A Abhyankar HC Chen, And KY Ho (2005) the Long-Run Performance of Initial Public Offering, Sotchastic Dominance Criteria

8/6/2019 A Abhyankar HC Chen, And KY Ho (2005) the Long-Run Performance of Initial Public Offering, Sotchastic Dominance Criteria

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Working Paper

The Long-Run Performance of Initial Public Offerings:

Stochastic Dominance Criteria

Abhay Abhyankar+

Hsuan-Chi Chen++

Keng-Yu Ho+++

March, 2005

Abstract

We examine the long-run performance of IPOs using the idea of stochastic dominance. The analysis is a first

attempt using a non-event study methodology to evaluate long-horizon performance. We find that there is no

first-order stochastic dominance relation between the IPO portfolio and the benchmark of a broad index or a

portfolio including either small size or low book-to-market stocks. However, those benchmarks second-order

stochastically dominate the IPO portfolio. When using a portfolio including both small size and low

book-to-market stocks as benchmark, there is a clear dominance of the IPO portfolio over the benchmark for both

first- and second-order stochastic dominance tests. These results generally imply that the question of assessing

portfolio performance between IPO firms and benchmark portfolios depends critically on the specific construction

or the cumulative distribution function of the benchmark portfolios, and potentially explain the extent of sample

dependent results in the literature.

Keywords: Stochastic Dominance; Initial Public Offerings; Long-Run Performance

JEL Classification: D81; G11; G30


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1. Introduction

There is large literature on long-run abnormal stock price performance following corporate events.

For initial public offerings (IPOs), Ritter (1991) finds an average underperformance of 27%, relative to

matched non-IPO firms, over a three-year post-offer period.1 However there is some debate about the

extent of this underperformance. For example, Brav, Geczy, and Gompers (2000) and Eckbo and Norli

(2004), find that the magnitude of the underperformance is small and not statistically significant. There

is a general consensus that the measurement of long-run abnormal returns, using an event study approach,

is fraught with many econometric difficulties.2 Some recent studies question whether the issue of IPO

underperformance could be resolved using an event study framework (see Schultz, 2003, Dahlquist and

De Jong, 2003, and Viswanathan and Wei, 2004). In a careful study, Viswanathan and Wei (2004) show

that expected long-run abnormal returns using an event study methodology are negative in any fixed

sample. Furthermore, they show that the statistical tests used in long-horizon event studies have low

power when endogenous variation in the number of events is correctly accounted for. Given these

findings it is of great interest to study long-run abnormal performance using an alternative methodology

for comparing IPO firm returns to commonly used benchmark portfolio returns.

In traditional long-run event studies, abnormal returns to a portfolio long in IPO firms and short in the

benchmark portfolio are computed and their economic and statistical significance are analysed. Our

main purpose in this paper is to explore, using the idea of stochastic dominance, whether investors with

specific preferences would choose to invest in an IPO portfolio relative to a set of benchmark portfolios

commonly used in the literature.3 We therefore compare whether the cumulative distribution of the


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returns to an IPO portfolio stochastically dominate that of a benchmark portfolio. There are several

advantages to using the idea of stochastic dominance. First, we can compare the entire return

distributions of the event and benchmark portfolios instead of just the mean portfolio return. More

importantly, we do not need to specify an asset pricing model to estimate expected returns. Finally, we

can allow for simple assumptions about investor preferences in the comparison of IPO firm portfolios

versus benchmark portfolios; for example, non-satiation in the case of first-order stochastic dominance

(FOSD) and risk aversion in the case of second-order stochastic dominance (SOSD). This is important

since the view of investors towards various benchmarks depends crucially on their risk preferences and

investment goals.

Our main results are as follows. First, we find no evidence of any first-order stochastic dominance

relation between the IPO portfolio and a broad index benchmark portfolio or a benchmark portfolio of

either small size or low book-to-market stocks. Second, we find that all of these benchmark portfolios

second-order stochastically dominate an IPO portfolio. Third, we find, using both first- and

second-order stochastic dominance tests, a clear dominance of the IPO portfolio over a benchmark

portfolio that includes both small size and low book-to-market stocks. In other words, our results imply

that an investment in a portfolio of IPO stocks is preferred to one in a portfolio of non-IPO stocks having

similar firm characteristics if investors prefer more wealth to less (first-order stochastic dominance) or are

risk averse (second-order stochastic dominance). Our main results remain robust to a variety of

partitions of our data set. We find, for example that our main results remain unchanged even when we

exclude the internet bubble period from sample. Further, we also find that our results are largely

unchanged even when we divide the IPO sample into venture-backed and non-venture backed


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dominance. In Section 4 we describe our empirical results, and Section 5 concludes the paper.

2. Review of the Prior Research

Comprehensive surveys of the literature on long-run stock price performance of firms after

corporate events are available in Fama (1998) and Ritter (2003). Here we provide a brief and selective

review of prior research on the long-run performance of IPOs.

Ritter (1991) is the first to study the long-run performance of firms following IPOs. He finds that

the three-year average buy-and-hold abnormal return of IPO firms is -27.39% relative to a portfolio of

size/industry matched firms. Ritter (1991) further reports that, in his sample, small issuers rather than

larger firms are the worst performers. In a follow-up study, Loughran and Ritter (1995) find that the

annual average buy-and-hold abnormal returns are -6.70% for IPO firms relative to size matched

benchmark firms. Over a five-year period they find that the IPO issuers underperform non-issuers of

similar size by 50.70%.

However, other authors find little or no evidence of underperformance following IPOs. For example,

Brav, Gzecy, and Gompers (2000) find an equally-weighted buy-and-hold abnormal return of 6.60% and a

value-weighted buy-and-hold abnormal return of 1.40% over five years for IPO issuers relative to a

size/book-to-market benchmark portfolio. They also report an average monthly abnormal return of

-0.37% for an equally-weighted and -0.11% for a value-weighted IPO portfolio using a calendar-time

approach. Eckbo and Norli (2004) also find no evidence of long-run underperformance for IPO firms

when they use both unconditional and conditional factor models to estimate expected returns.

In a recent review, Ritter and Welch (2002) use IPO data from 1980-2001 and find a three-year

buy-and-hold abnormal return of -5.10% relative to a size/book-to-market matched firm. However,


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sample period studied.

Empirical researchers face many methodological problems when using the event study approach to

measure abnormal performance over long horizons. The first is the effect on standard statistical tests of

the non-normality of the long-run abnormal returns. Several authors, for example Lyon, Barber, and Tsai

(1999), Mitchell and Stafford (2000), Ang and Zhang (2002), and Bacmann and Dubois (2002) among

others, have addressed this issue. A second problem is the choice of a model for expected returns (see

Eckbo, Masulis, and Norli, 2000 and Eckbo and Norli, 2004). Finally, empirical researchers also need to

address the question of whether to use value-weighted versus equally-weighted portfolios for the event

firms (see Fama, 1998) and how to deal with cross-correlations across firms in event time (see Fama,

1998 and Mitchell and Stafford, 2000) that affect statistical inference.

Several recent papers have raised issues about the application of the event study approach to the

analysis of abnormal performance over long horizons. For example, Schultz (2003) argues that firms are

more likely to issue equity when the market valuation is high and this result in equity sales being

concentrated at peak markets even though companies cannot determine these peaks ex-ante. He terms

this as pseudo market timing. Schultz then shows, using a simple example and simulations, that pseudo

market timing results in the probability of observing long-run underperformance ex-post far exceeding

50%. Building on Schultz (2003), Viswanathan and Wei (2004) study the effect of endogenous events

(like IPOs) on the measurement of long-run abnormal returns in an event study framework. They

provide a formal proof that when returns predict events, the expected event abnormal return in any fixed

sample is negative. They also find that long-run event studies have low power when endogenous

variation in the number of events is correctly accounted for. A general conclusion made from these


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Barber, and Tsai (1999) note, the measurement problems in this approach are treacherous and the

econometric problems make inference difficult. In addition, recent work by Viswanathan and Wei (2004)

casts doubts on whether event study methodology would be able to resolve the issue of long-term

abnormal performance following IPOs. In this paper therefore we turn to an alternative method to study

the relative performance between an IPO firm portfolio and a benchmark firm portfolio based on the idea

of stochastic dominance.

3. Data and Methodology

3.1. Data

Our sample of IPO firms is collected from Thomson Financial Securities Data (SDC) U.S. Common

Stock Initial Public Offerings database. It consists of 6,961 IPOs over the period 1977-2002. The

sample IPO firms meet the following criteria: (1) The IPOs involve common stocks only. Consistent with

previous IPO research, we exclude unit offers, real estate investment trusts (REITs), closed-end funds,

American Depositary Receipts (ADRs), and reverse leveraged buyouts. (2) The IPO firms have return

data in the Center for Research in Security Prices (CRSP) database. (3) The offer price is greater than or

equal to $5. We present in Figure 1 the distribution of the number of IPOs and the aggregate amount of

gross proceeds.

We construct the IPO portfolio, used in our stochastic dominance tests, as follows. For a given month,

we calculate the return on the 3-year calendar-time IPO portfolio by including all the IPOs that have gone

public during the prior 36 months.4 To avoid the impact of underpricing, we do not include the return of

the first trading month after the firm just goes public. Given our sample period, we are able to analyse

separately the period 1980/07-1998/12 that excludes the internet bubble period from 1999/01-2002/12.


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IPOs without the association of prestigious underwriters based on whether the Carter and Manaster ranks

of leading underwriters are greater than 8 (see Carter and Manaster, 1990). The updated underwriter

reputation rank is collected from Carter, Dark, and Singh (1998) and Loughran and Ritter (2004). 5 The

underwriter rank ranges from 0 to 9 and is based on the hierarchy of tombstone announcements.

We present, in Table 1, descriptive statistics of IPO calendar-time portfolio returns and the

corresponding returns of six benchmark portfolios: (i) the CRSP NYSE/AMEX/NASDAQ

value-weighted index, (ii) the Nasdaq Composite index, (iii) the Fama-French smallest size decile

portfolio, (iv) the Fama-French lowest book-to-market ratio decile portfolio, (v) the Fama-French smallest

size/lowest book-to-market ratio quintile portfolio, and (vi) the Fama-French smallest size/lowest

book-to-market ratio decile portfolio. We find that the mean IPO portfolio return is 0.96% per month for

all the IPOs during 1980/07-2002/12. The venture backed IPOs and non-venture backed IPOs have

similar mean returns, but non-venture-backed IPO portfolio returns are less volatile. Finally, IPOs

associated with prestigious underwriters have higher mean returns compared to the IPOs associated with

non-prestigious underwriters but both portfolio returns have similar standard deviations.

3.2. Methodology

We begin with a brief description of stochastic dominance relations as applied in our specific

context to compare the cumulative return distributions from an IPO firm portfolio and a set of benchmark

portfolios. Next we describe the statistical tests used in our empirical work.

Decision-making under uncertainty concerns the choice between random payoffs and is an important

topic in economics and finance. The idea of stochastic dominance offers a general decision rule

provided the utility functions share certain properties. Specifically, we study whether, given investor


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commonly used in the long-run event studies.6 In other words, we examine whether an investor with

specific preferences prefers a portfolio of IPO firms relative to an investment in a benchmark portfolio.

We compare the cumulative return distributions of our two candidate portfolios using the first two

orders of stochastic dominance. These are defined as follows. A cumulative distribution function G is

said to first- and second-order stochastically dominates a cumulative distribution function distribution F

if:

);();( 11 FzGz , (1)

);();( 22 FzGz , (2)

wherezis the joint ordered data points of the two samples and where:

)();(1 zFFz = , (3)

, (4) ==zz

dtFtdttFFz0

10

2 );()();(

I1(z;G) and I2(z;G) are analogues of Equation (3) and (4) in the case of the cumulative distribution

function G.

The economic intuition behind the two orders of stochastic dominance is as follows. First order

stochastic dominance, as in Equation (1) above, implies that the cumulative density function G is

everywhere to the right of cumulative density function F. In other words, investors prefer G to F

regardless of their risk preferences as long as their utility function is monotonically increasing, i.e., more

wealth is better than less. Under second order stochastic dominance, we see from Equation (2), that the

area under G is everywhere smaller than that under F. In other words, investors who prefer G to F are

required to be risk-averse, i.e., investors with monotonically increasing and concave utility function.


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Kolmogorov-Smirnov (K-S) test that is commonly used in the statistics literature to compare sample

distributions. 7 The null hypothesis, in these tests, is that cumulative distribution function G

stochastically dominates cumulative distribution functionFfor thejth order (this hypothesis also includes

the case where the two distributions are equal everywhere) while the alternative is that stochastic

dominance fails at some points. These hypotheses can be more compactly written as:

H0: zFzGz jj allfor);();(

, (5)

: zFzGz jj somefor);();( > . H1 (6)

ns) to be ranked. Linton, Maasoumi, and Whang (2004) propose the following test

statistic:

The Barrett and Donald (2003) test assumes that the returns are i.i.d. while Linton, Maasoumi, and

Whang (2004) tests can accommodate serial correlation in the data and general dependence among the

prospects (distributio

));();((sup FzGzNSD jjz

j = , (7)

where the operator Ij can be shown as:

=

=

==N

i

j

ii

N

i

Xjj XzzXjN

zN

Fzi

1

1

1

))((1)!1(

11)1;(

1);( , (8)

=

=

==N

i

j

ii

N

i

Yjj YzzYjN

zN

Gzi

1

1

1

))((1)!1(

11)1;(

1);( . (9)

A key difference between the Linton, Maasoumi, and Whang (2004) and Barrett and Donald (2003)

tests lies in the method used for constructing empirical p-values. Specifically, Barrett and Donald (2003)

use the multiplier and bootstrap methods to obtain simulated p-values while Linton, Maasoumi, and


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dependence and for autocorrelation in the returns and in this paper we rely on results based on these tests

since Table 1 shows that the portfolio returns are serially correlated. The Linton, Maasoumi, and Whang

(2004) subsampling method requires computing (N-b+1) times the test statistic for subsamples of size b

and they show that:

1,...,1for));();((sup ,,, +== bNiFzGzbSD ijijz

The subsampling procedure randomly chooses a block of observations from the original data rather

than a number of individual observations and is thus able to account for data dependency

ij . (10)

. The

es for rejecting the null hypotheses are:

RejectH0 if

approximate p-values and the decision rul

+

=

+

1

1

, )(1

1

1~bN

i

jijj

N

SDSD

b

p , (11)

wher

plot of empirical p-values over a

we follow this in our work.

4.

etween 2

e is the specified significance level.

As Linton, Maasoumi, and Whang (2004) highlight, choosing the subsample size is important but

difficult since a subsample size good for size distortion is not good for statistical power. In empirical

applications Linton, Maasoumi, and Whang (2004) recommend using a

range of subsample size and

Empirical Results

We now turn to the results of the statistical tests for stochastic dominance between the IPO portfolio

relative to a set of benchmark portfolios using calendar-time returns. We focus our empirical analysis on

results based on the test for stochastic dominance in Linton, Maasoumi, and Whang (2004). We choose

the range for the subsample size b, required for the Linton, Maasoumi, and Whang tests, to be b


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4.1.

n the two portfolio returns.

il in the following subsections.

4.1.

Results from the Whole IPO Sample during 1980-2002

We present, in Table 2, results of our tests for first- and second-order stochastic dominance between

the IPO portfolio using all IPOs during 1980/07-2002/12 and each of a set of benchmark portfolio returns.

Our tests follow a two-step procedure: First, we test whether the benchmark portfolio stochastically

dominates the IPO portfolio return. Second, we report p-values of tests for the converse hypothesis, i.e.,

whether the IPO portfolio stochastically dominates the benchmark portfolio. The results of our

statistical tests can be interpreted as follows. Suppose we fail to reject the first step that the benchmark

portfolio stochastically dominates the IPO portfolio but reject in the second step that the IPO portfolio

stochastically dominates the benchmark portfolio, we can then conclude that the benchmark portfolio

stochastically dominates an IPO portfolio.10 However if we reject or fail to reject both steps of the test,

we can only conclude that there is no stochastic dominance relation betwee

We discuss the empirical results in more deta

1 First-Order Stochastic Dominance

We begin with tests for first-order stochastic dominance (FOSD). Figure 2 shows the FOSD relation

and empirical p-values between the IPO portfolio and each of the six benchmarks. When using two

broad indices there is no evidence of a FOSD relation between the IPO portfolio and the CRSP

value-weighted (VW) index or Nasdaq Composite index. Our results imply that the IPO and the

benchmark cumulative return distribution functions cross-over at some points. Hence, for investors that

prefer more wealth to less (i.e., for the case of first-order stochastic dominance), comparing the mean

portfolio returns using traditional measures may not fully reflect the difference between the IPO portfolio


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Next, we test for FOSD between the IPO portfolio return and the two benchmark portfolios: (i) the

Fama-French smallest size decile (Size D1) portfolio and (ii) the Fama-French lowest book-to-market

ratio decile (BTM D1) portfolio.11 We find that for both the null hypothesis and the converse null

hypothesis the p-values are statistically significant at the 5% level. These results imply that there is no

FOSD relation between the IPO firm portfolio and the two Fama-French portfolios. In other words,

investors that only prefer more wealth to less would be indifferent between the returns to an investment

eith

prefer an IPO portfolio to a portfolio consisting of both small size and low book-to-market

rati

er in an IPO or in a portfolio consisting of small size or low book-to-market ratio stocks.

We note that Brav, Geczy, and Gompers (2000) find that IPO firms are likely to be firms that are

small in size and have low book-to-market ratios. We therefore use benchmarks that proxy for firms

with these attributes. We use the following two Fama-French portfolios for this purpose; the smallest

size/lowest book-to-market ratio quintile (Size/BTM Q(1,1)) portfolio, and the smallest size/lowest

book-to-market ratio decile (Size/BTM D(1,1)) portfolio. In contrast to the results using the previous

four benchmarks, we find that the IPO portfolio significantly dominates the Fama-French size/BTM

Q(1,1) and D(1,1) portfolios in the first order. These results imply that investors that prefer more wealth

to less would

o stocks.

Overall, we find that there is no stochastic dominance relation between an IPO portfolio relative to a

broad index portfolio or a portfolio that includes either small size or low book-to-market stocks.

However, there is a clear first-order stochastic dominance relation of the IPO portfolio over a portfolio

that contains both small size and low book-to-market stocks. In other words, our results imply that an


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Fam -French Size/BTM portfolios.a

4.2

t our main results.

4.3

d or non-venture backed IPOs, respectively. We discuss

s.

4.3.

Results from the IPO Sample Excluding the Internet Bubble Period

We analyse for stochastic dominance a sub-sample of IPO stocks and benchmark portfolios over the

period 1980/07-1998/12 that excludes the internet bubble period. We do this sub-period analysis as a

robustness check. Table 3 shows that our main results remain qualitatively similar to those for the full

sample period, 1980/07-2002/12. However, there are some differences between the performance of IPO

portfolios relative to the benchmarks for the full sample period and for the period prior to the internet

bubble. For example, using the Nasdaq Composite index and the Fama-French Size D1 portfolio as

benchmarks, we find that, during 1980-1998, there is no SOSD relation between the IPO portfolio and the

benchmarks, but these two benchmarks SOSD the IPO portfolio during 1980-2002 period. In general

however we conclude that excluding the internet bubble period does not affec

Results from Venture Backed IPOs and Non-Venture Backed IPOs

Tables 4 and 5 report the first-order and second-order stochastic dominance relation between each of

the benchmarks and portfolios of venture backe

the results further in the following subsection

1 First-Order Stochastic Dominance

Figure 4 shows the first-order stochastic dominance (FOSD) relation and empirical p-values between

the venture backed IPO portfolio and each of the six benchmarks. We find that there is no FOSD

relation between the venture backed IPO portfolio and each of the following four benchmarks: CRSP VW

index, Nasdaq Composite index, the Fama-French Size D1 portfolio, and the Fama-French BTM D1

portfolio. The findings suggest that investors who only prefer more wealth to less would be indifferent


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Size/BTM D(1,1) portfolio. These results imply that investors who only prefer more wealth to less

would prefer an IPO portfolio consisting of venture-backed firms to a portfolio consisting of both small

size

ealth than less would choose non-venture IPOs

rath

portfolios in respect of their first-order stochastic

4.3.

and low book-to-market ratio stocks.

Figure 5 shows the FOSD relation and empirical p-values between the non-venture backed IPO

portfolio and each of the six benchmarks. We find that using the first four benchmarks of broad indices

and portfolios consisting of either small size or low book-to-market stocks, there is no FOSD relation

between the non-venture backed IPO portfolio and each of the benchmarks. We note that such support

of no FOSD relation is weak when we use the Fama-French BTM D1 portfolio as benchmark. However,

we find FOSD of non-venture backed IPO portfolio over both Fama-French Size/BTM Q(1,1) and D(1,1)

portfolios, which implies that investors, who prefer more w

er than portfolios constructed by small growth stocks.

To summarize, our general conclusion based on the above results is that we find little difference

between venture backed and non-venture backed IPO

dominance relations to each of the six benchmarks.

2 Second-Order Stochastic Dominance

Figure 6shows the results for tests of second-order stochastic dominance (SOSD) relation between

the venture backed IPO portfolio and each of our six benchmark portfolios. We find that the venture

backed IPO portfolio is stochastically dominated in the second order by each of the following four

benchmarks: CRSP VW index, Nasdaq Composite index, the Fama-French Size D1 portfolio, and the

Fama-French BTM D1 portfolio. These results suggest that risk-averse investors would choose a broad

index or a portfolio including small size or low book-to-market ration stocks rather than the venture


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prefer a venture-backed IPO portfolio to a portfolio consisting of both small size and low book-to-market

ratio stocks. In their Table I, Brav and Gompers (1997) report that venture-backed IPOs underperform

various benchmarks except for the size and book-to-market portfolio. Our stochastic dominance tests

are

dominance tests are overall consistent with their results except

for th

in terms of second-order stochastic dominance relations to each of the six benchmark

4.4

restigious

e results furthermore in the following subsections.

overall consistent with their results using IPOs from the early 1970s to 1992.

Figure 7 shows the SOSD relation and empirical p-values between the non-venture backed IPO

portfolio and each of the six benchmarks. We find that using the first four benchmarks of broad indices

and portfolios consisting of either small size or low book-to-market stocks, there is a SOSD relation of

benchmarks over the non-venture backed IPO portfolio, except for the case of Nasdaq Composite index.

However, our results show that the non-venture backed IPO portfolio SOSDs both Fama-French

Size/BTM Q(1,1) and D(1,1) portfolios. In other words, investors who are risk averse would choose a

non-venture IPO portfolio to a portfolio consisting of small growth stocks. Similarly, Brav and Gompers

(1997) report that nonventure-backed IPOs underperform various benchmarks except for the size and

book-to-market portfolio. Our stochastic

e case of Nasdaq Composite index.

In general, we find that there is little difference between venture backed and non-venture backed

IPO portfolios

portfolios.

Results from IPOs Associated with Prestigious and Non-Prestigious Underwriters

Tables 6 and 7 present the first-order and second-order stochastic dominance relation between each

of the benchmarks and IPO portfolio associated with prestigious underwriters or non-p

underwriters, respectively. We discuss thes


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benchmarks: CRSP VW index, Nasdaq Composite index, the Fama-French Size D1 portfolio, and the

Fama-French BTM D1 portfolio. The findings suggest that investors, that only prefer more wealth to

less, would be indifferent between an IPO portfolio of firms associated with prestigious underwriters and

our benchmark portfolio. In contrast, we find that an IPO portfolio consisting of firms that have

prestigious underwriters significantly FOSDs both the Fama-French Size/BTM Q(1,1) and D(1,1)

portfolios. These results imply that investors, who only prefer more wealth to less, would prefer an IPO

por

lth to less, would choose non-prestigious IPOs rather than portfolios constructed by

sma

riter

dominance relations to each of the six benchmarks.

4.4.

tfolio to a portfolio consisting of both small size and low book-to-market ratio stocks.

Figure 9 shows the results for FOSD relation between the IPO portfolio consisting of firms with

non-prestigious underwriters and each of our six benchmark portfolios. We find that using the first four

benchmarks of broad indices and portfolios consisting of either small size or low book-to-market stocks,

no evidence of any FOSD relation between the non-prestigious underwriter IPO portfolio and each of the

benchmarks. We note that the support for no FOSD relation is weak when using Nasdaq Composite

index as benchmark. However, we find that an IPO portfolio associated with non-prestigious

underwriters FOSDs Fama-French Size/BTM Q(1,1) and D(1,1) portfolios. This implies that investors,

who prefer more wea

ll growth stocks.

To sum up, we find little difference between prestigious underwriter and non-prestigious underw

IPO portfolios in regard to first-order stochastic

2 Second-Order Stochastic Dominance

Figure 10 depicts the results of our tests for the SOSD relation between the prestigious underwriter

IPO portfolio and each of our six benchmarks. We find that an IPO portfolio associated with prestigious


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underwriter IPO portfolio. Similarly, Carter, Dark, and Singh (1998) report that IPOs associated with

prestigious underwriters (CM rank not less than 8) underperform CRSP VW index by 12.6% using the

IPO sample from 1979 to 1991. In contrast, we find that prestigious underwriter IPO portfolio SOSDs

both the Fama-French Size/BTM Q(1,1) and D(1,1) portfolios. These results imply that investors who

are risk-averse would prefer an IPO portfolio than a portfolio consisting of both small size and low

book-to-market ratio stocks. In other words, the IPO stocks are preferable to non-IPO stocks with

sim

uld choose non-prestigious underwriter IPOs rather than portfolios

consi

folios with regard to their second-order stochastic dominance relations to each of the

b

ilar characteristics.

Figure 11 shows the results of our tests for the SOSD relation between the non-prestigious

underwriter IPO portfolio and each of the six benchmarks. When using the first four benchmarks of

broad indices and portfolios consisting of either small size or low book-to-market stocks, there is a SOSD

relation of benchmarks over the IPO portfolio associated with non-prestigious underwriters. Carter,

Dark, and Singh (1998) report that IPOs associated with non-prestigious underwriters (CM rank less than

8) underperform CRSP VW index by more than 26% using IPOs from the period 1979-1991.

Furthermore, using Fama-French Size/BTM Q(1,1) portfolio as benchmark, we find that there is no

SOSD relation between the IPO and benchmark portfolios. However, we find evidence of SOSD of

non-prestigious underwriter IPO portfolio over the Fama-French Size/BTM D(1,1) portfolio implying that

investors, who are risk averse wo

sting of small growth stocks.

In summary, we find little difference between prestigious underwriter and non-prestigious

underwriter IPO port

six enchmarks.


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statistical tests for stochastic dominance. There are several distinct advantages of using the idea of

stochastic dominance to evaluate relative returns to an event firm and a benchmark portfolio as is done in

long-run event studies. First, we are able to compare the entire return distributions of an IPO portfolio

and a benchmark portfolio using stochastic dominance criteria rather than only the mean or median

returns as seen in the traditional event studies. Second, the stochastic dominance approach does not

require the use of a specific asset pricing model to correct for risk. Finally, we can incorporate simple

risk

y, as a robustness check, our main results do not change when we exclude the internet

bub

preferences, such as non-satiation or risk aversion, while comparing the portfolio returns.

Our main results are as follows. First, we find that there is no first-order stochastic dominance

relation between the IPO portfolio and the benchmark of a broad index or a portfolio including either

small size or low book-to-market stocks. We further find that those benchmarks second-order

stochastically dominate the IPO portfolio. However, when we use a portfolio including both small size

and low book-to-market stocks as benchmark, there is a clear dominance of the IPO portfolio over the

benchmark for both first- and second-order stochastic dominance tests. In other words, our results imply

that an investment in a portfolio of IPO stocks is preferred to one in a portfolio of non-IPO stocks having

similar firm characteristics if investors prefer more wealth to less (first-order stochastic dominance) or are

risk averse (second-order stochastic dominance). In general, our results imply that the question of

assessing portfolio performance between IPO firms and benchmark portfolios depends critically on the

specific construction or the cumulative distribution function of the benchmark portfolios. This could

potentially explain the extent of sample dependent results in the literature highlighted by Ritter and Welch

(2002). Finall

ble period.


20/41

non-venture backed IPOs seem to dominate the benchmark slightly more than the venture backed IPOs do.

As for the case of underwriter reputation, our results again indicate that there is not much difference

between prestigious underwriter and non-prestigious underwriter IPO portfolios for their first- and

second-order stochastic dominance relations to each of the six benchmarks. However, we can still

observe that IPOs associated with prestigious underwriters seem

to dominate the benchmark slightly more

than

un abnormal performance so that we can understand

more about the new issuance of equity securities.

the IPOs associated with non-prestigious underwriter do.

Many issues make the measurement of abnormal performance over long horizons difficult. These

include the identification of benchmark models, the use of buy-and-hold versus cumulative abnormal

returns, the use of value- versus equally-weighted portfolios, corrections for cross-correlations in event

time returns, accounting for time variation in risk over the event window, and the non-normality of

long-run abnormal returns. More recently doubts have been expressed over whether event studies can be

a useful tool to measure the long-run performance for endogenous events like IPOs. Our paper is a first

attempt at using an alternative methodology that provides a new insight to the literature that has relied

mainly on the event study methodology. Further research is warranted to develop empirical tools that

mitigate the various biases in measuring the long-r


21/41

Appendix A

Barrett and Donald (2003) Test Statistics

The Barrett and Donald (2003) test statistic is:

));();((sup NjMjz

j FzGzMN

MNS

+

= , (A1)

where the operator Ij are given by:

=

=

==N

i

j

ii

N

i

XjNj XzzXjN

zN

Fzi

1

1

1

))((1)!1(

11)1;(

1);( , (A2)

=

=

==M

i

j

ii

M

i

YjMj YzzYjM

zM

Gzi

1

1

1

))((1)!1(

11)1;(

1);( . (A3)

The test statistics for stochastic dominance beyond the first order (e.g. second and third order

stochastic dominance) do not have closed-form limiting distributions. As a result, p-values need to be

obtained by simulation (see also McFadden, 1989). Barrett and Donald (2003) propose two methods to

obtain simulated p-values; by simulation and by bootstrapping.

The first test statistic (KS1) using simulation to obtain the exact p-values is:

));((sup * Njz

F

j FzS = . (A4)

The second test statistic (KS2) is:

));();(1(sup **, NjMjz

GF

j FzGzS = , (A5)

where )( MNN += .

In both cases, the probability that a test statistic using random variables exceeds that using the


22/41

whereR is the number of replications used in the simulation, and is the specified significance level.

The other method to obtain exact p-values used by Barrett and Donald (2003) tests is the bootstrap.

An advantage of the bootstrap relative to the multiplier method is that we now do not necessarily need to

characterize the distribution. The first test statistic (KSB1) using the bootstrap is:

));();((sup *, NjNjz

F

bj FzFzNS = , (A8)

where is the analogue of Equation (A2) for a random sample of size N drawn from

.

);( *Nj Fz

},...,{ 1 NXX=

The second test statistic (KSB2) using the bootstrap is:

))

;()

;((sup**,

1, NjMjz

GF

bj FzGzMN

MN

S +

= , (A9)

where is the analogue of Equation (A3) for a random sample of size M drawn from the

combined sample , and is the analogue of Equation (A2) for a random

sample of sizeNdrawn from the combined sample

);( *Mj Gz

},...,,,...,{ 11 MN YYXX= );( *Nj Fz

},...,,,...,{ 11 MN YYXX= .

Finally, the third test statistic (KSB3) using the bootstrap is:

)));();(());();(((sup **,2, NjNjMjMjz

GF

bj FzFzGzGzMN

MNS

+

= , (A10)

where is the analogue of Equation (A3) for a random sample of size Mdrawn from the sample

, and analogue of Equation (A2) for a random sample of sizeNdrawn from the

sample In this case the two draws are independent.

);( *Mj Gz

},...,{ 1 MYY= );(*

Nj Fz

},...,{ 1 NXX= .


23/41

RejectH0 if =

R

r

j

F

rbj

F

bj SSR

p1

,,, )(1

1~, (A11)

RejectH0 if

=

R

rj

GF

rbj

GF

bjSS

Rp

1

,

,1,

,

1,)(1

1~, (A12)

RejectH0 if =

R

r

j

GF

rbj

GF

bj SSR

p1

,

,2,

,

2, )(1

1~, (A13)

where R is the number of replications used in the bootstrap simulation, and is the specified

significance level. To sum up, we use two test statistics using simulation and three that use

bootstrapping to obtain the p-values used to test for various orders of stochastic dominance. In the case

of first-order stochastic dominance since an analytic solution is available we are not required to use either

simulation or bootstrapping to obtain the exact p-value.


24/41

References

Anderson, G.. (1996). Nonparametric tests of stochastic dominance in income distributions. Econometrica

64, 1183-1193.

Ang, J.S. and Zhang, S. (2002). Choosing benchmarks and test statistics for long horizon event study.

Working Paper, Florida State University.

Bacmann, J.F. and Dubois, M. (2002). Long-run abnormal stock performance: Some additional evidence.

Working Paper, University of Neuchatel.

Barrett, G. and Donald, S. (2003). Consistent tests for stochastic dominance. Econometrica 71, 71-104.

Brav, A., Geczy, C., and Gompers, P.A. (2000). Is the abnormal return following equity issuances

anomalous? Journal of Financial Economics 56, 209-249.

Brav, A. and Gompers, P.A. (1997). Myth or reality? The long run underperformance of initial public

offerings: Evidence from venture and nonventure capital-backed companies, Journal of Finance 52,

1791-1821.

Carter, R. and Manaster, S. (1990). Initial public offerings and underwriter reputation. Journal of Finance

45, 1045-1068.

Carter, R., Dark, F., and Singh, A. (1998), Underwriter reputation, initial returns, and the long-run

performance of IPO stocks. Journal of Finance 53, 285-311.

Dahlquist, M. and De Jong, F. (2003). Pseudo market timing: Fact or fiction. Working Paper, Stokholm

Institute for Financial Research.

Davidson, R. and Duclos, J-Y (2000). Statistical inference for stochastic dominance and for the

measurement of poverty and inequality. Econometrica 68, 1435-1464.


25/41

Fama, E.F. (1998). Market efficiency, long-term returns, and behavioral finance. Journal of Financial

Economics 49, 283-306.

Fama, E.F. and French, K.R. (1993). Common risk factors in the returns on stocks and bonds. Journal of

Financial Economics 33, 3-56.

Fong, W. M., Wong, W. K., and Lean, H. H. (2004). International momentum strategies: A stochastic

dominance approach. Journal of Financial Markets, forthcoming.

Huang, C-F and Litzenberger, R.H. (1988). Foundations for Financial Economics. Prentice-Hall.

Ingersoll, J.E. (1987) Theory of Financial Decision Making. Rowman and Littlefield.

Joy, O.M. and Porter, R.B. (1974). Stochastic dominance and mutual fund performance. Journal of

Financial and Quantitative Analysis 9, 25-31.

Linton, O., Maasoumi, E., and Whang, Y.-J. (2004). Consistent testing for stochastic dominance under

general sampling schemes. Review of Economic Studies, forthcoming.

Loughran, T. and Ritter, J.R. (1995). The new issues puzzle. Journal of Finance 50, 23-51.

Loughran, T. and Ritter, J.R. (2004). Why has IPO underpricing changed over time? Financial

Management 33, 5-37.

Lyon, J.D., Barber, B.M., and Tsai, C-L (1999). Improved methods for tests of long-run abnormal stock

returns. Journal of Finance 54, 165-201.

McFadden, D. (1989). Testing for stochastic dominance. In T.B. Fomby and T.K. Seo (Eds.), Studies in

the Economics of Uncertainty: In Honor of Josef Hadar. New York, Berlin, London and Tokyo:

Springer.

Mitchell, M.L. and Stafford, E. (2000). Managerial decisions and long-term stock price performance.


26/41

Porter, R.B. (1973). An empirical comparison of stochastic dominance and mean-variance portfolio

choice criteria. Journal of Financial and Quantitative Analysis 8, 587-608.

Porter, R.B. and Gaumnitz, J.E. (1972). Stochastic dominance vs. mean-variance analysis: An empirical

evaluation. America Economic Review 62, 438-446.

Post, T. (2003). Empirical tests for stochastic dominance efficiency. Journal of Finance 58, 1905-1931.

Ritter, J. (1991). The long-run performance of initial public offerings. Journal of Finance 46, 3-27.

Ritter, J.R. (2003). Investment banking and securities issuance. In G. Constantinides, M. Harris, and R.

Stulz (Eds.), Handbook of the Economics of Finance, 255-306. North Holland.

Ritter, J.R. and Welch, I. (2002). A review of IPO activity, pricing and allocations. Journal of Finance 57,

1795-1828.

Schultz, P. (2003). Pseudo market timing and the long-run underperformance of IPOs. Journal of Finance

58, 3483-587.

Tehranian, H. (1980). Empirical studies in portfolio performance using higher degrees of stochastic

dominance. Journal of Finance 35, 159-171.

Viswanathan, S. and Wei, B. (2004). Endogenous events and long run returns. Working Paper, Fuqua

School of Business, Duke University.


27/41

Table 1

Descriptive Statistics for the Monthly Returns on IPO and Benchmark Portfolios

(1980/07-2002/12, 270 Months)

CRSP VW Index is the CRSP NYSE/AMEX/NASDAQ value-weighted index, Fama-French Size D1 is the Fama-French

smallest size decile portfolio, Fama-French BTM D1 is the Fama-French lowest book-to-market ratio decile portfolio,

Fama-French Size/BTM Q(1,1) is the Fama-French smallest size/lowest book-to-market ratio quintile portfolio, and

Fama-French Size/BTM D(1,1) is the Fama-French smallest size/lowest book-to-market ratio decile portfolio. AC1 to

AC12 are the autocorrelation coefficients for the 1st, 2nd, 3rd, 5th, and 12th lags of each series. The p-values of the Ljung-Box

Q-statistic are in the parenthesis.

Mean St. Dev. AC1 AC2 AC3 AC5 AC12Value-Weighted All IPO 0.0096 0.086 0.149

(0.014)

-0.044

(0.037)

-0.052

(0.061)

-0.059

(0.136)

-0.104

(0.025)

Value-Weighted

Venture Backed IPO

0.0096 0.114 0.128

(0.034)

-0.024

(0.098)

-0.059

(0.133)

-0.044

(0.292)

-0.098

(0.035)

Value-Weighted

Non-Venture Backed IPO

0.0098 0.071 0.147

(0.015)

-0.067

(0.029)

-0.039

(0.057)

-0.060

(0.117)

-0.079

(0.066)

Value-Weighted

Prestigious Underwriter IPO

0.0107 0.087 0.141

(0.020)

-0.033

(0.056)

-0.031

(0.110)

-0.051

(0.224)

-0.101

(0.040)

Value-Weighted

Non-Prestigious Underwriter IPO

0.0044 0.084 0.171

(0.005)

-0.124

(0.002)

-0.096

(0.002)

-0.064

(0.006)

-0.102

(0.005)

CRSP VW Index 0.0106 0.046 0.044

(0.466)

-0.040

(0.617)

-0.026

(0.764)

0.056

(0.702)

-0.017

(0.784)

Nasdaq Composite Index 0.0103 0.069 0.113

(0.063)

-0.007

(0.175)

-0.034

(0.283)

-0.038

(0.460)

-0.071

(0.235)

Fama-French Size D1 0.0105 0.060 0.261

(0.000)

-0.010

(0.000)

-0.135

(0.000)

-0.078

(0.000)

-0.014

(0.001)

Fama-French BTM D1 0.0101 0.056 0.064

(0.288)

-0.023

(0.528)

0.023

(0.701)

0.053

(0.784)

-0.030

(0.845)

Fama-French Size/BTM Q(1,1) 0.0029 0.084 0.184

(0.002)

-0.029

(0.009)

-0.104

(0.006)

-0.047

(0.016)

-0.092

(0.031)

Fama-French Size/BTM D(1,1) -0.0010 0.088 0.233

(0.000)

-0.029

(0.001)

-0.080

(0.001)

-0.056

(0.002)

-0.040

(0.004)


28/41

Table 2

The Stochastic Dominance Relation between All IPO and Benchmark Portfolios

In this table we report the first-order and second-order stochastic dominance relation between the value-weighted IPO portfolio

using all IPOs during 1980/07-2002/12 and each of the benchmark portfolios. B means benchmark stochastically dominates

IPO; I means IPO stochastically dominates benchmark; N means no stochastic dominance relation between the two

portfolios. We use a 5% significance level as a criterion. LMW Test is the Linton, Maasoumi, and Whang test, and BD

Test is the Barrett and Donald test.

CRSP VW

Index

Nasdaq

Composite

Index

Fama-French

Size D1

Portfolio

Fama-French

BTM D1

Portfolio

Fama-French

Size/BTM Q(1,1)

Portfolio

Fama-French

Size/BTM D(1,1)

Portfolio

LMW Test

First-Order N N N N I I

Second-Order B B B B I I

BD Test

First-Order N N N N N I

Second-Order B N B B N I

Table 3

The Stochastic Dominance Relation between All IPO and Benchmark Portfolios without Internet Bubble Period


using all IPOs during 1980/07-1998/12 and each of the benchmark portfolios. B means benchmark stochastically dominates

IPO; I means IPO stochastically dominates benchmark; N means no stochastic dominance relation between the two

portfolios. We use a 5% significance level as a criterion. LMW Test is the Linton, Maasoumi, and Whang test, and BD


CRSP VWIndex

NasdaqComposite

Index

Fama-FrenchSize D1

Portfolio

Fama-FrenchBTM D1

Portfolio

Fama-FrenchSize/BTM Q(1,1)

Portfolio

Fama-FrenchSize/BTM D(1,1)

Portfolio

LMW Test


Second-Order B N N B I I

BD Test

First-Order N N I N N I

Second-Order B N N N I I


29/41

Table 4

The Stochastic Dominance Relation between Venture Backed IPO and Benchmark Portfolios


using venture backed IPOs during 1980/07-2002/12 and each of the benchmark portfolios. B means benchmark stochastically

dominates IPO; I means IPO stochastically dominates benchmark; N means no stochastic dominance relation between the

two portfolios. We use a 5% significance level as a criterion. LMW Test is the Linton, Maasoumi, and Whang test, and BD


CRSP VW

Index

Nasdaq

Composite

Index

Fama-French

Size D1

Portfolio

Fama-French

BTM D1

Portfolio

Fama-French

Size/BTM Q(1,1)

Portfolio

Fama-French

Size/BTM D(1,1)

Portfolio

LMW Test


Second-Order B B B B N I

BD Test


Second-Order B B B B N N

Table 5

The Stochastic Dominance Relation between Non-Venture Backed IPO and Benchmark Portfolios


using non-venture backed IPOs during 1980/07-2002/12 and each of the benchmark portfolios. B means benchmark

stochastically dominates IPO; I means IPO stochastically dominates benchmark; N means no stochastic dominance relation

between the two portfolios. We use a 5% significance level as a criterion. LMW Test is the Linton, Maasoumi, and Whang

test, and BD Test is the Barrett and Donald test.

CRSP VWIndex

NasdaqComposite

Index

Fama-FrenchSize D1

Portfolio

Fama-FrenchBTM D1

Portfolio


Portfolio


Portfolio

LMW Test


Second-Order B N B B I I

BD Test


Second-Order B N N N N I


30/41

Table 6

The Stochastic Dominance Relation between Prestigious Underwriter IPO and Benchmark Portfolios


using prestigious IPOs during 1980/07-2002/12 and each of the benchmark portfolios. B means benchmark stochastically

dominates IPO; I means IPO stochastically dominates benchmark; N means no stochastic dominance relation between the

two portfolios. We use a 5% significance level as a criterion. LMW Test is the Linton, Maasoumi, and Whang test, and BD


CRSP VW

Index

Nasdaq

Composite

Index

Fama-French

Size D1

Portfolio

Fama-French

BTM D1

Portfolio

Fama-French

Size/BTM Q(1,1)

Portfolio

Fama-French

Size/BTM D(1,1)

Portfolio

LMW Test


Second-Order B B B B I I

BD Test


Second-Order B N B B N I

Table 7

The Stochastic Dominance Relation between Non-Prestigious IPO and Benchmark Portfolios


using non-prestigious IPOs during 1980/07-2002/12 and each of the benchmark portfolios. B means benchmark

stochastically dominates IPO; I means IPO stochastically dominates benchmark; N means no stochastic dominance relation

between the two portfolios. We use a 5% significance level as a criterion. LMW Test is the Linton, Maasoumi, and Whang

test, and BD Test is the Barrett and Donald test.

CRSPVW

Index

NasdaqComposite

Index

Fama-FrenchSize D1

Portfolio

Fama-FrenchBTM D1

Portfolio


Portfolio


Portfolio

LMW Test


Second-Order B B B B N I

BD Test

First-Order N B B B N I

Second-Order B B B B N N


31/41

Figure 1

Distribution of Initial Public Offerings by Year, 1980-2002

Our sample of initial public offerings is collected from Thomson Financial Security Data and it is composed of 6,961 initial public offerings from 1977-2002 meeting the following

criteria: (1) the offerings involve common stocks only. Unit offers, REITs, closed-end funds, and ADRs are excluded; (2) the IPO firms must have return data in CRSP; (3) theoffer price is greater than or equal to $5.

0

100

200

300

400

500

600

700

800

1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002

Year

N

umber

0

10000

20000

30000

40000

50000

60000

US

DMillion

Number of IPOs Aggregate Gross Proceeds (in million)

30


32/41

Figure 2

Empirical P-Values for First-Order Stochastic Dominance Tests using All IPOs (Linton, Maasoumi, and Whang Test)

Figure 2A to 2F show the plots of empirical p-values on both steps of the FOSD tests: (i) the Benchmark Portfolio FOSDs IPO Portfolio test and (ii) the IPO Portfolio FOSDs

Benchmark Portfolio test, using six calendar-time portfolio benchmarks.

31


33/41

Figure 3

Empirical P-Values for Second-Order Stochastic Dominance Tests using All IPOs (Linton, Maasoumi, and Whang Test)

Figure 3A to 3F show the plots of empirical p-values on both steps of the SOSD tests: (i) the Benchmark Portfolio SOSDs IPO Portfolio test and (ii) the IPO Portfolio SOSDs


32


34/41

Figure 4

Empirical P-Values for First-Order Stochastic Dominance Tests using Venture Backed IPOs (Linton, Maasoumi, and Whang Test)



33


35/41

Figure 5

Empirical P-Values for First-Order Stochastic Dominance Tests using Non-Venture Backed IPOs (Linton, Maasoumi, and Whang Test)



34


36/41

Figure 6

Empirical P-Values for Second-Order Stochastic Dominance Tests using Venture Backed IPOs (Linton, Maasoumi, and Whang Test)



35


37/41

Figure 7

Empirical P-Values for Second-Order Stochastic Dominance Tests using Non-Venture Backed IPOs (Linton, Maasoumi, and Whang Test)



36


38/41

Figure 8

Empirical P-values for First-Order Stochastic Dominance Tests using IPOs Associated with Prestigious Underwriters (Linton, Maasoumi, and Whang Test)



37


39/41

Figure 9

Empirical P-values for First-Order Stochastic Dominance Tests using IPOs Associated with Non-Prestigious Underwriters (Linton, Maasoumi, and Whang Test)



38


40/41

Figure 10

Empirical P-values for Second-Order Stochastic Dominance Tests using IPOs Associated with Prestigious Underwriters (Linton, Maasoumi, and Whang Test)



39


41/41

Figure 11

Empirical P-values for Second-Order Stochastic Dominance Tests using IPOs Associated with Non-Prestigious Underwriters (Linton, Maasoumi, and Whang Test)



40

Documents

A Abhyankar HC Chen, And KY Ho (2005) the Long-Run Performance of Initial Public Offering, Sotchastic Dominance Criteria