Agreeing to Disagree: Why IPOs are Underpriced? James R. Booth Arizona State University Department of Finance College of Business Tempe, AZ 85287 Tel: 480-965-5698 Fax: 480-965-8539 Email: james.booth@asu.edu Lena C. Booth Thunderbird- American Graduate School of International Management Department of World Business Glendale, AZ 85306 Tel: 602-978-7418 Fax: 602-843-6143 Email: [email protected]JEL Classification code : G24; G32 Key words: Initial pub lic offerings, un derpricing, initia l returns, divergence ofopinion, ownership constraint, and liquidity requirements. Current draft: July 2003
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Existing explanations of IPO underpricing are applicable to only one market
and/or a particular issuing procedure. Global evidence on IPO underpricing presents
a challenge to these explanations (see Jenkinson and Ljungqvist (2001) and Ritter
(2003) for summaries). In this study, we develop a new explanation for initial
underpricing that is robust to different financial markets and issuing procedures.
Our explanation is based on the presence of divergence of opinion and ownership
restrictions at the time of the initial offering. The role of divergence of opinion in
asset pricing was presented in earlier work (see Miller (1977)). Recently, it has
received increased attention in studies of price setting, particularly in the presence
of short-selling constraints.1 However, no study has formally examined the role of
divergence of opinion in the relation between IPO offer price and secondary market
price.2 In the current paper, we argue that the combination of divergence of opinion
and ownership restrictions produces initial underpricing across all issuing
procedures, even if market participants (issuers and investment banks) seek to
eliminate it. Thus, our explanation for initial underpricing differs from traditional
models where underpricing is used to cheat, signal, reward, entrench, and/or
protect one or more parties involved in the IPO. Our explanation also deals with
immediate secondary market consideration, a phenomenon that is generally
ignored in previous IPO underpricing models.3
1 These studies include Houge et. al. (2001) , Geczy et.al. (2002), D’Avolio (2002), Duffie et. al. (2002),among others.2 Miller (1977) does mention that ignoring or incorrectly estimating divergence of opinion may lead toinitial underpricing. The problem is that this naïve investment banker model is not very satisfying inthe global IPO context where investment bankers often do not set the offer price.3 An exception is Booth and Chua (1996) in which underpricing serves to compensate investors forinformation production and secondary market liquidity considerations.
of opinion arises. This is consistent with recent treatments of the costs of shorting
stocks.4
The foundation for this type of opinion divergence can be traced as far back
as Keynes (1937) and Williams (1938). Tobin (1958) suggests, “When Keynes refers
to uncertainty in the market, he appears to mean disagreement among investors
rather than subjective doubt in the mind of an individual investor”. Williams (1938)
appeared to have a similar notion in describing an individual investor’s demand
curve. He argues that investors are presumed to formulate their own single point
estimate of asset values; and each investor then invests his/her entire funds in the
assets with the highest excess value over the market price. The key issue for
investors, thus, is not how much to invest, but rather which asset to invest in. Each
investor has a perfectly elastic demand curve at prices below the subjective
assessed value. However, the market demand curve slopes down because
investors have heterogeneous opinions about the asset values.5 Implicit in this
discussion is the notion that investors have wealth constraints that limit the amount
of each security that they can purchase. Otherwise, the investor who values it most
highly will hold all the securities.
From this discussion, we can see that divergence of opinion can cause the
aggregate demand curve for a firm’s shares to slope downward even if individual
investors do not have uncertainty about possible return distributions. Modern
notions of divergence of opinion generally derive from Knight (1921). Here the idea
is that divergence of opinion derives from uncertainty about the possible return
distribution. This may be why Miller (1977) and Houge et. al. (2001) do not attempt
to distinguish between divergence of opinion and uncertainty.
4 See Duffie (2002), D’Avolio (2002), Geczy et.al. (2002), Houge et. al. (2001). A similar framework isalso used by Hong and Stein (2003).5 For a discussion of how this relates to the portfolio problem in the CAPM, see Mayshar (1983).
It is not crucial to our analysis at to which form of divergence of opinion
applies. It is only important that investors disagree about value and that one group
does not have superior information over another; or if one group of investors has
superior information, the other group does not know, or alternatively it disagrees.
Thus our framework excludes the asymmetric information frameworks of Rock
(1986), Beatty and Ritter (1986) and Benveniste and Spindt (1989), among others.
Their models would provide a slight complication to current analysis related to the
transition from offer price to secondary market price. Since the transition is not well
defined in their models, we will leave the discussion of it to later. We next develop
the aggregate demand curve for IPO shares in the presence of divergence of
opinion.6
B. The Aggregate Demand Curve
With the above assumptions, we can derive the aggregate demand curve for
a particular IPO in the presence of ownership constraints. For simplicity, we assume
investors are risk neutral in their demand for shares and assume investor’s opinions
about value are drawn from a normal distribution.
A key difference in our framework is that we assume wealth constraints on
individual purchases are not binding. Thus unlike Miller (1977) and Morris (1996),
we do not assume that wealth constraints limit investors to purchase a single share
in either the initial offering or the secondary market. As in traditional auction
theory, they treat this as a benign assumption. For IPOs, the ownership allocation
decision is crucial. Even if we assume the issuer does not care about ownership
6 When a firm first chooses to go public, we might expect high divergence of opinion as suggested byMiller (1977). He wrote, “The divergence of opinion about a new issue are greatest when the stock isissued. Frequently the company has not started operations, or there is uncertainty about the successof new products or the profitability of a major business expansion.”
dispersion either for retaining control (as in Brennan and Franks (1997)) or for
secondary market liquidity (as in Booth and Chua (1996)), the stock exchange
imposes restrictions on both the minimum number of shares and shareholders a
firm needs to have in the public float to qualify for listing.7 These considerations are
crucial in developing the aggregate demand curve for shares at the offering. It is
not only the position of the aggregate demand curve (i.e. the cumulative
distribution of the number of investors with opinions of value greater than or equal
to a given value) that is important, the distribution of individual demand curves that
make up this aggregate demand curve is crucial as well.8
Most early work on asset pricing consequences of divergence of opinion
ignores the ownership dispersion issue and/or imposes wealth constraints that limit
investors to only one share of many. For example, Miller (1977) assumes investors
can only afford one share in the secondary market (he does not consider the initial
offering). He concludes that if N>1 shares are available, the presence of divergence
of opinion means that the secondary market price will be set by the N investors who
are the most optimistic about value. Without divergence of opinion or an imposed
wealth constraint then N=1. In other words the investor who values it the most will
purchase all the shares.
In our framework, we assume no wealth constraint since average issue
proceeds in an IPO is approximately $35 million. A single institutional investor can
afford to purchase an entire issue if permitted. At least two restrictions may limit
investors demand; one is that in U.S. regulations, one effectively becomes an
insider if ownership exceeds 5% of available shares. The other is that if ownership
7Previous studies tend to focus on getting the shares into the hands of the original purchasers and not
on what happens even minutes after the shares are distributed (i.e. how do prices adjust so as to getinitial underpricing).8
In traditional auction theory, it is usually assumed that the number of investors exceeds the availablesupply of the asset being auctioned and that only the highest bidder will receive the asset.
becomes too concentrated (i.e., the number of shareholders fall below the minimum
required by the exchange), then the shares will face delisting due to a decline in
liquidity. Thus, we assume no investor will seek to purchase more than 5% of
available shares unless they are seeking control.
For convenience, we assume each investor is allowed to buy only one share
block at the offering. Thus a minimum number of share blocks have to be sold to
minimum number of investors for a firm to successfully go public. As in Williams
(1938), we assume that each investor has a perfectly elastic demand curve at
prices below the subjective assessed value for up to 4.99% of available shares. The
aggregate demand curve is downward sloping because investors have
heterogeneous opinions about the value of the shares and N> NMIN investors must
own shares. This leads to the same conclusion as in Miller (1977), i.e. when there
are N share blocks available, the market clearing price for the shares will be set by
the N investors who are the most optimistic about value (with N> 1).
In Figure 1, the aggregate demand curve for the share blocks of a given firm
is represented by DD. This is a constrained demand curve in the sense that one
investor is allowed to purchase only one share block. The demand curve
represented by D’D’ is more inelastic, representing greater divergence of opinion
about the value.9
Insert Figure 1 Here
C. The Supply Curve: To Go or Not to Go Public?
9 For simplicity, we assume that investors are risk neutral. Their individual demand curves are perfectlyelastic at prices equal to or below their assessed value of the shares of firm A or B. If we allow anyform of risk aversion, their demand curves and hence the aggregate demand curves will become moreinelastic.
In developing the supply curve for shares, we need to keep in mind that
going public means offering shares in a very specific way. This consideration is
usually not discussed in models of IPO underpricing.10 In other words, price is not
the only consideration. Firms choose to go public when they believe they can sell
the shares to a dispersed investor base (i.e. achieve liquidity for the shares) and still
receive the minimum price at which they are willing to sell part of the firm. This
means the discussion of the supply of shares has to focus on the number of
shareholders (each receiving one share block for convenience). Thus the different
sections of the supply curve for share blocks (SB) is represented by:
(1) SB/Smin >=SBmin/Smin if OP>Pmin and N>=Nmin potential shareholders;
(2) SB/Smin = 0 if OP>Pmin and N< Nmin potential shareholders;
(3) SB/Smin = 0 if OP< Pmin and N>=Nmin potential shareholders; or
(4) SB/Smin = 0 if OP< Pmin and N<Nmin potential shareholders.
This highlights the impact of restrictions on shares and share blocks. Consider
the U.S. listing requirements on Nasdaq and NYSE. The minimum number of public
shares required for listing is 1.1 million. Thus the supply curve has to be either 0,
equal to, or greater than 1.1 million shares. Additionally, the public float portion of
these shares must be owned by at least 400 investors for NASDAQ NMS listing
(NYSE listing requires 2,000 shareholders).11 This means that these 1.1 million
shares have to be issued to at least 400 investors (Nmin investors) in order to be
qualified for listing at NASDAQ NMS. This represents the minimum number of share
blocks (SBmin) required for going public. If we go beyond the exchange minimums
for liquidity purposes, then the number of share blocks will have to be even greater
10 Exceptions include Booth and Chua (1996), Brennan and Franks (1997), among others.11 The minimum number of round lot shareholders required for NASDAQ NMS listing under certainstandard was 800. As of April 2003, all the standards for NASDAQ NMS have a minimum of 400shareholders and 300 shareholders for NASDAQ Small-Cap.
(SB>SBmin). Figure 2 provides the relevant supply curves for share blocks with at
least the minimum number of shares.
Insert Figure 2
In Figure 2, we see that the current owners decide to go public only if the
demand curve for their share blocks is such that they can receive an offer price
greater than Pmin. If they go beyond the minimum exchange requirements on share
blocks to create additional liquidity, they will need additional demand, or
alternatively, they will have to lower the offer price. Issuing shares to more than
the minimum number of investors is likely necessary to ensure continued listing.
That is because the minimum number of shareholders needed for continued listing
in NASDAQ NMS is also 400. If shares were offered to only 400 investors, and if an
existing shareholder sells all his/her shares to another shareholder in the secondary
market, the firm would have violated the minimum requirement on the number of
shareholders.12 This means that the decision to go public at a reasonable price
shifts from the simple question of “how highly valued are our shares?” to “how
highly valued are our shares by at least the minimum number of investors?” In
Figure 2, offer price is determined when the aggregate demand curve and the
supply curve intersect. With demand at DD, offering more than the minimum
number of share blocks means the offer price have to be lowered.13
The decision to withdraw an offering is also influenced by the same
considerations. We illustrate that in Figure 3. We first assume that divergence of
12 It is not necessary to offer more than the minimum number of shares to ensure continued listing forNASDAQ NMS. The number of shares needed in the public float to ensure continued listing is 750,000.13 We exclude at this stage the notion in Booth and Chua (1996) that increasing the supply of sharesmay cause investors to value them more highly due to increased expectations regarding liquidity.
opinion is relatively low, as illustrated in the aggregate demand curve DD. At
SB/Smin >SBmin/Smin, the current owners of the firm will choose to go public and sell a
fraction of the firm because OP is above Pmin. This is possible because there are at
least N>Nmin investors who are willing to pay a price equals to OP. If the current
owners cannot receive at least Pmin at the minimum level of liquidity desired, they
will choose not to go public, or if they have previously decided to start the going
public process, they will withdraw the issue.
Insert Figure 3 here
As illustrated above this may occur because of higher divergence of opinion,
represented by the steeper aggregate demand curve D’D’. (As mentioned earlier,
SB/Smin is required to go public to ensure continued listing.) This means there are
not enough investors who are willing to pay Pmin (i.e. N<Nmin investors) for the
shares, thus the firm will have to withdraw the public issue.14 The firm can proceed
with selling part of the firm to a smaller group of investors who value it more highly
in a private transaction. This may explain why the vast majority of firms that
withdraw an IPO do not come back to the market at a later date.15 The above
argument implies that as divergence of opinion increases, the likelihood of
achieving the necessary conditions for the firm to go public will be reduced.
14 If the investment banker decides to go ahead with the issue by offering the shares at P min andabsorbing the unwanted shares, price will drop in the secondary market and results in overpricing. This is done only if the investment banker estimates that the loss from absorbing the unwanted sharesis less than the forgone underwriter spread had the issue been withdrawn, ignoring any reputationeffects.15 Evidence by Dunbar (2002) shows that only 9% of firms that are withdrawn attempt a second publicoffering at a later date. It is likely that many of these firms were subsequently sold in privatetransactions.
relaxed, thus resulting in initial underpricing (OP<MP and IR>0). In our framework,
investors A and B have different estimates of value because they have
heterogeneous opinions. Unlike the asymmetric information models such as Rock
(1986) and others, we do not assume that B is less informed than A (or visa versa)
and thus adverse selection in allocations does not affect behavior.16
We argue that case (4) represents the most realistic scenario of the IPO
market. We believe that heterogeneous opinions exist about the IPO shares.
Wealth constraint is usually not binding as one or a few institutional investors can
easily buy up the entire issue (even though they usually do so because of control
and liquidity reasons). Because of ownership dispersion constraint, the offer price
has to be set at or below the market clearing price, resulting in an oversubscription
for the shares. With secondary market trading, the price will be bid up, which
results in positive initial underpricing. This means that initial underpricing is
unintentional and is a natural by-product of divergence of opinion and ownership
dispersion constraint.
To summarize, in order to achieve zero initial underpricing (i.e. offer price
equal to the secondary market price), one or more of the following conditions must
hold. First, no divergence of opinion exists among investors. Second, a wealth
constraint is binding, both at the offering and in the secondary market. This would
also mean there is no trading in the secondary market until either new information
arrives or some investors holding the shares receive a liquidity shock. Third, there
is no restriction on the concentration of ownership such that the single most
optimistic investor gets the entire offering. If this occurs, the firm does not go
16 If we add that, it will only increase underpricing. It will also lead to additional complications as notedby Rock (1986) since lowering offer price will lead to increased informed demand.
is relaxed, trading price will rise to where aggregate demand intersects supply at
SBmin/Smin.17 In the case of low divergence of opinion, the price run-up will be less
(from OP to MPD) than in the case of high divergence of opinion (from OP to MPD’).18
This suggests that in successful offerings, initial underpricing increases with the
level of divergence of opinion.
Insert Figure 4 Here
Besides divergence of opinion, the variation in initial underpricing can also
result from how the shares are being rationed at the offering. If more shares are
allocated to investors with higher valuation, initial underpricing will be less
compared to if all investors receive the same number of shares or if more shares
are allocated to investors with lower valuation.
The explanation thus far (and many previously developed explanations)
seems to treat initial underpricing as a direct cost to the issuer at the time the
shares are sold.19 This, of course, is not always the case. In Miller (1977)’s model,
higher level of divergence of opinion leads to a higher secondary market price. This
is due to his assumption that the marginal investor holds an opinion of value above
the average of all possible investors for these shares. Here we have illustrated that
higher divergence of opinion leads to larger initial underpricing. Our result,
17 We can also illustrate this by assuming that new investors who do not receive shares in the IPO
appear in the secondary market. Either way we are illustrating the possibility that prices will rise in thesecondary market if some investors who receive allocation in the IPO are selling their shares. Typicallythey will sell on the first day only if they can get a price higher than the offer price they paid.18 It is possible that if some existing investors continue to buy in the secondary market and very fewnew investors appear, the exchange’s mandated minimum could be violated. In that case,underpricing will be even more severe.19 An exception to this is the information production framework of Booth and Chua (1996). In theirframework, initial underpricing is designed to allow investors to recoup pre-bid information costs. Tothe degree that this information production may enhance secondary market liquidity (and thusestimates of value), underpricing does not represent a cost to the firm over and above what theywould have received for the shares in the absence of this information production.
however, is not dependent on the relative valuation of the marginal versus average
investor. As long as ∂D’D’/∂P> ∂DD/∂P, then initial underpricing will be a positive
function of divergence of opinion.
Our result suggests a more complex relation between initial underpricing and
issue proceeds discussed in earlier studies. Previous studies have defined initial
underpricing as money left on the table (see Loughran and Ritter (2002)), i.e. the
issue proceeds could have been larger if the issue was not underpriced. Our
analysis suggests that at least part, if not all, of this initial underpricing is a natural
consequence of divergence of opinion. Depending on the positions of the aggregate
demand curves, higher level of divergence of opinion may lead to higher offer
prices and hence larger amount of proceeds. This suggests that higher initial
underpricing may not be costly to the issuing firm in terms of proceeds forgone. We
illustrate this in Figure 5. When the level of divergence of opinion is high, the
aggregate demand curve (D’D’) intersects the supply curve SB/Smin at OPD’, resulting
in a higher offer price and hence larger issue proceed than when the level of
divergence of opinion is lower. At the same time, the higher level of divergence of
opinion also leads to higher initial underpricing.20 This scenario represents an
alternative rationale to the irrational issuer explanation suggested by Brealey and
Myers (page 389).
Insert Figure 5 Here
We next consider how divergence of opinion impact initial underpricing under
alternative share allocation mechanisms. This also provides a basis for discussing
20 If the demand curves are positioned in such a way that the intersections with supply curve occur tothe right of the crossover point of the two demand curves, higher level of divergence of opinion willlead to lower offer price and lower issue proceeds, but higher initial underpricing.
competitive auction. Second, they limit how much each individual non-competitive
bidder may receive. This is very similar to exchange listing requirements and
Securities and Exchange Commission’s restrictions on ownership dispersion. 21 The
form of the constraint on competitive bidders suggests that the Treasury is
concerned about the secondary market liquidity of their debt. This is reflected in
the limit on bids for new bills, taking into account existing holding of near identical
secondary market securities. Since rationed bidders can fulfil their excess demand
in the secondary market, this will have the effect of raising secondary market
prices. Not surprisingly, the amount of underpricing for Treasury is low compared to
the uncertain world of the IPO market. A more surprising finding is that
underpricing exists in the Treasury bill market at all. While technically a Treasury
auction is an auction of new bills (primary securities), virtually identical instruments
are already trading in the secondary market. These instruments take the form of
previously issued bills, notes, and bonds with identical maturities, and securities
offered through a when issued market before the auction.22
From this comparison with the Treasury auction market, one can only
conclude that underpricing should be more severe in the issuance of securities with
less certain cash flows, especially in light of more rigid stock exchange restrictions
on initial ownership dispersion. While the focus here has been on Treasury
securities, virtually every study of the pricing process of corporate debt finds the
same conclusions about initial underpricing.23
21 See U.S. Treasury 356.22 Limitations on Auction Awards. Noncompetitive bidders are limited to $1million for bills and $5 million for notes and bonds. Competitive bidders are limited to purchase notmore than 35 % of the public offering less their net long positions as reported under 356.13, which isbasically their positions in similar instruments in the secondary market.22 The presence of initial underpricing for new T-bills in a market with perfect substitutes appears tocontradict the notion of lack of market spanning as a reason for initial underpricing (see Mauer andSenbet (1992)).23 See, for example, Ederington (1974), Weinstein (1978), Booth and Smith (1986) Datta et. al. (1997),among others.
Our sample of IPOs from 1988-2000 is obtained from the Thomson Financial
Securities Data new issues database. IPOs with an offer price below $5.00 per
share, unit offers, REITs, closed-end funds, banks and S&Ls, ADRs, and partnerships
are excluded. Our sample does not include best efforts offers because they are
typically very small and are not covered by Thomson Financial. The initial sample
consists of 4,385 IPOs that have been issued during the 13-year period.25 We
excluded 63 issues where we could not determine whether the price ranges were
revised up or down. These are the issues in which the price ranges have been either
narrowed or widened. This reduced the sample to 4,322. The sample is further
reduced to 3,406 due to missing data in the variable firm’s earnings prior to IPO.
The final sample with complete data is 3,010 IPOs, after adjusting for additional
missing data in the variables such as ratio of retained shares to public float,
underpricing, and the intended use of proceeds.
Underpricing is defined as the percentage change between the offer price
and the first day closing market price of the IPO. Average underpricing is the equal
weighted average of the individual IPO underpricing each month. In the cross-
sectional analysis, we use variables shown in previous studies to be important in
explaining IPO underpricing as control variables. Year Trend is a variable taking on
values of 1 to 13 for years 1988 to 2000. As there is a wide variation in
underpricing each year, especially in the mid to late 1990s, we control for the trend
in the cross-sectional regressions.26 In the monthly underpricing regression, we
25 We start our sample from 1988 because the price range revision data is largely not available in Thomson Financial before that.26 To check for robustness, we also use a dummy variable for each year. The results are very similar.
We use three variables to proxy for the market-wide divergence of opinion.
First, we use the volatility index VIX and VXN. VIX and VXN are daily indices
obtained from the CBOE websites. VIX is calculated by taking a weighted average of
the implied volatility from eight calls and puts on the S&P 100 index, with thirty
calendar days to expiration. VXN is calculated using the same methodology as VIX,
but based on the implied volatility of Nasdaq-100 Index (NDX) options. Since VXN is
available only from 1995, forecast values based on a simple regression are used for
1988-1994. The coefficient estimates of the regression are obtained from regressing
VXN on constant and VIX for the period 1995-2000. For the cross-sectional analysis,
we use VIX-30days, the median VIX 30days prior to the IPO date as a proxy for
divergence of opinion.27 For the monthly regressions, we use means and medians
of VIX and VXN for the month. We conjecture that when the implied volatility of
stock indices is high, divergence of opinion among investors is high.
We use the cumulative daily returns of NASDAQ stocks 30 calendar days
(approximately 21 to 22 trading days) prior to the IPO date as another market-wide
proxy of divergence of opinion (NASDAQ-30days). NASDAQ returns are obtained
from CRSP. The cumulative NASDAQ return prior to the IPO has been used in
previous studies in explaining IPO underpricing. For example, Bradley and Jordan
(2002) and Loughran and Ritter (2003) find that when the cumulative NASDAQ
return 15 trading days prior to the IPO is large, underpricing is high. We conjecture
that when expected returns in the market are high, divergence of opinion is likely to
be high. For the monthly regressions, NASDAQ returns are the monthly returns
obtained from CRSP. Another variable we use to proxy for market-wide divergence
of opinion is the average underpricing for the firms going public in the 30 calendar
27 For robustness check, we also use mean of VIX 30 days prior to the IPO date, VIX on the IPO date,mean and median of VXN 30 days prior to the IPO date. The results are very similar.
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Are there sufficient number of investors to go public?
Pmin
SB/Smin
SBmin/Smin
44
D’D’ represent sufficient demand for the firm to go publicabove Pmin if the supply curve is SBmin/Smin. However, D’D’ doesnot intersect SB/Smin (supply curve necessary to ensurecontinued listing) at a price equal to or above Pmin for the firm to
OPD is the the offer price forDD demand curve (lowdivergence of opinion)
OPD’ is the offer price for D’D’demand curve (highdivergence of opinion)
SBmin/Smin is the supply curvefor minimum share blocks
SB/Smin is the supply curve for
share blocks more than theminimum (necessary to ensurecontinued listing)
Figure 5
Possible Impact of Divergence of Opinion on Offer Price and Issu e
Proceeds
Share Block/Sharemin
D
D’
D’
OPD
OPD’
SBmin /Smin
46
At higher level of divergence of opinion (D’D’), offer price andhence issue proceeds are higher. The initial underpricing ishigher too (the arrows represent initial underpricing.).
Summary statistics of the firm characteristics and the average underpricing each year from 1988-2000
The data is from Thomson Financial Securities. Underpricing is defined as the percentage change between the offer price and the first dayclosing market price of the IPO. Due to missing data, total number of observations available for underpricing, firms with earnings data, andfirms with use of proceeds data are 4,114, 3,406, and 4,045 respectively. The underwriter’s rank is obtained from Loughran and Ritter (2003).
Table IISummary statistics of firms going public from 1988-2000 characterized by various measures of
divergence of opinion.
The data is from Thomson Financial Securities. T-test is the test of mean differences of issue characteristics between firms withnegative versus positive earnings, tech versus non-tech firms, firms whose intended use of proceeds is to repay debt versus forother purposes, firms with versus without price revision, and firms with final offer price out of filing price range versus in range.Standard deviations are in parentheses. * and ** denotes statistically significant at the 0.01 and 0.05 level respectively.
Table IIITests of mean differences in underpricing for IPOs with high versus low
levels of divergence of opinion (Sample period from 1988-2000)
The data is from Thomson Financial Securities. T-test is the test of mean differences inunderpricing between firms with negative versus positive earnings, tech versus non-tech
firms, firms whose intended use of proceeds is to repay debt versus for other purposes,firms with versus without price revision, and firms with final offer price out of filing pricerange versus in filing price range. Standard deviations are in parentheses. * and ** denotesstatistically significant at the 0.01 and 0.05 level respectively.
Average Underpricing (%)1988-2000 1988-1998 1999-2000
Table IVTOBIT of Magnitude of Price Revisions on Different Proxies of Divergence
of Opinion
The data is from Thomson Financial Securities from 1988-2000. Revision-Magnitude is the absolute
value of ((Offer price – Midprice) / Midprice) where Midprice is the average of the high and low prices inthe preliminary price range. Year trend is a variable taking on values of 1 to 13 for years 1988 to 2000;VC-Backed is a binary variable which takes on a value of 1 if the IPO is backed by venture capitalists;High Ranked is the underwriter’s rank obtained from Loughran and Ritter (2003) with a ranking equalto 8 or above takes on a value of 1, zero otherwise. Overhang measures the ratio of retained shares topublic float. VIX-30days is the median VIX 30days prior to the IPO date. VIX is calculated by taking aweighted average of the implied volatility from eight calls and puts on the S&P 100 index, with thirtycalendar days to expiration. NASDAQ-30days is the cumulative daily returns of NASDAQ stocks 30 daysprior to the IPO date. Underpricing-30days is the average underpricing for the firms going public in the30 days before the IPO date. Z-statistics are in parentheses. Huber/White robust covariances areused. *, **, and *** denotes statistically significant at the 0.01, 0.05 and 0.10 level respectively.
Table VOLS Regressions of Underpricing on Different Proxies of Divergence
of Opinion
The data is from Thomson Financial Securities from 1988-2000. Underpricing is defined
as (first day closing market price - offer price) / offer price. Year trend is a variable taking onvalues of 1 to 13 for years 1988 to 2000; VC-Backed is a binary variable which takes on a valueof 1 if the IPO is backed by venture capitalists; High Ranked takes on a value of 1 is theunderwriter ranking equals to 8 or above, zero otherwise; Overhang measures the ratio of retained shares to public float; Revision-Magnitude is the absolute value of ((Offer price –Midprice) / Midprice) where Midprice is the average of the high and low prices in thepreliminary price range; Revised takes on a value of one if the filing price range is amended,and a value of zero otherwise; Out-of-range takes on a value of 1 if the final offer price is out of range, and zero if the final offer price is in the range; VIX-30days is the median VIX 30daysprior to the IPO date. VIX is calculated by taking a weighted average of the implied volatilityfrom eight calls and puts on the S&P 100 index, with thirty calendar days to expiration.NASDAQ-30days is the cumulative daily returns of NASDAQ stocks 30 days prior to the IPOdate. Underpricing-30days is the average underpricing for the firms going public in the 30 daysbefore the IPO date. T-statistics are in parentheses and they are corrected forheterokedasticity using White test. * and ** denote statistically significant at the 0.01 and 0.05
Table VIVolatility index as a measure of divergence of opinion (Sample
period: 1988-2000)
Multiple regression analysis of average monthly underpricing on number of IPOs in thecorresponding month, time trend, monthly Nasdaq returns, and arithmetic mean and median
of volatility indices, VIX and VXN, in the corresponding month. Average underpricing is theequal weighted average of the individual IPO’s underpricing each month. VIX and VXN are dailyindices and they are obtained from the CBOE websites. VIX is calculated by taking a weightedaverage of the implied volatility from eight calls and puts on the S&P 100 index, with thirtycalendar days to expiration. VXN is calculated using the same methodology as VIX, but basedon the implied volatility of Nasdaq-100 Index (NDX) options. Since VXN is available only from1995, forecast values based on a simple regression are used for 1988-1994. The coefficientestimates of the regression are obtained from regressing VXN on constant and VIX for theperiod 1995-2000. Average monthly underpricing and the total number of IPOs are obtainedfrom Jay Ritter’s website. Time trend is a sequential number taking on values of 1 for January1988 to 156 for December 2000. T-statistics are in parentheses and they are corrected forheterokedasticity using White test. * and ** denote statistically significant at the 0.01 and 0.05levels respectively.
Dependent Variable: Average Monthly Underpricing (%)