When are announced initial public offerings completed?

MARIE-CLAUDE BEAULIEU* WILLIAM R. SODJAHIN**

August 2008

* RBC Chair in Financial Innovations, Centre interuniversitaire sur le risque, les politiques économiques et l’emploi (CIRPÉE), Département de Finance et Assurance, Faculté des Sciences de l’Administration, Université Laval, CANADA Telephone: 418-656-2926, email: Marie-Claude.Beaulieu@fas.ulaval.ca. ** Ph.D Candidate, Département de Finance et Assurance, Faculté des Sciences de l’Administration, Université Laval, CANADA Telephone: 418-656-2131, ext. 4689, email: william.sodjahin.1@ulaval.ca. W. Sodjahin is grateful for financial support from Institut de Finance Mathématique de Montréal (IFM2). M.-C. Beaulieu gratefully acknowledges funding from the Social Sciences and Humanities Research Council of Canada (SSHRC), Fonds Québecois pour la Recherche sur la Société et la Culture (FQRSC) and Institut de Finance Mathématique de Montréal (IFM2). The authors thank Jean Bédard, Jean-Marie Gagnon, Michel Gendron, Simon Gervais and seminar participants at Université Laval, at the doctoral consortium at AFFI 2008 and the 12th Annual International Conference on Real Options, for their comments.

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When are announced initial public offerings completed?

August 2008

Abstract

This paper explores the information content in the time that elapses from the announcement until the execution of initial public offerings (IPOs). Given that IPOs are raised in a context of information asymmetry and adverse selection, the external preparation delay for an IPO is important for public investors, issuers and bankers. We propose a model that formalizes the optimal external timing of an IPO using a real option framework. Our empirical investigations explore the determinants of the waiting period and how this period affects investors’ beliefs, the market reaction, as well as the probability of an underwriter switch or of a change in syndicate size. We find strong evidence that the IPO waiting period produces information, the quantity of which increases with syndicate size. We also provide evidence that the length of the waiting period is strongly related to cash pressure, pre-IPO leverage and post-IPO investment as well as managerial incentives. Further empirical results reveal that a shorter waiting period generates higher levels of heterogeneity in investors’ beliefs about the IPO firm’s future prospects and also increases the underwriter’s chance of being retained for a subsequent seasoned equity offering (SEO). Surprisingly, we find no link between the waiting period and underpricing in an IPO, but a strong link between the SEO and its first-day return. Overall, our results suggest that while issuers and underwriters benefit from shorter waiting periods, managers and investors benefit from longer waiting periods. JEL classification: G24 and G32. Key words: IPO, subsequent SEO, real option, waiting period, syndicate size, syndicate size and underwriter changes, managerial incentives.

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I- Introduction

Firms intent on going public face a timing issue. A substantial body of academic

research on initial public offerings (IPOs) documents the clustering of IPOs in a hot market

called a “hot issue market” (Ibbotson and Jaffe, 1975; Ritter, 1984; and Ibbotson, Sindelar and

Ritter, 1988, 1994; among others). However, few studies have investigated the external timing

of an individual IPO.1 This paper proposes a model that formalizes the optimal external

timing for an IPO using real option, derives underpricing, examines comparative statics and,

finally, presents related empirical evidence.

The external preparation delay is important because a long waiting period can alleviate

the concerns of public investors regarding the issuer’s financial health and reduce the

information asymmetry and adverse selection risk that characterize IPOs. The waiting period

not only reduces information asymmetry and adverse selection risk for investors, but also

provides issuers and bankers with more information2 about the best possible price the IPO

may reach (e.g., Hanley, 1989; Edelen and Kadlec, 2005). First, our empirical investigation

addresses not only the determinants of waiting period length in general, but focuses on that

period’s relation to underwriting syndicate size and to managers’ and directors’ incentives.

Second, the paper studies the implications of the waiting period length for certain IPO

anomalies as well as for major decisions such as a change in syndicate size (reduce, maintain

or increase) or a switch in lead underwriter at a subsequent seasoned equity offering (SEO).

Overall, focusing on the waiting period is justified because it is another means of

1 It is the external preparation delay or the time that elapses between the filing and offer dates. Note that the IPO decision date itself is internal to the company and non-observable. Only the official announcement date or filing date can be observed to the public. According to Draho (2004), investment banks provide three distinct services during the period between the filing and offer dates. Firstly, they provide administrative preparation of the prospectus and advice on setting the offering terms. Secondly, banks underwrite the offering by committing to bear underwriting risk in whole or in part. Finally, they place shares with investors. 2 This information may be private or public and may include spillovers.

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understanding equity offering decisions and their implementation. It also furthers our

understanding of how the waiting period contributes to alleviating the information asymmetry

and adverse selection risk that are prominent in IPO markets. Furthermore, a better

understanding of waiting period determinants and effects would help firms to strategically

manage them.

I- 1 Literature review

Several studies (see Ritter, 1984, and Lowry, 2003, among others) suggest that firms

tend to undertake IPOs when market conditions are favorable, which leads to fluctuations in

IPO volume over time. IPOs are characterized by clustering over both time and industry (e.g.,

Lowry and Schwert, 2002). Lowry (2003) suggests that when information asymmetry is high,

firms are more likely to delay their IPOs and choose alternative types of financing. In the

same way, Alti (2005) shows that a high offer price, which is associated with low information

asymmetry, triggers more IPOs. Other papers have linked the timing of IPOs to product

market competition3 (see Maksimovic and Pichler, 2001; Benveniste, Busaba and Wilhelm,

2002; among others) and the decision to go public to the outcomes of recent and current

offerings (Benveniste, Ljungqvist, Wilhelm and Yu, 2003).

The literature suggests many reasons why firms go public. These include a

diversification motive (Leland and Pyle, 1977), outside monitoring (Holmström and Tirole,

1993, and Bolton and Von Thadden, 1998), liquidity (Amihud and Mendelson, 1988) and

private benefits of control (Zingales, 1995; Benninga, Helmantel and Sarig, 2005).

While a substantial body of IPO literature focuses on market timing, IPO motivations,

links between asymmetry, uncertainty and underpricing (Beatty and Ritter, 1986, among

others), little has been said about the external timing of an individual IPO (i.e., the waiting 3 There may be an incentive to delay the offerings since some competitors that are not yet public can benefit from the information produced.

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period) and how that waiting period relates to underwriting syndicate size, the subsequent

SEO decision and IPO anomalies.

The idea that IPO timing is optimally chosen when firms exercise their option to go

public is used in Draho (2000) and Brada and Ma (2007). Logue (1973) positively relates

underpricing to the market return during the waiting period. Other authors study the partial

adjustment of IPO prices to private and public information revealed during the waiting period

(e.g., Hanley, 1989; Edelen and Kadlec, 2005). However, these authors do not tackle the

determinants of the length of the waiting period per se. Concerning syndicate size, Corwin

and Schultz (2005) find that prices offered are more likely to be revised in response to

information with larger syndicates. These authors also analyze the relation between

underwriters and factors that may affect syndicate size. Note that the findings of Corwin and

Schultz (2005) reinforce the role of syndicate size in the IPO process and the importance of

studying how changes in syndicate size at subsequent SEOs relate to the waiting periods of

IPOs and SEOs.

I- 2 Research issue and objectives

This paper seeks to answer two fundamental research questions: (1) What is the

information content of the IPO waiting period? What factors explain the length of this

period?4 (2) What are the consequences of the delay? and Who, ultimately, benefits from the

IPO waiting period?

Our objective is twofold: to explain the determinants of waiting period length for IPOs

and provide insight into the effects of that length. To this end, this paper, following authors

like Draho (2000) and Brada and Ma (2007), proposes a model that formalizes the optimal

4 Although the theoretical external preparation delay is set at 120 days (see Draho, 2004, page 183), as we will show, the actual delay varies substantially across firms.

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external timing of an IPO by means of real option modeling and uses the same framework to

derive IPO underpricing. The paper also empirically tests the research questions presented

above.

Note that this article is the first to present a model that incorporates underwriting

syndicate size, jumps in firms’ cash flows as well as the time-inconsistent preferences5 of

issuing firms and to analyze their effects on the external timing and underpricing of IPOs. We

include syndicate size in the model because of its significance in terms of IPO costs, as raised

recently by Corwin and Schultz (2005). These authors find that underwriter spreads increase

with syndicate size, suggesting that it is not always costless to add additional co-managers to

the IPO syndicate. The model also incorporates cash flow jumps to account for the risk of

drops in a firm’s cash flows due to product market competition, as well as the potential impact

of such cash flow jumps on IPO timing (see Maksimovic and Pichler, 2001; Benveniste,

Busaba and Wilhelm, 2002; among others). Following recent papers on IPOs that have

separately examined technology intensive firms because of their high level of expected

growth (see Loughran and Ritter, 2004, and Jaggia and Thosar, 2004, among others) we

introduce a time-inconsistent preference factor to account for the particularity of firms such as

high-tech firms, which value future cash flows over present cash flows. We further analyze

how time inconsistent preferences affect the external timing of individual IPOs.

This paper is also the first to empirically investigate the determinants of the IPO

waiting period and its implications. Our empirical investigation, controlling respectively for

certain characteristics of the firm as well as market conditions, focuses on the relation

5 These preferences help characterize high-tech or growth firms that typically bet on the future and can be more patient. In fact, their capital structure means they place greater emphasis on future cash flows than on present cash flows. Note that unlike most papers on time inconsistent preferences (Phelps and Pollak, 1968; Laibson, 1997; Harris and Laibson, 2004; Grenadier and Wang, 2007; among others), we model patience (that is, the fact that more weight is given to future cash flows than to present ones) rather than the impatience typically used to characterize these preferences.

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between waiting period length and underwriting syndicate size on the one hand, and between

waiting period length and managers’ and directors’ incentives on the other hand. To

determine who benefits from the waiting period length, we study the period’s impact on the

following aspects: underpricing, heterogeneity in investors’ beliefs, money left on the table,

pricing, the probability of an underwriter switch or of a change in underwriting syndicate size

at a subsequent SEO, and market return at the subsequent SEO date.

I- 3 Model predictions and empirical results

Predictions derived from the model show that the IPO waiting period increases with

syndicate size and downward jump risk (risk of profit drop due to product market

competition) and decreases with the time inconsistent preferences of issuing firms.

Predictions also show that underpricing decreases as the waiting period lengthens. First, these

findings suggest that a larger syndicate reduces net IPO proceeds for the firm, reducing its

incentive to go public and making a wait more valuable. On the other hand, the larger the

syndicate, the greater the risk of competition and disagreement between syndicate members

will be, potentially setting back IPO completion. Second, these predictions indicate that a

higher risk of profit drop due to product market competition will lead private firms to

complete their IPO later due to the information disclosure inherent in IPOs (see Maksimovic

and Pichler, 2001; Benveniste, Busaba and Wilhelm, 2002). These predictions suggest that

when private firms value future cash flows over present cash flows, the IPO will be completed

sooner, certainly for investment motives. Finally, the longer the waiting period, the lower the

underpricing return will be since a long waiting period reduces adverse selection risk and

information asymmetry.

Our empirical results are generally consistent with model predictions. We find

evidence that waiting periods produce information. After controlling for endogeneity in

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syndicate size choice, results show, consistent with our model’s predictions that the IPO

waiting period is more likely to be longer as syndicate size increases. Furthermore, time-

inconsistent preferences as proxied by our high-tech dummy are negatively related to the

waiting period.

We also find that the waiting period is determined by three factors, namely cash

pressure, investment and leverage. Note that the first two factors may also capture time-

inconsistent preference since firms that bet more on the future than standard firms, have less

cash and invest more (e.g., R&D and others forms of investments). Results provide evidence

that the greater the cash pressure on private firms, the sooner IPOs are completed. The results

also provide evidence that although investment is not a significant motive for IPOs as argued

by Pagano et al. (1998), investment expedites IPO completion. Likewise, when private firms

are overleveraged, IPOs are completed sooner as suggested by the trade-off theory of capital

structure (see Dittmar and Thakor, 2007, among others). In contrast, we find that a downward

jump risk indicator does not significantly affect the length of the waiting period. Moreover,

results reveal that firms that remunerate managers with options and provide loans to exercise

options are more likely to have a longer IPO waiting period, suggesting that the negotiation of

stock options may set back IPO completion. In contrast, directors’ incentives do not

significantly affect the IPO waiting period. Furthermore, we find that the waiting period is

shorter in a hot market, which is consistent with the fact that firms tend to undertake IPOs

when market conditions are favorable (see Ritter, 1984, and Lowry, 2003). Furthermore, we

find both Hanley’s (1993) partial adjustment effect and James and Wier’s (1990) leverage

effect as well as a downward jump risk impact on underpricing, but no significant effect of the

waiting period.

The results of our examination of who benefits from the waiting period reveals that a

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shorter waiting period (which implies more informational asymmetries and higher adverse

selection risk) generates higher levels of heterogeneity in investors’ beliefs about the IPO

firm’s future prospects. Surprisingly, our findings do not show that underpricing significantly

decreases with the waiting period. We do find, however, that the issuer is more likely to

subsequently switch underwriters when the IPO waiting period is long.

To further improve our understanding of the variations in delay, we provide additional

evidence on the relation between syndicate size and waiting period from multinomial model

estimates of changes in syndicate size at a subsequent SEO. Results show that:

(a) Firms are more likely to reduce syndicate size when the IPO waiting period is long, and

the announced SEO is more likely to be completed early when the syndicate size is reduced;

(b) Firms are more likely to increase rather than reduce syndicate size when the IPO waiting

period is shorter, and the completion of the announced SEO is more likely to be set back

when the syndicate size is increased rather than reduced.

Finally, our analysis sheds light on how the waiting period affects the market reaction

to the SEO. Empirically the relation is strong and positive, meaning that the longer the SEO

waiting period, the better the first-day market reaction. Furthermore, at the subsequent SEO

date, the market reacts negatively to higher post-IPO risk.

Overall, these findings complement in many ways the existing literature on IPO timing

and the role of underwriting syndicates. All in all, our findings suggest that issuers and

underwriters benefit from a shorter IPO waiting period because of cash pressure, investment

and leverage for the issuing firms and the underwriter’s chance of being retained for a

subsequent SEO. In fact, since directors’ incentives have no significant impact on the IPO

waiting period, directors would work in the interest of the issuing firms to change

underwriters at the subsequent SEO when the IPO waiting period is long. Conversely,

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investors benefit from longer waiting periods since a longer IPO waiting period reduces

heterogeneity in beliefs and the market reacts positively to a longer SEO waiting period.

Moreover, the length of the IPO waiting period can be subject to agency conflicts since unlike

the issuing firm, the manager may benefit from a longer waiting period to negotiate the post-

IPO stock option terms6.

The remainder of the paper is organized as follows. Section II develops the model

incorporating underwriting syndicate size, possible jumps in firms’ cash flows, and issuing

firms’ time-inconsistent preferences; it also derives the optimal external timing for an IPO,

which is the time elapsed from the announcement date to the effective date. Underpricing is

also examined and comparative static results are produced. Empirical results are presented in

Section III. Section IV concludes.

II. The model

In this section, IPO external timing is modeled in a real option framework. Our model

integrates underwriting syndicate size, possible jumps in firms’ cash flows, and issuing firms’

time-inconsistent preferences in a general real option framework for IPOs used by authors like

Draho (2000) and Brada and Ma (2007). Recall that we include syndicate size because the

recent findings of Corwin and Schultz (2005) show that underwriter spreads increase with

syndicate size, suggesting that it is not always costless to add additional co-managers to the

IPO syndicate. The jump in firms’ cash flows is modeled to account for possible drops in

firms’ cash flows due to product market competition as well as the jump’s importance with

respect to IPO timing (see Maksimovic and Pichler, 2001; Benveniste, Busaba and Wilhelm,

2002). Time-inconsistent preferences capture high-tech firms that place greater value on 6 For example, while the issuer can set a very high strike price, the manager need more time to have a good idea of the full subscription offer price and negotiate to lower the strike price of their option.

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future cash flows than present cash flows, in accordance with recent IPO research that

separately examined technology intensive firms given their high level of expected growth (see

Loughran and Ritter, 2004, and Jaggia and Thosar, 2004). We present the firm valuation and

the timing decision along with comparative statics and derive the IPO underpricing. The

model relies on the following assumptions:

Assumption 1: The firm’s market value is greater than its private value once the underwriting

spread is taken into account.7

Assumption 2: The firm does not issue immediately, otherwise the timing decision would be

irrelevant.

II.1 Firm valuation

We assume that a private firm has the option to go public at any time from the date the

IPO program is known to the public. The IPO is assumed to be irreversible, both the private

firm and the public investors are risk averse and time evolves continuously. The private

company generates an instantaneous profit flow tπ , with an initial profit level 0π at the date

the IPO announcement is made. The profit of a private firm is expected to grow at a constant

rate rμ > ,8 where r is the risk-free rate. Profits remain subject to random disturbances in the

market. The stochastic evolution of the private firm’s profits allows for a downward Poisson

jump to account for shocks in demand due to new entrants and technological development.9

The idea here is to assess the influence of potential competition on the IPO timing. Moreover,

many papers suggest that there is an incentive to delay the offerings because of product

market competition (see Maksimovic and Pichler, 2001; Benveniste, Busaba and Wilhelm,

7 This condition guarantees the incentive to go public. 8 If rμ < , no rational public investor would buy the stock. 9 In fact, the resulting competition will reduce the firm’s profits.

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2002). Thus, it is assumed that a mixed diffusion process describes dynamics of the private

firm’s profits according to the stochastic differential equation:

d dt dz dqπ μ σ φπ

= + − (1)

where the terms dz and dq are independently distributed processes representing respectively

an increment to a standard Wiener process and a continuous-time Poisson process. The

parameterθ is the intensity parameter of the Poisson process, measuring the frequency of a

jump, and 0 1φ≤ ≤ is the percentage change in profit flows if the Poisson event occurs. The

parameter σ is the instantaneous standard deviation excluding the impact of the Poisson

jump.

The random variable ratio of profit flow at time t , tπ , to the profit flow at time zero can be

written as

( )20 exp 1 2 .t t tt z qπ π μ σ σ φ⎡ ⎤= − + −⎣ ⎦ (2)

Public investors will form conditional expectations about the profit flow π for time t . The

expectation at time t of profit π is:

( )0 0( | ) .ttE e μ φθπ π π −= (3)

The value of the firm is then computed as the expected present discounted value of this profit

stream. To distinguish between the discount rates of entrepreneurs of high-tech or growth

firms and those of other types of firms, we assume time-inconsistent preferences of the

issuing firms and study their impact on external IPO timing and underpricing. Indeed, these

firms bet more on the future than standard firms and are more patient since they have less

cash and invest more (e.g., R&D), which implies that they place greater value on future cash

flows than present cash flows. Consequently, time is divided in two: the “present” period and

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all future periods.10 The present period, as in Harris and Laibson (2004) and Grenadier and

Wang (2007), last for a random duration of time ( )T t− . During that period, cash flows are

discounted exponentially with discount rate pρ by the private firm and mρ by public investors

in such a way that p mρ ρ> .11 In future periods, cash flows are discounted by the additional

factor [ )1,1δ ε∈ + , where ε is positive but small enough to keep the discount rate reasonable.

This additional discount factor determines the level of the entrepreneur's time-inconsistency.

Let ( , )D t s be the intertemporal discount function and { },i p m∈ . We have

[ )[ )

( )

( )

f

f

i ,( , )

i , ,

i

i

s t

s T

s

s

e t TD t s

e T

ρ

ρδ

− −

− −

∈

∈

⎧⎪= ⎨∞⎪⎩

(4)

as in Harris and Laibson (2004) and Grenadier and Wang (2007), ( )T t− has an exponential

distribution with mean 1 λ . In fact, this distribution is often used to model the waiting period

before a specific event. Using the intertemporal discount function ( , )D t s , the value of the

firm as the expected present discounted profit stream is

( ) ( )( ) ,i i

iTi s t s T tt T s s i it T

E E e ds e dsρ ρπ

δλ κ πυ π π δ πλ κ κ

∞− − − − ⎛ ⎞+⎡ ⎤= + = ⎜ ⎟⎢ ⎥⎣ ⎦ +⎝ ⎠∫ ∫ (5)

where i iκ ρ μ φθ= − + . In the case of time consistency ( 1δ = ), the value of the firm is:

.i

t ti i i

π δλ κ πκ λ κ κ

⎛ ⎞+< ⎜ ⎟+⎝ ⎠

Applying Ito’s lemma to (5), we obtain:

10 The present period represents the short- and medium-term horizons, while all future periods stand for long-term horizons. 11 Since the entrepreneur bears the cost of industry-wide idiosyncratic risk, he will discount firm profits at a higher rate. Note that both risk-adjusted rates are greater than the profit growth rate so that p mρ ρ μ> > .

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[ ]' '' 2 1( ) ( )

( ) ( ) ( ) .

ii i i

t t t t t ti i

i i it t t

d d d dt dz dq

dt dz dq

δλ κυ π υ π υ π μπ σπ π φλ κ κ

μυ π συ π υ π φ

⎛ ⎞+= + = + −⎜ ⎟+⎝ ⎠= + −

(6)

Thus, firm valuations by the entrepreneur and by public investors share the same stochastic

properties as the profit flow.

Private firms that go public incur issuing costs. These costs include direct

administrative costs, C ,12 and underwriting spread, ψ , as a percentage of the issue proceeds

(see Lee, Lockhead, Ritter and Zhao, 1996). Corwin and Schultz (2005) show that underwriter

spreads increase with syndicate size, suggesting that it is not always costless to add additional

co-managers to the IPO syndicate. Consequently, we allow the underwriter spreads to

positively depend on S , syndicate size, such that '( ) 0Sψ > , ''( ) 0Sψ < and 0 ( ) 1Sψ< < .

Then net proceeds to the private firm from the IPO, ( )tπΩ , are

( )( ) 1 ( ) .m

tt m m S Cδλ κ ππ α ψ

λ κ κ⎛ ⎞+

Ω = − −⎜ ⎟+⎝ ⎠ (7)

where α is the ratio of shares sold to the public.

II.2 Timing decision

The value to the private firm of owning a fraction α of the firm consists in cash flows

received in dividends up to the effective date of the sale and the IPO proceeds at that date.

The value is defined as

( *) ( ) ( *)( ) ( *) | .p it s t

t s ttF E e ds e

τ π ρ ρ τ ππ απ π π+ − − −⎡ ⎤= + Ω⎢ ⎥⎣ ⎦∫ 13 (8)

12 These costs include filing fees, legal expenses and other administrative costs. 13 This value assumes that the trigger point of the IPO occurs before the shift in the discount factor, which is reasonable since the timing decision we are dealing with is external IPO timing. This external preparation delay (waiting period) is more likely to occur in the short and medium terms than in the long term. Note that the shift in the discount factor still affects the value of F through the net IPO proceeds, Ω .

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The trigger point *π is the critical profit level at which the firm goes public and

( *)τ π is the first time the process π reaches *π . Thus, when the private firm’s profits reach

*π , the firm goes public immediately. The first term in equation (8) is the present value of

the dividend stream accumulated by the firm until the IPO is undertaken and the second term

is the present value of net IPO proceeds.

If ( *) 0τ π = , the firm goes public at the announcement date, the waiting period is zero

and ( *) ( *)F π π= Ω . The entrepreneur’s objective is to choose between waiting and

accumulating more dividends from owning α shares and going public to obtain the payoff

( *)πΩ . The firm must choose the timing strategy that maximizes the value ( )tF π , which can

be broken down into two parts: the immediate dividend and the discounted value of going

public. The Bellman equation for the optimal external IPO timing is:14

( ) [ ]1( ) max ( ), ( ) | .1 pF dt E F d

dtπ π απ π π π

ρ

⎧ ⎫⎪ ⎪= Ω + +⎨ ⎬+⎪ ⎪⎩ ⎭

(9)

In the continuation region, the second term is larger than the first one and the equilibrium

condition derived from equation (9) is

[ ]( ) ( ) | .pF dt dt E dFρ π απ π π= + 15 (10)

Using stochastic dynamic programming (see equation (9)) and expanding ( )dF π using

Ito’s lemma (in equation (10)) leads to the mixed diffusion-jump processes in the following

second-order differential equation:

[ ]2 2 '' '1 ( ) ( ) ( ) ( ) ( ) (1 ) ( ) 02

p p p p pF F F Fσ π π ρ κ π π ρ θ π θ φ π ρ κ π+ − − + + − + − = (11)

The optimal IPO timing ( *)τ π is determined by solving equation (11) under the

14 Similar to Dixit and Pindyck (1994, p.109). 15 Terms of second order ( 2dt ) are dropped since they become infinitesimally small much faster than dt.

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following boundary conditions:

(0) 0,F = (12)

( )( *) 1 ( ) ,m

tm mF S Cδλ κ ππ α ψ

λ κ κ⎛ ⎞+

= − −⎜ ⎟+⎝ ⎠ (13)

( )' 1 ( )( *) .

m

m m

SF

ψδλ κπ αλ κ κ

−⎛ ⎞+= ⎜ ⎟+⎝ ⎠

(14)

The first condition (12) states that the value of going public is worthless if firm value

equals zero. Conditions (13) and (14) are the value-matching and smooth-pasting conditions,

respectively, at the trigger point *π .

Proposition 1 presents the solution to equation (11) under the boundary conditions. It

characterizes the optimal IPO realization.

Proposition 1: The value of the firm to the entrepreneur prior to the IPO realization is

( ) ,p

p pF A β δλ κ ππ π αλ κ κ

⎛ ⎞+= + ⎜ ⎟+⎝ ⎠

(15)

where 1β > and the solution to the nonlinear equation is:

21 ( 1) ( ) ( ) (1 ) 02

p p p βσ β β ρ κ β ρ θ θ φ− + − − + + − = .

The trigger point *π is given by

( )( )1 ( ) 1* .

1 m p

m m p pS

Cψδλ κ δλ κ

λ κ κ λ κ κ

βπβ α −+ +

+ +

⎛ ⎞= ⎜ ⎟− −⎝ ⎠

(16)

The entrepreneur chooses to execute the IPO at { }( *) inf 0 \ * ,ss tτ π π π= > = ≥ where 0t =

is the announcement date and ( *)τ π the IPO waiting period.

The value of A is given in Appendix I.

Proof: See the Appendix I.

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Proposition 1 states that the firm should execute the IPO when *sπ π≥ . The threshold *π is

basically influenced by syndicate size, issue size, the time-inconsistent preference factor and

the size of the jump in the firm’s profits. The following corollary describes how these

parameters affect external IPO timing.

Corollary 1:

Holding all other parameters constant, the optimal IPO waiting period:

i) increases with the syndicate size, S ;

ii) decreases with the time-inconsistent preference factor, δ ;

iii) increases with the size of the jump in the firm’s profits, φ .

Proof: See Appendix I.

The impact of a large syndicate, S , on the waiting period is positive. Indeed, a larger

syndicate increases the underwriting spread, which in turn lowers the private firm’s net IPO

proceeds, reducing its incentive to go public and making a wait more valuable for the firm.

Furthermore, a large syndicate may wait longer to realize the IPO because there is greater risk

of competition between syndicate members, which may mean it takes longer to find

synergies16. Indeed, as reported by Corwin and Schultz (2005): “Practitioners tell us that

underwriters continue to compete with each other even after the syndicate has been

established.” Conversely, an increase in the patience factor δ will increase the market

valuation for any given profit level and the incentive to go public. Consequently, firms with

time-inconsistent preferences such as high-tech or growth firms will complete their IPO

sooner. A large jump in profits φ decreases the market valuation for any given profit level

and the incentive to go public. Thus, when there is the threat of a drop in profit due to new

16 There may be for instance a disagreement in setting offer price.

18

entrants, private firms will go public later. This result is consistent with papers suggesting that

there is an incentive to delay the offerings because of product market competition (see

Maksimovic and Pichler, 2001; Benveniste, Busaba and Wilhelm, 2002).

II.3 Numerical illustration

In this section, we proceed to numerical analyses of the model to illustrate the

magnitude of the critical value of *π at which it is optimal to realize the IPO. We also

consider comparative statics for the values of the underlying parameters of Corollary 1, that

is, S , δ and φ . The following parameter values are held constant throughout the three

examples presented: 0.2α = and 1C = . The entrepreneur is selling 20 percent of the shares

to the public and the fixed cost of the IPO is normalized to $1 million.

Table I summarizes the values of the parameters used to analyze the impact of

syndicate size, time-inconsistent preferences and uncertainty on the IPO trigger point. These

values are based on the literature. ψ is set to 7 percent since this rate is the most common

(Chen and Ritter, 2000, among others). The values of pρ and mρ are based on Draho (2000).

INSERT TABLE I ABOUT HERE

INSERT FIGURE 1 ABOUT HERE

The effect of the underwriting spread ( )Sψ on *π is shown in Figure 1. The

underwriting spread is representative of the syndicate size S since '( ) 0Sψ > . Increasing the

syndicate size raises *π and extends the waiting period. As mentioned earlier, a larger

syndicate reduces net IPO proceeds to the private firm, diminishes the incentive to go public

and makes waiting more valuable. Furthermore, a larger syndicate increases the risk of

competition among syndicate members, potentially setting back IPO completion.

19

INSERT FIGURE 2 ABOUT HERE

The effect of time-inconsistent preferences represented by δ on *π is depicted in

Figure 2. It shows that when private firms value future cash flows over present cash flows, the

IPO will be completed sooner. Time-inconsistent preferences increase market valuation for

any given profit level and thereby increase the incentive to go public and the relative urgency

of the IPO completion. Thus, firms such as high-tech or growth firms that value future cash

flows over present cash flows will complete their IPO sooner, probably for investment

motives.

INSERT FIGURE 3 ABOUT HERE

Figure 3 shows the impact of the jump amplitude φ in the Poisson event on the IPO

trigger point *π . While *π increases with the market volatility σ (as in standard option

pricing), this increase is greater for higher amplitudes, as observed in the cases of 0φ = ,

0.25φ = and 0.5φ = . When the risk of profit drop due to product market competition is

higher, private firms will go public later given the information disclosure inherent in IPOs

(see Maksimovic and Pichler, 2001; Benveniste, Busaba and Wilhelm, 2002). Table A1 in the

Appendix I shows the dependence of β and *π on various values of σ for different cases of

φ .

II.4 Underpricing

Underpricing is derived under the assumption that the price offer is the price as

estimated by the manager. Thus, we define the initial underpricing return UP as the

difference, at *π , between the market value which is the firm’s net value to public investors

20

( *)mnυ π and the offer value which is the firm’s net value to the manager17 ( *)pnυ π ,

normalized by the latter.

The firm’s net value to public investors is the latter value less issuing costs:

( ) ( )*( *) 1 ( ) ( *) 1 ( ) .m

m mm mn S C S Cδλ κ πυ π α αψ υ π α αψ

λ κ κ⎡ ⎤⎛ ⎞+⎡ ⎤= − − = − −⎢ ⎥⎜ ⎟⎣ ⎦ +⎝ ⎠⎣ ⎦

(17)

The firm’s net value to the manager is:

( ) ( )*( *) 1 ( ) ( *) 1 ( ) .p

p pp pn S C S Cδλ κ πυ π α αψ υ π α αψ

λ κ κ⎡ ⎤⎛ ⎞+⎡ ⎤= − − = − −⎢ ⎥⎜ ⎟⎣ ⎦ +⎝ ⎠⎣ ⎦

(18)

Then,

( )( )1 ( ) ( *)( *) ( *) 1.

( *) 1 ( ) ( *)

mm p

p p

S Cn nUPn S C

αψ υ πυ π υ πυ π αψ υ π

− −−≡ = −

− − (19)

The purpose of our analysis is to examine the variation in the underpricing return UP

as a function of the external IPO delay and to deduce direct, indirect and total effects for

syndicate size, issue size and the time-inconsistent preference factor, as well as the size of the

jump in firm profits. Proposition 2 below gives the relation between underpricing and the IPO

waiting period.

Proposition 2: The underpricing return UP decreases with the IPO waiting period.

Proof. See Appendix I.

The longer the waiting period, the lower the underpricing return. Indeed, a longer

external delay reduces information asymmetry since it can alleviate investor concerns about

the financial health of the private firm issuing. Moreover, Rock (1986), Beatty and Ritter

17 Recall that p mρ ρ> .

21

(1986) and Ellul and Pagano (2006) document a positive relation between the underpricing of

an IPO and investors’ uncertainty with respect to the value of the issuer. Figure 4 below

illustrates the negative relation between underpricing and the waiting period.

INSERT FIGURE 4 ABOUT HERE

The effects of syndicate size ( S ), time-inconsistent preferences level (δ ), and the

jump amplitude (φ ) on underpricing UP are undetermined. The total effect for each

parameter depends on whether direct or indirect effects (through *π ) dominate.18 Our

empirical investigation will provide insight into these effects.

III. Empirical analysis

In this section we test the hypotheses derived from the model and carry out further

investigations.

III. 1 Empirical implications of the model

From Propositions 1 and 2 and Corollary 1, we can express our empirical implications as

follows:

(I1) Waiting periods increase with syndicate size and downward jump risk (risk of drop in

profit flow). They decrease with the time-inconsistent preference factor.

(I2) Underpricing decreases as the waiting period lengthens.

III. 2 Determinants of the IPO waiting period

In this section we study the determinants of the waiting period. Our empirical 18 The indirect effects are: * 0

* ( )UP

Sπ

π ψ∂ ∂

<∂ ∂

, * 0*

UP ππ δ∂ ∂

>∂ ∂

and * 0*

UP ππ φ∂ ∂

<∂ ∂

. The direct effects are 0( )

UPSψ

∂>

∂,

0UPδ

∂<

∂ and 0UP or

φ∂

< >∂

.

22

investigation, controlling respectively for certain characteristics of the firm and market

conditions, focuses on the relation between waiting period length and underwriting syndicate

size on the one hand, and between waiting period length and managers’ and directors’

incentives on the other hand.

The hypothesis of the link between waiting period length and underwriting syndicate

size is stated in implication (I1) of the model. The firm’s situation includes not only

downward jump risk and time-inconsistent preferences as presented in I1, but also cash

pressure, post-IPO investment and pre-IPO leverage19. Firms mainly use the proceeds of the

offerings for holding cash, financing investments and repaying debt. As such, cash pressure is

one factor that may determine waiting period length. Indeed, IPOs are more likely to be

completed early when firms lack cash. Moreover, we test for the importance of investment

and trade-off theory of capital structure20 motives in setting the length of the waiting period.

Although investment alone does not justify IPOs (see Pagano et al., 1998), we expect that

needed investment will quicken IPO completion. In fact, firms that issue stocks to finance

investment opportunities will be more impatient to receive offering proceeds and carry out

their investment, in which case the IPO will be completed sooner. Likewise, overleveraged

private firms will not wait long to bring their capital structure to an optimal level in

accordance with the trade-off theory (see Dittmar and Thakor, 2007, among others).

Therefore, along with implication I1, we test the relation of the waiting period to cash

pressure, the waiting period to post-IPO investment and, finally, the waiting period to pre-IPO

leverage:

19 Note that, the time-inconsistent preferences factor may also be characterize by cash pressure and investment since firms that bet more on the future than standard firms, have less cash and invest more (e.g., R&D and others forms of investments). 20 According to the trade-off theory, issuance decisions move the firm’s capital structure toward an optimum obtained by a trade-off between marginal costs and the benefits of debt.

23

(H1) The waiting period decreases with cash pressure.

(H2) The waiting period decreases with post-IPO investment.

(H3) The waiting period decreases with pre-IPO leverage.

Furthermore, we examine whether post-IPO managers’ and directors’ incentives have any

correlation to waiting period length. Indeed, we expect the waiting period to be longer in the

presence of incentives such as stock options. In fact, negotiating and setting stock option

terms may set back IPO completion since managers require a good idea of the full

subscription offer price before negotiating stock option terms such as strike price and number

of options. Note that, issuer doesn’t need much time since he can set a very high strike price.

Thus, we test whether the waiting period increases with post-IPO managers’ and directors’

incentives:

(H4) The waiting period increases with post-IPO managers’ and directors’ incentives.

We test hypothesis H4 controlling for market conditions. Market variables include market

timing21 and post-IPO performance.

III. 3 Who benefits from the waiting period?

To answer this question, after the study of the determinants of the IPO waiting period

presented above, we analyze its implications of this delay. First, we study the impact of the

IPO waiting period on underpricing as stated in implication I2 of the model. Moreover, we

analyze the effects of IPO waiting period on the level of heterogeneity in investors’ beliefs,

money left on the table, pricing and the probability of an underwriter switch at a subsequent

21 IPO waiting delays may be shorter in hot markets or longer in cold markets.

24

SEO. We also examine the link between the probability of a change in syndicate size at a

subsequent SEO and the following aspects: waiting periods (for IPOs and SEOs), switching

underwriter and underwriter rank. Finally, we investigate whether the first-day market

reaction to the SEO depends on the SEO waiting period.

III. 4 Data and variable definitions

Our dataset consists of a sample of 690 IPOs retrieved from Bloomberg with data

available in the Center for Research in Security Prices (CRSP) daily master files. All

accounting data are collected from Compustat, while managers’ and directors’ incentives data

are sourced from Institutional Shareholder Services (ISS). Due to the availability of ISS data,

our sample covers the period from January 2003 to December 200522 for IPO announcements.

Our measure of underwriter prestige is based on the Tombstone underwriter reputation rank

developed by Carter and Manaster (1990). The adjusted Carter-Manaster ranks we use are

obtained from Jay Ritter’s web page at http://bear.cba.ufl.edu/ritter/Rank.pdf.

Our variable choices and definitions are inspired by earlier literature:

Waiting period is the number of calendar days from the initial filing date to the offer date. See

Hanley (1993) and Edelen and Kadlec (2005).

Underwriting syndicate size is measured by the number of managing underwriters, since

synergy problems and competition between syndicate members are more likely to occur

between managing underwriters than between non-managing underwriters.

Downward jump risk: Downward jumps occur when returns are negative and larger in

absolute value than the absolute value of the mean of returns over the post-IPO year. We 22 Note that we find many results consistent with previous studies that cover longer time periods. For instance, the average underpricing, money left on the table and gross proceeds in our sample are very close to the average values for 6,816 IPOs over the 2001−2005 period (see the website of Jay Ritter: http://bear.cba.ufl.edu/ritter/work_papers/IPOsMarch2006.ppt). We also find various effects, such as Hanley’s (1993) partial adjustment effect and James and Wier’s (1990) leverage effects.

25

define downward jump risk as the standard deviation of daily jump returns, calculated using

both jump and non-jump days over the post-IPO year. The value for the jump return is zero on

non jump days.

Time inconsistent preferences factor: Since this factor characterizes firms that place greater

value on future cash flows than present cash flows, high-tech firms are used to capture time-

inconsistent preferences. Using Fama-French industry classification, high-tech firms include

firms with SIC code 3570-3579, 3622, 3660-3692, 3694-3699, 3810-3839, 4800-4899, 7370-

7379, 7391 and 8730-8734. Note that the time-inconsistent preferences factor may also be

reflected by cash pressure and investment since this factor characterizes firms that bet more

on the future than standard firms, have less cash and invest more (e.g., R&D). Thus we define

cash pressure and investment as follow:

Cash pressure: the indicator for cash pressure is total cash held divided by net sales. Note that

cash pressure increases when this cash ratio decreases;

Investment is measured, over the post-IPO year, following Dittmar and Thakor (2007) by

capital expenditures to sales ratio.

Leverage is measured, over the pre-IPO year, by total debt divided by total capital invested,

and multiplied by 100.

“Underpricing”=First-day return = 100% x (Closing price – offer price)/offer price.

Money left on the table = number of shares sold x (closing price – offer price).

First-day turnover is the first-day trading volume divided by the number of shares issued.

Market adjusted SEO first-day return is the difference between the first-day return and that of

the market value-weighted index.

Managers’ and directors’ incentives

• Dirsubstock: equals 1 if directors are subject to stock ownership requirements (0

26

otherwise) in the year following IPO completion;

• Dirownership: equals 1 if directors’ and officers’ ownership as % of shares

outstanding is greater than 5 percent and less than or equal to 30 percent

(otherwise it is equal to 0) in the year following IPO completion;

• Stockplan: takes the value of 1 when company managers are remunerated with

options in the year following IPO completion and 0 otherwise;

• Loansoption: takes the value of 1 when the company provides loans to executives

to exercise options in the year following IPO completion and 0 otherwise.

• Overall incentives takes the value of 0 when Dirsubstock, Dirownership, Stockplan

and Loansoption take simultaneously the value of 0 and 1 otherwise.23 Since

specific incentives sometimes affect the decisions surrounding an IPO, Overall

incentives allows us to determine their overall effect as well as their simultaneity.

III. 5 Descriptive statistics

Table II presents company descriptive statistics (Panel A) and offering characteristics

(Panel B), IPO costs and money left on the table (Panel C), and market conditions and

aftermarket performance (Panel D).

INSERT TABLE II ABOUT HERE

The average size of the firms, measured by total assets, is $907.75 million. The median is far

lower at $120.97 million, indicating positive skewness. However, the median leverage

(47.14%) is very close to the mean (48.94%). The average post-IPO investment is 6.80%,

more than twice the median of 2.63%.

As it appears in Panel B, the characteristics of our market-adjusted 23 It takes the value of 1 if any of these four variables takes the value of 1.

27

underpricing⎯mean (8.98%), median (1.24) and standard deviation (22.37)⎯are very close

to those observed by Carter et al. (1998): (8.08%), median (2.38) and standard deviation

(17.38). Nominal gross proceeds, turnover and syndicate size exhibit positive skewness as

with firm size. The average underpricing, money left on the table and gross proceeds in our

sample are very close to the average values for 6,816 IPOs over the 2001−2005 period (see

Jay Ritter website: http://bear.cba.ufl.edu/ritter/work_papers/IPOsMarch2006.ppt). The

average rank of lead underwriters is high, 8.0 on Carter and Manaster’s 0-9.1 scale. The

median of 9.1 is the highest rank. For comparison, the average (median) in Corwin and

Schultz (2005) and Habib and Ljungqvist (2001) is respectively 7.67 (8.10) and 7.26 (8.75).

The gross spread includes underwriting fees, management costs and selling concessions. The

mean gross spread is 0.92 (6.04%). The median of 0.90 (6%) is very close. The trend for gross

spread to be exactly 7%, documented by Chen and Ritter (2000),24 is less pronounced in our

sample (52%).

The average waiting period is 113.58 days25, which is lower than the theoretical 120

days mentioned in Draho (2004). The median is even lower (95 days). The waiting period is

highly volatile (79.72), which justifies studying the determinants of its length.

In Panel D we observe that market conditions at the IPO announcement date exhibit

low volatility and a median slightly higher than the mean (respectively 3.89% and 3.65%).

Market conditions are proxied by the return of the market value-weighted index in the 3-

month period leading to the IPO announcement. Let us define mtr as the return of the market

value-weighted index at date t .This return results from a buy-and-hold strategy calculated as

24 The authors documented this trend for over 90% of medium-sized IPOs in the mid to late 1990s. Note that this trend is weaker and affects 60% of Habib and Ljungqvist’s (2001) sample covering the 1991−1995 period. 25 The average is relatively high because there is a minimum administrative delay for preparation of the prospectus, advice on setting the offering terms and shares placing.

28

(1 ) 1mttBHR r= + −∏ .

Panel D also presents two 12-month post-IPO stock price performances.26 The

unadjusted performance exhibits a positive mean (16%) and median (5.74%) and high

volatility (55%). We observe that although the average market-adjusted aftermarket

performance is not negative, it is weak and close to zero (0.67%). The median is negative (-

9.13%) and consistent with the long-run underperformance of IPO firms documented in the

literature. Let us now define itr as the return of the IPO company i on date t and ( )imE r as the

return of the market value-weighted index. The market-adjusted aftermarket performance can

be computed as

(1 ) (1 ( ))i it imt tBHAR r E r= + − +∏ ∏ ,

III. 6 Regression results

This section presents and discusses tests of empirical implications directly drawn from

the model, in particular implications (1) and (2), and carry out further investigations. Our

results are organized into two parts: determinants of the IPO waiting period and consequences

of this delay. In order to ultimately answer the question of who benefits from the delay, our

investigation of the determinants of the IPO waiting period is performed in two steps. The

first step focuses on the relation between waiting period length and underwriting syndicate

size while the second step studies the relation between waiting period length and managers’

and directors’ incentives.

III. 6. 1 Determinants of the IPO waiting period

Let us recall our first hypothesis:

26 A 12-month horizon was selected because it is the longest for which data are available for all offerings in the sample.

29

(I1) Waiting periods increase with syndicate size and downward jump risk (risk of drop in

profit flow). They decrease with time-inconsistent preferences.

We conduct a two-stage least squares (2SLS) regression of the waiting period

determinants, allowing the choice of syndicate size to be endogenous. While the waiting

period may depend on syndicate size, the choice of syndicate size may also depend on how

long firms are willing to wait. The positive and significant coefficient of the estimated Inverse

Mills Ratio (IMR), an endogeneity indicator, comfort the choice of a 2SLS allowing for

simultaneity of the syndicate size choice. Details regarding the computation of the IMR and

the estimation technique of the impact of the estimated IMR on the waiting period can be

found in Appendix II.

Results of the 2SLS regressions are presented in Table III below.

INSERT TABLE III ABOUT HERE

In Panel A of Table III, the average (median) length of the waiting period is 106.43

days (91.5 days) for IPOs with one lead manager, versus 124.73 days (99.5 days) for IPOs

with more than one lead manager. The differences between the means and medians of the two

groups are statistically significant at 1%, suggesting that IPOs with larger syndicates wait

longer, as predicted by our model.

Panel B of the table presents the results of the 2SLS regressions. The estimates allow

for the simultaneity of syndicate size choice. The dependent variable in the first-stage least

squares regression is the natural logarithm of the syndicate size. As observed in Panel A of

Table AII, syndicate size is strongly and positively determined by offering size, lead

underwriter prestige and the NYSE/AMEX listing dummy. The second-stage regressions

30

address the waiting period length issue controlling for potential endogeneity. We present the

model in Column 1 to show that the waiting period does not significantly depend on offering

size, gross spread, price revision, post-IPO risk, firm size or the NYSE/AMEX listing

dummy. The downward jump risk coefficient is insignificant. The model’s F-statistic is only

significant at 10% level despite the significance of syndicate size at the 1% level. Column 2

shows that, controlling for underwriter rank, Syndicate size exhibits a positive and significant

coefficient, as predicted by our model and depicted in Figure 1. This result suggests that a

large syndicate is more likely to set back IPO completion. Note however that, a large

underwriting syndicate size has key advantages to help stock promotion since each syndicate

members has its clients. The coefficient of High-tech is negative and significant, meaning that

firms are not homogeneous with respect to how long they are willing to wait given their type

of preferences. This result is also consistent with our model’s predictions, as shown in Figure

2.

Panel B of Table III also presents the tests of hypotheses 1, 2 and 3. Let us recall these

hypotheses:

(H1) The waiting period decreases with cash pressure.

(H2) The waiting period decreases with post-IPO investment.

(H3) The waiting period decreases with pre-IPO leverage.

We observe, as conjectured, that the coefficient of Cash/Sales is positive and significant at

the 1% level. Also as expected, we find that the coefficient of Investment is negative and

strongly significant (p<0.001 for both). These results indicate that the greater the cash

pressure on firms (low Cash/Sales ratio), the sooner the IPOs are completed. These results

also suggest that although investment is not the main motive for IPOs (see Pagano et al.,

31

1998), it can quicken IPO completion. The sign and significance of Cash/Sales and

Investment are consistent with our model predictions, as shown in Figure 2. In fact, the time-

inconsistent preferences factor may also be reflected by cash pressure and investment since

this factor characterizes firms that bet more on the future than standard firms, have less cash

and invest more (e.g., R&D). Lastly, also as expected, the coefficient of Leverage is negative

and strongly significant (p<0.001 for both) suggesting that when private firms are

overleveraged, IPOs are completed sooner as suggested by the trade-off theory of capital

structure.

Table IV below presents the results of our examination of the link between waiting period

and post-IPO managers’ and directors’ incentives.27

INSERT TABLE IV ABOUT HERE

Panel A shows that when there are managers’ and directors’ incentives or, more

specifically, when managers are remunerated with options or the firm grants them loans to

exercise their options after the firm becomes public, the IPO waiting period is significantly

longer. This result is consistent with Hypothesis 4, which stated that:

(H4) The waiting period increases with post-IPO managers’ and directors’ incentives.

Panel B presents ordinary least squares (OLS) regressions of the natural logarithm of the

waiting period for managers’ and directors’ incentives, controlling for market timing and

aftermarket performance. The results of this multivariate analysis are consistent with those

obtained earlier in Panel A in a univariate setting. Post-IPO managers’ and directors’

incentives are positively associated with the waiting period. However this result seems to be

27 The number of observations for our regressions is reduced due to data availability in the ISS database for managers’ and directors’ incentives.

32

more driven by managers’ incentives since only stockplan and loansoption are significant.

More precisely, firms that remunerate managers of public firms with options and grant loans

so they can exercise options are more likely to be those with a longer IPO waiting period.

This result, in accordance with Hypothesis 4, suggests that the negotiations and the setting of

stock option terms may set back IPO completion. Indeed, managers need to have a good idea

of the full subscription offer price before setting stock option terms such as strike price and

number of options. We also find that the waiting period is shorter in a hot market. This is

consistent with the fact that firms tend to undertake IPOs when market conditions are

favorable (see Ritter, 1984, and Lowry, 2003). However, we find no evidence of a significant

correlation between waiting period and aftermarket performance.

III. 6. 2 Who benefits from IPO waiting period length?

In order to answer this question, this section analyzes the implications of the IPO

waiting period. The first investigation concerns the link between underpricing and the waiting

period. We go on to study the link between the level of heterogeneity in investors’ beliefs and

the waiting period, as well as how the waiting period affects money left on the table, pricing,

the probability of an underwriter switch or of a change in underwriting syndicate size at a

subsequent SEO, and firm stock return at the subsequent SEO date.

A- Effect of IPO waiting period on underpricing

Table V presents the tests of Implication 2, which states that:

(I2) Underpricing decreases as the waiting period lengthens. The relation of underpricing

to syndicate size, downward jump risk and time-inconsistent preferences is undetermined.

INSERT TABLE VI ABOUT HERE

33

In Panel A of Table V, the average (median) level of initial return (underpricing) is

equal to 10.32% (4%) for IPOs with a long waiting period, versus 7.83% (0.36%) for IPOs

with a short waiting period. Although the difference between the means of the two groups is

not statistically significant, the difference between the medians is significant at the 5% level.

The unexpected sign of the finding may be explained by the fact that longer waiting periods

can be a signal of “more difficult” IPOs that need more premiums to convince investors to

participate.

In Panel B of Table V, we run robust least squares regressions for the impact of the waiting

period on underpricing. Surprisingly, we find no evidence of the expected negative relation

between waiting period and underpricing. The waiting period coefficient is negative as

predicted by the model but not significant in either model presented. We find that

underpricing increases with gross spread. Our results confirm the existence of both Hanley’s

(1993) partial adjustment effect and James and Wier’s (1990) leverage effect, as well as a

firm size effect found in earlier literature (e.g., Ritter (1984), Megginson and Weiss (1991),

Lowry and Murphy (2007)). Indeed, the coefficient of the variable Upward price revision is

positive and significant at the 1% level. This result suggests that underpricing is significantly

greater when the offer price exceeds the midpoint of the filing range (Hanley, 1993).

Furthermore, the coefficient for Leverage is negative and significant, which means that prior

credit relationships significantly reduce underpricing because the presence of a credit

relationship reduces uncertainty (James and Wier, 1990). Likewise, the coefficient of

Ln(assets) is negative and significant at the 1% level, which is consistent with the fact that

smaller firms are perceived as riskier, leading to greater underpricing. Lastly, consistent with

the expected relation between underpricing and uncertainty, firms with high downward jump

risk are more underpriced.

34

B- Effects of IPO waiting period on belief heterogeneity, pricing and money left on the

table

This subsection seeks to analyze the relation between waiting period and heterogeneity

in investors’ beliefs. We test whether a shorter waiting period (which implies greater

information asymmetry and higher adverse selection risk) generates higher levels of

heterogeneity in investors’ beliefs about the IPO firm’s future prospects. Following a number

of empirical papers (see, e.g., Bamber, 1987, and Bamber, Barron and Stober, 1997), we use

trading activity to proxy for heterogeneous beliefs among investors. Thus, we expect a

negative impact of the waiting period on the first-day turnover (first-day trading volume

divided by the number of shares issued), consistent with the results of many papers that

examine the correlation between trading volume and information asymmetry (see, e.g.,

Milgrom and Stokey, 1982, and Chae, 2005). This subsection also examines the links between

pricing (defined as pricing at the upper limit of the price range) and waiting period on the one

hand and between money left on the table (MLT) and waiting period on the other. Since the

waiting period is positively associated with syndicate size, which is in turn positively related

to underwriter spreads (Corwin and Schultz, 2005), we expect respectively negative and

positive effects of the waiting period on pricing and MLT. Results are presented in Table VII

below:

INSERT TABLE VI ABOUT HERE

The first column of Table VI presents a robust least squares regression of the first-day

turnover determinants. We find, as conjectured, a negative and significant impact of the

waiting period on the heterogeneity in investors’ beliefs proxied by first-day investors’

trading activity. A natural interpretation of this negative relation is that the information

35

asymmetry and adverse selection risk inherent to short waiting periods increase differences in

beliefs among investors, which in turn generates volume. We also find that heterogeneity in

investors’ beliefs increases with offering size and pre-IPO earnings. Finally, we observe that,

controlling for the offering size, firm size has a negative impact on heterogeneity in investors’

beliefs.

The second column of Table VI reports a logistic regression of IPO pricing: the

dependent variable is the IPO priced at the upper limit of the price range dummy variable.

Although the waiting period exhibits the expected sign, it is not significant. Pricing, like

turnover, is significantly positively and negatively related to offering size and firm size

respectively.

The third column of Table VI presents a robust least squares regression analyzing how

the waiting period affects money left on the table. The waiting period coefficient exhibits the

expected sign but is insignificant. As for turnover and pricing, MLT is significantly positively

and negatively affected by offering size and firm size respectively. Moreover, the STD return

coefficient is positive and significant at the 5% level, suggesting that firms which leave

money on the table are more likely to be volatile.

C- Does the IPO waiting period affect the probability of changing underwriter at a

subsequent SEO?

To be included in the sample, an SEO had to occur within 18 months of the IPO and

be the firm’s first SEO. There are 190 first SEOs, representing about 28% of our initial IPO

sample.28 We test whether issuers with a long IPO waiting period are more likely to change

underwriter at a subsequent SEO. Indeed, we study whether a relatively shorter waiting period

28 Note that this proportion was about 21% in Jegadeesh et al. (1993).

36

increases the lead underwriter’s chance of being retained for a subsequent SEO. Assuming

that the probability of switching lead underwriter is characterized by a logistic distribution,

we conduct logit estimations over a dichotomic variable that takes the value of 1 when the

issuer changes lead underwriter at a subsequent SEO and 0 otherwise.

INSERT TABLE VII ABOUT HERE

Table VII presents the logit regressions estimates. The independent variable of

primary interest is the waiting period. We find in all specifications presented a significant

positive relation between the IPO waiting period and the probability of changing underwriter

at a subsequent SEO. This result indicates that the shorter the IPO waiting period, the less

likely the lead underwriter is to be changed, meaning that lead underwriters may benefit from

a shorter IPO waiting period. Furthermore, consistent with Krigman et al. (2001), Brav and

Gompers (2003) and Ljungqvist and Wilhelm (2005), issuers are less likely to change when

they have a more reputable IPO underwriter and more likely to change when they have a more

reputable SEO underwriter. Also, the longer the time elapsed between the IPO and the SEO,

the more likely issuers are to switch underwriter.

D- Probability of changing syndicate size at a subsequent SEO

Regarding the importance of syndicate size (Corwin and Schultz, 2005) and as further

investigation of the relation between syndicate size and waiting period, we explore the

determinants of the probability of changing syndicate size between the IPO and the

subsequent SEO. As mentioned earlier, studying changes in syndicate size is very different

from focusing on changes in underwriter since the firm can keep the same lead manager but

reduce or increase the size of the syndicate. Precisely, we relate issuing firms’ decision of

whether or not to reduce the syndicate size between the IPO and the first SEO to underwriter

37

changes, IPO and SEO waiting periods and other potential determinants such as IPO

syndicate size, IPO and SEO sizes and ranks. Table VIII reports the coefficients from

multinomial logistic regressions, modeling the decision to reduce, increase or maintain

syndicate size. Positive or negative coefficients in “size reduction” and “size increase”

equations suggest that the independent variable is associated with a higher or lower

probability of choosing to reduce or to increase the syndicate size.

INSERT TABLE VIII ABOUT HERE

Model 1 in Table VIII focuses on how the decision to change syndicate size is shaped

by offering characteristics (initial IPO return, IPO size and IPO gross spread), syndicate

characteristics (IPO syndicate size and IPO underwriter rank) and waiting periods (IPO and

SEO waiting periods and days from IPO to SEO announcement) in particular. The overall

explanatory power of the models is good, in term of the pseudo R2 at 30.17%. Among offering

characteristics, issuers are less likely to reduce syndicate size (scenario 1) and more likely to

increase rather than reduce syndicate size (scenario 3) with a larger IPO. In contrast, the

effect of IPO size on the probability of increasing syndicate size (scenario 2) is not

statistically significant. Furthermore, we find that issuers are more likely to reduce syndicate

size (scenario 1) and less likely to increase it (scenario 2), with a large IPO syndicate. Finally,

we find that the SEO waiting period (time elapsed from SEO announcement to completion)

has a negative and significant impact on the probability of reducing syndicate size and a

positive and significant effect on the likelihood of increasing, rather than decreasing,

syndicate size. Consistent with the strong impact of syndicate size on the waiting period that

we found earlier, these results suggest that firms that reduce syndicate size are more likely to

complete the announced SEO sooner.

38

Model 2 provides results from estimation of the same model, including underwriter

change variables. The model’s general fit improves substantially. For instance, IPO size, IPO

syndicate and SEO waiting period remain strongly significant with the same sign as in

scenarios 1 and 3 while the underwriter change is positively and significantly related to the

likelihood of reducing syndicate size (scenario 1) as well as the likelihood of increasing

syndicate size (scenario 2).

Model 3 provides results from estimation of the same model including SEO size

instead of IPO size, the change to a higher-ranked lead manager dummy and, in particular, the

IPO waiting period. The model’s general fit improves again. The IPO syndicate size and the

SEO waiting period are still strongly significant with the same sign as in scenarios 1 and 3.

Again, we observe that issuers are less likely to reduce syndicate size (scenario 1) and more

likely to increase it (scenario 2) and to increase rather than reduce syndicate size (scenario 3)

with a large SEO. The change for a higher ranked lead manager dummy is only significant in

scenario 2. We conclude that firms that increase syndicate size are more likely to change for a

more prestigious lead manager. Finally, we find that issuers are more likely to reduce

syndicate size (scenario 1) and less likely to increase it (scenario 2) when the IPO waiting

period is longer. This result indicates that the shorter the IPO waiting period, the more likely

the syndicate size is to be maintained or increased rather than reduced.

E- Does the market react at the subsequent SEO to a syndicate size change and the SEO

waiting period?

The results presented earlier show the importance of syndicate size and the

determinants of a syndicate size change between the IPO and the subsequent SEO. These

findings naturally raise the question: Does the market react to a change in syndicate size?

39

Since a longer waiting period is associated with lower adverse selection risk, we also explore

whether long SEO waiting periods are positively related to the first-day market reaction. To

answer these questions we perform robust least squares regressions analyzing how a syndicate

size change and the SEO waiting period affect the adjusted SEO first-day return.29 We control

for SEO size, gross spread, syndicate size, underwriter rank, post-IPO price volatility (STD

return), prospect indicator (Market-to-book), syndicate size and underwriter changes. Results

are presented in Table IX below:

INSERT TABLE IX ABOUT HERE

We find that a syndicate size change does not significantly affect the first-day market

adjusted return. Underwriter change has no effect either. In contrast, we find a strong positive

relation between the SEO waiting period and the first-day market adjusted return. This result

indicates that a longer SEO waiting period is associated with a positive first-day market

reaction. Indeed, as mentioned earlier, longer waiting periods are associated with lower

adverse selection risk. Furthermore, the first-day market adjusted return for the SEO is

negatively and significantly affected by post-IPO price volatility, meaning that at a

subsequent IPO, markets react negatively to higher post-IPO risk.

IV. Summary and conclusion

This paper begins by asking why the IPO waiting period varies so widely across firms.

To answer that question, we propose a model that formalizes the optimal external timing of

IPOs using a real option framework, derive its underpricing implications and examine the

model comparative statics. To the best of our knowledge, this article presents the first model

29 The market value-weighted index return is used for the adjustment.

40

to incorporate underwriting syndicate size (see Corwin and Schultz, 2005), the risk of a drop

in firms’ cash flows due to product market competition (Maksimovic and Pichler, 2001;

Benveniste, Busaba and Wilhelm, 2002) and time-inconsistent preferences to capture firm

characteristics such as those of high-tech firms,30 since these firms place greater value on

future cash flows than present cash flows. This paper is also the first to empirically investigate

the determinants of the IPO waiting period and the implications of this delay.

Results generated by the model reveal that the IPO waiting period increases with

syndicate size and downward jump risk (risk of drop in profit flow due to product market

competition) and decreases with time-inconsistent preferences. The model also leads to the

conclusion that a longer delay leads to less underpricing.

These findings complement the existing literature on IPO timing and the role of the

underwriting syndicate. First, our predictions from the model suggest that a larger syndicate

reduces net IPO proceeds to the private firm, diminishes the incentive to go public and makes

waiting more valuable. On the other hand, the larger the syndicate, the greater the risk of

competition and disagreement between syndicate members, which may set back IPO

completion. In addition, the results indicate that a greater risk of profit drop due to product

market competition will induce private firms to complete their IPO later because of the

information disclosure inherent in IPOs (see Maksimovic and Pichler, 2001; Benveniste,

Busaba and Wilhelm, 2002). These predictions suggest that when private firms value future

cash flows over present cash flows, the IPO will be completed sooner, certainly for

investment motives. Finally, the longer the waiting period, the lower the underpricing return

will be since a long waiting period reduces adverse selection risk and information asymmetry.

Overall, the results of our empirical tests are in line with our model’s predictions. We 30 This follows papers like those of Loughran and Ritter (2004), who separately examined technology intensive firms, and Jaggia and Thosar (2004), who studied high-tech IPOs.

41

find evidence that waiting periods produce information. Indeed, as our model predicted, we

find that syndicate size is positively and strongly correlated to the length of the waiting

period. Also consistent with our model’s prediction, time-inconsistent preferences are

negatively related to the waiting period. Moreover, three factors affect the waiting period:

cash pressure (lack of cash), investment and leverage. These results provide evidence that

cash pressure on private firms will induce them to complete the IPO sooner. Likewise, when

private firms are overleveraged, IPOs are completed earlier, consistent with the trade-off

theory of capital structure. The findings also provide evidence that although investment is not

a significant motive for IPOs as argued by Pagano et al. (1998), investment expedites IPO

completion. In contrast, we find that a downward jump risk indicator has no significant effect

on the waiting period.

Additional investigations reveal that private firms that remunerate managers with

options and provide loans to exercise options are more likely to have a longer IPO waiting

period, which suggests that negotiations of stock option terms may set back IPO completion.

Indeed, managers need to have a good idea of the full subscription offer price before

negotiating stock option terms such as strike price and number of options. In contrast,

directors’ incentives do not significantly affect the IPO waiting period. Furthermore, we find

that waiting periods are shorter in a hot market, which is consistent with the fact that firms

tend to undertake IPOs when market conditions are favorable (see Ritter, 1984, and Lowry,

2003).

Concerning the consequences of the waiting period, we find both Hanley’s (1993)

partial adjustment effect and James and Wier’s (1990) leverage effect as well as a downward

jump risk impact on underpricing but no significant effect of the waiting period. Surprisingly,

our results do not show that underpricing decreases as the waiting period lengthens.

42

Empirical results also show that heterogeneity in investors’ beliefs about the IPO

firm’s future prospects is greater for shorter waiting periods, which are characterized by

higher adverse selection risk and information asymmetry. However, we also find that the

issuer is more likely to switch underwriters when the IPO waiting period is long.

The relation between syndicate size and waiting period is also supported by our

multinomial model estimates of the determinants of a change in syndicate size at a subsequent

SEO. Results indicate (a) that issuers are less likely to reduce syndicate size with a shorter

IPO waiting period, and the SEO waiting period is more likely to be shorter when the

syndicate size is reduced; and (b) that issuers are more likely to increase rather than reduce

syndicate size with a shorter IPO waiting period, and the SEO waiting period is more likely to

be longer when syndicate size is increased rather than reduced.

Finally, our analysis shows the effects of the waiting period on the SEO first-day

market reaction. We find a strong positive relation between the SEO first-day return and the

SEO waiting period, meaning that the longer the SEO waiting period, the better the first-day

market reaction will be, since waiting periods reduce adverse selection risk and information

asymmetry. Furthermore, at the subsequent SEO date, the market reacts negatively to higher

post-IPO risk.

Overall, in light of our findings, we conclude that issuing firms benefit from a shorter

IPO waiting period since it relaxes their cash pressure, balances their leverage and helps

realize investment earlier. Underwriters also benefit from a shorter waiting period as it

increases their chance of being retained for a subsequent SEO. In fact, since directors’

incentives do not significantly affect the IPO waiting period, directors would work in the

interest of the issuing firms to change underwriters at the subsequent SEO when the IPO

waiting period is long. In contrast, investors benefit from longer waiting periods since a

43

longer IPO waiting period reduces heterogeneity in investors’ beliefs. This result is reinforced

in the long run because the market reacts more positively to a longer SEO waiting period.

Moreover, the length of the IPO waiting period can be subject to agency conflicts since unlike

the issuing firms, a longer waiting period may benefit to the manager for his negotiations of

the post-IPO stock option terms.

44

Appendix I

Proposition 1

According to Dixit and Pindyck (1994), the solution to the second-order differential equation

(11) will have the form

( ) .p

p pF A β δλ κ ππ π αλ κ κ

⎛ ⎞+= + ⎜ ⎟+⎝ ⎠

(AI1)

where A and 0β > are constants to be determined. The first term in (AI1) is the solution to

the homogeneous part of (AI1) and the second term is the particular solution to (AI1).

Replacing ( )F π by A βπ in equation (11) yields the nonlinear equation:

21 ( 1) ( ) ( ) (1 ) 02

p p p βσ β β ρ κ β ρ θ θ φ− + − − + + − = . (AI2)

The value of β is obtained as solution to (AI2).

From the smooth pasting condition (14),

( )1 ( )* 1 .m p

m m p p

SA β ψπ δλ κ δλ κπ α

β λ κ κ λ κ κ−⎛ ⎞⎛ ⎞ + +

= −⎜ ⎟⎜ ⎟ + +⎝ ⎠ ⎝ ⎠ (AI3)

Substituting this into the value matching condition gives

( ) ( )1 ( )* 1 * * 1 ( ) ,m p p m

m m p p p p m m

SS C

ψπ δλ κ δλ κ δλ κ π δλ κ πα α α ψβ λ κ κ λ κ κ λ κ κ λ κ κ

−⎛ ⎞ ⎛ ⎞ ⎛ ⎞⎛ ⎞ + + + +− + = − −⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ + + + +⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎝ ⎠

( ) ( )1 ( ) 1 ( )* 1 1* ,m p m p

m m p p m m p p

S SC

ψ ψπ δλ κ δλ κ δλ κ δλ κα απβ λ κ κ λ κ κ λ κ κ λ κ κ

− −⎛ ⎞ ⎛ ⎞⎛ ⎞ + + + +− − − = −⎜ ⎟ ⎜ ⎟⎜ ⎟ + + + +⎝ ⎠ ⎝ ⎠ ⎝ ⎠

( )1 ( )1 1* 1 ,m p

m m p p

SC

ψδλ κ δλ καπβ λ κ κ λ κ κ

−⎛ ⎞⎛ ⎞ + +− − =⎜ ⎟⎜ ⎟ + +⎝ ⎠⎝ ⎠

( )( )1 ( ) 1* .

1 m p

m m p pS

Cψδλ κ δλ κ

λ κ κ λ κ κ

βπβ α −+ +

+ +

⎛ ⎞= ⎜ ⎟− −⎝ ⎠

(AI4)

45

Assumption 1 ensures that the denominator of *π is positive.

Substituting *π into (A4) gives

( )1

1

1 ( )( 1) 1 .m p

m m p p

SA

C

ββ β

β β

ψβ δλ κ δλ κ αβ λ κ κ λ κ κ

−

−

−⎛ ⎞− + += −⎜ ⎟+ +⎝ ⎠

(AI5)

Corollary 1:

Holding all other parameters constant,

i)

( )( )*

1 ( ) 1

00

* * ( ) ( ) 0.( )

m

m m

m p

m m p pS

S SS S S S

δλ κ πλ κ κψδλ κ δλ κ

λ κ κ λ κ κ

π π ψ ψψ

++

−+ ++ +

>>

∂ ∂ ∂ ∂= = >

∂ ∂ ∂ ∂−

ii)

( )( )( )( )1 ( ) 1

1 ( ) 1

* * * .m m p p

m p

m m p p

S

S

AB

ψλ λλ κ κ λ κ κ

ψδλ κ δλ κλ κ κ λ κ κ

π π πδ

−

+ +

−+ ++ +

−∂= − = −

∂ −

Assumption 1 ensures that B is positive. The numerator A is positive if ( )Sψ is small. Since

the fraction of the issue proceeds paid as underwriting spread is small

* 0.πδ

∂<

∂

Figure 2 confirms this sign.

iii) Since the value of β that satisfies (AI2) can only be found numerically, we present

numerical results in Table 1 and Figure 3. These results show that the IPO trigger point *π

increases with σ and this increase is greater for higher jump size φ .

46

Table AI: Dependence of β , *π , φ , andσ

β *π σ

0.5φ = 0.25φ = 0φ = 0.5φ = 0.25φ = 0φ =

0.0 4.51 2.40 1.30 7.18 3.06 1.460.1 3.53 2.18 1.28 7.80 3.30 1.540.2 2.60 1.86 1.24 9.08 3.86 1.740.3 2.09 1.62 1.20 10.73 4.65 2.070.4 1.78 1.47 1.16 12.72 5.62 2.500.5 1.59 1.36 1.12 15.06 6.79 3.050.6 1.46 1.28 1.10 17.76 8.14 3.690.7 1.37 1.23 1.08 20.82 9.70 4.450.8 1.30 1.18 1.07 24.27 11.45 5.310.9 1.25 1.15 1.06 28.11 13.42 6.281 1.21 1.13 1.05 32.34 15.59 7.36

Proposition 2

( )( )

1 1

2*

(1 ( )) 0.* (1 ( ))

m p

m m p p

p

p p

UP S CS C

δλ κ δλ κλ κ κ λ κ κ

δλ κ πλ κ κ

αψπ αψ

+ ++ +

++

−∂= − − <

∂ ⎡ ⎤− −⎣ ⎦

47

Appendix II

Before investigating the determinants of the waiting period, we first study the probability of

choosing a syndicate size with more than one lead manager and analyze the syndicate size

effect on the waiting period. Indeed, the risk of competition between syndicate members

(Corwin and Schultz, 2005) mentioned earlier becomes relevant when there is more than one

lead manager. We then study if the waiting period reveals any incremental information about

syndicate size.

Let siX be a vector of the market information set explaining the choice of syndicate size for

IPO i . The syndicate size variable S takes the value of 1 when there is more than one lead

manager and 0 when there is only one lead manager. Thus, the syndicate size for IPO i is

modeled as follows:

1 ' 00

s si i

iif X u

Sotherwise

θ⎧ + >= ⎨⎩

(AII1)

If certain unobserved characteristics increase the likelihood of choosing a larger syndicate,

thus further lengthening the waiting period, we should find a positive value for sβ in the

following regression:

ˆ* s s ssπ γ β λ ε= + + (AII2)

Under the assumption that siu is normally distributed, sλ is the inverse Mills ratio (IMR)

computed as in Barnow et al. (1981). We define (.)φ as the density probability function. (.)Φ

is the cumulative probability function and [ ].1 is an indicator function such that: [ ]11 1S= = if

1S = and [ ]01 1S= = if 0S = . We have

[ ] [ ]1 0( | , 1) 1 ( | , 0) 1s s s ss S SE u X S E u X Sλ = == = × + = × .

48

We then estimate equation (AII1) using a probit model since siu is assumed normally

distributed.

We then proceed to estimate equation (AII3) using least squares with adjusted standard errors

(Heckman, 1979).

[ ] [ ]1 0

ˆ ˆ( ' ) ( ' )ˆ 1 1ˆ ˆ( ' ) 1 ( ' )

s s

s S Ss s

X XX X

φ θ φ θλθ θ= =

−= × + ×Φ −Φ

(AII3)

Results are presented in Table AII below.

INSERT TABLE AII ABOUT HERE

Panel A of Table AII reports the probit syndicate size choice. The likelihood of

choosing more than one lead manager is strongly and positively determined by offering size

and lead underwriter prestige. We also find significantly larger syndicate sizes as the offer

price exceeds the midpoint of the filing range. IPOs listed on the NYSE or the AMEX are also

likely to positively affect syndicate size. Panel B represents a standard error adjusted least

squares regression for the waiting period. Results reveal a positive and significant coefficient

of the estimated inverse Mills ratio. This result suggests that certain unobserved

characteristics increase the likelihood of choosing a larger syndicate, thus further lengthening

the waiting period.

49

Table AII Syndicate size effect This table presents the results of conditional syndicate size effect on the waiting period. Panel A reports the robust probit syndicate size choice. The dependent variable takes the value of 1 when there is more than one lead manager and 0 when there is only one lead manager. Waiting period is the number of calendar days from the initial filing date to the offer date. Panel B represents the least squares regression for waiting period with the estimated inverse Mills ratio (IMR) as explanatory variable. Offering size is the natural logarithm of the gross proceeds. The gross spread includes underwriting fees, management costs and selling concessions. Jay Ritter’s updated Carter and Manaster (1990) ranks are used as a measure of underwriter reputation. Upward price revision is a dummy variable that takes the value of 1 when the offer price exceeds the midpoint of the filing range and 0 otherwise. Ln(assets) is the natural logarithm of the total assets. Heteroscedasticity-consistent p-values are provided in parentheses. *** and ** indicate a significance level of respectively 1% and 5%. Panel A: Probit model for syndicate size

Coefficient p-value

Intercept Offering characteristics Offering size Gross spread Underwriter prestige Underwriter rank Price revision Upward price revision Firm size Ln(assets) Market NYSE/AMEX listing

-4.831*** 0.458*** 0.302 0.248*** -0.344** 0.029

0.472***

(0.000)

(0.000)

(0.248)

(0.000)

(0.035)

(0.595)

(0.005)

Diagnostics Pseudo R2 Wald

2

χ test: coeff.=0 No. of observations

27.92% 101.75*** (0.000) 485

Panel B: Second-pass regression: Log (1+ waiting period) Intercept Inverse Mills ratio

4.560*** 0.095**

(0.000)

(0.013) Diagnostics R2 F-statistic No. of observations

0.93% 6.28** (0.013) 485

50

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0 0.05 0.1 0.150

5

10

15

20

25

30

35

ψ(S)

π*

Figure 1: The effect of syndicate size ( )Sψ on the critical value *π , measured in millions of dollars (which increases with the IPO waiting period).

1 1.05 1.1 1.15 1.2 1.254

4.5

5

5.5

δ

π*

Figure 2: The effect of time inconsistent preferences or patience factorδ

on the critical value *π , measured in millions of dollars (IPO waiting period).

55

0 0.2 0.4 0.6 0.8 10

5

10

15

20

25

30

35

σ

π*

φ=0.5 φ=0.25φ=0

φ=0.5φ=0.25φ=0

Figure 3: The effect of the drop amplitudeφ in profit flows

on the critical value *π , measured in millions of dollars (IPO waiting period).

0 5 10 15 20 25 30 35 400.228

0.23

0.232

0.234

0.236

0.238

0.24

0.242

0.244

π*

UP:

Und

erpr

icin

g

Figure 4: Underpricing and IPO critical value *π , measured in millions of dollars (IPO waiting period).

56

Table I Definitions and values of model parameters

Parameters Definitions Values δ Time inconsistency preferences or patience factor 1.125

λ Fraction of the issue proceeds received by underwriter

0.1

θ Intensity parameter of the Poisson process 0.1

mρ Discount rate by public investors 0.12

pρ Discount rate by the private firm 0.13

( )Sψ Underwriting spread 0.07

C Fixed direct expenses 1

α Fraction of shares to be sold to public investors 0.2

φ Jump amplitude of the Poisson event 0.25

57

Table II

Descriptive sample statistics The sample covers 690 IPOs retrieved from Bloomberg with data available in the Center for Research in Security Prices (CRSP) daily master files. Panel A tabulates three firm characteristics. Assets is the annual total assets in the fiscal year prior to the IPO. Leverage is the total debt divided by total capital invested, and multiplied by 100. Investment is measured, over the post-IPO year, following Dittmar and Thakor (2007) by capital expenditures to sales ratio. Panel B reports various offering characteristics. The offer price is in $ and the nominal gross proceeds are the total amount issued. Underpricing=First-day return = 100% x (Closing price – offer price)/offer price. Underpricing is adjusted to the market value-weighted index return. First-day turnover is the first-day trading volume divided by the number of shares issued. We use Jay Ritter’s updated Carter and Manaster (1990) ranks as a measure of underwriter reputation on a scale from 0 (lowest) to 9.1 (highest). Underwriting syndicate size is measured by the number of managing underwriters. Waiting period is the number of calendar days from the initial filing date to the offer date. Panel C presents IPO total cost and money left on the table. The gross spread includes underwriting fees, management costs and selling concessions. Money left on the table = number of shares sold x (closing price – offer price). Panel D summarizes market conditions and aftermarket performance. The market conditions are proxied by the return of the market value-weighted index in the 3-month period leading to the IPO announcement. 12-month adjusted performance is post-IPO stock price performance adjusted to the market value-weighted index return.

Variable description

Mean Median Standard deviation

First quartile

Third quartile

Panel A: Firm characteristics Assets, in millions of $ Leverage, in % Investment, in % Panel B: Offering characteristics Offer price Nominal gross proceeds, in millions of $ Underpricing unadjusted return, in % Underpricing adjusted return, in % First-day turnover, in % Carter-Manaster underwriter reputation rank Syndicate size IPO waiting period, calendar days High-tech IPO waiting period, calendar days Non high-tech IPO waiting period, calendar days Panel C: IPO costs and money left on the table Gross spread Money left on the table, in millions of $ Panel D: Market conditions and aftermarket performance Market conditions-3 months (%) 12-month unadjusted performance (%) 12-month adjusted performance (%)

907.75 48.94 6.80

15.23 249.88

9.08 8.98

21.19 8.00 1.51

113.48 111.37 113.92

0.92 15.79

3.65 15.99 0.67

120.97 47.14 2.63

15 130

1.43 1.24

15.34 9.1

1.00 95 91 96

0.90 1.21

3.89 5.74

-9.13

5192.77

648.65 0.13

5.23 351.28 22.41 22.37 30.09 1.77 0.74

79.72 87.86 78.03

0.31 53.03

0.05 0.55 0.59

30.76 3.06

0.9

12 66

0 -0.003

0.06 7.10

1 71 69 72

0.68 0

-1.06 -11.72 -30.06

448.59 89.47 7.16

19.75 275

13.68 13.63 27.53 9.10

2 131 137 129

1.12 14.85

7.43 33.54 20.56

58

Table III Two-stage least squares (2SLS) regressions explaining syndicate size and the waiting period This table presents the results of tests for hypotheses 1, 2 and 3. Syndicate size is the number of lead managers. Waiting period is the number of calendar days from the initial filing date to the offer date. Panel A presents the mean and median values of the waiting period depending on the syndicate size dummy. It also reports p-values of mean comparisons (with unequal variance) and Mann-Whitney comparisons of the waiting period between the two groups. Panel B presents 2SLS regressions explaining syndicate size and waiting period as well as a robust least squares regression of the impact of syndicate size on the waiting period. It also tests the effects of uncertainty, patience factor, leverage and investment on the waiting period. Downward jump risk is defined as the standard deviation of daily jump returns, calculated using both jump and non-jump days over the post-IPO year. The value for the jump return is zero on non jump days. Downward jumps occur when returns are negative and larger in absolute value than the absolute value of the mean of returns over the post-IPO year. The patience factor is proxied by the high-tech firm dummy. The first-stage regression is estimated by robust ordinary least squares (OLS) regression of the natural logarithm of the syndicate size, and the fitted value from this regression is used as the waiting period instrument in the second-stage OLS regression. Leverage is the total debt divided by total capital invested, and multiplied by 100. Investment is measured by the capital expenditures to sales ratio. Ln(assets) is the natural logarithm of total assets. Offering size is the natural logarithm of the IPO gross proceeds. The gross spread includes underwriting fees, management costs and selling concessions. Underwriter rank is Jay Ritter’s updated Carter and Manaster (1990) ranks. Upward price revision is a dummy variable that takes the value of 1 when the offer price exceeds the midpoint of the filing range and 0 otherwise. The NYSE/AMEX listing dummy takes the value of 1 if the IPO is listed on the NYSE or AMEX, and 0 otherwise. Heteroscedasticity-consistent p-values are provided in parentheses. ***, ** and * indicate a significance level of respectively 1%, 5% and 10%. Panel A: Univariate evidence

IPO waiting period Syndicate size

Mean Median No. of observations

No. lead managers =1

No. lead managers >1

p-Value (comparison tests)

106.43

124.73

0.005***

91.5

99.5

0.004***

424

266

Panel B: Multivariate evidence

First stage Second stage

Syndicate size ( S ) IPO waiting period ( *π )

Log(1+ *π ) Log(1+ *π )

Log( S )

(1) (2)

Intercept Offering characteristics Offering size Gross spread Underwriter prestige Underwriter rank Price revision Upward price revision

-0.661*** (0.000)

0.129*** (0.000) -0.015 (0.785)

0.035*** (0.001)

-0.060*

4.974*** (0.000)

-0.033 (0.509) 0.059

(0.603)

-0.039* (0.086)

-0.017

4.848*** (0.000)

-0.027 (0.124)

59

Variables of the model Syndicate size ( S ) (Instrument) Downward jump risk (φ ) High-tech (δ ) Cash pressure and investment Cash/Sales Investment Leverage Leverage Firm size Ln(assets) Market NYSE/AMEX listing Diagnostics R-squared F-statistic No. of observations

(0.086)

0.020* (0.083)

0.168*** (0.000)

37.65%

46.16*** (0.000)

485

(0.797)

0.241*** (0.003) -1.001 (0.855)

-0.009 (0.672)

0.028 (0.702)

2.45% 1.72

(0.093) 474

0.173** (0.047)

-0.181** (0.050)

0.0004*** (0.005)

-1.061*** (0.000)

-0.0001*** (0.000)

6.84% 10.94*** (0.000)

422

60

Table IV IPO waiting period and post-IPO managers’ and directors’ incentives This table presents the results of tests for Hypothesis 4. The dependent variable is the natural logarithm of the waiting period. Panel A presents univariate evidence of the relation between waiting period and post-IPO managers’ and directors’ incentives. Panel B presents the analysis in a multiple regression framework. Hot (cold) market dummy equals 1 for months in which the market level (which is the level of the market index on the last trading day of the month) is in the top (bottom) quintile, and 0 otherwise. Market conditions-3 months are proxied by the return of the market value-weighted index in the 3-month period leading to the IPO announcement. Aftermarket performance is the 12-month post-IPO stock price performance adjusted to the market value-weighted index return. Dirsubstock equals 1 if directors are subject to stock ownership requirements in the year following IPO completion and 0 otherwise. Dirownership equals 1 if directors’ and officers’ ownership as % of shares outstanding is greater than 5 percent but less than or equal to 30 percent in the year following IPO completion (otherwise it is equal to 0). Stockplan takes the value of 1 when the company’s managers are remunerated with options in the year following IPO completion and 0 otherwise. Loansoption takes the value of 1 when the company provides loans to executives for exercising options in the year following IPO completion and 0 otherwise. Overall incentives takes the value of 0 when Dirsubstock and Dirownership and Stockplan and Loansoption take simultaneously the value of 0 and 1 otherwise. There are fewer observations due to data availability in the ISS database. Heteroscedasticity-consistent p-values are provided in parentheses. ***, ** and * indicate a significance level of respectively 1%, 5% and 10%. Panel A: Univariate evidence

IPO waiting period Diff. mean Mean Median p-value

Yes 150 89 Directors’ ownership No 118.08 102

(0.514)

Yes 133.93 115 Directors’ and officers’ ownership (5%-30%) No 114.85 99

(0.052)*

Yes 252.71 229 Stock option plan No 115.89 101

(0.043)**

Yes 133.82 111 Loan for option exercise No 104.65 92

(0.000)***

Yes 131.53 110 Overall incentives No 105.24 92

(0.000)***

61

Panel B: Multivariate evidence

Dependent variable =log(1+IPO waiting period)

Model 1 Model 2

Intercept Marketing timing Hot market dummy Cold market dummy Market conditions-3months Post IPO performance Aftermarket performance Post IPO incentives Dirsubstock Dirownership Stockplan Loansoption Overall incentives Diagnostic R2 F-statistic (coeff.=0) No. of observations

4.540*** (0.000)

-0.285*** (0.000) -0.083 (0.352) 0.234 (0.644)

-0.021 (0.690) 0.152 (0.475) 0.068 (0.305) 0.594*** (0.002) 0.251*** (0.001)

9.91% 7.420***

(0.000) 359

4.564*** (0.000) -0.234*** (0.006) -0.120 (0.184) 0.136 (0.790)

-0.021 (0.683) 0.249***

(0.001)

6.33% 7.610***

(0.000) 366

62

Table V IPO waiting period and underpricing

This table presents the results of tests for Implication 2 of the model. Underpricing=First-day return = 100% x (Closing price – offer price)/offer price. Waiting period is the number of calendar days from the initial filing date to the offer date. Panel A presents the mean and median values of Underpricing depending on the waiting period dummy. It also reports p-values of mean comparisons (with unequal variance) and Mann-Whitney comparisons of the Underpricing between the two groups. Panel B presents robust least squares regressions explaining the impact of the waiting period on Underpricing. It also tests the effects of syndicate size, uncertainty and patience factor on Underpricing. Syndicate size is the number of lead managers. Downward jump risk is defined as the standard deviation of daily jump returns, calculated using both jump and non-jump days over the post-IPO year. The value for the jump return is zero on non jump days. Downward jumps occur when returns are negative and larger in absolute value than the absolute value of the mean of returns over the post-IPO year. The patience factor is proxied by the high-tech firm dummy. Offering size is the natural logarithm of the gross proceeds. The gross spread includes underwriting fees, management costs and selling concessions. Underwriter rank is Jay Ritter’s updated Carter and Manaster (1990) ranks. Upward price revision is a dummy variable that takes the value of 1 when the offer price exceeds the midpoint of the filing range and 0 otherwise. Leverage is the total debt divided by total capital invested, and multiplied by 100. Investment is measured by the ratio of capital expenditures to sales. Ln(assets) is the natural logarithm of total assets. The NYSE/AMEX listing dummy takes the value of 1 if the IPO is listed on the NYSE or AMEX, and 0 otherwise. Heteroscedasticity-consistent p-values are provided in parentheses. ***, ** and * indicate a significance level of respectively 1%, 5% and 10%.

Panel A: Univariate evidence

Underpricing IPO waiting period

Mean Median

IPO waiting period ≥ median

IPO waiting period < median

p-Value (comparison tests)

10.32

7.83

(0.149)

4.00

0.36

(0.019)** Panel B: Multivariate evidence

Underpricing (UP)

(UP1) (UP2)

Intercept Offering characteristics Offering size Gross spread Underwriter prestige Underwriter rank Price revision Upward price revision Variables of the model IPO waiting period (Log(1+ *π ))

-7.911 (0.226)

11.061*** (0.000)

0.642 (0.220)

9.565*** (0.000)

0.244 (0.809)

-12.496* (0.069)

1.995** (0.031)

10.255*** (0.000)

0.451 (0.393)

9.420*** (0.000)

0.285 (0.779)

63

Syndicate size ( S ) Downward jump risk (φ ) High-tech (δ ) Leverage Leverage Firm size Ln(assets) Diagnostics R-squares F-statistic No. of observations

-0.858 (0.315)

225.71** (0.050) 0.306

(0.854)

-0.0005* (0.064)

-1.230** (0.010)

23.94% 16.57*** (0.000)

471

-1.501 (0.120) 261.70** (0.029) 0.088

(0.957)

-0.0005** (0.048)

-1.678*** (0.001)

24.49% 15.00*** (0.000)

471

64

Table VI Turnover, pricing, money left on the table (MLT) and the IPO waiting period This table presents the results of tests for the effects of the waiting period on first-day turnover, pricing and money left on the table. The first regression is a robust OLS regression of the first-day turnover. The second regression is a logistic regression of the pricing, where the dependent variable is the IPO priced at the upper limit of the price range dummy variable. The last regression is a robust OLS one of the money left on the table. Money left on the table = number of shares sold x (closing price – offer price). Offering size is the natural logarithm of the gross proceeds. Waiting period is the natural logarithm of the number of calendar days from the initial filing date to the offer date. Market conditions are proxied by the return of the market value-weighted index in the 3-month period leading to the IPO announcement. Ln(assets) is the natural logarithm of the total assets. High-tech is the high-tech firm dummy. STD return is the standard deviation of a time series of 255 daily raw returns for each IPO. EPS is the earnings per share in the fiscal year prior to the IPO. Heteroscedasticity-consistent p-values are provided in parentheses. *** and ** indicate a significance level of respectively 1% and 5%. Estimation method OLS Logit OLS

Dependent variable Turnover Pricing at the upper limit MLT

Intercept Offering size IPO waiting period Market conditions-3months Ln(assets) High-tech STD return EPS-1*0.01 Diagnostics R2 (pseudo for Logit) F-statistic (Wald

2

χ test: coeff.=0) No. of observations

0.222 (0.119)

0.105*** (0.000) -0.081** (0.046) 0.077 (0.712)

-0.029*** (0.000) 0.070

(0.144) 1.292

(0.423) 0.002***

(0.000)

9.04% 12.58***

(0.000)

452

-2.329** (0.041)

0.751*** (0.000)

-0.177 (0.272)

-1.696 (0.418)

-0.213** (0.014)

-0.054 (0.827) 1.851

(0.824) -0.190

(0.611)

4.87% 12.58***

(0.002)

437

-120.27*** (0.001)

30.99*** (0.000) 1.054 (0.804) -17.40 (0.583)

-4.824*** (0.000) 4.259 (0.417)

466.12** (0.044) -0.059 (0.789)

21.09% 5.100***

(0.000)

451

65

Table VII Does the IPO waiting period affect the probability of an underwriter switch at a subsequent SEO? This table presents the logit regression estimates of the probability of an underwriter switch at a subsequent seasoned equity offering (SEO). The dependent variable is a dummy that is assigned the value of 1 if the firm issues its first seasoned equity within 18 months of the IPO and uses a different lead underwriter from the lead underwriter used in the IPO. Independent variables include Size of SEO, defined as the natural logarithm of the gross proceeds from the SEO. Underwriter rank is Jay Ritter’s updated Carter and Manaster (1990) ranks. Underpricing=First-day return = 100% x (Closing price – offer price)/offer price. Heteroscedasticity-consistent p-values are provided in parentheses. *** and ** indicate a significance level of respectively 1% and 5%.

Dependent variable= 1 if issuer changes lead underwriter at a subsequent SEO

Model 1 Model 2 Model 3

Intercept IPO waiting period Size of SEO IPO underwriter rank SEO underwriter rank Underpricing Log (days from IPO to SEO announcement) Diagnostics Pseudo R2 Wald

2

χ test coeff.=0 No. of observations

-0.625 (0.763) 0.668** (0.021)

-0.888*** (0.000)

-0.579** (0.027)

0.718** (0.049)

13.86% 24.47***

(0.000)

180

-0.604 (0.771)

0.665** (0.022) -0.855*** (0.001)

-0.611** (0.026)

0.140* (0.051)

-0.005 (0.401)

13.76% 24.53***

(0.000)

179

-6.146* (0.069)

0.608** (0.043)

-0.931*** (0.000)

-0.533** (0.026)

0.644** (0.044)

1.127** (0.013)

17.68% 31.70***

(0.000)

180

66

Table VIII Multinomial logistic regressions modeling the decision to change syndicate size This table presents the results of multinomial logistic regressions modeling the decision to reduce, increase or maintain syndicate size between the IPO and the subsequent SEO. Scenarios 1 and 2 represent respectively the decision to reduce and to increase rather than maintain syndicate size (model default: comparison group). Scenario 3 represents the decision to increase rather than reduce syndicate size (model default: comparison group). The dependent variable is -1 for syndicate size reduction, 1 for size increase and 0 for size maintenance. We relate a firm’s switching decision to Offering characteristics, Syndicate characteristics, Underwriter switch and Waiting periods. Underpricing=First-day return = 100% x (Closing price – offer price)/offer price. IPO and SEO are the total amounts issued. The gross spread includes underwriting fees, management costs and selling concessions. Syndicate size is the number of lead managers. Underwriter rank is Jay Ritter’s updated Carter and Manaster (1990) ranks. Waiting period is the natural logarithm of the number of calendar days from the filing date to the offer date. Coefficient p-values are provided in parentheses. ***, ** and * indicate a significance level of respectively 1%, 5% and 10%.

Scenario 1 Scenario 2 Scenario 3

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

Offering characteristics Underpricing Log IPO size Log SEO size IPO gross spread SEO gross spread Syndicate characteristics IPO syndicate size IPO underwriter rank SEO underwriter rank Underwriter switch =1 if underwriter switch =1 if switch for higher ranked Waiting periods IPO waiting period Log (days from IPO to SEO announcement) SEO waiting period Intercept Diagnostics McFadden pseudo-R2

Wald2

χ test (all coeff.=0) No. of observations

-0.037 (0.222) -1.994*** (0.002) 0.987 (0.537) 3.975*** (0.000) 0.208 (0.617) -0.273 (0.761) -1.206*** (0.000) 2.041 (0.769) 30.17% 100.25*** 188

-0.066 (0.122) -2.259*** (0.004) 1.166 (0.522) 5.017*** (0.000) -0.175 (0.758) 2.090** (0.033) -0.082 (0.941) -1.361*** (0.001) 2.583 (0.760) 39.00% 127.99*** 187

-0.058 (0.144) -2.433** (0.021) 3.210** (0.019) 4.513*** (0.000) 0.247 (0.693) 2.126* (0.070) 2.340** (0.046) 0.247 (0.693) -1.494*** (0.006) -10.516 (0.289) 44.87% 129.32*** 173

0.00005 (0.994) 0.107 (0.709) -0.657 (0.359) -1.065** (0.016) -0.066 (0.582) 0.190 (0.647) -0.279 (0.113) 0.775 (0.792) 30.17% 100.25*** 188

0.002 (0.789) 0.357 (0.258) -0.752 (0.304) -1.421*** (0.003) 0.405** (0.049) 1.636*** (0.000) -0.282 (0.554) -0.259 (0.192) -1.902 (0.574) 39.00% 127.99*** 187

-0.005 (0.536) 0.794** (0.044) -1.051* (0.079) -1.747*** (0.003) 0.551** (0.044) 3.484*** (0.000) -0.200 (0.615) -0.500 (0.373) 0.095 (0.748) -3.493 (0.371) 44.87% 129.32*** 173

0.037 (0.228) 2.101*** (0.003 -1.643 (0.334 -5.041*** (0.000) -0.274 (0.519) 0.463 (0.629 0.927** (0.010) -1.266 (0.863) 30.17% 100.25*** 188

0.068 (0.114) 2.617*** (0.001) -1.918 (0.309 -6.439*** (0.000) 0.581 (0.325) -0.453 (0.662) -0.200 (0.863) 1.102** (0.010) -4.485 (0.610) 39.00% 127.99*** 187

0.053 (0.193) 2.433*** (0.003) -3.210*** (0.004) -4.513*** (0.000) 0.304 (0.651) 1.358 (0.274) -2.540** (0.036) -0.126 (0.917) 1.589*** (0.008) 7.023 (0.499) 44.87% 129.32*** 173

67

Table IX Does the market react at the subsequent SEO to a syndicate size change and the SEO waiting period? This table presents the first-day market reaction at the subsequent SEO to syndicate size change between the IPO and the first SEO and to the SEO waiting period. The dependent variable is the market adjusted SEO first-day return which is the difference between the first-day return and that of the market value-weighted index. The two independent variables of primary interest are the SEO waiting period and syndicate size reduction dummy. SEO size is the natural logarithm of the gross proceeds. The gross spread includes underwriting fees, management costs and selling concessions. Syndicate size is the number of lead managers. Underwriter rank is Jay Ritter’s updated Carter and Manaster (1990) ranks. Waiting periods is the natural logarithm of the numbers of calendar days between the filing date and the offer date. STD return is the standard deviation of a time series of 255 daily raw returns for each IPO. Market-to-book is the monthly market-to-book ratio prior to the SEO. Heteroscedasticity-consistent p-values are provided in parentheses. *** and ** indicate a significance level of respectively 1% and 5%.

Dependent variable: Market adjusted SEO first-day return Model 1 Model 2 Model 3

Offering characteristics Log SEO size SEO gross spread Syndicate characteristics SEO syndicate size SEO underwriter rank Waiting periods SEO waiting period Risk STD return Prospect indicator Market-to-book Syndicate size and underwriter switch =1 if syndicate size reduced =1 if switch for lower ranked Intercept Diagnostics R2 F-statistic No. of observations

-0.004 (0.338) 0.005

(0.437)

0.003 (0.480)

0.009*** (0.007)

-0.253**

(0.022)

0.0002 (0.420)

-0.010 (0.598)

5.39%

2.97***

169

-0.003 (0.569) 0.004

(0.485)

-0.001 (0.800)

0.008**

(0.013)

-0.252** (0.020)

0.0002 (0.438)

-0.003 (0.749)

-0.005 (0.786)

5.26% 2.39**

168

-0.004 (0.352) 0.005

(0.440)

0.003 (0.496)

0.009*** (0.007)

-0.255**

(0.019)

0.0002 (0.437)

0.001 (0.897)

-0.010 (0.606)

5.42% 2.56**

169