Pseudo Market Timing and the Long-Run Underperformance of IPOs

Paul Schultz

University of Notre Dame

October 16, 2001.

Comments of Robert Battalio, Utpal Bhattacharya, Long Chen, Shane Corwin, Margaret Forster,Charles Hadlock, Naveen Khanna, Tim Loughran, Wayne Mikkelson, Ralph Walkling and seminarparticipants at the University of Notre Dame and Michigan State University are gratefullyacknowledged. Blunders etc are the sole preserve of the author.

Abstract

Numerous studies document long-run underperformance by firms following initial public offerings or

seasoned equity offerings. In this paper, I show that such underperformance is very likely to be

observed ex-post even in an efficient market. The premise is that more firms issue equity at higher stock

prices even though they cannot predict future returns. Ex-post, issuers will seem to time the market

because there will usually be more offerings at market peaks than when stock prices are low.

Simulations based on observed market parameters suggest that even when ex-ante expected abnormal

returns are zero, median ex-post underperformance for equity issuers will be significantly negative and

very close to what is actually observed.

1In a seminal study, Ritter (1991) shows that IPOs underperform relative to indices and

matching stocks in the three to five years after going public. Similar underperformance following

seasoned offerings is reported by Loughran and Ritter (1995), Spiess and Affleck-Graves (1995), Lee

(1997) and others. At the aggregate level, Baker and Wurgler (2000) find that stock market returns

are lower following years when equity accounts for a large proportion of total financing. The poor

performance of IPOs has also been found in other markets and at other times. Arosio, Giudici and

Paleari (2001), Keloharju (1993), Lee, Taylor and Walter (1996), Levis (1993), and others report

poor long-run performance in a number of other countries. Gompers and Lerner (2000) show that

IPOs issued between 1935 and 1972 performed poorly in the years after issue. Schlag and Wodrich

(2000) even report poor long-run performance for German IPOs issued before World War I.

Ritter (1991), Lerner (1994), Loughran and Ritter (1995, 2000), Baker and Wurgler (2000)

and Hirshleifer (2001) discuss a behavioral explanation for poor performance subsequent to equity

offerings. These authors suggest that stock prices periodically deviate from fundamental values and that

managers and investment bankers take advantage of overpricing by selling stock to overly optimistic

investors. While this explanation is broadly consistent with the evidence, it is an anathema to those who

believe markets are efficient. Indeed, it strikes at the reason market efficiency matters - without it

markets will fail to allocate capital optimally.

Others suggest that when excess returns are properly measured, the evidence for long-run

underperformance following offerings disappears. Brav et al. (2000) find that post-issue IPO returns

are similar to those of firms with similar size and book-to-market characteristics and that SEO returns

covary with similar nonissuing firms. Eckbo et al. (2000) show that leverage and its attendant risk is

significantly reduced following equity offerings while liquidity is increased. They claim that as a result of

these changes in leverage and liquidity, firms that have recently issued equity are less risky than

benchmark firms. However, those who favor behavioral explanations for underperformance point out

that IPOs have significantly underperformed market indices, and few would claim that IPOs are less

risky than an average stock.

In this paper, I examine a phenomenon that I refer to as pseudo market timing and show that it

2can explain the poor long-run performance of stocks that have recently issued equity. The premise of

the pseudo market timing hypothesis is that the more firms can receive for their equity, the more likely

they are to issue stock even if the market is efficient and managers have no timing ability. In this case,

equity sales will be concentrated at peak prices ex-post even though companies cannot determine

market peaks ex-ante. As a result of this pseudo market timing, the probability of observing long-run

underperformance ex-post may far exceed 50 percent. Simulations using the distribution of market and

IPO returns and the relation between the number of offerings and market levels over 1973-1997 reveal

that underperformance of more than 25 percent in the five years following an offering is not surprising or

unusual in an efficient market.

The remainder of the paper is organized as follows. Section I provides a simple example of

pseudo market timing. In Section II I estimate the relation between the number of IPOs and the level of

indices of past IPOs and the market. I then simulate sample paths of stock returns and IPOs and show

that observed underperformance is not unusually large given realistic parameters. In Section III I

discuss how other aspects of IPO and SEO performance are consistent with the pseudo market timing

explanation for long-run underperformance. In Section IV I discuss other anomalies. Section V offers a

summary and conclusions.

I. Pseudo Market Timing

A. A simple example.

The premise of the pseudo market timing hypothesis is that more firms go public as the level of

stock prices increases even though managers cannot predict future returns. This could be because

higher stock prices imply more investment opportunities and firms go public to take projects.

However, the reason why higher stock prices result in more offerings is unimportant for the pseudo

market timing explanation. Firms could issue more equity at higher prices because they believe it results

in less earnings dilution, because they incorrectly believe stock prices are too high, or for any other

reason. What is important is that managers in effect use trigger prices to determine when to take their

stocks public.

3 Pseudo market timing is best explained with an example. To keep things as simple as possible,

we examine one period returns following offerings rather than multiperiod returns. We assume that

each period the market earns a return of +5% or -5% with equal probability. The aftermarket return of

IPOs is equal to the market return plus an excess return of either + 10% or - 10%. Positive and

negative excess returns are equally likely, are unpredictable, and are independent of the return on the

market. Private firms that are potential IPOs are assumed to earn the same returns as recent IPOs. For

simplicity, the price of all recent IPOs and the per share value that all private firms could get for an IPO

is the same. At time zero it is $100. For this example, we assume that no companies go public if stock

prices for potential IPOs are $89 or less, there is one IPO if prices are between $89.01 and $94, two

IPOs if prices are between $94.01 and $99.00, three IPOs if prices are between $99.01 and $104.00,

four IPOs for prices between $104.01 and $109.00, five IPOs for prices between $109.01 and

$114.00, and six IPOs for prices greater than $114.

We consider the number of IPOs issued in periods zero and one, and examine their single-

period aftermarket excess returns. In each period, there are four possible combinations of market

returns and IPO excess returns: a positive market return and a positive excess return, a positive market

return and a negative excess return, a negative market return and a positive excess return, and a

negative market return and a negative excess return. We examine returns and excess returns over two

periods, so there are 42=16 equally likely possible paths for stock returns and excess returns. Each row

of Table I corresponds to one of these paths.

Consider the price path shown in the first row of the table. This is the one in which the market

rises each period and IPOs earn excess returns each period. At time 0, IPO stock prices are $100 and

three firms go public. The market return is 5% the next period and each IPO earns an excess return of

10%. At the period 1 IPO price of $115, six additional firms go public. Each of these six IPOs earns

the market return of 5% and an excess return of 10%. In total, for this path, there are nine IPOs; three

at time 0 and six at time 1. If we calculate event-time average excess returns, we weight each individual

IPO equally and find mean excess returns of 10% and mean market returns following IPOs of 5%.

Of course, there are sixteen equally likely stock price paths and only one will occur. Table I

4reveals that when average aftermarket excess returns are calculated in event time, that is weighting

each IPOs return equally, mean excess returns are positive for four paths and negative for 12 paths.

Thus even though the expected aftermarket return for any individual IPO is zero, there is a 75%

probability that the observed mean aftermarket return will be negative. Again, this occurs because of

pseudo market timing: there are more offerings when IPO prices are higher. This can be seen in the

third row of the table. In this path, excess returns are positive for IPOs that go public in period 0 and

negative for IPOs in period 1. However, because of the rise in stock prices, there are more IPOs

issued at time 1 than at time 0. Thus in event time, the mean excess return across all IPOs on this path

is negative. Notice however that if excess returns were calculated in calendar time, that is weighting

each of the two months equally, the mean excess returns of the IPOs would be zero.

I reiterate that managers have no timing ability. In this example, the decision to go public is a

response to current price levels and is not made because future returns are predictable. As an

illustration, four of the paths in the example have a stock price of $115 at time 1. On each of the four

paths, six IPOs are issued at time 1. The aftermarket excess return for IPOs issued at time1 is positive

for two of the paths and negative for the other two. Ex-ante, the number of IPOs is uncorrelated with

future excess returns.

I emphasize that although the probability of observing a price path where aftermarket returns

are negative is 75%, IPOs are never a bad investment ex-ante. In each case, whether prices are high or

low, each IPO is equally likely to have a positive or negative excess return in the aftermarket. A critical

point is that if you weight the price paths by the number of IPOs on each, the expected return is zero.

Those price paths with the highest excess returns also have the most offerings.

Although this example is simple, it captures the key features of pseudo market timing. First, the

likelihood of observing abnormal returns in event time far exceeds 50 percent even though the ex-ante

expected excess return of every IPO is zero. This is because the number of IPOs increases with higher

stocks prices and, ex-post, IPOs will cluster when prices are near their peak. Second, excess returns

are negative in event time and zero in calendar time.

Note that this example, and pseudo market timing, rely on two important but realistic

5assumptions. First, it is assumed that at higher levels of stock prices, more firms will go public. Second,

it is assumed that excess returns of IPOs are positively correlated cross-sectionally. Both of these

assumptions are borne out empirically. Two other assumptions that were made to simplify the model

are not important. The results are unchanged if more than two periods are considered or if aftermarket

returns are calculated over more than one period. The example becomes much more complicated

though.

Another way to think of pseudo market timing is that investing in IPOs is like a game in which

you double your bet if you win. If IPOs perform well, the market increases (doubles) its bet the next

period as even more firms go public than in the previous period. With a strategy of doubling your bets,

the probability of going broke is 100% even though each bet is fair. Similarly, if the number of IPOs

increases after IPOs have done well in the aftermarket, the likelihood of losing money on average is

high even though each IPO is a fair bet.

B. Pseudo Market Timing and Expected Long-Run Abnormal Returns

It is very difficult to calculate the effect of pseudo market timing on the likelihood of observing

negative abnormal returns following IPOs. Hence an example was used in the previous section to

illustrate that the chances of observing negative abnormal returns may far exceed 50%. It is much easier

to show how pseudo market timing affects the expected value of long-run abnormal returns. Many

studies, including Ritter (1991) and Spiess and Affleck-Graves (1995) estimate average long-run

cumulative abnormal returns around equity offerings as follows:

6Now consider the expected average cumulative abnormal return. It is the expectation of the

product of the total abnormal return, that is the numerator of (1), and 1/N. From elementary statistics,

the expectation of a product is the product of the expectations plus the covariance. Thus

E CAR EN

E r r CovN

r rj mn

N

e

E

j mn

N

e

E( ) ( ) ( ),e ,e ,e ,e=

-

+

-

== ==

1 1

11 11 (2).

Equation (2) does not appear in the literature in discussions of expected cumulative abnormal returns

because researchers make the implicit assumption when calculating (1) that N, the number of offerings,

is constant and exogenous. It is not. Because the number of offerings over the sample period is

positively related to past abnormal returns, there is a positive covariance between the excess returns in

the early part of the sample period and the total number of offerings N. Or, equivalently, there is a

negative correlation between the excess returns and 1/N. Consider an efficient market where the

expected return of the IPO firms is equal to the expected return of the market or matching firm. In this

case, the first term in (2) is zero. That is, there is no real market timing. It is the second term, the

covariance between the returns and the inverse of the number of offerings that leads to a negative

expected value for the cumulative abnormal returns. This is the effect of pseudo market timing on ex-

post returns.

As an aid to intuition, consider what happens when IPOs at the beginning of a sample period

perform very poorly. There may be no future IPOs and the mean abnormal returns for IPOs will be

7stuck at the level of the poorly performing early IPOs. On the other hand, if IPOs in the early part of

the sample period perform well, their positive abnormal returns will be dampened because additional

IPOs with zero expected abnormal returns will follow.

Equation (2) can be used to calculate the expected abnormal return in the example of Table I.

The expected average excess return in (2) is equivalent to the average of excess returns across possible

paths. Averaging the mean IPO excess returns in the second to last column of Table I across the 16

rows yields a mean of -.02095. The critical negative covariance between the reciprocal of the number

of offerings and the total excess return in (2) can be obtained for the example of Table I. First, the sum

of the excess returns, that is

e

E

j mn

Nr r

= = -

1 1( ),,e ,e

is calculated by multiplying the mean IPO excess return in the second to the last column by the number

of IPOs in the last column. The covariance between the total abnormal returns and the reciprocal of the

number of offerings shown in the last column is -.02095, the expected average excess return.

II. Can Pseudo Market Timing Explain Long-Run Underperformance of IPOs and SEOs?

The previous section shows that, even in an efficient market, average abnormal returns

following offerings are likely to be negative if the covariance between returns and the number of future

offerings is positive. In this section, I use simulations to see if this effect is strong enough to explain the

observed underperformance of IPOs and SEOs over 1973-2000. As a first step, I create IPO and

SEO indices by compounding aftermarket returns of recent IPOs and SEOs. I then estimate the relation

between levels of the CRSP value-weighted market index and the IPO (SEO) index and the number of

offerings. Then, using estimated relations between index levels and the number of offerings and between

market and IPO returns, I simulate long-run aftermarket abnormal returns of IPOs and SEOs over

1973 - 2000 under the assumption that the ex-ante abnormal return is zero. I find that the median

simulated underperformance is very similar to actual abnormal returns over the 1973 - 2000 period. In

8other words, the observed underperformance of IPOs and SEOs is what we would expect if the ex-

ante excess returns of all stocks making offerings was zero but pseudo market timing resulted in more

equity sales when stock prices were high.

A. Data

Securities Data Corporation (SDC) is the source of information on the number of IPOs and

SEOs over the 1973 - 1997 period. I exclude all offerings by funds, investment companies and REITs

(SIC codes 6722, 6726 and 6792) as well as offerings by utilities (SIC codes 4911 - 4941), and

banks (6000 - 6081). Table II provides data on the distribution of the number of offerings each month.

The mean number of IPOs per month is 26.8 while the mean number of SEOs is 26.0. The distribution

of each is right-skewed as evidenced by a median of 21 IPOs and 20 SEOs. The number of IPOs per

month ranges from 0 to 107 while the number of SEOs ranges from 1 to 104. The first-order

autocorrelation is .85 for the monthly number of IPOs and .83 for the monthly number of SEOs.

For comparison with the simulations to follow, I use the CRSP tapes to calculate returns for

each IPO or SEO for up to 60 months following the offering. Many studies of long-run performance

after equity offerings use sophisticated techniques for estimating abnormal performance. Here, to keep

from diverting attention from the issue of pseudo market timing, I use the simplest possible way of

calculating abnormal performance: each month I subtract the CRSP value or equal-weighted index

return from the stock return. Results are shown in Table III.

The first three rows of the table report calendar-time returns. Here, the return and abnormal

returns are averaged across stocks for each calendar month, and the equal-weighted mean of the

calendar month means is reported. The mean excess returns for IPOs was 0.02% relative to the CRSP

value-weighted index and -0.12% relative to the CRSP equal-weighted index. Neither excess return is

significantly different from zero. For SEOs, calendar-time excess returns based on the value-weighted

index are not significant, while excess returns calculated with the equal-weighted index are -.30% per

month, with a t-statistic of -2.40. All told, evidence for long-run underperformance is weak when

calendar-time returns are examined.

1The regressions are similar to those reported by Loughran, Ritter and Rydqvist (1994). They regress annual IPOvolume on the level of the stock market and future GNP growth rates for 15 countries. The coefficient on the market level ispositive in 14 of the 15 regressions, and positive and significant at the 5% level in 12 of the 15 regressions. A difference is that

9

For the next three rows, mean returns and excess returns are calculated for each event-period

month. That is, I calculate the mean return and excess return across all offerings for the first month

following the IPO (SEO) , second month following the offering and so forth. Grand means are then

calculated across the 60 months of the event period. These are reported in the table. Here, the

evidence for underperformance is strong. The mean excess return per month is

-.49% for IPOs when measured against the value-weighted index and -.194% when measured against

the equal-weighted index. SEO excess returns are of similar magnitude. All monthly excess returns are

highly significant. When the monthly excess returns relative to the CRSP value-weighted index are

summed over a five year period, the cumulative abnormal returns are -29% for IPOs and -23% for

SEOs.

B. Estimating the Relation Between Price Levels and the Number of Offerings

In the example in Section I, I assumed a relation between the number of IPOs and stock prices.

Here, for realistic simulations, I first estimate the relation between the number of IPOs or SEOs and

stock prices over 1973-1997. I cannot of course tell whether the values of private firms that are

potential IPOs are high or low relative to historic values, so I compile an index of recent IPOs as a

proxy for the value of potential IPOs. Similarly, I compile an index of SEOs to proxy for the value of

those stocks that could conduct SEOs. The value of the IPO and SEO indices are set to 100 at the

beginning of February 1973. For each month, an average return is calculated for all firms listed on

CRSP that had an IPO (SEO) in the 60 prior months. The index level at the beginning of the month is

multiplied by one plus the average return during the month to get an index level for the beginning of the

succeeding month. I also calculate a market index that is set equal to 100 at the beginning of February

1973 and then changed by the return on the CRSP value-weighted index each month. The number of

IPOs (or SEOs) is then regressed on the levels of the market and the IPO (or SEO) index at the

beginning of each month from February 1973 through December 1997.1

my regressions include the level of past IPOs as well as the market level.

10

Results are reported in Table IV. The first row of the table describes the regression of the

number of IPOs on the level of the IPO index. The coefficient on the IPO index is .0539, indicating that

the number of IPOs increases with the index of past IPO returns. The t-statistic, based on

heteroskedasticity-consistent standard errors, is a highly significant 21.69. The second row of the table

provides results of the regression of the number of IPOs on the level of the market index. The

coefficient on the market index is positive and significant, implying that there are more IPOs when the

level of the market is high. The third regression in the table includes the level of both indices and a time

variable to pick up any intertemporal variation in the number of IPOs. The time variable is just a

sequential numbering of the months of the sample period. When both indices are included, the

coefficient on the market index switches sign and the coefficient on the IPO index increases

dramatically. The levels of the indices are highly correlated, and thus both are positively related to the

number of IPOs when considered alone. However, the number of IPOs is affected more by the level of

the IPO index, and that is reflected in the regression with both indices. In the fourth row of the table, I

include the square root of each index to account for non-linearities in the relation between the number

of offerings and the index level. This regression produces the highest R2, .8010, and estimates from that

regression are used as a base case in the simulations. The last four rows show the analogous

regressions with the number of seasoned equity offerings as the dependent variable. The results are

similar to the IPO regressions. In particular, the number of SEOs is much more strongly related to the

level of the SEO index than to the level of the CRSP value-weighted market index.

Figures 2a and 2b graph the actual and fitted number of IPOs and SEOs for the regressions

that use the levels of the market and recent IPOs, the square roots of the levels, and the time since

January 1973 as independent variables. It is apparent that the regressions do a very good job of fitting

the number of offerings in sample, particularly for IPOs.

Nevertheless, there are problems with using ordinary least squares regressions to estimate the

relation between the levels of the market and IPO (SEO) index and the number of offerings. First, the

number of offerings may be predicted to be less than zero. Fig. 2 shows that this is an infrequent

2If the predicted number of offerings is negative in any simulation, it is set to zero.

3The sample includes IPOs and SEO s starting January 1973 and thus aftermarket returns start with February 1973.

11

occurrence in the estimations, but it may become important in the simulations.2 A second problem with

the OLS regressions is heteroskedasticity: the variance of the number of offerings is positively related to

the expected number. As an alternative, I estimate Poisson regressions in which the Poisson parameter

is a function of the market level, the level of the IPO (or SEO) index and time. When the number of

offerings is generated with a Poisson process, the number will never be negative and the variance of the

number of offerings in a month is equal to the expected number. In this case, goodness-of-fit tests

indicate overdispersion; that is the heteroskedasticity is even greater than explained by the Poisson

regressions. Thus Poisson parameters are estimated with an overdispersion parameter (negative

binomial regression). Estimates for 1973-2000 are shown in Table IV Panel B.

Poisson regression estimates are similar to OLS estimates in that the number of offerings in a

month is far more closely tied to the level of the IPO or SEO index than to the level of the market

index. In these regressions, like the OLS regressions, the best fits are obtained when the square root of

the market and IPO (SEO) index levels and time are used in addition to the levels.

Because the OLS and Poisson regression estimates are so similar, the simulations based on the two

types of regressions produce comparable results. So, except for a sensitivity analysis, I only report

simulations based on the OLS regressions. Results of simulations based on the Poisson regressions are

available from the author.

C. Simulations of Aftermarket Performance

For the simulations, I estimate the distributions of the monthly return on the CRSP value

weighted index using all months from February 1973 through 19973. Over this time, the mean monthly

return is .0112 and the standard deviation is .0452. I also estimate the relation between the returns on

IPOs and SEOs by regressing an equal-weighted average return from all IPOs (or SEOS) from the

previous 60 months on the CRSP value-weighted index return using all months from February 1973

through December 1997. The slope coefficient for IPOs is 1.31 with a residual standard deviation of

12

.0427. The slope coefficient for the SEO portfolio is also 1.31 but with a residual standard deviation of

.0262.

I run 1,000 simulations of sample paths for IPOS and 1,000 for SEOs. To simulate returns of

the market each month, I first generate a return from the normal distribution using the mean and

standard deviation of the monthly return on the CRSP value-weighted index over 1973 - 1997. The

return on the portfolio of IPOs is generated by multiplying the market return by the slope coefficient of

1.31 and adding a residual return that is generated from a normal distribution with a mean of zero and a

standard deviation of .0427. I do not add the intercept coefficient from the regression to the simulated

IPO portfolio return. Instead, I subtract .003454 from the IPO return each month so that the expected

return on the IPO portfolio and the market are identical. For the beginning of the first month of a

simulated sample path of returns and offerings, the level of the IPO index and market index are both set

to 100. At the beginning of each succeeding month, the simulated level of the market portfolio and of

the IPO portfolio are obtained by multiplying the previous months level by one plus the previous

months simulated return. The number of IPOs in a month is then obtained from the simulated levels of

the IPO index and market using the estimated coefficients from the regression of the monthly number of

IPOs on time, the market level, the IPO index level, the square root of the market level and the square

root of the IPO index. Each simulated sample path of returns and offerings is 300 months (25 years)

long. The procedure used with SEOs is identical but uses the coefficients and standard deviations

estimated for SEOs.

Excess returns for IPOs during a calendar month are the difference between the IPO index

return and the market return during a month. It is worth emphasizing that ex-ante expected excess

returns for each month are set equal to zero by construction. Event-period abnormal returns are

obtained for each IPO in a simulated sample path by cumulating abnormal returns in the calendar

months before or after the offering as in (1).

Simulation results are reported in Table V. For each of 1,000 simulations, mean cumulative

abnormal returns are calculated for a variety of event periods. Panel A of TableV reports the

distribution of simulated mean cumulative abnormal returns across the 1,000 simulations. For example,

13

the distribution of cumulative excess returns in the 36 months prior to an IPO is described in the second

column of the table. The median excess return, across the 1,000 simulations, is 15.59% over the 36

months prior to an IPO. I emphasize medians rather than means in this table because the distribution of

cumulative returns is highly right-skewed, and the mean may be significantly affected by a few very large

returns. In this case, the mean excess return is 16.75% over the 36 months prior to an IPO, with a t-

statistic of 22.98. Further examination of the table reveals that excess returns are positive in periods

prior to IPOs even though the ex-ante excess returns are zero. This is simply a result of the number of

IPOs increasing as the level of the IPO index rises.

Of more interest are the excess returns following IPOs. Table V shows that cumulative

abnormal returns following IPOs decline monotonically with the length of the holding period. The last

column of the table shows the distribution of the cumulative excess returns in the 60 months after an

IPO. The median, across the 1,000 simulated samples of the average excess returns is, -21.32%. This

is close to the actual sample period cumulative abnormal returns of -29%. So to reiterate, even when

ex-ante excess returns are zero, we will observe mean event period excess returns for the 60 months

after IPOs of less than -21.32% half of the time. The likelihood of finding that IPOs underperform in the

60 months after the offering is 74.1%, and there is a ten percent chance of observing excess returns of

less than -54.20%. Given the relation between the number of offerings and the levels of the IPO and

market indices, it is not surprising that IPOs underperform in reality. Even in an efficient market, where

IPOs are not systematically under or over priced, it is the most likely result.

In Panel B of Table V, I report distributions of 60 month cumulative abnormal returns from the

simulations when calendar months are weighted equally and following months with heavy or light

offering activity. For comparison, the second column of the table repeats the distribution of simulated

cumulative abnormal returns from Panel A. The following column reports the distribution of simulated

cumulative abnormal returns for the 60 months following every calendar month. That is, cumulative

abnormal returns are estimated regardless of whether there were any offerings that month and all

months are weighted equally. Here, the median cumulative abnormal return is 0.48%, while the mean

cumulative abnormal return is -0.23%. This is as expected. In the simulations, expected abnormal

14

returns were set equal to zero. The next column of the table, labeled ex-post calendar returns, shows

the distribution of cumulative abnormal returns when all months are weighted equally but are only

included when there is at least one offering during the month. Note first that the mean and median

simulated abnormal returns in this case are negative. As a result of the pseudo timing, even calendar

period abnormal returns may be negative because months with no offerings, when prices tend to be low

ex-post, are excluded. Note also that the simulated abnormal return in this case is not as negative as the

event period excess returns. Pseudo market timing produces much greater underperformance in event

time than calendar time.

The last two columns of the table show cumulative abnormal returns following months of light

and heavy offering activity. A light activity month is defined as one in which the number of simulated

offerings is in the bottom quartile of months with at least one offering. A heavy month is defined as one

in which the number of simulated offerings is in the top quartile of months with at least one offering.

Simulated cumulative abnormal returns are much more negative following months of heavy offering

activity than in typical months. Simulated cumulative abnormal returns are actually positive following

months of light offering activity. These results are similar to those reported with actual IPOs and are

cited by those who favor the behavioral explanation for long-run performance as strong evidence of

market timing ability by managers and underwriters. But in these simulations, there is no timing ability.

Abnormal returns must be negative after months with heavy offering activity. If they were positive, the

heavy activity months would be followed by months with even larger numbers of offerings and thus the

heavy activity months would no longer be classified as having heavy activity.

Panel C of Table V provides the distributions of wealth relatives and market returns across the

1,000 simulations. The median wealth relative for the 36 months following an IPO is .8545. This means

that the ratio of the wealth from investing in IPOs to the wealth from investing in the market at the same

time is .8545. At the end of the 60 months subsequent to an IPO the median wealth ratio across all

simulated sample paths is .7860. For comparison, Loughran and Ritter (1995) report average wealth

ratios of .80 at the end of the three years after an IPO and .70 at the end of the five years after an IPO.

The next column reports the distribution of the average market return over the 300 month

15

sample paths. Recall that the mean return in the simulations is set equal to 1.12% per month, the

observed return on the value-weighted index over 1973-1997. Thus it is not surprising that both the

median and mean of the average market returns are 1.12%. However, market returns are lower

following offerings. The next column shows the distribution of market returns in the 36 months following

IPOs. The median market return is now 0.96% while the mean is 0.94%. Similar results are reported in

the next column for the 60 months following IPOs. Paired sample t-tests of the returns on the market in

all sample months with the mean returns of the market following IPOs are 14.63 for 36 months and

14.05 for 60 months. That market returns are low subsequent to IPOs is an artifact of more firms going

public when the level of the IPO index is high, and of the IPO index being correlated with the level of

the market. These simulated results resemble Baker and Wurglers (2000) finding that the market return

is lower following years when a large portion of capital is raised from equity offerings.

The last column of the table reports the distribution of the number of IPOs per month across the

1,000 simulations The median number is 18 while the mean is 86.5. Recall that over 1973-1997 the

number of IPOs per month averaged 26 with a range from 0 to 107. That the mean is far higher than

median is a result of a right-skewed distribution for the simulated number of IPOs. However, the mean

of 86.5 offers per month is not an unreasonable number if, say, the market had performed well in 1974-

75 or the 1987 crash had not occurred. The correlation between the number of IPOs in a simulation

and the mean excess return in the 60 months after IPOs is .4554.

The simulations of returns around SEOs are reported in Table VI. The simulated number of

SEOs in a month is generated using the estimated coefficients from the last equation in Panel A of Table

IV. The market return is again assumed to be normally distributed with a monthly mean of 1.12% and a

standard deviation of 4.52%. As before, the return on the SEO portfolio for a month is simulated by

multiplying the return on the market index by the coefficient from a regression of SEO returns on market

returns and adding a constant chosen so that the ex-ante excess returns on SEOs equal zero. The

idiosyncratic return of the SEO portfolio is simulated from a normal distribution with a mean of zero and

a standard deviation of 2.62% per month. This is the standard deviation of the residuals from the

regression of SEO returns on the market over 1973 - 1997. Excess returns are again calculated by

16

subtracting the market return from the return of the SEO portfolio.

The results for SEOs are similar to the findings for IPOs. Panel A of Table VI reveals that the

median and mean of the excess returns from the 1,000 simulated sample paths are positive before

SEOs and negative afterwards. The last column of the table, showing cumulative abnormal returns in the

60 months following an SEO is particularly instructive. The median aftermarket performance across the

1,000 sample paths is -18.24%. Because cumulative abnormal returns are right-skewed, the mean

return in the 60 months after the SEO is higher, but it is still -11.81%. Of course, researchers working

with real data only observe one sample path of stock returns and SEOs. The results in the last column

of the table indicate that there is a 67.7% chance that the researcher will observe negative abnormal

returns in the 60 months after SEOs even if the ex-ante excess returns are zero. There is a 10% chance

that the researcher will observe returns of less than -49.63% and a 25% chance of returns less than -

34.76%.

Results in Panel B of Table VI are similar to those reported earlier for IPOs. Calendar

abnormal returns are close to zero. The cumulative abnormal returns following months with light offering

activity are 6.83%, while the cumulative abnormal returns following months of heavy offering activity are

-26.44%.

Panel C of Table VI provides the distribution of wealth relatives and aftermarket returns for the

36 and 60 months following SEOs. The table reveals that, for any given sample path of 25 years worth

of stock returns and SEOs, there is a 50% chance of observing a wealth relative of less than .8443 for

60 months following SEOs even when the ex-ante excess returns are zero. There is 25% chance of

observing a wealth relative less than .7067 and a 10% chance of observing a wealth relative of less than

.6188. The table also indicates that the return on the market as a whole is likely to be lower than

normal following SEOs.

The number of SEOs generated in each simulation varies widely, but is typically higher than was

actually observed. The correlation between aftermarket excess returns and the number of offerings is

.5239.

4Mitchell and Stafford (2000) conclude that cross-sectional correlation of abnormal returns across firms results inoverstated significance for buy-and-hold returns in most studies of abnormal returns.

17

D. Sensitivity Analysis

The simulations employed here are based on specific assumptions relating the number of

offerings to the levels of the market and IPO (SEO) indices and on a particular way of measuring

abnormal returns. If pseudo market timing is to serve as an explanation for poor long-run performance

it should be robust with respect to these factors. In Table VII I report the distribution of simulated

cumulative abnormal returns in the 60 months following offerings under different assumptions. Panel A

shows results for IPOs. For comparison, the second column provides the distribution of cumulative

abnormal returns in the 60 months following IPOs for the base case - that is the simulations reported in

Table V.

The following column provides the distribution of buy and hold excess returns. Buy and hold

returns for the 60 months after an offering a calculated as

BHAR r rtIPO

tMkt

tt= + - +

==( ) ( )1 1

1

60

1

60 (3)

In a sense, my focus on cumulative abnormal returns understates the magnitude of pseudo market

timing. Most studies of long-run performance use buy and hold excess returns, which, as Fama (1998)

observes, are particularly low.4 This is also true for the buy and hold abnormal returns simulated here.

Median buy and hold abnormal returns are -36.55% as compared to -21.32% in the base case. The

following column, labeled linear model for number of offers, reports cumulative abnormal returns when

the number of IPOs per month is based on the regression in Table IV that includes IPO and market

index levels but not their square roots. Results are slightly stronger than for the base case.

Size matched excess returns are in the fifth column of the table. They are simulated by first

matching each IPO (SEO) over 1973 - 1997 with another firm of near equal market capitalization.

IPO (SEO) capitalizations are obtained by multiplying the offering price by the number of shares

outstanding after the IPO. Matching firm sizes are the capitalizations as of the end of the previous

calendar year. If a match leaves the CRSP tape it is replaced by another with a capitalization as close

5 In the other simulations, I estimate parameters over 1973-1997 to simulate abnormal returns to be compared withactual abnormal returns over 1973-2000. That is, I replicate a researcher who used the maximum time period to estimate abnormalreturns but only included offerings with at least three years of aftermarket data. Because the number of offerings in a month is ahighly nonlinear function of the parameters in the Poisson regressions, I try to keep the number of simulated offerings close tothe actual number by simulating 20 years of IPOs rather than 25. I also estimate the relation between number of offerings andindex levels using data from 1973 - 2000 to utilize a wider range of parameter inputs.

18

as possible to the IPO. No firm listed on CRSP less than five years is eligible for a match. No match

firm is used more than once during a calendar month. Matches are quite close in size to the IPOs. The

ratio of the match size to the IPO size has a 10th percentile of .9983 and a 90th percentile of 1.0017.

Match firm and IPO returns are then used to generate levels of the match firm and IPO index

for each calendar month over 1973-1997. Estimates of the relation between the levels of these indices

and the number of IPOs are used then to simulate the number of IPOs each month. Excess returns are

the difference between the IPO returns and returns on the matched stocks. As before, expected

abnormal returns are set to zero. Table VII shows that cumulative abnormal returns based on firms

matched on size are similar to the cumulative abnormal returns estimated in the base case.

In the next column of the table, the number of IPOs in each month in the simulations are

generated using the Poisson regression from Table IV with the market index level, IPO index level, the

square roots of the index levels and the time since the first month as independent variables. The

simulations produce results that are very similar to those obtained with OLS regressions. The median

underperformance of IPOs in the 60 months following an offering is

-19.57%. Although not shown, the underperformance is particularly strong following months with heavy

IPO issuance and the market return is itself lower than usual following offerings.5

The next column shows simulations based on rearranging actual returns. Rather than simulating

returns based on a normal distribution, I randomly rearrange the monthly returns on the CRSP value

weighted index and the monthly excess returns of IPOs over 1973-1997 to form a time series of levels

of the market and recent IPOs. The number of offerings each month is then based on the same

regression used in the base case. One result of this is that median and mean underperformance is

reduced to -13.83% and -12.54%, but the probability of observing underperformance increases to

94.4%. The range of IPO and market index levels are greatly reduced by rearranging the actual returns,

19

and thus the number of offerings is close to the actual number. The mean number of offerings is 9,876

while the median is 8,067.

Simulations in which observations are discarded if the number of offers is extreme are

described in the next column. Here, the 100 simulations with the highest number of offers and the 100

simulations with the lowest number of offers are discarded from the base case of 1,000 simulated paths

of stock returns and offerings. Results are very similar to, but slightly stronger than the base case.

Simulations based on the doubled variance use the same techniques and parameters as in the

base case but the variance of the residual return on the IPO index is doubled. Mean and median

underperformance are now greater than before. The point of these simulations is to demonstrate that the

negative abnormal performance brought about by pseudo market timing is greater when the correlation

between the IPOs and benchmark is lower - even if the expected return on both are the same. This

could explain why underperformance is particularly pronounced for smaller IPOs - they have more

idiosyncratic risk.

Panel B of Table VII duplicates Panel A with SEOs. As with IPOs, results are much stronger

when buy and hold excess returns are used, but unlike IPOs are considerably weaker when actual

returns are rearranged. As a whole, results seem robust to the way in which excess returns are

calculated and the relation between the number of offerings and the level of market and IPO or SEO

indices. Other characteristics of the simulations, like abnormal returns over different time periods or

following months of heavy or light issuing activity are not shown, but are also very similar to the base

case results in Tables V and VI.

III. Distinguishing Between Explanations for Long-Run Underperformance

The pseudo market timing discussed here competes with two other explanations for the poor

long-run performance of equity issuing firms. The behavioral explanation is that stock prices are subject

to fads and managers and investment bankers time the market to issue stock when it is overpriced. As a

result of cognitive biases investors never figure out that managers are taking advantage of them. The

20

poor risk adjustment explanation posits that IPOs and SEOs have not underperformed after properly

adjusting for risk. All three of these explanations can explain why IPOs and SEOs have performed

poorly in the long-run. However, pseudo market timing more satisfactorily accounts for other

characteristics of IPO and SEO aftermarkets. Some of these other characteristics are as follows.

A. Measures of Operating Performance are Also Poor Following Equity Offerings

Jain and Kini (1994) find that operating return on assets and operating cash flows deflated by

assets decline for IPO firms relative to firms in the same industry after their offering. Likewise,

Mikkelson, Partch, and Shah (1997) find that operating returns on assets decline following IPOs and

that the decline is especially large for the smallest and newest companies. Similarly, Loughran and Ritter

(1997) report that in the four years following an SEO, operating income divided by assets, profit

margins, and return on assets decline for firms that conduct SEOs relative to matched firms that did not

issue equity.

The decline in operating income following equity offerings suggests that the poor return

performance is not just a symptom of incorrect risk adjustment. Note that it is consistent with both the

behavioral and pseudo market timing explanations for long-run underperformance. The pseudo market

timing hypothesis says that the observed underperformance of IPOs is real ex-post, but that it is

unpredictable ex-ante.

B. Poor Aftermarket Performance is Observed in Other Countries and at Other Times

Ritter (1998) summarizes studies of long-run performance following IPOs in thirteen countries.

IPOs underperform in eleven of them. In one of the papers, Lee, Taylor and Walter (1996) find that

Australian IPOs underperform by over 46% in the subsequent three years. In another, Keloharju

(1993) finds that Finnish IPOs underperformed the Finnish value-weighted index by 26.4% in the three

years following their offerings. Similarly, Aussnegg (1997) shows that IPOs of Austrian firms cluster

after bull markets and that IPOs underperform by an average of 74% in the five years after an offering.

In a paper not discussed in Ritter (1998), Arosio, Giudici, and Paleari (2001) report mean buy-and-

21

hold abnormal returns of -11.53% over three years for Italian IPOs over 1985 to 1999.

Studies of IPOs in earlier periods also document underperformance. Gompers and Lerner

(2000) study the aftermarket performance of over 3,600 IPOs from 1935 to 1972. Buy and hold

returns calculated in event time are 12.6% less than the CRSP value-weighted index in the three years

following IPOs and 29% less when a five year period is used. Schlag and Wodrich (2000) report that

German IPOs from 1870 to 1914 underperformed relative to indices of seasoned equities in the same

industry groups in the three to five years following their IPOs.

These results again suggest that the ex-post underperformance of IPOs and SEOs is real and

not an artifact of data mining or a chance occurrence. The consistency of the results across countries

and times seems more consistent with either the behavioral or pseudo market timing explanation for

underperformance than with poor risk-adjustment.

C. Offerings Occur at Market Peaks

Lerner (1994) examines 350 privately held biotech firms between 1978 and 1992. He then

compares their financing choices - whether they go public or get private venture capital financing. He

shows that they are more likely to go public when the level of a biotech index is near a local peak.

Keloharju (1996) studies Finnish IPOs over 1984-1989. Over half of the IPOs in his sample were

issued in 1988. He notes that the Finnish market peaked in April 1989 and the value-weighted index

declined 58.1% from then until December 1991. Korajczyk, Lucas and McDonald (1990) observe that

U.S. seasoned offerings cluster in some years and that these years follow market-wide price runups.

On average, the difference between the market return and the return on T-bills is about 48% in the two

years prior to a seasoned offering. Likewise, Loughran and Ritter (1995) find a mean return of 72% in

the year preceding a seasoned offering and about half of this is from a market-wide runup.

It is plainly the case that the number of equity offerings varies a great deal over time, and that

equity offerings are more common when the market is high. The poor risk-adjustment hypothesis is

silent on this, but it is predicted by both the behavioral and pseudo market timing explanation.

22

D. Excess Returns After Equity Offerings are Significant in Event Time but not Calendar Time

Loughran and Ritter (1995), and Loughran and Ritter (2000) observe that excess returns

following equity offerings are much lower when measured in event time than in calendar time. When

returns are measured in calendar time each month is weighted equally while each issue is weighted

equally in event time. Loughran and Ritter (2000) suggest that if issuers are able to time their offerings

to take advantage of mispricings, we would expect more offerings prior to poor returns, and thus

waiting each month equally rather than each offering will understate the abnormal returns.

The difference between returns measured in calendar time and event time is also observed in

studies of offerings in other countries and at other times. Schlag and Wodrich (2000), in their study of

German IPOs from 1870 to 1914, find significant underperformance in event time but not in calendar

time. lvarez and Gonzlez (2001) find that Spanish IPOs issued over 1985-1997 underperform in

event time but not in calendar time. Gompers and Lerner (2000) determine that over 1935 to 1972,

buy and hold abnormal returns are negative in event-time following IPOs, but disappear when

calculated in calendar time. Over the entire time period, IPO returns measured on a calendar time basis

are very similar to returns on the market.

This result is predicted by the behavioral explanation for poor long-run performance. However,

results in Table V and VI clearly demonstrate that pseudo market timing also results in much greater

abnormal performance in event time than calendar time. Poor risk-adjustment does not explain this

finding.

E. Performance is Particularly Poor Following Periods of Heavy IPO Issuance

Ritter (1991) and others observe that long-run performance is particularly poor for IPOs issued

during periods when a lot of companies go public. In contrast, IPOs issued during cold markets

perform well. Behavioralists claim that this is evidence that firms issue equity when they know their

stock is overpriced. However, as shown in the simulations, pseudo market timing also results in

especially poor performance following periods of heavy IPO market activity even when ex-ante

23

abnormal returns on all IPOs are zero. Particularly poor performance following periods of heavy

issuance is not predicted or explained by the poor risk adjustment explanation for IPO

underperformance.

F. Performance is Also Poor After Debt and Convertible Debt Issuance

Spiess and Affleck-Graves (1998) examine stock returns around offerings of straight and

convertible debt. They report large positive excess returns for a companies stock prior to debt issues.

Holding period returns in the five years following an offering are 14% less for straight issues than for

matching stocks. Following the issuance of convertibles, the stocks underperform matching firms by

37%.

Poor long-run performance following debt issues is consistent with the pseudo market timing

explanation for poor performance. It appears inconsistent with the behavioral explanation. If managers

can time the market and issue stock when it is overpriced, why would they instead issue debt?

G. Managers do not Exploit Underperformance for Personal Gain

If firms can time equity issuance to take advantage of overvaluation of their stock, we would

expect managers to also gain by taking advantage of misvaluations. However, Lee (1997) shows that

stocks underperform following seasoned equity offerings of primary stock, but, when insiders sell their

own shares in a secondary seasoned offering, subsequent performance is not significantly different from

that of matching firms. Lee (1997) also shows that, while primary SEOs perform poorly in the three

years following the offering, performance is unrelated to insider trading around the offering.

Lees results are consistent with the pseudo market timing explanation for long-run

underperformance. On the other hand, Lees evidence contradicts the assertion of behavioralists that

managers are able to time the market with equity issues.

To summarize, there are three explanations for the poor performance of IPOs and SEOs: the

behavioral explanation, the poor risk-adjustment explanation, and the pseudo market timing hypothesis.

Each is consistent with the poor performance of IPOs and SEOs but they differ in their ability to explain

24

other characteristics of the long-run returns. Poor-risk adjustment seems incapable of explaining the

relation between the number of IPOs and subsequent returns, the poor operating performance of firms

following offerings and the robustness of the anomaly over time and across countries. The behavioral

explanation for the poor long-run performance of equity issuers does correctly predict the relation

between the number of IPOs and subsequent returns and the difference between calendar and event-

time returns. However, it does not explain why firms choose to issue debt at market peaks or why

insiders do not seem to exploit their timing ability. In short, only the pseudo market timing explanation

seems consistent with all the facts about the long-run performance of equity issuers.

IV. Other Anomalies

Since the original study by Ritter (1991), a number of papers have reported abnormal

performance following various corporate actions. Typically these actions follow stock price runups (or

decreases) and thus may be explained by the same pseudo market timing that occurs with equity

offerings.

Loughran and Vijh (1997) note that a merger in which the target is acquired for stock is

equivalent to an offering of stock in which the proceeds are used to buy another company. Loughran

and Vijh examine post acquisition returns for tender offers and mergers when the offering was for stock

or for cash. They find that in the five years following the acquisition, firms that merged with another firm

and paid with stock earned abnormal returns of -25%. Acquiring firms that made a tender offer and

paid cash had average abnormal returns of 61.7% in the five years following the acquisition. Agrawal,

Jaffe, and Mandelker (1992) examine post-merger performance of acquiring firms for an exhaustive

sample of NYSE mergers over 1955 to 1987. Thee mergers typically occur after abnormally strong

performance by the acquiring company. They find that the acquiring companies earn cumulative

abnormal returns of about -10% in the five years following the acquisition.

Webb (1999) studies pre and post-listing performance for stocks that moved from Nasdaq to

the NYSE or AMEX or from the AMEX to the NYSE. Stocks typically perform well before listing.

6One anomaly that pseudo market timing does not seem to explain is the continued positive (negative) abnormalperformance by following initiation (omission) of dividends documented by Michaely, Thaler and Womack (1995).

25

However, after listing, the same firms underperform relative to matching firms, with the

underperformance concentrated in the firms that performed best prior to listing.

Hand and Skantz (1998) find that market-wide returns are significantly higher before carveouts

than afterwards. This result holds for both value-weighted and equal-weighted market indices.

Further, returns before and after are negatively correlated. Hand and Skantz interpret their findings to

mean that either managers or underwriters of their firm's carve-outs can successfully time the market.

That is, they not only know when their stock is over or underpriced, they know when the market as a

whole is too high or low.

Lakonishok and Vermaelen (1990) investigate the long-run performance of 258 stocks in the

24 months following repurchase tender offers over 1962-1986. They document that repurchased

stocks outperform a value-weighted index by 23.11% and an equal-weighted index by 12.34% in the

two years following the tender offer. When a size benchmark is used, abnormal returns still exceed

8.5%. Ikenberry, Lakonishok, and Vermaelen (1995) find even more pronounced underperformance

for value stocks.

Billet, Flannery, and Garfinkel (2001) examine stock returns following announcements of bank

loans over 1980 to 1989. They find mean buy and hold abnormal returns of -53% for the five years

following the loans. Their findings appear to be robust with respect to the benchmark used to evaluate

returns.

In most of these studies, the authors conclude that their findings are suggestive of market

inefficiency. But, in each case, the pseudo market timing discussed here could be the culprit.6 Positive

abnormal returns precede debt offerings, acquisitions, NYSE listings, and carveouts, while negative

abnormal returns follow these events. It is likely that, ex-post, these events are occurring when the

prices of the types of companies that issue debt, or make acquisitions, or list on the NYSE, or carve-

out divisions are at peaks. Likewise, firms that repurchase their own stock are likely to do so when, ex-

post, their stock prices are at bottoms. These anomalies bear further examination to see if they are just

26

further examples of pseudo market timing.

V. Summary and Conclusions

In this paper, I propose that the poor long-run performance of equity-issuing firms is real, but is

not indicative of any market inefficiency. The premise of the pseudo market timing explanation for

underperformance is that more firms go public when they can receive a higher price for their shares. As

a result, ex-post there are more offerings at peak valuations than at lower prices. This is pseudo market

timing. The issuing companies didnt know prices were at a peak when they issued stock. If prices had

kept rising, even more offerings would have been forthcoming until prices eventually fell and offerings

dried up. Using simulations with parameters estimated from historical data, I show that pseudo market

timing can easily lead to a level of ex-post underperformance similar to that documented for IPOs and

SEOs over the past 25 years.

Researchers who believe that firms intentionally issue equity when they know their shares are

overpriced point to several pieces of evidence to support their view. One is that underperformance is

much stronger in event time than in calendar time. They claim that this is a result of firms successfully

timing the market and conducting more offerings at market peaks. The pseudo market timing

explanation also has more firms issuing equity at market peaks, but notes that this will occur ex-post if

managers choose to issue more equity when prices are higher even if prices are correct ex-ante. A

second piece of evidence is that IPOs issued during the periods when the most firms go public

underperform far more than IPOs issued when few firms go public. This is also consistent with pseudo

market timing. If IPOs performed well after periods of heavy equity issuance, even more firms would

go public and the heavy issuance periods would no longer be defined as periods of heavy issuance. A

third observation that is offered as evidence in favor of the behavioral explanation is that smaller firms

that issue equity underperform the most. Loughran and Ritter (2000) argue that these stocks are most

likely to reflect cognitive biases because their small size prevents arbitragers from correcting their

mispricing. This is also consistent with my explanation for the poor performance of equity issuing firms.

27

It is likely that smaller firms returns will have lower correlations with their benchmarks than other firms.

The lower the correlation between the returns of the equity issuing firm and its performance benchmark,

the greater the underperformance ex-post, even if ex-ante expected returns are equal.

Pseudo market timing is also consistent with observations that seem to contradict the behavioral

explanation for long-run underperformance. One such observation is that stocks underperform

following issues of straight or convertible debt as well as equity. If managers can tell when their stock is

overpriced and can regularly fool investors by selling overpriced equity, why would they choose to

issue debt? The pseudo market timing explanation says that managers raise cash when stock prices are

high but have no particular incentive to issue equity because they cannot time the market. A second

apparent contradiction for the behavioral explanation for long-run underperformance is that managers

do not seem to exploit mispricing by selling their own shares at the same time that firms issue equity.

Again, this is consistent with the pseudo market timing outlined here. Managers do not take advantage

of mispricing in their personal trades because corporate decisions to issue equity are not driven by

mispricing of equity.

The primary implication of pseudo market timing for the methodology of long-run performance

studies is that event-time returns should be avoided in favor of calendar time returns if the probability of

the event in question is related to past stock returns. The number of stock repurchases, mergers, debt

offerings and listings are all likely to be related to past returns. Thus the anomalous long-run

performances following these events may all bear reexamination in light of the pseudo market timing

phenomenon.

The most important implication of this work is that IPOs and SEOs are not bad investments,

and should not be avoided. It is true that over the last 25 years they have underperformed market

indices. The probability is much greater than 50% that, on average, they will underperform over the

next 25 years as well. But, ex-ante, any individual IPO or SEO can be expected to provide a fair rate

of return.

28

Table I. An example of pseudo market timing. Each period, zero IPOs occur if prices are $89 or less, one IPO occurs if prices are between$89.01 and $94.00, two occur for prices between $94.01 and $99.00, three IPOs occur if prices are between $99.01 and $104.00, fourIPOs occur for prices between $104.01 and $109.00, five IPOs are issued if prices are between $109.01 and $114.00 and six IPOs areissued if prices exceed $115. Each period the market earns a return of either +5% or -5%. Each return is equally likely. IPOs earn the marketreturn plus an excess return of either +10% or -10%. Each excess return is equally likely and independent of the market return. In each period,there are four equally likely possible combinations of market returns and excess returns to IPOs. Over two periods there are 42=16 equallylikely paths of market returns, IPO excess returns, and IPO issues.

29

Priceat 0

Issuedat 0

ExcessReturn0 to 1

MarketReturn0 to 1

Priceat 1

Issuedat 1

ExcessReturn1 to 2

MarketReturn1 to 2

Numberof IPOs

# IPOsFollowed by +/-

Excess Return

# IPOsFollowed by

+/- Mkt Return

Mean ExcessReturn

100 3 .10 .05 115 6 .10 .05 9 9 / 0 9 / 0 .10

100 3 .10 .05 115 6 .10 -.05 9 9 / 0 3 / 6 .10

100 3 .10 .05 115 6 -.10 .05 9 3 / 6 9 / 0 -.03

100 3 .10 .05 115 6 -.10 -.05 9 3 / 6 3 / 6 -.03

100 3 .10 -.05 105 4 .10 .05 7 7 / 0 4 / 3 .10

100 3 .10 -.05 105 4 .10 -.05 7 7 / 0 0 / 7 .10

100 3 .10 -.05 105 4 -.10 .05 7 3 / 4 4 / 3 -.01

100 3 .10 -.05 105 4 -.10 -.05 7 3 / 4 0 / 7 -.01

100 3 -.10 .05 95 2 .10 .05 5 2 / 3 5 / 0 -.02

100 3 -.10 .05 95 2 .10 -.05 5 2 / 3 3 / 2 -.02

100 3 -.10 .05 95 2 -.10 .05 5 0 / 5 5 / 0 -.10

100 3 -.10 .05 95 2 -.10 -.05 5 0 / 5 3 / 2 -.10

100 3 -.10 -.05 85 0 .10 .05 3 0 / 3 0 / 3 -.10

100 3 -.10 -.05 85 0 .10 -.05 3 0 / 3 0 / 3 -.10

100 3 -.10 -.05 85 0 -.10 .05 3 0 / 3 0 / 3 -.10

100 3 -.10 -.05 85 0 -.10 -.05 3 0 / 3 0 / 3 -.10

30

Table II. The distribution of the number of offerings per month.The number of offerings is obtained for each month from January 1973 through December 1997 fromSecurities Data Corporation. Offerings with SIC codes 4911-4941 (utilities), 6000 - 6081 (banks),6722, 6726, 6792 (funds and investment cos) are excluded.

Monthly Number of InitialPublic Offerings

Monthly Number of SeasonedEquity Offerings

Mean 26.80 26.02

Median 21 20

Minimum 0 1

Maximum 107 104

1st Order Autocorrelation .85 .83

31

Table III. Aftermarket returns for IPOs and SEOs.Excess returns are calculated for the 60 calendar months and 60 event months following every offeringfrom January 1973 through December 1997. Excess returns are the difference between the IPO orSEO returns and the CRSP value-weighted or equal-weighted index. Average excess returns, asshown in the table, are calculated weighting each calendar month or each event month equally.Offerings by firms with SIC codes 4911-4941 (utilities), 6000 - 6081 (banks), 6722, 6726, 6792(funds and investment cos) are excluded.

IPOs SEOs

Mean t-statistic Mean t-statistic

Calendar Time Returns 1.126% 2.73 0.954% 2.68

Calendar Time Value-Weighted Excess Returns 0.020% 0.08 -0.152% -0.90

Calendar Time Equal-Weighted Excess Returns -0.123% -0.89 -0.295% -2.40

Event Time Returns 0.850% 13.66 0.957% 17.52

Event Time Value-Weighted Excess Returns -0.490% -8.10 -0.377% -7.07

Event Time Equal-Weighted Excess Returns -0.194% -3.39 -0.186% -3.59

32

Table IV. Panel A. Regressions of numbers of IPOs and SEOs each month on time, a market index based on returns on the CRSP value-weighted portfolio, and indices based on returns of past IPOs or SEOs. The time variable is set equal to one in January 1973 and incrementedby one each month. The market, IPO and SEO indices are set to 100 for the end of January 1973 and then are assumed to earn the samereturn as the portfolio of all firms with IPOs or SEOs in the prior 60 months. T-statistics are shown in parentheses under coefficient estimates.White estimates of standard errors are used in calculating t-statistics. Firms with SIC codes 4911-4941 (utilities), 6000 - 6081 (banks), 6722,6726, 6792 (funds and investment cos) are excluded.

Dependent Variable Intercept Time MarketIPO or SEO

Index Market1/2IPO or SEO

Index1/2 R2

Monthly Number IPOs 2/73 - 12/97 -0.7002(-0.69)

0.0539(21.69)

.6473

Monthly Number IPOs 2/73 - 12/97 9.1734(6.19)

0.0363(13.11)

.4483

Monthly Number IPOs 2/73 - 12/97 -1.9744(-2.60)

-0.1439(-7.11)

-0.0571(-10.14)

0.1533(18.78)

.7797

Monthly Number IPOs 2/73 - 12/97 -18.2452(-2.39)

-0.2934(-5.60)

-0.1406(-8.60)

0.2126(8.36)

5.0570(5.93)

-2.4533(-2.73)

.8010

Monthly Number SEOs 2/73 - 12/97 4.3041(3.72)

0.0687(18.86)

.5217

Monthly Number SEOs 2/73 - 12/97 11.4551(8.82)

.0300(13.90)

.4208

Monthly Number SEOs 2/73 - 12/97 -0.4819(-0.48)

-0.2041(-7.45)

-0.0776(-7.51)

0.3004(10.69)

.6736

Monthly Number SEOs 2/73 - 12/97 11.9871(1.29)

-0.0904(-2.05)

-0.0383(-1.53)

0.2774(4.00)

-2.9151(-2.71)

0.9847(0.50)

.6801

33

Table IV Panel B. Poisson regressions with an overdispersion parameter (negative binomial regressions) of numbers of IPOs and SEOs eachmonth on time, a market index based on returns on the CRSP value-weighted portfolio, and indices based on returns of past IPOs or SEOs.The time variable is set equal to one in January 1973 and incremented by one each month.

Dependent Variable Intercept Time MarketIPO or SEO

Index Market1/2IPO or SEO

Index1/2Pseudo

R2

Monthly Number IPOs 2/73 - 12/00 .8913(8.79)

.0078(7.24)

-.0023(-16.65)

.0037(11.41)

.1258

Monthly Number IPOs 2/73 - 12/00 -1.6753(-9.22)

-.0000(-0.01)

-.0032(-7.35)

-.0868(-4.77)

.3700(15.48)

.1958

Monthly Number IPOs 2/73 - 12/00 -3.8675(-13.61)

-.0232(-9.53)

-.0027(-7.23)

-.0042(-10.42)

.2056(5.93)

.4496(19.37)

.2246

Monthly Number SEOs 2/73 - 12/00 1.9699(24.72)

.0003(0.29)

-.0017(-12.03)

.0059(10.48)

.0897

Monthly Number SEOs 2/73 - 12/00 .2182(0.98)

.0011(3.31)

-.0028(-2.74)

-.1897(-7.61)

.4153(9.70)

.1197

Monthly Number SEOs 2/73 - 12/00 -1.2394(-3.21)

-.0117(-4.51)

-.00005(-0.12)

-.0049(-4.46)

-.0526(-1.36)

.5181(10.84)

.1267

34

Table V. Simulations of IPO aftermarket excess returns. I run 1,000 simulations of a 25 year period of IPO returns. I calculate the mean event excess return for each IPO in each simulation for periodsbefore and after the IPO. Estimates are based on actual data for 1/73 - 12/97. The expected return on the market each month is .0112, with avariance of .00204. The return on the portfolio of recent IPOs is -.00345 +1.3084 x market return. The constant is chosen so that IPOs havethe same expected return as market. The variance of the residuals is .00182. The relation between the number of IPOs and the level of theCRSP value-weighted index and the IPO index is estimated over 1973-1997. The number of IPOs in a month is given by -18.245 -.2934*month-.1406 x value of markett-1 + .2126 x (IPO indext-1) + 5.0571 x (value of markett-1)

-2.4533 x (IPO indext-1) . Returns are

cumulated over event periods by summing abnormal returns for each month.Panel A. Cumulative abnormal returns around IPOs.

Cumulative Abnormal Returns

Months -36, -1 -24,-1 -12, -1 -3, -1 -1 1 1 - 3 1 - 12 1 - 24 1 - 36 1 - 60

Median .1559 .1086 .0618 .0158 .0054 -.0052 -.0152 -.0589 -.1064 -.1485 -.2132

Mean .1675 .1178 .0639 .0169 .0057 -.0044 -.0128 -.0486 -.0897 -.1207 -.1609

Standard Error .0073 .0051 .0027 .0007 .0002 .0002 .0007 .0027 .0052 .0075 .0114

t-statistic 22.98 22.88 23.50 23.80 23.81 -18.89 -18.54 -17.87 -17.24 -16.06 -14.16

10th Percentile -.1011 -.0708 -.0367 -.0090 -.0030 -.0124 -.0366 -.1411 -.2708 -.3814 -.5420

25th Percentile .0355 -.0251 .0165 .0040 .0013 -.0088 -.0261 -.1014 -.1838 -.2603 -.3810

75th Percentile .2884 .2039 .1091 .0286 .0098 -.0008 -.0025 -.0100 -.0090 -.0091 .0126

90th Percentile .4517 .3133 .1666 .0446 .0153 .0052 .0154 .0629 .1230 .1824 .2973

Percentage < 0 19.9% 18.9% 19.2% 19.1% 18.7% 78.5% 78.4% 78.0% 76.0% 75.7% 74.1%

35

Table V, Panel B. Calendar-period cumulative abnormal returns and event-period cumulative abnormal returns in the 60 months after an offering for light months(lowest quartile of number of offerings) and heavy months (highest quartile of number of offerings). Quartiles are based on months with at leastone offering. Calendar excess returns are an equal weighted average of excess returns across all months. Ex-post calendar excess returns arecalendar excess returns conditioned on at least one IPO in the previous 60 months.

EventExcess Return

Calendar ExcessReturn

Ex-Post CalendarExcess Return

Light Months ExcessReturn

Heavy MonthsExcess Return

Median -.2132 .0048 -.0765 .0734 -.2969

Mean -.1609 -.0023 -.0648 .0225 -.2397

Std. Error .0114 .0081 .0089 .0097 .0144

t-statistic -14.16 -0.28 -7.25 2.32 -16.64

10th Percentile -.5420 -.3398 -.4074 -.4029 -.7454

25th Percentile -.3810 -.1702 -.2611 -.2013 -.5232

75th Percentile .0126 .1747 .1334 .2491 -.0024

90th Percentile .2973 .3205 .3066 .3773 .3383

36

Table V, Panel C. Event period wealth relatives and market returns following IPOs. Wealth relatives are obtained by dividing 1 plus the total return on the IPOsby 1 plus the total return by the simulated market. The market return is the average calendar month return. Market returns in 1-36 and 1-60 arethe average monthly returns in the 36 and 60 event month period returns following IPOs.

Wealth Relative 1-36

Wealth Relative 1-60

MarketReturn

Market Return 1-36a

Market Return 1-60b

Number of IPOsper Monthsc

Median .8545 .7860 .0112 .0096 .0099 18.0

Mean .9118 .8985 .0112 .0094 .0096 86.5

Std. Error .0078 .0129 .0001 .0002 .0001 5.0

10th Percentile .6816 .5686 .0077 .0029 .0039 1.6

25th Percentile .7637 .6619 .0094 .0066 .0071 3.3

75th Percentile .9908 .9834 .0130 .0127 .0127 96.8

90th Percentile 1.2042 1.3490 .0145 .0153 .0150 240.4a The difference between return on market overall and return in the 36 months after an IPO is .00183 per month with a t-statistic 14.63. b The difference between return on market overall and return in the 60 months after an IPO is .00154 per month with a t-statistic 14.05.c Correlations of total number of offerings and 5-year excess returns: .5262.

37

Table VI. Simulations of aftermarket SEO cumulative abnormal returns.I run 1,000 simulations of a 25 year period of SEO returns. I calculate the mean event excess return for each SEO in each simulation forperiods before and after the SEO. Estimates are based on actual data for 1/73 - 12/97. The expected return on the market each month is.0112, with a variance of .00204. The return on the portfolio of recent SEOs is -.0035 +1.3143 x market return. The constant is chosen so thatSEOs have the same expected return as market. The variance of the residuals is .00069. The relation between the number of SEOs and thelevel of the CRSP value-weighted index and the SEO index is estimated over 1973-1997. The number of SEOs in a month is given by 11.9871- .0904*month-.0383 x value of markett-1 + .2774 x (SEO indext-1) - 2.9151 x (value of markett-1)

+0.9847 x (SEO indext-1) . Returns are

cumulated over event periods by summing abnormal returns for each month.Panel A. Cumulative abnormal returns around SEOs.

Cumulative Abnormal Returns

-36, -1 -24,-1 -12, -1 -3, -1 -1 1 1 - 3 1 - 12 1 - 24 1 - 36 1 - 60

Median .1174 .0855 .0487 .0131 .0045 -.0041 -.0120 -.0468 -.0848 -.1269 -.1824

Mean .1473 .1060 .0583 .0155 .0053 -.0029 -.0088 -.0337 -.0625 -.0858 -.1181

Standard Error .0056 .0038 .0020 .0005 .0002 .0002 .0006 .0025 .0048 .0071 .0111

t-statistic 26.34 27.54 29.17 30.20 30.73 -13.89 -13.82 -13.59 -12.99 -12.13 -10.63

10th Percentile -.0409 -.0236 -.0076 -.0020 -.0006 -.0103 -.0311 -.1171 -.2277 -.3331 -.4963

25th Percentile .0208 .0207 .0145 .0043 .0016 -.0072 -.0217 -.0840 -.1606 -.2302 -.3476

75th Percentile .2458 .1759 .0928 .0237 .0081 .0008 .0020 .0084 .0257 .0464 .0954

90th Percentile .3839 .2702 .1419 .0372 .0126 .0062 .0202 .0747 .1412 .2155 .3627

Percent < 0 19.1% 17.9% 14.9% 13.6% 13.4% 71.7% 72.1% 71.4% 70.7% 69.7% 67.7%

38

Table VI. Panel B. Calendar-period cumulative abnormal returns and event-period cumulative abnormal returns in the 60 months after anoffering for light months (lowest quartile of number of offerings) and heavy months (highest quartile of the number of offerings). Quartiles arebased on months with at least one offering. Calendar excess returns are an equal weighted average of excess returns across all months. Ex-postcalendar excess returns are calendar excess returns conditioned on at least one IPO in the previous 60 months.

EventExcess Return

Calendar ExcessReturn

Ex-Post CalendarExcess Return

Light Months ExcessReturn

Heavy MonthsExcess Return

Median -.1824 .0037 -.0181 .0683 -.2644

Mean -.1181 -.0032 -.0295 .0303 -.2038

Std. Error .0111 .0073 .0077 .0069 .0148

t-statistic -10.63 -0.44 -3.81 4.38 -13.81

10th Percentile -.4963 -.3023 -.3337 -.2754 -.7556

25th Percentile -.3476 -.1566 -.2264 -.0773 -.5026

75th Percentile .0954 .1529 .1462 .1703 .0779

90th Percentile .3627 .2891 .2891 .2596 .4140

39

Table VI, Panel C.Event period wealth relatives and market returns following SEOs. Wealth relatives are obtained by dividing 1 plus the total return on the IPOsby 1 plus the total return by the simulated market. The market return is the average calendar month return. Market returns in 1-36 and 1-60 arethe average monthly returns in the 36 and 60 event month period returns following IPOs.

Wealth Relative 1-36

Wealth Relative 1-60

Return onMarket

Return onMarket 1-36a

Return onMarket 1-60

# of SEOs perMonth

Median .8963 .8443 .0112 .0103 .0105 73.9

Mean .9632 .9696 .0112 .0101 .0103 168.5

Standard Error .0075 .0127 .0001 .0001 .0001 7.77

10th Percentile .7370 .6188 .0077 .0047 .0053 5.0

25th Percentile .8053 .7067 .0094 .0076 .0080 17.3

75th Percentile 1.0714 1.1203 .0130 .0132 .0130 219.2

90th Percentile 1.2643 1.4581 .0145 .0155 .0152 456.1a The difference between return on market overall and return in the 36 months after an SEO is .00104 per month with a t-statistic 9.75. b Difference between return on market overall and return in the 60 months after an SEO is .00088 per month with a t-statistic 8.80. c The correlations of total number of offerings and 5-year excess returns is .5966.

40

Table VII. Sensitivity Analysis. Ex-post excess returns for IPOs (SEOs) are simulated when ex-ante excess returns are zero. In each case, theexcess returns are simulated for 60 months following an offering. The base case refers to the cumulative abnormal returns in Table V, (or VI)where the number of IPOs (SEOs) each month is based on the level of previous IPOs (SEOs), the level of the market, the square root of thelevels and the number of months since the beginning of the simulated calendar period. Buy and hold excess returns are the difference betweenthe cumulated return of each IPO (SEO) and of the market over the 60 months following the offering. The linear model for number of offers isbased on regressing the number of IPOs (SEOs) each month over 1973-1997 on the level of the index of previous IPOs (SEOs), the level ofthe CRSP value-weighted index and the number of months from January 1993. Size match excess returns are simulated by first matching eachIPO(SEO) over 1973 - 1997 with another firm of near equal market capitalization. IPO (SEO) capitalizations are obtained by multiplying theoffering price by the number of shares outstanding after the IPO. Matching firm sizes are the capitalizations as of the end of the previouscalendar year. If a match leaves the CRSP tape it is replaced by another with a capitalization as close as possible to the IPO (SEO). No firmlisted on CRSP less than five years is eligible for a match. No match firm is used more than once during a calendar month. Match firm and IPO(SEO) returns are then used to generate levels of the match firm and IPO (SEO) index for each calendar month over 1973-1997. Estimates ofthe relation between the levels of these indices and the number of IPOs (SEOs), estimated as in the base case, are then used to simulate thenumber of IPOs each month. In the Poisson regression simulations, the relation between the number of IPOs (SEOs) in a month is estimatedusing the same variables as the base case but in a Poisson regression with an overdispersion parameter. Simulations based on rearrangingactual returns involve randomly rearranging the returns on the CRSP value weighted index and randomly rearranging the residual from aregression of the returns on the recent IPO (SEO) index on the CRSP value-weighted index. In the Windsorized simulations observations arediscarded if the number of offers is extreme are based on simulating 1,000 paths of stock returns and offerings and then discarding the 100 withthe highest number of offers and the 100 with the lowest number of offers. Double variance simulations use twice the variance of the residualreturn on IPOs (SEOs) over 1973-1997 in simulations.

41

Panel A. IPOs

BaseCase

Buy and HoldExcessReturns

Linear Modelfor Number of

Offers

Size MatchExcessReturns

PoissonRegression

RearrangeActual

Returns

WindsorizeBased on

Number Offers

Use DoubleActual

Variance

Median -.2132 -.3655 -.2376 -.1567 -.1957 -.1721 -.2348 -.2636

Mean -.1609 -.2765 -.1844 -.1324 -.1435 -.1808 -.1985 -.2281

Std. Error .0114 .0201 .0124 .0160 .0110 .0039 .0113 .0129

t-statistic -14.16 -13.72 -14.81 -8.30 -13.07 -45.98 -17.58 -17.66

10th Percentile -.5420 -.8600 -.6023 -.7355 -.5184 -.3494 -.5498 -.6941

25th Percentile -.3810 -.6402 -.4369 -.4610 -.3709 -.2516 -.3883 -.4810

75th Percentile .0126 -.0711 .0169 .1809 .0501 -.1025 -.0349 -.0188

90th Percentile .2973 .5427 .3398 .5178 .3176 -.0329 .2180 .2959

Percent < 0 74.1% 77.6% 74.2% 62.4% 71.2% 94.4% 78.6% 76.2%

42

Panel B. SEOs

BaseCase

Buy and HoldExcessReturns

Linear Modelfor Number of

Offers

Size MatchExcessReturns

PoissonRegression

RearrangeActual

Returns

WindsorizeBased on

Number Offers

Use DoubleActual

Variance

Median -.1824 -.3392 -.1711 -.1473 -.1845 -.0498 -.1866 -.2121

Mean -.1181 -.2063 -.1121 -.1063 -.1363 -.0489 -.1449 -.1473

Std. Error .0111 .0204 .0108 .0131 .0103 .0031 .0114 .0119

t-statistic -10.63 -10.10 -10.39 -8.11 -13.22 -15.82 -12.74 -12.40

10th Percentile -.4963 -.8897 -.4880 -.6163 -.4813 -.1640 -.5085 -.5491

25th Percentile -.3476 -.5843 -.3389 -.4011 -.3523 -.1154 -.3546 -.3997

75th Percentile .0954 .1188 .0881 .1593 .0618 .0096 .0630 .0720

90th Percentile .3627 .6439 .3570 .4559 .3092 .0816 .2928 .3682

Percent < 0 67.7% 70.1% 68.1% 63.0% 68.9% 72.3% 69.9% 69.2%

43

Agrawal, Anup, Jeffery Jaffe, and Gershon Mandelker, 1992, The pos