Working Paper Series

_______________________________________________________________________________________________________________________

National Centre of Competence in Research Financial Valuation and Risk Management

Working Paper No. 580

The Dynamics of Going Public

Maria Cecilia Bustamante

First version: December 2005 Current version: November 2008

This research has been carried out within the NCCR FINRISK project on

“Dynamic Corporate Finance and Financial Innovation”

___________________________________________________________________________________________________________

The Dynamics of Going Public

Maria Cecilia Bustamante�

This Draft: November 2008First Draft: December 2005

Abstract

This paper develops a signalling game in which the decision to raise public equityis a real option of the �rm. Firms may use multiple signals to reveal their type:the timing of the IPO, the fraction of shares issued and the underpricing of shares.The model provides a tractable approach for solving signalling games in a real optionsframework and predicts both IPO activity and underpricing conditional on adverseselection. In periods where adverse selection is less relevant (hot markets), there ishigher IPO volume, younger �rms go public and �rms with worse investment prospectsare overvalued. In periods where adverse selection is more relevant (cold markets),there is lower IPO volume, �rms with better investment prospects accelerate their IPOand underprice more their shares with respect to worse �rms to avoid imitation. Thepaper provides a rational approach to analyze underpricing and market timing. Theempirical tests support the predictions that better �rms go public earlier and underpricemore their shares during cold IPO markets.

Keywords: IPOs, SEOs, real options, signalling games, asymmetric information.JEL Classi�cation Numbers: D82, G14, G31, G32

�University of Lausanne, Swiss Finance Institute. E-mail: mariacecilia.bustamante@unil.ch. I amgrateful to Christopher Hennessy, Ron Giammarino, Dmitry Livdan, Erwan Morellec, Christine Parlour,Enrique Schroth, Ilya Strebulaev, Gunther Strobl, Rene Stulz, Deszo Szalay, Alexander Wagner, ChristopherYung and seminar participants at the University of Lausanne, Universidad Torcuato di Tella and Universityof California, Berkeley. I thank all comments received at the UBC Winter Finance Conference and theWFA Annual Meetings 2008, Hawaii. An earlier version of this paper won the SFI Annual Award 2006 forthe Best Working Paper by a PhD student in Switzerland. All errors are my own. Financial support bythe Swiss National Centre of Competence in Research "Financial Valuation and Risk Management" (NCCRFINRISK) is gratefully acknowledged.

1 Introduction

Ever since Ibbotson (1975) �rst documented large underpricing in initial public o¤erings

(IPOs), there has been a growing literature on IPOs. The study of IPOs gained further

attention during the 1990s with the work by Ritter (1991) on long run underperformance,

and the increased IPO activity until the burst of the NASDAQ bubble. Most of the theory

on IPOs, though, is static in nature: it posits multi period set-ups where the time at which

�rms become public is taken as given. For instance, the papers by Rock (1986) and Welch

(1989) provide alternative explanations to underpricing where the time at which the �rm

goes public is deterministic. This paper adds to the current literature in IPOs by analyzing

the decision to go public as a real option of the �rm. The framework emphasizes that both

the timing to raise public equity and the underpricing of new issues are relevant to explain

the decision to go public.

In line with Welch (1989), Grinblatt and Hwang (1989) and Allen and Faulhaber (1989),

there is asymmetric information between managers and market players. Since the single

managing shareholder of the �rm has better information about his �rm�s future cash �ows,

he may signal information about the true value of the �rm through the going public strategy.

This paper explores a dynamic signalling game of the decision to raise public equity, where

�rms reveal their type through both dynamic signals such as the timing to do a public

o¤ering and static signals such as the fraction of shares issued and the underpricing of

shares. While the static signals have been widely studied elsewhere (see Vandemaele, 1997,

for a survey), this also considers timing to raise public equity in the presence of asymmetric

information. The model is thus strongly related to the literature on real options and

asymmetric information motivated by Grenadier (1999).

Several contributions follow from analyzing the decision to go public in the current

framework. First, this paper adds to the study of real options and asymmetric information

in considering the impact of signalling on the option exercise strategies of �rms. When

�rms fully reveal their type (separating equilibrium), �rms with better investment projects

go public earlier to make imitation more costly. When �rms do not reveal their type (pooling

equilibrium), �rms with worse investment projects accelerate the decision to go public to

enhance the pricing of their shares. The timing to raise public equity thus depends both

on �rm characteristics and on the incentives of �rms to reveal their type in equilibrium.

The model then characterizes the timing to go public according to the degree of adverse

selection in the market (Tirole, 2007). In periods where adverse selection is more relevant

(cold markets), good �rms optimally decide to signal their type to market players by antici-

pating their public o¤ering and there is relatively low IPO volume. In periods of relatively

1

low adverse selection (hot markets), the costs of signalling for good types are larger than the

undervaluation implied by pooling and there is increased IPO activity. The model further

demonstrates that the average expected average age of issuers and the average fraction of

shares issued increase with adverse selection.

Second, the paper provides a tractable approach to model underpricing in a real options

set-up. While there has been a growing literature on option exercise strategies and run-up

e¤ects, this literature solves for the timing to exercise the option assuming fully revealing

strategies, and de�nes underpricing as the di¤erence between the actual value of the �rm

and its prior expected value by market players.1 This paper relaxes this assumption and

shows that underpricing also depends on adverse selection. When market beliefs imply

high underpricing costs at the public o¤ering, �rms may have no incentives to reveal their

type to outside investors.

This paper highlights that both underpricing and the option exercise strategies of �rms

are jointly determined in equilibrium. The model provides a rational approach to analyze

underpricing and market timing of public equity issues. In fully revealing separating equi-

libria, underpricing is endogenously determined such that market beliefs are self-ful�lling

and the strategies of issuers are incentive compatible. In pooling equilibria, IPO strategies

are not informative to market players, all �rms issue simultaneously and there is mispric-

ing in equilibrium. The timing to raise public equity is thus functionally related to the

underpricing of shares, and depends on the �rms�incentives to signal their type to outside

investors.

Finally, the paper demonstrates that underpricing relates to the shadow cost of signalling

for issuers. In least cost separating equilibria, the underpricing provided by �rms with

good investment projects depends on the shadow cost of incentive compatibility constraints

on their optimal IPO strategies. Underpricing increases when the �rms with better and

worse investment projects are relatively more similar, such that �rms with worse investment

projects �nd it less costly to imitate better �rms.2 The paper then provides a positive role

for underpricing in IPO markets. Underpricing is a mechanism through which �rms with

good investment projects transfer their signalling costs to new shareholders.

The implications on underpricing are then directly translated into announcement e¤ects.

The model predicts non negative short-run abnormal returns for issuing stocks when �rms

fully reveal their type. Better �rms convey higher abnormal returns to new shareholders

1Carlson et al (2006a) provide a real options model of SEOs with announcement e¤ects. Other paperson real options and announcement e¤ects are Carlson et al (2006b), Morellec and Zdhanov (2005) andHackbarth and Morellec (2007).

2This statement relates underpricing to the distribution of �rm types. See Figure 2.

2

and thus re-allocate part of their signalling costs as abnormal returns to outside investors.

The paper highlights that the timing to exercise an option and abnormal returns are func-

tionally related in equilibrium. This result di¤ers signi�cantly from the approach in existing

literature in which option exercise strategies are solved independently of the announcement

e¤ects they induce.

The signalling model in this paper predicts the behavior of �rms according to the degree

of adverse selection in the market. During periods of relatively low adverse selection (hot

markets), there is clustering of IPOs, a higher trading volume, a lower average expected age

of issuers, and overvaluation of bad types by market players. During periods of relatively

high adverse selection (cold markets), IPOs are distributed in time according to �rm type,

trading volume of issuing stocks decreases, there is a higher average expected age of issuers

and good types e¢ ciently underprice their shares to signal their type to outside investors.

These predictions match the empirical evidence on hot and cold IPO markets for a sample

of US public o¤erings between 1980 and 2005.

The dynamic set-up of the model can also explain the strategy to raise public equity in

subsequent public o¤erings (SEOs); the option to go public in itself implies the option do a

SEO. When the �rm has more than one growth option, multiple o¤ering strategies enable

managers to allocate the costs of asymmetric information across time. Managers optimally

decide on the number of public o¤erings to perform based on the trade-o¤ between higher

underpricing costs in fewer o¤erings or higher underwriting fees with more SEOs. The

dynamic implications of the strategy to go public are then strongly related to the empirical

�ndings by Denis (1991) and Derrien and Kecskés (2007), who show that multi-stage o¤ering

strategies are intended to lower the costs of going public.

The empirical section of the paper further complements the available literature by pro-

viding supporting empirical evidence for the signalling explanation for IPO underpricing

and highlights IPO timing as a relevant feature of the going public decision. Using a sam-

ple of US public o¤erings between 1980 and 2005, I show that underpricing is positively

related to the probability of obtaining a high common equity score by Standard and Poors

(S&P) in the incoming years of the o¤ering.3 This result complements Michaely and Shaw

(2004) who �nd no supporting empirical evidence for the signalling explanation on under-

pricing. The probability of getting a high common stock score by S&P is also negatively

and signi�cantly related to the age of issuing �rms in IPOs at NYSE and to the age of

issuing �rms at SEOs. To my understanding, this is the �rst empirical test on signalling

in IPOs based on underlying measures of �rm quality.

3See Section 4.

3

The paper is divided in �ve sections. Section 2 describes the basic IPO model and

its main results. Section 3 discusses the extension to SEOs. Section 4 tests the model

empirically. Section 5 concludes. All proofs are provided in the Appendix.

1.1 Related literature

This paper is related to several strands of literature in �nancial economics. In line with

the papers by Welch (1989), Grinblatt and Hwang (1989) and Allen and Faulhaber (1989),

I explain IPO underpricing using a model of signalling. Benninga, Simon and Helman-

tel (2005) study IPO timing by examining the trade-o¤ between an entrepeneur�s private

bene�ts and the gains from diversi�cation for a �rm in isolation. This paper incorporates

IPO timing in a signalling game in which managers convey information to outside investors

through underpricing, market timing and the fraction of shares issued. This paper thus

provides a rational approach to study underpricing and market timing of IPOs.

The paper also contributes to the literature of real options and asymmetric information.

Grenadier (1999) presents a model with imperfect information where agents infer the private

signals through option exercise strategies. Lambrecht and Perraudin (2003) consider the

impact of incomplete information and preemption on investment strategies. Grenadier and

Wang (2005) solve for a screening game in a real options framework where better �rms have

incentives to delay their investment. I hereby model a signalling game i a real options

framework where good �rms accelerate the option to go public in cold markets and delay

it otherwise.

The model is also related to Carlson, Fisher and Giammarino (2006a) who provide a

model for SEOs where the decision to raise public equity is a real option of the �rm. The

results by Carlson et al (2006a) assume that the timing of the SEO is always informative

and determine abnormal returns as the di¤erence between the actual value of the �rm at the

SEO and its prior expected �rm value. This paper relaxes this assumption and shows that

when option exercise strategies are informative conditional on �rms� incentives to reveal

their type, announcement e¤ects depend on the optimal timing of public o¤erings.

Other related papers include Lucas and McDonald (1990), Pastor and Veronesi (2003)

and Alti (2005). Lucas and McDonald (1990) present a model of equity issues and screening

and predict that good types also optimally delay their o¤ering when subject to screening.4

This paper predicts that asymmetric information erodes the option value of waiting to go

public upon revelation; this is because in signalling games good types (and not bad types)

4This is analogous to Grenadier and Wang (2005).

4

bear the cost of asymmetric information.5 Pastor and Veronesi (2003) provide a model

of rational IPO waves in which low required returns cause investment-driven issuance and

low average returns follow. In this paper, hot and cold IPO markets are linked to the

distribution of good and bad investment options. Alti (2005) develops a model to explain

IPO clustering in hot markets assuming asymmetric information among outside investors.

This paper complements Alti (2005) and predicts IPO clustering conditional on the degree

of adverse selection among issuers; in this paper �rms behave di¤erently according to market

conditions and the quality of their growth options.

Several implications of the paper match the empirical evidence by Chemmanur, He and

Nandy (2007). First, the authors explore the relationship between ex ante product market

characteristics and the going public decision; this paper derives the going public strategy of

the �rm as a function of �rms�characteristics. Second, the authors show that �rms with

larger sales growth and productivity are more likely to go public. The optimal strategy

of �rms in separating equilibria is a function of the productivity of their growth options.

Third, the authors estimate a probit model of the decision to go public as a function of �rm

characteristics; this paper provides a closed form solution for such probability. Finally, the

authors study the dynamics of a �rm�s product market performance before and after the

IPO; they conclude that sales growth exhibit an inverted U-shaped pattern with peak in

the year of the o¤ering. The dynamics of �rm cash �ows around the IPO in this model are

in line with this observation.

The empirical section of the paper further contributes to the existing empirical evidence

on signalling in IPOs. Michaely and Shaw (1994) compare the winners�curse and signalling

explanations for underpricing in IPOs and �nd no empirical support for signalling predic-

tions. This paper shows that better �rms e¤ectively underprice more their shares in IPOs

as suggested by Ibbotson (1975).

2 Basic IPO model

2.1 Main assumptions

Consider a private �rm with both assets in place and a growth option to invest. The �rm

is all equity �nanced and it is run by a manager who is the single shareholder. Assets in

place generate a continuous stream of cash �ows (Xt)t�0 governed by the di¤usion

dXt = �Xtdt+ �XtdZt; X0 > 0 (1)

5This is analogous to Grenadier and Wang (2005).

5

where Wt is a standard Brownian motion under drift � and volatility �:

The �rm has a growth option to invest which enables the manager to expand �rm size

and update cash �ows by a factor � > 1: The �rm increases capacity at a cost of investment

I: There are two di¤erent types of �rms j = L;H according to the quality of their growth

options, such that �L < �H . While managers know the true value of their growth options,

market players only know that high types occur with probability p and low types occur with

probability (1� p) : This implies that there is asymmetric information between managersand market players.

The option to invest can be funded by either the internal funds or public capital. The

manager of �rm j can decide to stay private and fund investment with internal funds.

Alternatively, he can decide to go public and fund investment with both internal funds and

public capital. The optimal time to go public depends on the relative costs of internal

funding vis a vis the costs of public capital. Without loss of generality, the decision to

raise public equity and the decision to invest are assumed to be made simultaneously at the

IPO. I denote by �j the percentage share of �rm j traded publicly at the time of investment

I.

The costs of public capital include both underwriting fees and underpricing costs at the

public o¤ering. Underwriting fees are composed of a �xed cost f and a variable cost which

depends on the value of the shares sold by �rm j at the o¤ering. Underwriting fees are

given by

Fj = [c�j � f ] (2)

Following Altinkiliç and Hansen (2000), marginal underwriting fees are an increasing func-

tion of �j so that is even and larger than 1: The functional form of underwriting fees is

in line with U -shaped average spreads acknowledged both theoretically and empirically.6

Fixed costs f initially cause scale economies, but as issue size increases diseconomies of

scale emerge in the spread due to rising placement costs.

Underpricing costs at the o¤ering result from the asymmetric information between the

manager and market players. Ex-ante underpricing arises if the manager optimally chooses

to sell the shares of the �rm at a percentage discount �j � 1. In that case, managers

optimally choose to underprice their shares to convey information to market players (Grin-

blatt and Hwang, 1989). I denote ex-ante underpricing as underpricing only throughout

the paper. In addition, the shares sold by �rm j can be mispriced at the public o¤ering

due to the inability of market players to infer �rm type out of the signals provided by

6The spread is the percentage di¤erence between underwriting fees and gross proceeds at the publico¤ering. For a discussion on U -shaped spreads, see Altinkiliç and Hansen (2000).

6

the manager. Ex-post underpricing Uj (either positive or negative) is thus the di¤erence

between the value of the �rm under perfect information Vj and the market price of the

�rm Pj once the o¤ering has been announced. Whenever ex-ante underpricing di¤ers from

ex-post underpricing in equilibrium, �rms are mispriced by market players and can either

be overvalued or undervalued.

2.2 Benchmark under perfect information

Consider �rst the case of perfect information. The manager�s problem is to maximize �rm

value Vj by choosing the optimal time to do the IPO Tj , the optimal fraction of shares

issued �j and the optimal discount on prices �j : Given the cash�ow process of the �rm (1),

the optimal time to do the IPO is determined by the optimal cash�ow threshold xj at which

the �rm triggers the decision to go public.

Using the standard real options approach, the manager chooses the threshold xj that

solves

rVj = �X@Vj@X

+�2

2X2@

2Vj@X2

+X (3)

subject to the boundary conditions

Vj jXt=x�j = [1� �j + �j�j ]�j�xj � I � Fj (4)

@Vj@X

����Xt=x�j

= [1� �j + �j�j ]�j�

(5)

where � stands as the di¤erence between the drift � of the cash�ow process and a constant

risk-free interest rate r.

The ordinary di¤erential equation (3) imposes an equality between the required rate of

return of the �rm and the expected return on the option to go public and the assets in place

of the �rm. The value matching condition in equation (4) imposes an equality between the

value of the �rm before going public and the pay-o¤ of the option to do the IPO. Thus, the

value of �rm on shelf equals, at the time of the public o¤ering, the surplus that the manager

extracts from the IPO net of underwriting fees and investment costs. The smooth pasting

condition in equation (5) ensures that the option to IPO is exercised along the optimal path

by requiring continuity of the slopes at the trigger threshold.

The manager also chooses the percentage amount of shares that maximizes Vj . The

7

optimality condition on �j at the cash �ow threshold x�j is given by

@Vj@�j

����Xt=x�j

= � [1� �j ]�j�xj � c [c�j � f ] �1

Finally, managers have no incentives to underprice their shares under perfect informa-

tion. Underpricing costs are equal to zero and ��j = 1.

Proposition 1 The optimal strategy to perform an IPO under perfect information S�j =

fx�j ;��j ; 1g is such that

x�j =

�I

�j � 1

��v�

v � 1

�(6)

��j =f

c(7)

where ��j = 1 and �rm value V �j�Xt;S

�j

�under perfect information is given by

V �j�Xt;S

�j

�=Xt�+

��j � 1�

x�j � I�

Xtx�j

!v(8)

where v > 1 denotes the positive root of the �rm�s ordinary di¤erential equation (3):

The optimal timing to do the IPO in (6) is a function of �rm characteristics: all else

equal, �rms with better investment projects go public earlier. The threshold x�j also

increases with investment costs, suggesting that the optimal IPO timing increases with the

scale of investment projects. Equation (7) re�ects that the fraction of shares of a �rm of type

j demanded by outside investors does not depend on �rm type under perfect information.

No �rm underprices under perfect information. Panel A in Table 1 illustrates quantitatively

the dependence of optimal IPO strategies on �rm type.

2.3 Equilibria under asymmetric information

Consider now the case where managers have private information about the type of growth

options of the �rm. The strategy derived in Proposition 1 under perfect information does

not necessarily hold in equilibrium, since low types may �nd it pro�table to mimic the

strategy of high types.

The IPO game is thus a signalling game with multiple signals and three players: outside

investors (the market) with no private information, and two �rms of di¤erent types. The

8

decisions of the game are the IPO strategies followed by each �rm. The transfers from

outside investors to issuers are the proceeds obtained at the IPO. The equilibrium strategy

of issuers is to maximize �rm value given the strategy of the other issuers and the beliefs

by market players.

A relevant condition such that there is a non-trivial signalling game is that lower types

have incentives to imitate higher types under asymmetric information. In particular, the

value of the option to go public for low types when imitating good types should be more

valuable than the their own IPO strategy under perfect information, namely

eVL (Xt;S�H)���Xt=x�H

> V �L (Xt;S�L)jXt=x�H (9)

where eVj indicates deviation. Since higher types optimally issue earlier (Proposition 1),

(9) must hold for any value of Xt � x�H . I assume (9) holds throughout the paper.

2.3.1 Separating Equilibria

In separating equilibria, outside investors infer �rm types through IPO strategies. Since

the �rm has multiple signals to convey information to market players, there are multiple

separating equilibria of the IPO game. This section focuses on the least cost separating

equilibria of the game such that all �rms maximize �rm value conditional on revealing their

type to outside investors in equilibrium.

A separating equilibrium exists as long as the value function of the managers complies

with single crossing conditions. The equilibrium strategies should also comply both with

individual rationality (IR) and incentive compatibility constraints (ICC).

The single crossing conditions in the IPO game re�ect the impact of signalling on �rm

value according to �rm type. I derive single crossing conditions for the whole IPO strategy

fxj ;�j ; �jg in the Appendix. First, the cost of accelerating the decision to go public is

strictly lower for high types. Second, better �rms �nd it more costly to issue public capital;

the value of their stake being sold in the market is higher than that of lower types. Since

�j enters linearly in the value function of �rm j and does not depend on type explicitly, the

single crossing conditions are those on xj and �j only. When �rms separate in equilibrium,

I show below that �j < 1 re�ects the shadow cost of signalling such that high types provide

higher underpricing.

Individual rationality (IR) constraints ensure that agents participate in the principal�s

mechanism, and are usually de�ned as the reservation value of the agent if he does not

participate in the game. In the current framework, though, IR constraints are implied by

9

the value matching conditions on �rm value: agents optimally decide to participate once

their growth option is in the money. The real options approach endogeneizes the reservation

value at which �rms decide to participate in the IPO game.

Incentive compatibility constraints (ICC) ensure that the manager of �rm j has no

incentives to imitate other types. The ICCs of the IPO game are then given by

eVL (Xt;SH)���Xt=xH

� V �L (Xt;S�L)jXt=xH (10)

eVH (Xt;S�L)���Xt=xH

� VH (Xt;SH)jXt=xH (11)

where xH is the cash �ow threshold of �rm H when �rms separate in equilibrium. The

relevant ICC for the signalling game is that of low types (10) due to single crossing.

As it is standard in signalling games, the low type performs its optimal equilibrium

strategy under perfect information. Meanwhile, the high type deviates from its strategy

under perfect information to prevent low types from imitating them. This framework

extends the concept of signalling to a real options framework in which the costs of signalling

also a¤ect the optimal timing in corporate decisions.

Under asymmetric information, the manager of �rm H maximizes �rm value subject to

two additional constraints. First, high types are constrained by the ICC of low types (10)

such that

�H

heVL (Xt;SH)� V �L (Xt;S�L)i���Xt=xH

= 0 (12)

where �H is the Lagrange multiplier of high types on the ICC of low types. The complemen-

tary slackness condition in (12) is such that either the constraint is binding and multiplier

is positive �H > 0; or the constraint is slack and �H = 0. The Lagrange multiplier �H > 0

re�ects the marginal cost for higher types of signalling its true type to investors.

The �rm must also ensure that the underpricing determined by managers equals the

underpricing implied by market players, namely

UH jXt=xH = (1� �H)�H�xj (13)

Since there is no mispricing in separating equilibria, condition (13) guarantees that beliefs

by market players are self-ful�lling.

Given conditions in (12)-(13), the problem of �rm H is thus given by

rVH = (r � �)X@VH@X

+�2

2X2@

2VH@X2

t

+X

10

subject to the boundary conditions

VH jXt=xH = [1� �H + �H�H ]�H�xH � I � FH � �H

heVL � V �Li (14)

@VH@Xt

����Xt=xH

= [1� �H + �H�H ]�H�� �H

"@ eVL@Xt

� @V�L

@Xt

#(15)

where the smooth pasting and value matching conditions (14)-(15) are constrained by the

ICC of the low types (10). The approach to solve for the problem of �rm H in this paper

is an alternative to the one proposed by Grenadier and Wang (2005) to solve for incentive

compatibility in real options set-ups.7 The interpretation of conditions (14)-(15) is similar

to the value matching and smooth pasting conditions in (4)-(5); (14)-(15) further account

for incentive compatibility in equilibrium.

The manager of �rm H also chooses the optimal fraction of shares that maximizes �rm

value where the condition

@VH@�H

����Xt=xH

= � [1� �H ]�H�xH � c [c�H � f ] �1 � �H

@ eVL@�H

(16)

is equal to zero. The last term in (16) shows that the optimal amount of shares issued in

equilibrium is a¤ected by the shadow cost of signalling.

Proposition 2 The least cost optimal separating equilibria of the IPO game are such that:

� Low types perform its optimal IPO strategy under perfect information S�L; and attain

�rm value V �L (Xt;S�L) ;

� High types follow the strategy SH = fxH ;�H ; �Hg given by

xH =(1� �H) (I + FH)

��vv�1

�[1� �H + �H�H ] �H�1� �H [(1� �H) �L+�H�H�H�1]

�H =f

c� 1c

"�H(�H�H � �L)c �1� �

H

� xH�+(1� �H) �Hc �1� �

H

� xsH�

# 1 �1

�H =I + FH +

hI+FLv�1

�xHxsL

�vi�H

�HxH�

� ((1� �H) �L � 1)�H�H

7 It is possible to show that both approaches yield the same result.

11

where �H > 0 is the shadow cost of incentive compatibility constraints. Firm value

VH (Xt;SH) is then given by

VH (Xt;SH) =Xt�+

�(1� �H + �H�H) �H � 1

�xH � I � FH

��Xtx�H

�v(17)

where v > 1 denotes the positive root of the �rm�s ordinary di¤erential equation (3):

Proposition 2 summarizes the optimal strategy to do an IPO when �rms reveal their

private information in equilibrium. The strategies of higher types in Proposition 2 di¤er

from those of Proposition 1 as long as the ICCs are binding for high types and thus �H > 0.

When �H = 0 and �H = 1, all strategies converge to the case of perfect information stated

in Proposition 1.

Proposition 2 shows that there are multiple separating equilibria that are incentive

compatible, depending on the combination between �H and all the signals issued by the

�rm. Two special cases are relevant. First, the manager of the �rm can reveal private

information to market players solely through the timing of the IPO and the fraction of

shares issued; in this case, the complementary slackness condition in (12) is attained with

�H > 0 and �H = 1: This equilibrium is in line with the literature motivated by Grenadier

(1999) where the timing of the exercise of growth options conveys information to market

players. Firms optimally signal their type through the two mechanisms outlined in the

single crossing conditions of the IPO game; better �rms optimally accelerate the time to go

public and issue a lower fraction of shares to convey information to outside investors.

Second, the manager can attain the same �rm value and reveal �rm type by means of

underpricing, such that �H = 0 and �H < 1. In this case, underpricing re�ects the shadow

cost of signalling in equilibrium; �rms with good investment projects substitute deviations

in IPO timing and the fraction of shares issued for positive underpricing at the IPO. This

alternative equilibrium is in line with Ibbotson�s (1975) conjecture that new issues can be

underpriced in order to "leave a good taste in investors�mouth". The di¤erence between

proceeds under perfect information and proceeds under asymmetric information is mainly

driven by underpricing. Also, low types do not have incentives to imitate high types since

the complementary slackness condition (12) is also binding.

Table 1 provides the calibrated version of the basic IPO model; it illustrates the di¤er-

ence between the strategies of �rms under perfect information and those under asymmetric

information. In all separating equilibria, higher types choose to go public earlier than their

�rst-best case under perfect information (xH < xL) to make imitation more costly. Panel B

considers the case where �H> 0 and �H = 1; high types reveal their type only through the

12

timing to go public and the fraction of shares issued. Panel C illustrates the case where

�H < 1 is the lowest; the timing to go public for higher types is the closest to their �rst-best,

and instead managers provide the underpricing such that �H < �L: The equilibrium strate-

gies for the timing to go public in Panel C are the closest to those of Panel A; signalling

costs in Panel C are mainly re-allocated to outside investors by means of underpricing.

The multiplicity of equilibria implied by Proposition 2 also provides a functional relation

between the di¤erent signals in equilibrium. In particular, the model suggests that the

static signals commonly reviewed in the IPO literature optimally depend on the time to

raise public equity. Figure 3 illustrates the comparative statics of the di¤erent signals used

by �rms in separating equilibria. All else equal, �rms that wait longer to issue (and thus

time their issue closer to �rst-best) must provide higher underpricing to ensure incentive

compatibility. This provides a rational explanation for the link between underpricing and

market timing when �rms reveal their type. Also, older (and larger) �rms issue a lower

fraction of equity in equilibrium. Finally, the multiplier �H for �rm H is increasing in �H ;

this illustrates the duality between underpricing and the shadow cost of signalling in the

model.

2.3.2 Pooling equilibria

In pooling equilibria, IPO strategies do not convey information to outside investors such

that there is mispricing in equilibrium. High types are undervalued and low types are

overvalued with respect to the expected market value E [Vj (Xt;Sp)]. Since all �rms issue

simultaneously, there is a higher supply of shares in the market and higher IPO activity.

Proposition 3 The pooling strategy of all �rms Sp = fxp;�p; �pg is such that

xp =

�I + Fp

(1� �p) �H + �p�p� � 1

��v�

v � 1

�

�p =f

c� 1c

24�1� �

�H

� c

�H�xp

351

�1

where �p = 1 and the value of �rm j under pooling is then given by

Vj (Xt;Sp) =Xt�+

�(1� �p) �j + �p�p� � 1

�xp � I � Fp

��Xtxp

�vwhile market players consider E [Vj (Xt;Sp)] = pVH (Xt;Sp) + (1� p)VL (Xt;Sp) :

13

Propositions 2 � 3 characterize the role of asymmetric information on IPO strategies.

Consider �rst the implications for timing. When �rms separate, the time to go public is a

signal and better �rms go public earlier to make imitation more costly. When �rms pool,

the timing to go public is not informative and worse �rms to go public earlier to enhance

the value of their shares. Consider now the fraction of shares issued. When �rms reveal

their type, high �rms issue a lower fraction of shares due to higher underpricing costs. In

pooling equilibria, all types issue a fraction �p where high types are underpriced by the

average �rm value. Finally, consider underpricing. High types are underpriced ex-ante in

separating equilibria and ex-post when �rms pool. Low types are fairly priced when there is

revelation in equilibrium, but they are overvalued when market players cannot di¤erentiate

across types. Table 1 illustrates numerically the di¤erences between separating and pooling

equilibria.

2.3.3 Implications for Hot and Cold Markets

A general criticism posed by Tirole (2007) on signalling games is that they are plagued by

multiplicity of equilibria. I hereby consider two re�nements to obtain clear-cut predictions

about hot and cold IPO markets.

The �rst re�nement selects the least cost separating equilibrium out the least cost sep-

arating equilibria in Proposition 2: The re�nement considers a Nash bargaining solution

to the equilibrium allocation between issuers and outside investors. While Proposition 2

derives multiple optimal separating equilibria based on the managers�optimization prob-

lem, the equilibrium allocation of the fraction of shares issued and underpricing should also

depend on the willingness of outside investors to buy new shares. Results in Figure 1

suggest that the equilibria in Proposition 2 imply a positive supply-type relation between

the fraction of shares issued and the o¤er price of shares at the IPO. Notice, however, that

outside investors may bene�t from underpricing in equilibrium; while it is true that issuers

optimally issue less shares for higher levels of underpricing (see Figure 1), underpricing

is a mechanism that re-allocates signalling costs of issuers as abnormal returns to outside

investors. The separating equilibrium allocation of undepricing and the fraction of shares

issued should thus satisfy both Proposition 2 and should ensure that the increase in �rm

value due to the IPO is allocated e¢ ciently between issuers and new shareholders. The

equilibrium separating allocation of the IPO game thus depends on the relative bargain-

ing power of issuers and outside investors. The empirical evidence on IPO underpricing

suggests that �rms e¤ectively underprice their shares in equilibrium.8 This �nding can be

8See Ritter (2003) for a survey on the empirical evidence on IPO underpricing and Table 2 for the

14

rationalized by considering some positive bargaining power of ouside investors during the

going public procedure. For the sake of simplicity, I assume that the least cost separating

equilibrium with �H = 0 in Proposition 2 is the least cost separating equilibrium of the

game that is preferred both by issuers and outside investors jointly. This corresponds to a

situation where issuers have little bargaining power and outside investors bene�t from high

underpricing.9 For the case of �H = 0 underpricing re�ects the most of the shadow costs

of signalling borne by issuers in equilibrium.

The second re�nement allows to predict when separating equilibria are the only possible

outcome under asymmetric information. Notice that for any given probability p, �rms with

better investment prospects have the option to either separate from low types or to pool

with them in equilibrium. When low types are relatively scarce and p is high, the expected

market �rm value for outside investors is closer the true price of high types; in this case,

the implied undervaluation of high types in pooling may be lower than the corresponding

signalling cost of revealing �rm type. Conversely, when high types are relatively scarce and

p is low, the implied cost of revealing �rm type to market players outscores the corresponding

mispricing due to lack of information. Maskin and Tirole (1992) provide a formal derivation

of this intuition to determine a range of p in which only separating equilibria can occur.10

In particular, this equilibrium re�nement builds upon optimal strategies under asymmetric

information and on the sets of beliefs of market players in pooling equilibria.

Proposition 4 De�ne the threshold p such that high types are indi¤erent between revealingtheir type through signalling or pooling with bad types in equilibrium In line with Maskin

and Tirole (1992), �rms optimally reveal their type when adverse selection becomes more

relevant (p 6 p) and may pool otherwise.

The optimal strategy of high types under asymmetric information is thus a function of

p: In scenarios where there is high share of low types in the market (p 6 p), asymmetricinformation erodes the option value of waiting to issue. Conversely, when there is a high

share of high types in the market (p > p), high types allow low types to cluster and the

optimal IPO strategies of both types change. In particular, the threshold p such that high

types are indi¤erent between revealing their type or pooling in equilibrium is given by

VH (Xt;SH)jXt=xH = VH (Xt;Sp)jXt=xHcorresponding working sample statistics.

9Note that a formal derivation of the optimal allocation requires de�ning the value function of outsideinvestors and making an assumption on the relative bargaining power of investors.10See Maskin and Tirole (1992) and Tirole (2007). Hennessy, Livdan and Miranda (2007) apply this

equilibrium re�nement in a dynamic signalling game of capital structure decisions.

15

Figure 2 illustrates the optimal strategy for high types under asymmetric information

as a function of p. When �rms with good investment opportunities are relatively more

scarce, high types optimally separate and follow the strategy in Proposition 2. Otherwise,

�rms pool in equilibrium and the optimal strategy of high types depends on p. When p

equals unity, the optimal strategy under pooling converges to the optimal strategy under

perfect information in Proposition 1.

Figure 3 further illustrates that p increases when signalling is relatively less costly in

equilibrium. Assuming a uniform distribution of types such that p = 0:5 and cash �ow

mark-ups are given by f� (1� ��) ; � (1 + ��)g ; the dispersion on cash-�ow mark-ups ��a¤ects the upper bound p such that high types optimally reveal their type when signalling

is less costly. When �� increases, the relative advantage of high types with respect to bad

types also increases, reducing the costs of revealing �rm type in equilibrium. The range of

separating equilibria (0; p] is increasing in the dispersion of cash�ows ��:

The main results of the signalling game can then be easily extended to explain the

evidence on hot and cold IPO markets. Denote hot markets are those states of nature

where adverse selection is less relevant such that p > p (Tirole, 2007).11 The de�nition of

hot and cold markets is related to the lemons problem. Whenever p < p; adverse selection

is more likely; �rms optimally reveal their type to market players and enter the market

sequentially. Conversely, when p > p; both good types and bad types issue simultaneously,

there is increased IPO activity and a positive probability of buying a lemon in equilibrium.

Figures 4 and 5 provide the empirical evidence for IPO and SEO strategies (respectively)

in a sample of US issuing �rms between 1980 and 2005.12 The working assumption to

discriminate among hot and cold markets is that hot markets correspond to the period

of intense IPO activity during the late 1990s (1998-2000). Figure 4 illustrates that IPO

strategies change signi�cantly conditional on hot or cold markets. During hot markets

�rm age is more concentrated on lower values, the average fraction of shares decreases

and average underpricing increases. The basic IPO model described in this paper matches

most of the empirical evidence in Figure 4: I show in the Appendix that for a change of

probabilities around p such that cold markets occur for p � " and hot markets occur forp+ ", the expected average age of issuing �rms decreases and the average fraction of shares

issued decreases during hot markets. Still, the model cannot match the empirical fact that

average underpricing increases during hot markets.

Figure 5 provides the empirical evidence for SEO strategies. The empirical evidence

11Note that hot markets need not be perfectly correlated with booms. Given the de�nition in the text,hot markets occur whenever there is an increase in the overall perception of p by market players.12See Appendix for details on database construction.

16

suggests that SEO: strategies are not signi�cantly di¤erent in hot and cold markets, respec-

tively. The model can rationalize such �nding if asymmetric information between managers

and market players is not economically signi�cant in subsequent stages of the going public

procedure.

The model thus characterizes the behavior of �rms according to the degree of adverse

selection in the market. During periods of relatively high adverse selection (cold mar-

kets), IPOs are distributed in time according to �rm type, trading volume of issuing stocks

decreases, there is a higher average expected age of issuers and good types e¢ ciently under-

price their shares to signal their type to outside investors.13 During periods of relatively

low adverse selection (hot markets), there is clustering of IPOs, a higher trading volume, a

lower average expected age of issuers, and a positive probability of buying a lemon.

Finally, notice that all results on ex-ante and ex-post underpricing translate into ab-

normal returns. When �rms reveal their type in equilibrium, abnormal returns to market

players translate into short-run abnormal returns or announcement e¤ects that are equal

to the percentage underpricing provided by �rms. When �rms do not reveal their type in

equilibrium, there may be either undervaluation or overvaluation of stocks due to mispricing

by market players.

Proposition 5 When p 6 p; �rms reveal their type in equilibrium and abnormal returns at

the IPO of �rm j are given by 1��j : When p > p, there may be either undervaluation of hightypes or overvaluation of low types. During hot markets, the average expected age of issuers

decreases and the average percentage amount of shares issued decreases. Furthermore, �rms

with good investment projects are undervalued and �rms with bad investment projects are

overvalued.

Proposition 5 complements the observation made in the Introduction that the optimal

timing and the corresponding announcement e¤ects of corporate decisions are intrinsically

related under asymmetric information. Since �rms behave strategically under asymmetric

information, announcement e¤ects vary according to �rms�incentives to reveal their type.

During cold markets, �rms with more productive investment opportunities go public earlier,

underprice their shares and there is fair pricing. During hot markets, instead, all �rms

issue simultaneously, IPO activity increases and there is mispricing in equilibrium.

13Note that all statements on volume and distribution of IPOs in time are conditional on the initial valueof cash �ows for all �rms.

17

3 SEOs

The basic IPO model does not incorporate the option to SEO explicitly. In the basic IPO

model, the value of the option to go public relates to funding of new investment projects

through public capital. Nonetheless, the option to SEO is embedded in the option to IPO;

as in any sequential real options problem, the value of the option to go public includes the

value of the option to do SEOs in subsequent stages. Since the current set-up assumes an

investment motive for equity issues, one potential way to incorporate SEOs explicitly is to

consider that �rms may have sequential investment plans with di¤erent implied investment

productivities (i.e. productivities �ij for each Stage i of the investment plan of �rm j).

When �rms have sequential investment plans or several growth options, the current set-up

raises the question of the optimal number of public o¤erings to perform.

In the case of perfect information, the optimal number of public o¤erings depends on the

investment plan of the �rm and the structure underwriting fees. While a �rm performing a

single o¤ering is subject to higher variable underwriting fees, a �rm performing two public

o¤erings pays �xed underwriting costs twice. In the presence of asymmetric information,

the optimal strategy also depends on the signalling costs borne by higher types in equilib-

rium. Multi-stage o¤ering strategies are thus partly intended to reduce uncertainty with

respect to �rm type, insofar they reveal more information about �rm characteristics and

thus reduce the issuance costs of asymmetric information. This is in line with Denis (1991)

and Derrien and Kecksés (2007).

The IPO-SEO model also extends to cases where asymmetric information survives the

announcement of the IPO. When �rms have several growth options and cannot convey

enough information about them at the IPO, asymmetric information prevails after the IPO

has been done. This happens whenever the amount of signals that each �rm can convey

at the IPO are not enough to reveal all the information about unknown parameters of the

sequential investment plan of the �rm. It is possible to show that there exists a commitment

proof separating equilibrium of the IPO game where (i) the ex-ante market beliefs by

market players at the IPO are compatible with the ex-ante beliefs by market players in

subsequent SEOs; and (ii) underpricing costs are decreasing in asymmetric information

across public o¤erings.14 Signalling costs are thus increasing in the amount of asymmetric

information; this result supports Baron (1982), who posits that issues characterized by

greater uncertainty tend to be more underpriced to compensate investors for learning about

their values.14The analytical proof of these statements is available upon request.

18

4 Testable implications and empirical evidence

I hereby discuss the economic signi�cance of IPO timing in the data and test the signalling

prediction that IPO strategies depend on �rm type during cold markets. Ritter (2003)

surveys the empirical literature on IPOs and concludes that there is little evidence on sig-

nalling explanations for IPO underpricing. This section complements the existing empirical

literature and provides supporting empirical evidence for signalling explanations of IPO un-

derpricing and market timing of equity issues. I discuss on database construction in the

Appendix.15

The paper emphasizes that the optimal IPO timing is a function of both �rm character-

istics and asymmetric information. While the empirical literature on IPOs does not focus

on IPO timing, several studies have demonstrated that the probability of doing an IPO

(Chemmanur, He and Nandy, 2007) and a SEO (Gomes and Phillips, 2007) is a function

of �rm characteristics. To the extent that the �rm endogenously determines the optimal

expected time to go public, this paper also provides a closed-form solution for the proba-

bility of raising public equity. The empirical evidence on the probability of doing an IPO

or a SEO as a function of �rm characteristics is thus supporting evidence for a real options

model of the decision to raise public equity.16 In the model, the expected age of �rms

raising public equity at time Tj is given by

E�Tj�=ln�xjX0

��

(18)

where � = �� �2

2 : Meanwhile, the probability Pr (0;Tij ] that �rm j raises public equity since

it starts operating until time Tj is given by

Pr (0;Tj ] = �

0@� ln�xjX0

�+ �Tj

�pTj

1A+ e 2��2 xjX0�

0@� ln�xjX0

�� �Tj

�pTj

1Awhere � is the is the standard normal cumulative probability distribution.17 The underlying

15The source for identifying IPOs and SEOs is the Securities Data Company�s (SDC) Deals Database; Ithen use the merged CRSP-Compustat database to obtain information on the issuing �rms��nancials.16Note that a static model in which IPO timing predetermined cannot predict the probability of doing an

IPO. This model would either predict the probability of doing an IPO to be equal to zero if the �rm is stillprivate and equal to 1 otherwise.17The closed-form solution for this probability can be computed from the hitting time distribution of the

Brownian motion. See Harrison (1985).

19

parameters explaining Pr (0;Tj ] are the same as those explaining E�Tj�:18

The signalling model in this paper suggests that optimal IPO strategies are function of

the quality of the �rms�growth options. Proposition 2 predicts that during cold markets

better �rms go public earlier, issue a higher lower of shares and underprice more. Proposi-

tion 3 predicts that during hot markets market players cannot infer �rm type from observed

IPO strategies. I thus use the S&P Common Equity rankings as a measure of �rm quality

and test these predictions empirically, both for IPOs and SEOs. The S&P Common Stock

ranking is an appraisal of past performance of a stock�s earnings and dividends and the

stock�s relative standing as of a company�s current �scal year-end; the score is mainly based

on the past growth and stability of earnings and dividends of �rms.19 To my understand-

ing, this is the �rst empirical test on signalling in IPOs based on underlying measures of

�rm quality.

With some exceptions, the S&P Common Stock rankings are usually unavailable at the

time of the IPO; still, several �rms in the sample are ranked by S&P once public. Table 2

shows the available information on stock rankings in the sample (SPRAT in Panels A to C).

Panel A shows that no �rms during the period 1998-2000 were given a ranking by S&P in

the incoming years after the IPO (with the exception of two observations assigned the lowest

score); this suggests that there is little information on �rm quality during hot markets. I

focus on the available observations for cold markets and estimate the probability of having

an S&P score above average after the o¤ering as a function of the observed IPO strategy,

�rm size (measured by LNSALES) and exchange dummies. I then consider the marginal

contribution of each element of the IPO strategy (namely, AGE, ALPHA and UNDP) to

increasing the probability of getting a high score in the future. The empirical approach

matches the idea that a separating equilibrium should be self-ful�lling in cold markets; the

probability of being of certain type upon observation of the corresponding IPO strategy

should be equal to one. The dependent dummy variable TYPEH (see Table 2) is equal

to one if the �rm is assigned a score above average (i.e. between 7 and 16) during the 8

incoming years after the o¤ering, and is equal to zero if the �rm is assigned a score below

average (i.e. between 18 and 21).20

18 The prediction on Pr (0;Tij] is conditional on p such that the probability of going public for bad types

is higher during hot markets (p < p).19The index is available since 1985 up to date. For further details, see COMPUSTAT User�s Guide,

Chapter 5, pp. 228-229.20The highest score in the S&P ranking is 7 (equal to an A+) and the lowest is 21 (equal to a C). A score

of 22 further indicates that the �rm is in reorganization, and 99 stands for liquidation. I consider the horizonof 8 years to obtain su¢ cient observations in all tests. Since S&P requires 10 years of data to construct therating, an horizon of 8 years once public is conservative.

20

Figure 6 and Table 3 provide the empirical evidence on the predictions for IPOs as a

function of �rm type. An increase in IPO underpricing induces a marginal increase in the

probability of having an S&P above average in the incoming years after the o¤ering. This

result is consistent with the prediction that better �rms underprice more their shares during

cold markets to "leave a good taste in investors�mouths" (Ibbotson, 1975). These results

complement Michaely and Shaw (1994), who compare the winner�s curse and the signalling

explanations for IPO underpricing and �nd no empirical support for signalling models.

Figure 6 and Table 3 further show that the predictions concerning the age of issuing

�rms are better matched by �rms listing in the NYSE. The relation between the age of

issuers and the probability of having a high S&P score in is hump shaped for all markets

on average; only mature �rms of the good type accelerate their decision to go public. For

NYSE listing �rms, though, the probability of being of the good type is decreasing in the

age of issuers at the IPO. These di¤erences in IPO strategies across stock exchanges can

be attributed to the di¤erent listing requirements in NYSE and NASDAQ; listing �rms in

NYSE for the �rst time are usually older and larger, as observed in Table 2.21

The distribution of the fraction of shares issued is also hump shaped for the whole

sample; the probability of being of a good type decreases when the fraction of shares issued is

larger than 50%. When the estimation is constrained to NYSE observations, the probability

of being of a good type is not signi�cantly a¤ected by the fraction of shares issued. Factors

such as corporate control or moral hazard by managers could contribute in the explanation

of optimal issuance policies.22

The availability of information is much higher for SEOs. I thus replicate the analysis

for SEOs without recent S&P scores prior to the o¤ering and compute the probability of

getting an S&P score above average in the future as a function of observed SEO strategies.

I consider the number of years since the IPO (YSIPO) as the relevant variable for SEO

timing.23 Figure 7 and Table 4 show that underpricing is not signi�cant in explaining

the probability of obtaining a high S&P score in the incoming years after the SEO. This

may imply that asymmetric information is not so relevant in explaining SEO policies. The

empirical results in Figure 7 and Table 4 support the predictions for SEO timing. Firms

raising public equity earlier are usually rated as better stocks irrespective of exchange listing.

This result is also consistent with the predictions of the model under perfect information,

21See Corwin and Harris (2001) for a discussion on these requirements.22See Tirole (2007).23 In the case of SEOs, it is important to control for the number of SEOs performed before the current

o¤ering, and the amount of years that the �rm has quoted on stock markets. Since AGE and YSIPO arehighly correlated, I consider YSIPO as the relevant variable for SEO timing and further incorporate "Numberof SEO" dummies in probit regressions.

21

where the optimal timing to raise public equity is negatively related to �rm type (Proposition

1).

5 Conclusions

This model addresses the option to raise public equity in a real options framework. The

optimal strategy to raise public equity results from the �rm�s value maximizing behavior

and depends on its fundamentals, its long term investment plan and its issuance costs of

public capital; it also depends on the strategy of other �rms in the market.

From the theoretical standpoint, the paper provides new insights to the current literature

of real options and IPOs. First, the model provides a tractable approach to solve for

signalling games in real options and relates the optimal timing to go public to hot and cold

IPO markets. In hot markets, �rms have incentives to pool and the timing to go public is

uninformative; in cold markets, asymmetric information erodes the option value of raising

public equity. Second, the model solves for underpricing endogenously in a real options

set-up, suggesting that the option exercise of �rms and underpricing must be solved jointly

in equilibrium. Finally, the model provides a rational approach to relate underpricing to

market timing of public o¤erings.

From the empirical standpoint, the paper highlights that the age of issuing �rms is

signi�cant to explain the decision to raise public equity. The empirical evidence on IPO

markets is in line with the predictions of the model; during hot markets the average ex-

pected age of issuers decreases, the average fraction of shares issued decreases and there is

overvaluation of �rms with worse investment projects. Most importantly, the paper com-

plements the empirical literature on signalling theories and provides supporting evidence

on the prediction that better �rms underprice more their shares (Ibbotson, 1975) and go

public earlier to reveal their type during cold markets.

The model can be extended in several ways. First, a natural extension is incorporate

discount e¤ects to provide a better rationale for hot markets and IPO waves (Pastor and

Veronesi, 2003). Second, it would be interesting to consider the impact of alternative

�nancing choices in the timing and structure of the going public strategy (Stein, 1991).

Third, it would be relevant to study managerial entrenchment and corporate control in the

decision to go public. As Myers (2000) has suggested, models should consider the rationale

for outside equity �nancing when insiders are not inclined to act in outside investors�inter-

ests. Finally, this paper assesses the option to go public from an investment perspective.

Assessing alternative motives to go public should provide further insights on the underlying

22

determinants of the going public strategy.

23

6 Appendix

6.1 Single Crossing Conditions

I prove that the IPO game complies with single crossing conditions in two steps. First,

Cho and Sobel (1990) show that if both the value functions of issuers and investors comply

with certain monotonicity conditions, then there exists a separating equilibrium as long as

the single crossing conditions hold for each signal in isolation. I thus prove that this is the

case. Second, I consider the single crossing conditions for each signal.

The mechanism implied by the signalling game in Section 2 is to determine an allocation

consisting of a decision for each �rm j and a vector of transfers from investors to �rms. In

the current set-up, decisions are the IPO strategy followed by each �rm and transfers are

the proceeds obtained by issuers at the o¤ering such that Tj is the transfer price paid by

market players to issuers for all shares sold at the IPO. The transfer Tj re�ects the market

value of the �rm as seen by market players. Since the proof of single crossing conditions

abstracts from any type of equilibrium concept, I �rst consider Tj as given. I elaborate on

this later on.

The value of the �rm Vj upon which issuers decide on their optimal IPO strategies is

then given by:

Vj (Xt;Sj) =Xt�+

�(1� �j) �j � 1

�xj + �jTj � I � Fj

� �Xtxj

�vwhere the xj and �j may take any value given xj > 0 and 0 < �j < 1.

Denote then Vj (Sj ; Tj) as the value function of �rm type �j given the set of signals

Sj = f�j ; xjg and the price paid by investors Tj : It then holds that:

1. The value function Vj (Sj ; Tj) of the issuer is continuous in Sj and Pj for any type �j :

2. The value function Vj (Sj ; Tj) of the issuer is increasing in Tj for any type �j :

3. The pay-o¤ function of investors is continuous in Sj and Pj for any type �j :and is also

strictly quasiconcave di¤erentiable in Tj for Xt � xj :

4. The pay-o¤ function of investors is a strictly increasing function of �j :

5. If �L < �H , SL > SH then VL (SL; TL) � VL (SH ; TH) implies VH (SL; TL) < VH (SH ; TH).

Conditions 1� 4 are standard regularity assumptions. The pay-o¤ function of investorsis proportional to Vj (Sj ; Tj) so it complies with Condition 3. Condition 5 states that if

24

two signal-action pairs yield the same utility to some type of issuer and one signal is lower

(componentwise) than the other, then all types prefer to send the lower signal. Denote

� � 1 such thatVL (SL; TL) = �VL (SH ; TH)

The proof of condition 5 then implies testing whether

VH (SL; TL)� VL (SL; TL) < VH (SH ; TH)� �VL (SH ; TH)

holds for any sets SL < SH .The inequality above then implies

(1� �L) (�H � �L) xL� � [FH (�L)� FL (�L)](1� �H) (�H � ��L) xH� � [FH (�H)� �FL (�H)]

< 1 <

�xLxH

�v(19)

which holds for any parameter values when SH < SL.

Given these su¢ ciency conditions by Cho and Sobel (1990), there exists a separating

equilibrium in the IPO game as long as signals xj and �j comply with single crossing

conditions separately. The single crossing conditions for the IPO game for each signal

issued by �rm j are given by

@

@�

24 @V1j@sj@Vj@Tj

35 7 0 (20)

where (20) measures the marginal change in �rm value Vj according to �rm type when �rms

choose signal Sj and receive transfer Tj .

Consider �rst the timing to do the IPO xj . The single crossing conditions for xj re�ect

that, all else equal, good types �nd it less costly to issue earlier, namely

@

@�j

24 @Vj@xj@Vj@Tj

35 = (1� v) (1� �j) 1��j

< 0 (21)

Consider now the fraction of shares issued �j . The derivative of �rm value with respect

to �1j at the threshold is such that, all else equal, better �rms �nd it more costly to issue

public capital, namely

@

@�j

24 @Vj@�j@Vj@Tj

35 = �xj�

�j< 0 (22)

The single crossing conditions (21) and (22) ensure that the incentive compatibility

constraint is binding and that there exists a separating equilibrium of the IPO game. The

25

ultimate value of Tj is then determined in equilibrium. Given conditions (21) and (22), a

separating equilibrium exists where market players infer �rm types issuers�strategies and

then Tj = �j�j�jxj� :

6.2 Implications for Hot and Cold Markets

Consider probability of being of the high type when �rms separate and the probability of

being of the high type when �rms pool around p such that �rms optimally separate at

p� " and pool at p+ ": The argument that the average age of issuers decreases during hotmarkets then implies

ln (xp) � p0 ln (xH) + (1� p0) ln (xL)

) p0 > 0 > �ln (xH)� ln (xL)ln (xL)� ln (xp)

which holds for any parameter values given xH < xp < xL: Using the same approach, the

statement on that the fraction of shares issued decreases during hot markets implies

�p < p0�H + (1� p0)�L

) p0 < 1 <�H � �L

(�H � �L) + (1� �H) �H

which holds for any parameter values given �H < 1:

6.3 Database construction

The source for identifying IPOs and SEOs is the Securities Data Company�s (SDC) Deals

Database. The sample considers common equity issues between January 1, 1980 and

December 31, 2005 for all US �rms excluding �nancial �rms (SICs 6000-6999) and regulated

industries (SICs 4900-4999). I then match the data obtained from this source to the merged

CRSP-Compustat database, to obtain information on �rms �nancials.

The main variables used throughout the empirical section that come from SDC are: (1)

the date of the issue; (2) the date when the company was founded; (3) the o¤er price of the

deal; (4) the stock price at close of o¤er/�rst trade; (5) the principal amount traded, for

all markets; (6) the main stock exchange on which the issuer�s stock trades. PROCEEDS

are thus equal to (5); UNDP is the percentage di¤erence between the (3) and (4); ALPHA

is the ratio of (5) over the market value of equity after the o¤er ((4) times item25 from

COMPUSTAT); NASDAQ and NYSE are dummies based on (6).

26

The variable describing �rm age (AGE) comes from two sources. First, for the �rms no

missing info on dates, AGE is the di¤erence between the date of the issue (1) and the date

when the �rm was founded (3) as stated by SDC. For �rms with (1) but no (2), I used the

year when the company was founded as reported in the database [Age Data (.xsl)] built by

Boyan Jovanovic and available online.24

Ex-ante �rm characteristics are taken from the merged CRSP-Compustat database.

The S&P Common Stock Rating is the underlying indicator for �rm quality (item282);

LNSALES is the log of sales (item12); CAPX to TA is the ratio of capital expenditures

(item128) and total assets (item6); TLTD is the sum total long term debt (item9) and long

term debt in current liabilities (item34); WK is working capital (item179). The dummy

INVGR has been built using the S&P long term credit rating reported in item280. Finally,

HOTMA is equal to 1 if IPO or SEO occurred during the hot IPO market period and 0

otherwise. The hot IPO market period is de�ned between the last quarter of 1998 and the

last quarter of year 2000. Alternative de�nitions of this period have no major impact on

results.

6.4 Parameter choice in Figures 1-2 and Table 1

The choice of parameters in the numerical example is determined in one of three ways using

the basic IPO model for i = 1. The �rst group of parameters is determined by direct or

indirect measurements conducted in other studies. Direct measurements include the annual

risk free rate r = 5%, the convenience yield on cash �ows � = 2; 5% and cash �ow volatility

� = 25%. The annual risk free rate r, the convenience yield on cash �ows � and cash �ow

volatility � are in line with the baseline parametrization of a SEO model by Carlson et al

(2006a).

The second subset of parameters is based on assumptions. Marginal underwriting fees

are linear (i.e. = 2) as in Altinkiliç and Hansen (2000). I assume a uniform distribution

of types such that p = 0:5.

The third set of parameters consists is intended to obtain realistic IPO moments with

respect to the empirical evidence. I consider I = 18 based on the mean capital expenditures

in the database. I set X0 = 0:8 such that the expected age of high types is 8 years at the

IPO. I set � = 2 and �� = 0:2 such that �H = � (1 + ��) and �L = � (1� ��) : I considerf = 6 and c = I such that the average expected underpricing is 8% and the fraction of

shares issued under perfect information is close to 25%.

24See http://www.nyu.edu/econ/user/jovanovi/.

27

References

[1] Allen, F., and Faulhaber, G. Signalling by underpricing in the IPO market, Journal

of Financial Economics 23, 303-323.

[2] Altinkiliç, O., and Hansen, R.S., 2000. Are there economies of scale in underwriting

fees? Evidence of rising external �nancing costs. Review of Financial Studies 13, 191-

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[3] Alti, A., 2005, IPO market timing, Review of Financial Studies 18, 1105-1138.

[4] Baron, D., 1982. A model of the demand for investment banking advising and distri-

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mance. Journal of Finance 61, 1009-1034.

[7] Carlson, M. D., Fisher, A. J. and Giammarino, R., 2006b. SEOs, Real Options, and

Risk Dynamics: Empirical Evidence, Working Paper.

[8] Chemmanur, T. J., He, S. and Nandy, D., 2007. The Going Public Decision and the

Product Market. AFA 2007 Annual Meetings.

[9] Cho, I., & Sobel, J., 1990. Strategic Stability and uniqueness in signalling games.

Journal of Economic Theory 50, 381-413.

[10] Corwin, S., & Harris, J., 2001 The Initial Listing Decisions of Firms that Go Public.

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[11] Denis, D. J., 1991 Shelf Registration and the Market for Seasoned Equity O¤erings.

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28

[14] Fundenberg, D., and Tirole, J., 1991. Game Theory. MIT Press.

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[17] Grinblatt, M., and Hwang, C., 1989. Signalling and the Pricing of New Issues. Journal

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[18] Hackbarth, D. and Morellec, E. Stock returns in mergers and acquisitions. Journal of

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namics, Working Paper.

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Economics 2, 235-272.

[21] Ibbotson, R., and Ja¤e,J., Hot issue markets. Journal of Finance 30, 1027-1042.

[22] Lambrecht, B. and Perraudin, W., 2003. Real options and preemption under incom-

plete information. Journal of Economic Dynamics & Control 27, 619�643.

[23] Lucas, D., and McDonald, R., 1990. Equity issues and stock price dynamics. Journal

of Finance 45, 1019-1043.

[24] Maskin, E. and Tirole, J., 1992. The principal-agent relationship with an informed

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[25] Michaely R. and Shaw W., 1994. The Pricing of Initial Public O¤erings: Tests of

Adverse Selection and Signaling Theories. The Review of Financial Studies 7, pp.

279-319.

[26] Morellec, E., and Zhdanov,A., 2005. The Dynamics of Mergers and Acquisitions.

Journal of Finance 77, pp 649-672.

[27] Myers, S., 2000. Outside Equity. Journal of Finance 55, 1005-1037.

[28] Oksendahl, B., 2000. Stochastic Di¤erential Equations: An Introduction with Appli-

cations. Springer.

29

[29] Pastor, L., and Veronesi, P., 2003. Rational IPO Waves. Journal of Finance 60,

1713-1757.

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[33] Welch, I., 1989. Seasoned O¤erings, Imitation Costs and the Underpricing of Initial

Public O¤erings. Journal of Finance 44, 421-449.

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of Corporate Finance 2, 227-259

30

Figure 1: Comparative Statics for High Typesin the basic IPO model

This �gure illustrates the comparative statics between the di¤erent signalswhen �rms fully reveal their private information at the IPO. Denote under-pricing as (1 � �j). The cash �ow threshold xj is increasing in underpricing;the timing to raise public equity is closer to that of perfect information when�rms provide higher levels of underpricing to outside investors. The fraction ofshares issued �j is decreasing in underpricing costs; �rms optimally issue lesswhen the issuance costs are higher. The Lagrange multiplier �j is increasingin �j ; this re�ects the duality between signalling costs and underpricing in themodel. Finally, the cash �ow threshold to raise public equity is decreasing in�j ; older (and larger) �rms issue lower percentages of equity in equilibrium.

0.85 0.9 0.95

0.9

1

1.1

x H

εH

0.85 0.9 0.95

0.214

0.215

0.216

0.217

αH

εH

0.85 0.9 0.950

0.1

0.2

0.3

χ H

εH

0.9 1 1.10.214

0.215

0.216

0.217

αH

xH

31

Figure 2: The Optimal Strategy for High Typesunder Asymmetric Information

This �gure illustrates the optimal IPO strategies for high types depending onthe level of adverse selection in the market. The solid black line in all chartsillustrates the optimal IPO strategy under asymmetric information. Whenp is relatively low and high types are relatively scarce, high types optimallyseparate in equilibrium. This is illustrated on the left-hand side of all chartswhen the probability of being of a high type is lower than 0.5. For high levelsof p, �rms optimally pool and IPO strategies are then a function of p. Theoptimal strategy of �rms under pooling converges to the optimal strategy ofhigh types under perfect information (dashed line in black) when p convergesto 1.

0.2 0.4 0.6 0.8 11.12

1.14

1.16

1.18

p

x H

0.2 0.4 0.6 0.8 1

0.2

0.22

0.24

0.26

p

αH

0.2 0.4 0.6 0.8 10.8

0.9

1

1.1

p

ε H

0.2 0.4 0.6 0.8 1

58

59

60

61

62

63

p

VH

32

Figure 3: Signalling costs for High Typesin the basic IPO model

This �gure illustrates that it is more costly for higher types to separate whenthe two types are more similar. Consider a uniform distribution of types suchthat �� re�ects the dispersion of the quality of growth options in the market.As �� increases, the high types try to make the issue unappealing to low typesby going public earlier earlier, issuing a lower percentage amount of equityand underpricing more their shares. The the upper bound on the probabilityof high types is increasing in ��; this suggests that separating equilibria aremore likely when signalling is less costly.

0.25 0.3 0.35 0.4 0.45

0.8

0.9

1

σθ

x H

0.25 0.3 0.35 0.4 0.45

0.22

0.23

0.24

0.25

σθ

αH

0.25 0.3 0.35 0.4 0.450.85

0.9

0.95

1

σθ

ε H

0.25 0.3 0.35 0.4 0.45

0.7

0.8

0.9

1

σθ

Upp

er B

ound

 on 

p

33

Figure 4: Distribution of Firm Age,Fraction of Shares Issued, Underpricing and Proceeds

for IPOs in the Working Sample

This �gure illustrates the kernel density distributions of AGE, ALPHA, UNDPand PROCEEDS for IPOs in the working sample.The dashed line correspondsto the observations during 1998-2000 and the solid line considers the remain-ing observations. The distribution of AGE, ALPHA, UNDP and PROCEEDSchanges signi�cantly during hot markets. During hot markets, AGE is moreconcentrated on lower values, the average ALPHA decreases, the averageUNDP increases and PROCEEDS are higher.

0.0

2.0

4.0

6.0

8.1

De

nsity

0 10 20 30 40Age of Is s u ing  Firms  ( IPOs )

01

23

4D

ens

ity

0 .2 .4 .6 .8 1Frac tion o f Shares  Is s ued  ( IPOs )

0.5

11.

5D

ens

ity

­ 1 ­ .5 0 .5 1U nderpr ic ing  ( IPOs )

0.0

05

.01

.01

5.0

2.0

25

De

nsity

0 50 100 150 200Proc eeds  ( IPOs )

34

Figure 5: Distribution of Firm Age,Fraction of Shares Issued, Underpricing

and Proceeds for SEOs in the Working Sample

This �gure illustrates the distribution of AGE, ALPHA, UNDP and PRO-CEEDS for SEOs in the working sample. The dashed line corresponds tothe observations during 1998-2000 and the solid line considers the remainingobservations. The distribution of AGE, ALPHA and UNDP does not changesigni�cantly during hot markets, suggesting that market players are betterinformed about �rm type during SEOs.

0.0

1.0

2.0

3.0

4.0

5D

ens

ity

0 10 20 30 40Age of Is s u ing  Firms  (SEOs )

05

1015

2025

De

nsity

0 .2 .4 .6 .8 1Frac tion o f Shares  Is s ued  (SEOs )

01

23

4D

ens

ity

­ 1 ­ .5 0 .5 1U nderpr ic ing  (SEOs )

0.0

05

.01

.01

5D

ens

ity

0 50 100 150 200Proc eeds  (SEOs )

35

Figure 6: Observed IPO Strategies and the Probability of Obtainingan S&P Common Stock Rating above Average

This �gure illustrates the marginal increments in the probability of being ratedabove average by SP due to observed IPO strategies. Results are conditionalon exchange listing, except for underpricing (UNDP). The predictions of themodel �t particularly well the empirical evidence on NYSE stocks, in whichthe age (AGE) of issuing �rms decreases with �rm type and the underpricingafter the �rst trading day (UNDP) increases with �rm type. The empiricalevidence for the fraction of shares issued (ALPHA) is ambiguous when consid-ering all markets jointly and not signi�cant for NYSE only. All correspondingprobit regressions are shown in Table 3.

AGE - All Markets AGE - NYSE onlyPredicted Values for  ­­ high

Pro

babi

litie

s an

d 95

% C

I

age0 20 40 60 80

0

.2

.4

.6

.8

Predicted Values for  ­­ high

Pro

babi

litie

s an

d 95

% C

I

age0 20 40 60 80

0

.2

.4

.6

.8

ALPHA- All Markets ALPHA- NYSE onlyPredicted Values for  ­­ high

Pro

babi

litie

s an

d 95

% C

I

alpha0 .5 1

0

.2

.4

Predicted Values for  ­­ high

Pro

babi

litie

s an

d 95

% C

I

alpha0 .5 1

0

.2

.4

.6

.8

UNDP - All Markets UNDP - NYSE onlyPredicted Values for  ­­ high

Pro

babi

litie

s an

d 95

% C

I

underpricing­.5 0 .5

0

.1

.2

.3

.4

Predicted Values for  ­­ high

Pro

babi

litie

s an

d 95

% C

I

underpricing­.2 0 .2 .4 .6

0

.5

1

36

Figure 7: Observed SEO Strategies and the Probability of Obtainingan S&P Common Stock Rating above Average

This �gure illustrates the marginal increments in the probability of being ratedabove average by SP due to observed SEO strategies. Results suggest thatasymmetric information is not as strong as for IPO strategies; the contributionof underpricing to the probability of being rated above average in the futureis not signi�cantly di¤erent from zero. The numbers or years since the IPO(YSIPO) that �rms wait until doing a SEO are negatively related to theprobability of being ranked above average in the future; this suggests thatbetter �rms issue earlier even under perfect information (Proposition 1). Allcorresponding probit regressions are shown in Table 4.

AGE - All Markets AGE - NYSE onlyPredicted Values for  ­­ high_seo

Pro

babi

litie

s an

d 95

% C

I

ysipo2, Winsorized fraction .010 5 10 15 20

.2

.3

.4

Predicted Values for  ­­ high_seo

Pro

babi

litie

s an

d 95

% C

I

ysipo2, Winsorized fraction .010 5 10 15 20

.4

.5

.6

.7

ALPHA- All Markets ALPHA- NYSE onlyPredicted Values for  ­­ high_seo

Pro

babi

litie

s an

d 95

% C

I

alpha0 .2 .4 .6

0

.2

.4

.6

.8

Predicted Values for  ­­ high_seo

Pro

babi

litie

s an

d 95

% C

I

alpha0 .2 .4 .6

.2

.4

.6

.8

1

UNDP - All Markets UNDP - NYSE onlyPredicted Values for  ­­ high_seo

Pro

babi

litie

s an

d 95

% C

I

undp0­.5 0 .5

.2

.3

.4

.5

Predicted Values for  ­­ high_seo

Pro

babi

litie

s an

d 95

% C

I

undp0­.5 0 .5

.2

.4

.6

.8

37

Table 1: A numerical example of the IPO Model

This table illustrates the main predictions of the model for IPOs. Panel A reports the case of perfectinformation. Panel B reports the optimal separating equilibrium. Panel C shows the optimal strategies inpooling for p=0.5. In separating equilibria, high types issue earlier and provide more underpricing to revealtheir type. In pooling equilibria, all �rms issue simultaneously.

Perfect Info Least Cost Sep. Eq. Pooling Eq.Panel A �H > 0; �H = 1 �H = 0; �H < 1L H L H L H L H

Going Public Strategy

xipo 2.474 1.160 2.474 0.849 2.474 1.147 1.153 1.153

�1 25.00% 25.00% 25.00% 21.80% 25.00% 21.37% 21.40% 21.40%

�1 1.000 1.000 1.000 1.000 1.000 0.835 1.000 1.000

�1 0.000 0.000 0.000 0.376 0.000 0.000 0.000 0.000

IPO Statistics

Underpricing 0.00% 0.00% 0.00% 0.00% 0.00% 16.53% 0.00% 0.00%

Underwriting cost 2.25 2.25 2.25 4.31 2.25 4.63 4.62 4.62

Gross Spread 5.68% 12.12% 5.68% 36.40% 5.68% 35.39% 29.24% 29.24%

Announcement E¤ect 0.00% 0.00% 0.00% 0.00% 0.00% 16.53% 0.00% 0.00%

Proceeds

Current value 39.58 18.56 39.58 11.84 39.58 13.10 15.79 15.79

At X0 8.56 11.31 8.56 11.07 8.56 8.11 9.71 9.71

Gross Spread 0.00 0.00 0.04 0.22 0.04 0.22 0.24 0.24

Actual Firm Value

At IPO 160.13 96.51 144.23 65.33 144.23 96.57 76.94 110.53

At X0 46.40 69.19 43.01 69.26 43.01 69.39 43.95 68.89

Expected Firm Value

At IPO 160.13 96.51 144.23 65.33 144.23 96.57 93.74 93.74

At X0 45.55 62.86 42.11 61.66 42.11 63.71 61.61 61.61

Ages and Probabilities

P ipo[0;5] 0.00% 67.66% 0.00% 0.00% 0.00% 70.14% 69.05% 69.05%

Age at xipo 25.57 8.27 25.57 1.12 25.57 8.00 8.12 8.12

38

Table 2: Working Sample Statistics

This table reports summary statistics on US public equity issues reported by SDC from 1980 to 2005.PROCEEDS are total proceeds. UNDP is the underpricing after the �rst trading day. ALPHA is thefraction of shares issued. LNSALES is the log of sales before the o¤ering. AGE is the age of the �rm.TYPEH equals 1 when SP rates common stocks above average within the next 8 years after the issue.

Panel A: All IPOs

80-97 and 01-05 98-00

N mean p50 sd N mean p50 sd

PROCEEDS 4576 48.915 21.000 98.094 449 104.608 66.000 141.600

UNDP 3775 0.067 0.075 0.303 435 0.305 0.352 0.400

ALPHA 3658 0.475 0.455 0.249 423 0.315 0.266 0.226

AGE 1732 14.859 8.000 19.399 256 9.598 5.000 11.399

LNSALES 4048 3.201 3.333 2.218 419 2.988 3.010 2.184

SPRAT 19 16.789 17.000 5.084 2 19.000 19.000 2.828

TYPEH 313 0.173 0.000 0.378 2 0.000 0.000 0.000

Panel B: IPOs at NYSE

80-97 and 01-05 98-00

N mean p50 sd N mean p50 sd

PROCEEDS 573 179.505 105.000 198.480 30 353.113 247.826 285.005

UNDP 520 0.060 0.064 0.240 29 0.103 0.147 0.244

ALPHA 445 0.463 0.414 0.291 26 0.413 0.403 0.273

AGE 284 23.493 13.000 27.225 17 18.059 12.000 21.767

LNSALES 531 5.770 5.745 1.578 31 6.941 6.912 1.411

SPRAT 10 15.900 17.500 5.915 0 . . .

TYPEH 56 0.250 0.000 0.437 0 . . .

Panel C: All SEOs

80-97 and 01-05 98-00

N mean p50 sd N mean p50 sd

PROCEEDS 5540 80.980 39.900 126.834 851 192.424 91.500 221.706

UNDP 5235 0.013 0.010 0.259 822 0.046 0.039 0.258

ALPHA 5274 0.181 0.152 0.141 789 0.168 0.142 0.132

AGE 2806 26.827 15.000 29.463 606 21.002 13.000 23.206

LNSALES 5430 4.823 4.814 2.259 837 4.865 4.871 2.236

SPRAT 1265 17.396 18.000 3.420 220 17.268 18.000 3.185

TYPEH 626 0.254 0.000 0.436 31 0.194 0.000 0.402

39

Table 3: Marginal E¤ects of IPO Strategieson the Probability of Having an S&P Common Stock Rating above Average

This table summarizes the estimation results of runing probit regressions on the dummyTYPEH as a function of IPO Strategies in the sample. TYPEH is equal to 1 if the issuing�rm receives a common stock rating by SP above average during the next 8 years afterthe sample. All coe¢ cients correspond to marginal increments in the probability of beingrated above average. All standard errors have been controlled for industry clustering.

VARIABLES (1) (2) (3) (4)

All Markets All Markets NYSE NYSE

AGE 0.0150** -0.0064**

(0.00613) (0.00290)

AGE2 -0.0002**

(7.31e-05)

ALPHA 0.885 0.940** 0.0142 0.210

(0.916) (0.450) (0.209) (0.174)

ALPHA2 -1.051 -1.106**

(0.882) (0.467)

UNDP 0.550** 0.440*** 0.111 0.576**

(0.258) (0.129) (0.316) (0.2651)

UNDP2 -0.835** -0.618**

(0.426) (0.274)

LNSALES 0.0270 0.0640*** 0.0545* 0.1081***

(0.0193) (0.0189) (0.0319) (0.0419)

Exchange Dummies Yes Yes No No

Clusters 8 8 5 5

Observations 98 149 37 45

Pseudo R2 0.292 0.221 0.106 0.380

Probability at x 0.214 0.201 0.243 0.242

*** p<0.01, ** p<0.05, * p<0.1

Robust standard errors in parentheses

40

Table 4: Marginal E¤ects of SEO Strategies on theProbability of Having an S&P Common Stock Rating above Average

This table summarizes the estimation results of runing probit regressions on the dummyTYPEH as a function of SEO Strategies in the sample. TYPEH is equal to 1 if the issuing�rm receives a common stock rating by SP above average during the next 8 years afterthe sample. All coe¢ cients correspond to marginal increments in the probability of beingrated above average. All standard errors have been controlled for industry clustering.

(1) (2) (3) (4)

VARIABLES All Markets All Markets NYSE NYSE

AGE -0.00413** -0.00411**

(0.00175) (0.00208)

ALPHA -1.477*** -2.663*** -3.360*** -1.254***

(0.500) (0.325) (0.634) (0.413)

ALPHA2 1.543** 3.400*** 4.805*** 1.137*

(0.774) (0.424) (1.240) (0.602)

UNDP -0.137 -0.0247 -0.169 0.00792

(0.123) (0.109) (0.193) (0.108)

LNSALES 0.0418** -0.0133 0.0252*** 0.0354*

(0.0167) (0.0270) (0.00520) (0.0183)

Exchange Dummies Yes Yes No No

# SEOs Dummy Yes Yes Yes Yes

Clusters 9 9 9 9

Observations 249 406 134 218

Pseudo R2 0.202 0.117 0.157 0.104

Probability at x 0.370 0.526 0.415 0.523

*** p<0.01, ** p<0.05, * p<0.1

Robust standard errors in parentheses

41