm’s industry. Firms are grouped into industries on
the basis of 3-digit SIC codes.
We regress the industry-adjusted ex-post growth rates of IPO firms on Lhu and a set
of control variables. We expect that once we control for ex-ante observable characteristics, issuers would differ only in terms of their unobservable quality of growth opportunities. Investors can deduce the unobservable growth potential of issuers from their
IPO timing and underpricing choices, such that high-quality issuers become highlyunderpriced leaders (Lhu ). Therefore, we expect a positive coefficient on Lhu in our
regression models. The coefficient estimates presented in Table 5 show that this is
indeed the case, such that the industry-adjusted asset, sales, and capital expenditure
growth rates of highly-underpriced leaders are much higher than the corresponding
growth rates of remaining hot market IPOs. The differences are economically significant up to 5 years after going public and statistically significant as well up to 3 years
after going public.
To provide additional evidence on the stronger ex-post growth performance of
highly-underpriced leaders, we compute the difference in mean industry-adjusted growth
rates of highly-underpriced leaders and remaining hot market IPOs. Our IPO timing
model suggests that the difference should be positive. Moreover, the difference should
remain positive after matching highly-underpriced leaders with remaining hot market
25
IPOs on the basis of pre-IPO observable characteristics. This is because, if the difference in post-IPO growth vanishes after controlling for pre-IPO observable characteristics, then our model’s main implication that highly-underpriced leaders are high-quality
firms trying to signal their unobservable type to investors would be wrong. Therefore,
we investigate matched differences as well as unmatched ones.
We employ propensity score matching techniques to obtain the matched differences.17
These techniques match firms that choose the treatment (leading a hot
market and issuing highly-underpriced shares) with those that do not on the basis
of pre-treatment observable characteristics (age, size, leverage, etc.). Consequently,
any treatment effect (significant difference in post-IPO growth) across the treatment
group (highly-underpriced leaders) and the control group (remaining hot market IPOs)
cannot be attributed to differences in pre-treatment observable characteristics.
The unmatched and matched differences between the mean industry-adjusted growth
rates of highly-underpriced leaders and remaining hot market IPOs are reported in Table 6.18 The column titled UM reports the unmatched differences. Those that are
titled NM, RM, and KM report matched differences according to different matching
techniques.
It is clear from the figures in panel A that the assets, sales and capital expenditures
of highly-underpriced leaders grow significantly more. For instance, their industryadjusted assets, sales, and capital expenditures grow on average 37.03%, 54.52% and
24.88% more 3 years after their IPOs on an unmatched basis respectively. Moreover,
highly-underpriced leaders continue to display a superior post-IPO growth performance
when the differences in means are calculated on a matched basis. For instance, the
smallest ∆Salesi figure in panel A suggests that the sales of a highly-underpriced
17
See Li and Zhao (2006) for an application of propensity score matching techniques in the context
of firm performance after seasoned equity offerings.
18
We do not report the means of each group to save space. The mean industry-adjusted growth rates
of highly-underpriced leaders are always positive, which mean that they grow faster than the public
firms in their industries.
26
leader grows on average 31.01% more 3 years after its IPO compared to a group of
other hot market IPOs that have the closest pre-IPO observable characteristics.
The figures in panel A provide strong evidence that the superior post-IPO growth
of highly-underpriced leaders cannot be attributable to their observable characteristics
at the time when they make this choice. In other words, the fact that some firms
choose to become highly-underpriced leaders is consistent with an incentive to signal
their unobservable superior growth potential to investors as predicted by our model.
Although the figures in panel A support our model’s arguments, they can also be
consistent with a counterargument that firms gain growth potential by leading IPO
waves. According to this counterargument, firms are identical in terms of their ex-ante
quality, but those that lead hot markets seize better growth opportunities, potentially
due to a first-mover advantage. However, the figures presented in panel B provide
evidence against this counterargument. In this panel, the treatment group contains all
leaders (i.e., not only highly-underpriced ones). The control group consists of the followers. The differences in means are economically small and statistically insignificant.
This suggests that leaders per se do not grow faster than followers ex post. Therefore,
the findings in panels A and B together imply that only highly-underpriced leaders experience a significantly stronger growth in assets, sales and capital expenditures after
going public. This contradicts the idea of a first-mover advantage, since if there was
such an advantage we would expect all leaders to grow significantly more ex post.
In summary, the findings in this section provide evidence that highly-underpriced
leaders experience a significantly stronger post-IPO growth in assets, sales, and capital expenditures than other hot market IPOs that have similar pre-IPO observable
characteristics. These findings support our model’s prediction that highly-underpriced
leaders are high-quality firms with better growth opportunities. They are inconsistent
with an alternative explanation that leaders become high-quality firms due to a first
mover advantage, since leaders as a group do not grow more than followers.
27
5.6
The relationship between IPO volume and average underpricing
Lowry and Schwert (2002) document a lead-lag relationship between monthly IPO
volume and average underpricing. They find that higher average underpricing leads to
higher volume. It is rather puzzling that more firms go public as average underpricing
increases, since underpricing is an indirect cost of going public. The authors argue
that this relationship can be due to releases of positive information, which are not fully
incorporated into offer prices (see Hanley (1993) and Loughran and Ritter (2002)). The
positive information increases future volume, whereas the partial adjustment of offer
prices in response to positive information increases current average underpricing. The
lead-lag relationship emerges as a result.
Our model’s outcome implies that this relationship is triggered by changes in market
conditions. Improvements in market conditions cause high-quality firms to lead hot
markets and issue underpriced shares, and low-quality firms to follow. High-quality
issuers have to underprice more when low-quality issuers are higher in numbers. This
causes periods of high underpricing to be followed by periods of high volume when the
market conditions keep improving, and creates the lead-lag relationship.
In order to investigate the causal relationships between market conditions, average
underpricing and IPO volume, we run third-order vector autoregressions (VAR), similar
to those in Lowry and Schwert (2002), using monthly data on average underpricing and
IPO volume. Dummy variables for the months of January and September are included
as exogenous variables to control for seasonality effects.19 The results are presented in
Table 7.
Granger F-tests for models (1) and (2) show that there is a significant relationship between current average underpricing and future IPO volume, but no significant
relationship between current IPO volume and future average underpricing. This is
the relationship documented by Lowry and Schwert (2002). However, the inclusion
19
Helwege and Liang (2004) note that fewer IPOs take place during January and September in the
US, due to the difficulties in scheduling road shows during vacation times.
28
of lagged market returns as an explanatory variable changes the results. The coefficient of the lagged market returns variable is positive significant in Models (3) and
(4). Moreover, the Granger F-test conducted on Model (4) shows that the relationship
between current underpricing and future volume loses its significance after controlling
for changes in market conditions. This finding is consistent with our model’s interpretation of the lead-lag relationship and shows that market conditions play a role in
explaining the time variation in underpricing and volume.
6
Conclusion
The purpose of this paper is to study the IPO timing decision of firms in hot markets.
In particular, we are interested in understanding why some firms lead an IPO wave,
whereas others initially wait and go public later on in the same wave. Our model
of IPO timing is based on two main assumptions: (1) the value of a firm’s growth
opportunities is uncertain and depends on the state of the economy; (2) some firms
have better growth opportunities than others and investors cannot recognize those
firms. The first assumption gives all firms an incentive to wait, whereas the second
one gives high-quality firms an incentive to move. This creates a tradeoff, such that
high-quality firms compare the value of their real option to go public with the value of
revealing their type to investors.
Our model’s outcome suggests that when the economy is likely to be bad, all firms
wait, since the real option to go public is very valuable in this case. However, when
there is sufficient probability of a good economy, high-quality firms move in order to
signal their type to investors. Furthermore, they underprice their shares in order to
prevent low-quality firms from mimicking their action. Even though they accept an
unfair valuation, this is still a better valuation than the one they would have got had
they waited to go public alongside low-quality firms.
These results provide us a theoretical framework of hot markets. According to
29
our model, hot markets are likely to be in either pooling equilibrium or separating
equilibrium with underpricing. In the former type of equilibrium, the average quality
of IPO firms is constant and the average underpricing is low throughout the hot market.
In the latter type of equilibrium, the average quality and underpricing are both initially
high and go down later in the hot market. The IPO market is likely to be in a separating
equilibrium with underpricing when the economic uncertainty is high, the number of
high-quality firms is low compared to the number of low-quality firms, and the quality
gap between the two types of firms is wide.
Our empirical findings show that average underpricing tends to be initially high at
the start of a hot market, but then it falls sharply as the hot market ensues. In general,
firms that lead hot markets underprice their issues more, after controlling for their preIPO characteristics. Investors value the growth opportunities of leaders significantly
more, and indeed highly-underpriced leaders meet the expectations of investors by
growing significantly more up to 5 years after going public.
Overall, our theoretical and empirical findings indicate that both average firm quality and underpricing need not be constant throughout a hot market. We provide evidence for the existence of hot markets in which high-quality firms signal their type by
becoming leaders and underpricing their issues.
A
Proofs of Propositions
We start with the proof of pooling equilibrium presented in Proposition 1. It is intuitive
that when q is small, all firms prefer to wait, since their growth opportunities are
unlikely to payoff at t = 1. If the economy turns out to be good at t = 1 (despite the
low probability) firms go public. In such a case, investors’ breakeven condition at t = 1
is:
(1 − αp )(pVg + (1 − p)Vb ) = I
30
Solving for αp yields Equation (2). Pooling is an equilibrium if no firm is willing
to deviate by going public at t = 0. This depends on what investors would believe
about the type of a firm that follows this out-of-equilibrium strategy. For instance,
if they would believe that such a firm is of low-quality, pooling is, clearly, always an
equilibrium. However, such a belief is against the Cho-Kreps intuitive criterion (see Cho
and Kreps (1987)), since low-quality firms are precisely the type of firms that would
not follow the out-of-equilibrium strategy. Therefore, consistent with this criterion,
we assume that investors believe high-quality firms would follow the out-of-equilibrium
strategy, since they have a very strong incentive to do so. Then, if an IPO were to take
place at t = 0, investors would believe their breakeven condition is:
(1 − αg )qVg = I
Solving for αg yields Equation (4). Then, high-quality firms can either pool with lowquality ones if the economy is good at t = 1 and retain an equity stake of fraction αp ,
or they can take the risk of going public at t = 0 and retain an equity stake of fraction
αg . They prefer to pool as long as:
αg qVg − c ≤ q(αp Vg − c)
This inequality is satisfied when q is less than or equal to q (see Equation (1)). Therefore, the IPO market is in a pooling equilibrium when q ≤ q, and high-quality firms
deviate when q > q.
Next, we prove Proposition 2, which describes a separating equilibrium without
underpricing in which high-quality firms go public at t = 0, and low-quality ones go
public at t = 1 if the economy is good. In equilibrium, investors’ beliefs should be
consistent with the actions of firms, such that they should value any firm that goes
public at t = 0 (t = 1) as a high-quality (low-quality) firm. Consequently, at t = 0,
31
firms can retain fraction αg of their equity, which is the maximum fraction that satisfies
investors’ breakeven condition when investors believe they are faced with high-quality
firms. Similarly, investors believe they are faced with low-quality firms at t = 1. Thus,
their breakeven condition at that time is:
(1 − αb )Vb = I
Solving for αb yields Equation (5). Separating without underpricing is an equilibrium if
it is optimal for high-quality firms to move and for low-quality ones to wait. Low-quality
firms can have an incentive to deviate, since if they move they would be valued as highquality firms by investors. Therefore, separating equilibrium without underpricing is
maintained as long as low-quality firms’ optimal action is to wait:
αg qVb − c ≤ q(αb Vb − c)
This inequality is satisfied when q is less than or equal to q ∗ (see Equation (3)).
Therefore, the IPO market is in a separating equilibrium without underpricing when
q < q ≤ q ∗ , and low-quality firms deviate when q > q ∗ .
We now provide a proof of Proposition 3, which deals with the separating equilibrium with underpricing. We showed above that the separating equilibrium without
underpricing breaks down when q > q ∗ , since low-quality firms move in order to mimic
high-quality firms. High-quality firms can prevent this by agreeing to retain an equity
stake of αu that is smaller than αg , such that low-quality firms become indifferent
between moving and waiting:
αu qVb − c = q(αb Vb − c)
Solving for αu yields Equation (7). Separating with underpricing is an equilibrium
32
as long as it is optimal for high-quality firms to underprice their issues. These firms
have to underprice more when q is high (i.e. ∂αu /∂q < 0). Consequently, when q
reaches a threshold, they are no longer better off by signaling their quality, and when
q exceeds that threshold they would rather pool with low-quality firms. This threshold
is determined by the following inequality:
αu qVg − c ≤ q(αp Vg − c)
which is satisfied when q is less than or equal to q (see Equation (6)). Thus, the
IPO market is in a separating equilibrium with underpricing when q ∗ < q ≤ q, and
high-quality firms deviate when q > q.
Finally, we prove Proposition 4. We argued that when q > q, high-quality firms
are better off by pooling with low-quality firms at t = 1. As in Proposition 1, whether
pooling is an equilibrium or not depends on investors’ belief about the type of firms
that go public at t = 0. Clearly, high-quality firms have an incentive to follow this
strategy, if investors would believe that an IPO at t = 0 is conducted by a high-quality
firm. But, under such a belief, given that q is high, low-quality firms would also have
an incentive to follow the same strategy to benefit from being valued as high-quality
firms. Therefore, we assume that, when q > q, if investors were to observe a firm
going public at t = 0, they would believe the firm is of high-quality with probability p.
Consequently, their breakeven condition would be:
(1 − αp0 )(pqVg + (1 − p)qVb ) = I
It is easy to show that αp0 is always less than or equal to αp , since q ≤ 1. Therefore,
both types of firms are better off by pooling at t = 1, since the fraction of equity they
would retain if they go public at t = 0 is smaller, let alone the uncertainty of going
public at t = 0. As a result, the IPO market is in a pooling equilibrium when q < q ≤ 1,
33
such that all firms wait at t = 0 and go public at t = 1 if the economy is good.
34
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37
q
1.0
0.8
q
0.6
q*
0.4
q
0.2
p
0.02
0.04
0.06
0.08
0.10
Figure 1: The model’s outcome.
The IPO market is in a pooling equilibrium in the white regions, in a separating
equilibrium without underpricing in the black region, and in a separating equilibrium
with underpricing in the gray region. The black region is bounded by q and q ∗ . The
gray region is bounded by q ∗ and q. p is the probability that a firm is of high-quality,
q is the probability that the economy is good at t = 1. The parameter values used for
this figure are {Vg , Vb , I, c} = {360, 120, 100, 20}.
38
150
125
100
75
Volume
50
25
0
1975q1
1980q1
1985q1
1990q1
1995q1
2000q1
2005q1
2010q1
Time
Figure 2: Hot markets between 1975 and 2010.
The area plot is the 3-quarter moving average IPO volume ma(3). Black, dark gray,
and light gray areas represent hot, warm, and cold quarters respectively. A quarter
is classified as hot (cold) if its ma(3) exceeds (falls short of) the historical average of
previous quarters by 50%. Quarters that are neither hot nor cold are classified as warm.
The line plot represents the historical average that goes back to 1960. Quarterly IPO
volume is deflated by the number of public firms in the previous quarter before ma(3)
is calculated. Public firms are identified as those that have a sharecode of 10 or 11 in
CRSP. The data on monthly IPO volume is obtained from Jay Ritter’s website. The
“net” volume variable is used. Net volume is regressed on “gross” volume between 1975
and 2010 and the estimated regression line is used to obtain estimates of net volume
between 1960 and 1974.
39
Table 1: A numerical example of separating equilibrium with underpricing
The top pair in parantheses is the range of underpricing over the range of q, where q ∈ (q ∗ , q).
The bottom pair in parantheses is (q ∗ , q). The IPO market is in a separating equilibrium with
underpricing when q lies in this range. Underpricing is defined in Equation (8). q ∗ and q are
defined in Equations (3) and (6) respectively. p is the probability that a firm is of high-quality.
Vg and Vb are the payoffs of growth opportunities for high- and low-quality firms if the economy
is good at t = 1. I and c are the investment and issuing costs respectively. For some calibrations
q ∗ exceeds q in which case the IPO market is never in a separating equilibrium with underpricing.
The ranges of underpricing and q are not reported in those cases.
Panel A: p=2.5%
c/I=20%
c/I=15%
c/I=10%
Vg /Vb =3
(0.00% , 105.26%)
(0.44 , 0.74)
(0.00% , 88.71%)
(0.42 , 0.68)
(0.00% , 62.50%)
(0.39 , 0.58)
Vg /Vb =2.5
(0.00% , 80.56%)
(0.50 , 0.77)
(0.00% , 67.62%)
(0.48 , 0.71)
(0.00% , 46.62%)
(0.45 , 0.62)
Vg /Vb =2
(0.00% , 52.94%)
(0.58 , 0.80)
(0.00% , 43.56%)
(0.57 , 0.75)
(0.00% , 27.87%)
(0.55 , 0.67)
Panel B: p=5.0%
c/I=20%
c/I=15%
c/I=10%
Vg /Vb =3
(0.00% , 54.05%)
(0.44 , 0.59)
(0.00% , 35.71%)
(0.42 , 0.52)
(0.00% , 9.62%)
(0.39 , 0.42)
Vg /Vb =2.5
(0.00% , 39.71%)
(0.50 , 0.63)
(0.00% , 24.45%)
(0.48 , 0.56)
(0.00% , 2.15%)
(0.45 , 0.46)
Vg /Vb =2
(0.00% , 22.58%)
(0.58 , 0.68)
(0.00% , 10.68%)
(0.57 , 0.61)
Panel C: p=7.5%
c/I=20%
c/I=15%
Vg /Vb =3
(0.00% , 21.98%)
(0.44 , 0.51)
(0.00% , 4.72%)
(0.42 , 0.43 )
Vg /Vb =2.5
(0.00% , 12.80%)
(0.50 , 0.54)
Vg /Vb =2
(0.00% , 1.37%)
(0.58 , 0.59)
40
c/I=10%
35
30
Average underpricing (%)
10
15
20
25
5
0
.Cold
.Warm
Q={0,1,2}
Q={3, 4, 5}
Q>5
Figure 3: Average underpricing during the course of a hot market.
The bars labeled “Cold” and “Warm” depict the level of average underpricing in cold
and warm quarters respectively. The remaining bars labeled Q = q represent the level
of average underpricing in the qth quarter of a hot market. A quarter is classified as
hot (cold) if its ma(3) exceeds (falls short of) the historical average in previous quarters
by 50%. A quarter is classified as warm if it is neither hot nor cold. Quarterly IPO
volume is deflated by the number of public firms in the previous quarter before ma(3)
is calculated. Public firms are identified as those that have a sharecode of 10 or 11 in
CRSP. The Nasdaq Bubble quarters (the last quarter of 1999 and the first quarter of
2000) are excluded. The average level of underpricing is 96.8% in these two quarters.
The data on monthly average underpricing is obtained from Jay Ritter’s website.
41
42
Sales−1
mean median
Cold
512.81
100.35
Warm
314.46
46.22
Leaders 143.48
31.99
Followers 156.90
33.55
Bubble 213.07
12.12
All
213.42
35.88
Obs.
4,988
IniR
mean median
Cold
12.46
6.25
Warm
14.59
5.65
Leaders 29.31
12.98
Followers 13.72
5.56
Bubble 100.64
65.00
All
20.04
7.50
Obs.
6,298
T P ro
mean
median
149.13
83.59
541.11
103.84
424.19
157.81
460.95
128.58
1251.79
413.01
493.31
127.99
5,055
Age
mean median
15.99
9.00
14.73
8.00
11.47
6.00
13.01
7.00
8.26
5.00
13.13
7.00
6,170
Panel A: Issue characteristics
Assets−1
mean
median
423.36
73.78
374.52
43.35
127.17
26.27
135.91
23.76
209.61
23.35
211.85
29.52
5,055
CapX−1
mean
median
8.70
5.65
9.76
5.78
11.33
7.67
10.50
6.20
11.57
7.70
10.42
6.44
4,938
P rof−1
mean median
3.92
13.90
-20.43
10.45
-8.12
14.65
-1.79
14.43
-61.24
-36.14
-9.94
12.84
4,972
Panel B: Pre-IPO firm characteristics
M toB0
mean
median
3.33
2.56
3.72
2.69
5.67
3.16
3.53
2.73
7.68
4.25
4.13
2.82
5,451
a percentage of total assets in y = −1.
Debt−1
mean median
26.32
18.98
24.82
11.82
22.13
10.50
26.46
12.58
18.84
3.75
24.93
11.60
5,044
SecS
mean median
19.16
0.00
12.40
0.00
13.36
0.00
10.69
0.00
2.21
0.00
11.81
0.00
6,298
V Cap
mean median
0.41
0.00
0.45
0.00
0.45
0.00
0.40
0.00
0.73
1.00
0.43
0.00
6,298
2010 dollars in y = −1 respectively. CapX−1 is capital expenditures, P rof−1 is EBITDA, Debt−1 is long-term debt in y = −1, all expressed as
variable equal to 1 if the IPO is backed by a venture capital firm. Sales−1 and Assets−1 are net sales and total assets measured in millions of
firm’s IPO and foundation years. SecS is the number of secondary shares offered as a percentage of total shares offered. V Cap is a dummy
is the market to book ratio in y = 0. T P ro is the total proceeds as a percentage of total assets in y = −1. Age is the difference between the
Mean and median values are reported. IniR is the initial percentage return between the offer price and the first trading day closing price. M toB0
Table 2: Descriptive Statistics
Table 3: Can investors distinguish leaders from followers?
Odds ratio estimates of logistic regression models are reported. The dependent variable is L, which is equal
to 1 if 0 ≤ Q ≤ 2 and to 0 if Q ≥ 2, where Q = q means that a firm went public during the qth quarter of a
hot market. Age is the difference between the firm’s IPO and foundation years. V Cap is a dummy variable
equal to 1 if the IPO is backed by a venture capital firm. SecS is the number of secondary shares offered as
a percentage of total shares offered. T P ro is the total proceeds as a percentage of total assets in y = −1.
Sales−1 is net sales measured in millions of 2010 dollars in y = −1. CapX−1 is capital expenditures,
P rof−1 is EBITDA, Debt−1 is long-term debt in y = −1 as a percentage of total assets in y = −1. Model
(4) excludes the IPOs that took place during the NASDAQ Bubble period. AUC is the area under the ROC
curve. Robust t-statistics are in parentheses. ***, **, and * stand for significance at 1, 5, and 10 percent
levels respectively.
Model
Age
V Cap
SecS
T P ro
(1)
(2)
(3)
(4)
0.99*
(-1.77)
1.16*
(1.80)
1.01***
(4.72)
1.00
(-0.34)
1.04*
(1.82)
1.01*
(1.79)
1.00**
(-2.11)
1.00*
(-1.78)
0.28***
(-12.53)
0.99*
(-1.85)
1.23**
(2.54)
1.01***
(3.89)
1.00
(0.38)
1.05**
(2.21)
1.01*
(1.93)
1.00***
(-3.14)
1.00**
(-2.39)
0.29***
(-11.74)
3,386
0.01
0.57
3,189
0.01
0.58
1.00*
(-1.74)
1.18**
(2.14)
1.01***
(5.35)
1.00
(-0.86)
ln(Sales−1 )
Con.
0.31***
(-17.16)
1.04*
(1.93)
1.01*
(1.81)
1.00
(-1.51)
1.00**
(-2.33)
0.33***
(-13.82)
Obs.
R-sq.
AUC
3,483
0.01
0.57
3,422
0.00
0.54
CapX−1
P rof−1
Debt−1
43
Table 4: Do leaders underprice more and do investors value the growth opportunities
of leaders more?
Coefficient estimates of OLS regression models are reported. IniR is the initial percentage return between
the offer price and the first trading day closing price. M toB0 is the market to book ratio in y = 0. L (Ls )
is the dummy for leaders, which is equal to 1 if 0 ≤ Q ≤ 2 (Q = 1) and to 0 if Q > 2 (Q > 1), where Q = q
means that a firm goes public during the qth quarter of a hot market. Age is the difference between the
firm’s IPO and foundation years. V Cap is a dummy variable equal to 1 if the IPO is backed by a venture
capital firm. SecS is the number of secondary shares offered as a percentage of total shares offered. T P ro
is the total proceeds as a percentage of total assets in y = 0. Sales−1 is net sales measured in millions of
2010 dollars in y = −1. CapX−1 is capital expenditures, P rof−1 is EBITDA, Debt−1 is long-term debt
in y = −1, all expressed as a percentage of total assets in y = −1. ∆Sales0 , ∆CapX0 , and ∆P rof0 are
the percentage growth rates in net sales, capital expenditures and EBITDA between y = −1 and y = 0
respectively. Bubble is a dummy variable, which is equal to 1 if the IPO took place during the bubble period
(4th quarter of 1999 or 1st quarter of 2000). All models include 3-digit SIC dummies. Robust t-statistics
are in parentheses. ***, **, and * stand for significance at 1, 5, and 10 percent levels respectively.
IniR
L
V Cap
SecS
T P ro
ln(Sales−1 )
CapX−1
P rof−1
Debt−1
M toB0
14.12***
(7.95)
Ls
ln(Age + 1)
IniR
M toB0
1.99***
(4.20)
1.73***
(3.34)
-4.01***
(-5.01)
7.43***
(4.52)
-0.21***
(-7.10)
-0.00
(-0.22)
0.65
(1.41)
0.02
(0.42)
-0.04**
(-2.37)
-0.06***
(-4.10)
11.11***
(3.48)
-3.88***
(-4.88)
7.27***
(4.49)
-0.18***
(-5.86)
-0.00
(-0.06)
0.40
(0.89)
0.03
(0.44)
-0.02*
(-1.88)
-0.06***
(-3.90)
-0.23
(-1.11)
0.65*
(1.86)
-0.01
(-1.29)
-0.00
(-0.80)
-0.11
(-1.43)
-0.04
(-1.15)
-0.01*
(-1.67)
0.00
(0.19)
1.74**
(2.52)
-0.21
(-0.96)
0.55
(1.54)
-0.02**
(-2.20)
-0.00
(-0.57)
-0.10
(-1.25)
-0.03
(-0.98)
-0.01
(-1.50)
0.00
(0.35)
75.08***
(9.21)
30.90***
(11.07)
74.00***
(9.03)
30.60***
(10.77)
1.61**
(2.03)
3.40***
(3.42)
1.30
(1.51)
3.21***
(3.07)
-0.08
(-0.37)
0.15
(0.36)
-0.00
(-0.39)
-0.00
(-1.32)
0.01
(0.11)
-0.05
(-1.14)
-0.00
(-0.60)
0.01
(1.06)
0.02***
(4.40)
0.00
(0.04)
0.00
(0.73)
1.18
(1.28)
1.31
(0.96)
3,386
0.27
3,168
0.27
3,366
0.06
3,150
0.06
2,878
0.07
∆Sales0
∆CapX0
∆P rof0
Bubble
Con.
Obs.
R-sq.
M toB0
44
45
1
Obs.
R-sq.
3,172
0.32
43.72***
(7.38)
ln(Age + 1) -13.91***
(-7.69)
V Cap
3.90
(1.29)
P Sec
-0.16***
(-2.69)
T P ro
0.01***
(4.11)
ln(Sales−1 -10.67***
(-8.99)
CapX−1
0.34***
(2.89)
P rof−1
-0.09*
(-1.65)
Debt
-0.10
(-1.62)
Bubble
40.82***
(4.54)
Con.
152.58***
(27.89)
Lhu
i
2,563
0.14
23.28***
(2.82)
-16.40***
(-6.39)
9.32**
(2.17)
0.02
(0.21)
0.01***
(3.27)
-6.48***
(-4.31)
0.66***
(3.77)
-0.04
(-0.88)
-0.04
(-0.74)
-10.17
(-0.80)
141.03***
(18.30)
∆Assetsi
3
2,048
0.11
15.16
(1.41)
-18.08***
(-5.68)
19.37***
(3.34)
-0.06
(-0.57)
0.01***
(4.81)
-6.79***
(-3.67)
0.65***
(2.60)
-0.01
(-0.27)
0.02
(0.23)
-11.02
(-0.77)
146.57***
(14.63)
5
3,065
0.29
38.52***
(6.01)
-11.38***
(-7.22)
11.73***
(3.81)
-0.16***
(-3.02)
0.00**
(2.03)
-14.49***
(-9.37)
0.64***
(4.25)
-0.16***
(-3.54)
-0.07
(-1.29)
50.98***
(5.00)
121.19***
(17.72)
1
2,468
0.26
29.88***
(3.51)
-13.72***
(-6.38)
21.71***
(4.98)
-0.11
(-1.53)
0.00
(0.58)
-16.66***
(-9.05)
1.15***
(5.85)
-0.26***
(-4.20)
0.00
(0.07)
12.37
(0.98)
139.96***
(15.69)
∆Salesi
3
1,985
0.20
24.47*
(1.93)
-13.30***
(-4.64)
27.05***
(4.50)
-0.14
(-1.30)
0.02*
(1.93)
-17.92***
(-7.47)
1.26***
(4.33)
-0.14
(-1.46)
0.06
(0.71)
20.28
(1.33)
139.85***
(11.33)
5
3,110
0.17
30.23***
(3.86)
-15.15***
(-5.78)
-9.29**
(-2.03)
-0.36***
(-3.56)
0.02**
(2.04)
-10.07***
(-6.49)
-2.68***
(-10.97)
0.12
(1.54)
0.10
(1.57)
3.89
(0.35)
180.11***
(19.65)
1
2,490
0.13
23.96**
(2.16)
-14.76***
(-4.23)
12.96**
(2.14)
-0.22*
(-1.69)
0.07***
(7.96)
-2.20
(-1.05)
-3.28***
(-8.66)
0.48***
(6.09)
0.13
(1.56)
-49.67***
(-3.69)
117.33***
(9.38)
∆CapXi
3
1,982
0.12
17.37
(1.36)
-20.42***
(-4.75)
18.90**
(2.46)
-0.37**
(-2.09)
0.06***
(4.65)
-4.13*
(-1.70)
-3.59***
(-6.88)
0.49***
(4.61)
0.23***
(2.65)
-32.04**
(-2.01)
139.56***
(9.06)
5
The output from OLS regression models are reported. Lhu is a dummy variable, which is equal to 1 if 0 ≤ Q ≤ 2 and the issuer’s underpricing
is in the top quartile of the sample. It is equal to 0 if Q > 2 or if 0 ≤ Q ≤ 2 and the issuer’s underpricing is in the bottom 3 quartiles of the
sample. ∆Assetsi is the percentage growth rate in total assets from y = −1 to y = i, which is calculated as 100 × ln(Assetsi /Assets−1 ) minus
the contemporaneous industry median based on 3-digit SIC codes. ∆Salesi and ∆CapXi are the percentage growth rates in net sales and capital
expenditures respectively. They are calculated in the same manner as ∆Assetsi . Age is the difference between the firm’s IPO and foundation
years. V Cap is a dummy variable equal to 1 if the IPO is backed by a venture capital firm. SecS is the number of secondary shares offered as a
percentage of total shares offered. T P ro is the total proceeds as a percentage of total assets in y = 0. Sales−1 is net sales measured in millions of
2010 dollars in y = −1. CapX−1 is capital expenditures, P rof−1 is EBITDA, Debt−1 is long-term debt in y = −1, all expressed as a percentage
of total assets in y = −1.
Table 5: Do highly-underpriced leaders grow more ex-post? (OLS regressions)
46
59.60
10.23
37.03
4.84
30.86
3.11
6.45
1.71
-3.83
-0.79
-7.53
-1.21
3
5
1
3
5
UM
1
i
-6.04
-0.94
-6.58
-1.31
7.84
1.91
14.36
1.25
21.81
2.42
44.73
6.21
NNM
-5.93
-0.97
-3.16
-0.66
6.19
1.58
21.63
1.97
28.56
3.33
48.98
7.06
T/C
UM
NNM
∆Salesi
RM
KM
T/C
UM
NNM
-5.93
-0.96
-3.19
-0.67
6.25
1.59
20.85
1.90
28.16
3.28
48.34
6.96
546/1,502
672/1,891
825/2,347
171/1,877
212/2,351
270/2,902
34.10
2.40
31.01
2.92
35.39
4.38
37.41
2.75
41.76
4.13
45.77
6.00
36.24
2.67
40.90
4.04
44.83
5.87
163/1,822
202/2,266
262/2,803
4.29
0.62
0.14
0.03
7.68
1.95
3.23
0.44
0.44
0.08
4.18
1.00
3.56
0.52
-1.14
-0.21
4.35
1.10
3.61
0.52
-1.20
-0.23
4.42
1.11
532/1,453
653/1,815
809/2,256
Panel B: Leaders vs followers
47.74
4.31
54.52
6.48
58.90
9.61
-8.79
-1.04
-9.33
-1.35
-1.58
-0.31
20.17
1.49
24.88
2.25
39.09
4.87
-2.10
-0.24
-7.12
-0.99
3.41
0.65
19.60
1.36
26.80
2.18
33.67
3.74
Panel A: Highly-underpriced leaders vs remaining hot market IPOs
∆Assetsi
RM
KM
-4.38
-0.54
-5.82
-0.85
1.27
0.25
18.95
1.39
26.18
2.25
34.77
4.13
-4.37
-0.54
-5.87
-0.85
1.53
0.31
18.93
1.38
25.85
2.22
34.61
4.11
∆CapXi
RM
KM
527/1,455
651/1,839
810/2,300
166/1,816
202/2,288
264/2,846
T/C
The differences in mean industry-adjusted growth rates are reported. The figures are in percentages. In Panel B, the treatment group is leaders
(L = 1) and the control group is followers (L = 0). In Panel A, the treatment group is leaders that are in the top quartile of the full sample’s
underpricing distribution, and the control group is followers and the remaining leaders. ∆Assetsi is the percentage growth rate in total assets
from y = −1 to y = i, which is calculated as 100 × ln(Assetsi /Assets−1 ) minus the contemporaneous industry median based on 3-digit SIC
codes. ∆Salesi and ∆CapXi are the percentage growth rates in net sales and capital expenditures respectively. They are calculated in the
same manner as ∆Assetsi . UM is the unmatched-difference of industry-adjusted percentage growth rates between the treatment and the control
groups. NNM, RM, KM are matched differences on the basis of a particular type of propensity score matching. NNM is a nearest neighbor
matching (10 neighbors are used). RM is a radius matching with caliper of 0.05. KM is a kernel matching. T/C gives the number of observations
in the treatment and the control groups. The pre-treatment variables used to estimate propensity scores are identical to those used in Table 5. t
statistics are reported underneath the differences in means.
Table 6: Do highly-underpriced leaders grow more ex-post? (Propensity Score Matching)
Table 7: The relationship between IPO volume and average underpricing
Coefficient estimates of third-order vector autoregressions involving monthly average underpricing IniRm
and monthly IPO volume V olm are reported. The data is obtained from Jay Ritter’s website. For the IPO
volume, “net count” variable is used. This variable does not count penny stocks, units, closed-end funds,
REITs acquisition companies, ADRs, limited partnerships, banks and S&Ls, and IPO firms that are not
listed on CRSP. The data on this variable is available from 1975 till 2010. Jan and Sep are dummy variables
that are equal to 1 if the month is January and September respectively. R1 is the return on the monthly
average level of the value-weighted index of all NYSE, AMEX, and NASDAQ stocks. Lt represents lag t of
a variable, where t ∈ {1, 2, 3}. The figures in parentheses are t-statistics and p-values in Panels A and B
respectively. ***, **, and * stand for significance at 1, 5, and 10 percent levels respectively.
Model
Regressand
(1)
(2)
(3)
(4)
IniRm
V olm
IniRm
V olm
Panel A: Regressors
L1.IniRm
0.52***
(10.34)
0.07**
(2.42)
0.49***
(9.47)
0.04
(1.29)
L2.IniRm
0.19***
(3.44)
-0.01
(-0.37)
0.20***
(3.64)
-0.00
(-0.03)
L3.IniRm
0.02
(0.48)
0.01
(0.24)
0.04
(0.74)
0.02
(0.73)
L1.V olm
-0.04
(-0.52)
0.59***
(13.19)
-0.08
(-1.05)
0.55***
(12.15)
L2.V olm
0.01
(0.16)
0.01
(0.14)
0.03
(0.30)
0.02
(0.40)
L3.V olm
0.01
(0.19)
0.28***
(6.35)
0.04
(0.58)
0.32***
(7.15)
Jan
5.50**
(2.03)
-12.86***
(-7.91)
5.05*
(1.87)
-13.36***
(-8.39)
Sep
6.52**
(2.35)
-7.44***
(-4.47)
6.50**
(2.36)
-7.46***
(-4.60)
0.53**
(2.33)
0.58***
(4.32)
L1.R1
Con.
3.96***
(2.85)
2.63***
(3.16)
3.54**
(2.54)
2.17***
(2.65)
Obs.
R-sq.
390
0.46
390
0.74
390
0.46
390
0.75
Panel B: Granger F-tests
Lagged Vol
Lagged IniR
0.30
(0.96)
1.24
(0.74)
9.38
(0.03)
47
5.73
(0.13)