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PhD Course in Corporate Finance
Initial Public O�erings
Ernst Maug1
Revised March 3, 2016
1Professor of Corporate Finance, University of Mannheim; Homepage:http://http://cf.bwl.uni-mannheim.de/de/people/maug/, Tel: +49 (621)181-1952, E-Mail: [email protected]. This note is made publiclyavailable subject to the condition that any user noti�es the author of its use.Please bring any errors and omissions to the attention of the author.
Ernst Maug PhD Course in Corporate Finance
The Model
Based on Rock (1986)
A company o�ers 1 share of its common stock for the �rst time in
an initial public o�ering (IPO). Value of company is uncertain:
V =
{V̄ with probability pV with probability 1− p
The share is o�ered at an initial o�ering price P0; the price cannot
be revised.
Ernst Maug PhD Course in Corporate Finance
There are two groups of investors:
Informed investors acquire information about the company.
They apply for 0 < QI ≤ 1 shares if and only if they expect to
break at least even, otherwise they do not apply for shares.
Uninformed investors do not acquire any information and only
know the probability distribution for �rm values. They apply
for QU ≥ 1 shares if and only if they expect to break at least
even, otherwise they do not apply for shares.
Note: If uninformed investors and informed investors apply for
shares, then demand exceeds supply. Assume also that the number
of shares cannot be increased in this case (no �Greenshoe option�).
Ernst Maug PhD Course in Corporate Finance
We also assume:
Investors cannot short sell the shares.
The information acquired by informed investors is of the form
of a binary signal σ ∈ {σ;σ} where:
Pr (σ = σ |V = V ) = Pr(σ = σ
∣∣V = V̄)
= 1− ε.
Hence ε is the error of the signal. Assume for now that ε = 0,
i. e. informed investors receive a perfect signal.
If demand exceeds supply, shares are rationed pro rata, i. e.
every investor receives a proportion 1
QU+QIper share ordered.
Ernst Maug PhD Course in Corporate Finance
From these assumptions it is easy to derive the decision rule of
informed investors:
Apply if P0 ≤ V ,Do not apply if P0 > V .
It is clear that the issuer will never issue shares below V , and no
investor will ever buy shares if P0 > V̄ . Hence P0 ∈[V , V̄
]and
the policy of the informed investor can be rewritten as:
Apply if V = V̄ ,Do not apply if V = V .
Ernst Maug PhD Course in Corporate Finance
Then we can write the incentive compatibility constraint for the
uninformed investors as follows:
pQU
QU + QI
(V̄ − P0
)+ (1− p) (V − P0) ≥ 0.
This implies that the o�ering price is bounded from above.
De�ne α ≡ QUQU+QI
. Then:
P0 ≤αpV̄ + (1− p)V
1− (1− α) p.
Uninformed investors will not participate if this constraint is
violated.
Ernst Maug PhD Course in Corporate Finance
This shows immediately that the o�er is underpriced. The average
price in secondary trading is:
P1 = pV̄ + (1− p)V .
Then the average IPO discount is:
∆IPO = P1 − P0 = pV̄
(1− α
1− (1− α) p
)+ (1− p)V
(1− 1
1− (1− α) p
)= p (1− p)
(V̄ − V
) 1− α1− (1− α) p
.
Ernst Maug PhD Course in Corporate Finance
Note that:
The variance of a Bernoulli random variable like �rm value is
p (1− p)(V̄ − V
)2, hence the IPO discount is closely related
to the uncertainty or volatility of the share price.
The IPO discount is zero only if α = 1 as long as volatility is
not zero. Hence, 1− α is a parameter for the degree of
adverse selection.
Exercise
Generalize the model above for the case where ε > 0 and informed
investors' information is only imperfect. Derive new expressions for
P0 and ∆IPO .
Ernst Maug PhD Course in Corporate Finance
Exercise
Extend the model of Rock (1986) to include underwriter price
support in the secondary market as follows. Assume the �rm hires
an underwriter who is committed to buy all shares from the �rm at
the price PF . The underwriter sells the shares in the IPO for P0
and agrees to buy shares back in the secondary market for some
support price P . Only investors who bought shares in the IPO can
sell them back at the support price.
Ernst Maug PhD Course in Corporate Finance
Solve the model using the following steps:
Assume that P ∈[V , V̄
]. Rewrite the condition for the
uninformed investors to participate in the IPO. Show that P0
becomes a function of P. Derive this function and showwhether it is decreasing or increasing.Write down the payo� of the underwriter. This must includethe payo� from buying shares from the �rm and selling themto investors, and the expected cost of price support, i. e. thecost of buying shares above their intrinsic value. (Hint:assume the underwriter buys these shares from investors andimmediately sells them in the secondary market for theintrinsic value P1). From this, what is the price PF theunderwriter can o�er the �rm and still make a positive pro�t?
Ernst Maug PhD Course in Corporate Finance
Assume many banks compete for underwriting the issue, so
the underwriter makes zero pro�ts in equilibrium and the
underwriter who buys the shares from the �rm at the highest
price PF conducts the o�ering. Which level of price support Pis o�ered in equilibrium? Verify the initial assumption that
P ∈[V , V̄
]. Hence, what is the equilibrium solution for P0
and PF ?
Show that the equilibrium has the following properties: (1) the
adverse selection problem is eliminated completely, and the
�rm receives a fair price of the stock, and (2) the IPO is
overpriced. Comment on this solution.
Note: Models of IPO price support were published by Chowdhry
and Nanda (1996) and Benveniste, BuSaba and Wilhelm (1996).
Ernst Maug PhD Course in Corporate Finance
Based on Benveniste and Wilhelm (1990)
Entrepreneur wants to take his �rm public and sell one share
to two investors. Each investor observes a signal that is either
good (g) with probability p or bad (b) with probability 1− p.
Once listed, shares are trading at a price Ps where
s ∈ {0, 1, 2}, the number of good signals:
Ps = P̄ − (2− s)α .
Ernst Maug PhD Course in Corporate Finance
The entrepreneur hires an investment bank that sells the
shares at o�ering prices PsO to the public and elicits the
information of the two investors by way of a mechanism
through direct revelation (the revelation principle applies).
The investment bank can choose the allocation qsg , qsb as a
function of the information investors reveal to the bank during
bookbuilding.
Let φ ≤ 1 be the minimum number of shares the entrepreneur
wishes to sell in the issue.
Let f ≥ φ/2 be the maximum each investor is willing to buy.
Ernst Maug PhD Course in Corporate Finance
The objective of the bank and the entrepreneur is to choose an
allocation and o�ering prices to maximize expected proceeds.
Shares not sold in the IPO will be sold in an SEO later:
Π = E (Ps)− p2(P2 − P2
O
)2q2g
−2p (1− p)(P1 − P1
O
) (q1g + q1b
)− (1− p)2
(P0 − P0
O
)2q0b
subject to the following constraints.
1 Sell at least φ and at most one share:
1 ≥ 2q2g ≥ φ1 ≥ q1g + q1b ≥ φ (1)
1 ≥ 2q0b ≥ φ
Ernst Maug PhD Course in Corporate Finance
2 Investors are willing to buy at most f shares each:
0 ≤ qsg , qsb ≤ f s = 0, 1, 2. (2)
3 It must be incentive compatible for the investor with good
information to reveal her information truthfully:
p(P2 − P2
O
)q2g + (1− p)
(P1 − P1
O
)q1g (3)
≥ p(P2 − P1
O
)q1b + (1− p)
(P1 − P0
O
)q0b (4)
= p(P1 + α− P1
O
)q1b + (1− p)
(P0 + α− P0
O
)q0b .(5)
Ernst Maug PhD Course in Corporate Finance
4 It must be incentive compatible for the investor with bad
information to reveal her information truthfully:
p(P1 − P1
O
)q1b + (1− p)
(P0 − P0
O
)q0b
≥ p(P1 − P2
O
)q2g + (1− p)
(P0 − P1
O
)q1g (6)
= p(P2 − α− P2
O
)q1b + (1− p)
(P1 − α− P1
O
)q0b .
5 Investors are not willing to pay more for shares than they are
worth (participation constraint):
Ps ≥ Ps0 s = 0, 1, 2. (7)
Ernst Maug PhD Course in Corporate Finance
Analysis
Rewrite Π as:
Π = E (Ps)− 2p[p(P2 − P2
O
)q2g + (1− p)
(P1 − P1
O
)q1g]
−2 (1− p)[p(P1 − P1
O
)q1b + (1− p)
(P0 − P0
O
)q0b]
Assume that only (4) is binding and that (6) is not binding. Then
substitute (4) into the �rst square brackets:
Π = E (Ps)− 2p[p(P1 + α− P1
O
)q1b + (1− p)
(P0 + α− P0
O
)q0b]
−2 (1− p)[p(P1 − P1
O
)q1b + (1− p)
(P0 − P0
O
)q0b]
= E (Ps)− 2[p(P1 − P1
O
)q1b + (1− p)
(P0 − P0
O
)q0b]
−2pα[pq1b + (1− p) q0b
].
Ernst Maug PhD Course in Corporate Finance
Now choose the allocation and prices as follows:
1 Π is increasing in P1
O and P0
O . Hence, choose P1
O = P1 and
P0
O = P0, so (7) is binding for s = 0, 1. Then the �rst term in
square bracket vanishes.
2 Π is decreasing in q0b and q1b, so choose these as small as
possible, so from (1), q0b = φ/2, q1b = f and q1g = φ− f .
Ernst Maug PhD Course in Corporate Finance
3 Rewrite (4) and choose(P2 − P2
O
)q2g so that (4) is just
satis�ed:
p(P2 − P2
O
)q2g = α (pf + (1− p)φ/2) .
Solving for P2
0gives:
P2
O = P2 − α[f
q2g+
(1− p)φ
2pq2g
]Clearly, an admissable solution is q2g = f and
P2
O = P2 − α[1 +
(1− p)φ
2pf
]. (8)
Note that
P2 − α− P2
O =α (1− p)φ
2pf> 0 . (9)
Ernst Maug PhD Course in Corporate Finance
4 With this, P2
O < P1 = P2 − α. Note that the left hand side of
(6) equals zero because the o�ering prices equal the
aftermarket prices from the �rst step. The right hand side of
(6) can be rewritten using (9):
0 ≥ p
(α (1− p)φ
2pf
)f + (1− p) (−α) q
φ
2= 0 ,
where we have used that P1
O = P1, q0b = φ/2, and q1b = f ,hence (6) is also satis�ed.
Ernst Maug PhD Course in Corporate Finance
Discussion
Underpricing is the expected di�erence between market price and
o�ering price:
E (Ps − PsO) = p2
(P2 − P2
O
)= p2α
[1 +
(1− p)φ
pf
].
Underpricing is therefore:
Increasing in α,
Increasing in φ,
Decreasing in f .
Ernst Maug PhD Course in Corporate Finance
Expected proceeds are:
E (Ps)− 2pα [pf + (1− p)φ/2]
The second expression represents the rents extracted by informed
investors.
The o�ering price is not monotonic (P2
O < P1
O = P1). If that would
be required, then choose P1
O < P1 and underpricing increases.
Ernst Maug PhD Course in Corporate Finance
Regular investors
Assume the bank can extract some of the rents of regular investors
and induce them to accept a loss L > 0. Then (7) becomes
Ps + L ≥ Ps0 s = 0, 1, 2. (10)
Clearly, the bank will then overprice some IPOs and increase the
o�ering amount.
Ernst Maug PhD Course in Corporate Finance
Motivation
Based on Khanna, Noe and Sonti (2008)
Puzzling observations about IPOs:
Hot issue markets: why do many �rms suddenly decide to go
public? What is the �window of opportunity�?
Underpricing is higher in hot markets than in cold markets.
Why do �rms not shift to markets where they have to leave
less money on the table?
Why does competition not eliminate banks' rents in hot
markets?
Why are �rms during hot markets younger, less pro�table, and
with less insider ownership?
Ernst Maug PhD Course in Corporate Finance
The Model
Economy has N entrepreneurs who may go public. Each is matched
with one of a continuum of underwriters:
A fraction ρ of projects is good (�G�) with payo� X = 1, 1− ρis bad (�B�) with payo� X = 0.
Going public has an opportunity cost w .
Each �rm bargains with the underwriter it is matched with
who sets the o�er price ps . Firms capture a fraction β of the
issue price, underwriters 1− β.Underwriters' bene�t from higher prices through higher fees;
they are penalized for overpricing IPOs.
Underwriters hire a quantity η ∈ [0, 1] of bankers who cost θand screen projects. With probability 1− η they receive an
uninformed signal U. With probability η they become perfectly
informed so that Pr (H |1) = Pr (L |0) = η.
Ernst Maug PhD Course in Corporate Finance
Solution
1 Average quality of the IPO pool is π = ρρ+α(1−ρ) , assuming
that all G projects and α of the B projects go public (�single
crossing�). This is the fundamental value of the shares.
2 There is no underpricing for s = L, H. There is underpricing
for s = U : p∗U < π.
3 The di�erence in issue prices between G and B �rms is βη. Gentrepreneurs issue with probability 1.
Ernst Maug PhD Course in Corporate Finance
A sequentially rational equilibrium is a triple (π, η, θ) such that:
1 B �rms play a mixed strategy: β (1− η) p∗U = w .
2 The market for bankers clears:
Nη (ρ+ α (1− ρ)) = Nη ρπ ≤ 1.
3 Underwriters hire screening labor (�bankers�) such that
∆V = θ.
4 Underpricing: p∗U < π.
Ernst Maug PhD Course in Corporate Finance
Proposition
The larger the pool of potential IPOs (N ↑) in an overheated
equilibrium, the lower the average quality of �rms that want to go
public (π ↓).
The higher the average quality of IPOs issued, the higher the
bene�t for B �rms to go public.
The higher the probability of screening, the lower the bene�t
for B �rms to go public. Hence, B's indi�erence condition
implies that a higher π has to be compensated by a higher η.
A higher N (or ρ) shifts the indi�erence curve in π − η−spaceto the right and equilibrium π down.
Fixed supply of bankers reduces π: A higher quality ρ or a
larger size N of the IPO pool reduces the quality of IPO
applicants.
Ernst Maug PhD Course in Corporate Finance
Hot and Cold Markets
Proposition
If the number of good projects ρN is below ββ−w , there exists an
equilibrium in which only good projects try to obtain funding. If ρNis above this cut-o�, some bad �rms apply for funding.
Implications:
There is a discontinuous shift at some point such that above
the threshold, there are more �rms apply for funds.
Such a shock is more likely to come from market-wide shocks
than from industry-speci�c IPO waves.
Ernst Maug PhD Course in Corporate Finance
Discussion
The story in a nutshell:
Hot markets are ignited for neoclassical reasons: The number
of good �rms that want to go public crosses a critical
threshold.
Once su�ciently many investment bankers are too busy
screening projects, the quality of screening declines, which
opens a �window of opportunity� for bad �rms.
Bad �rms are drawn into the market, which becomes even
more crowded, deteriorating the quality of screening further.
The quality of IPOs declines and the uncertainty about quality
increases, leading to more underpricing.
Ernst Maug PhD Course in Corporate Finance
Motivation
Based on Schultz (2008)
Question: Why do IPOs underperform in the long run?
Potential explanation:
behavioral e�ects: companies issue equity when the market isovervaluedproblem: violates market e�ciency
Alternative: Pseudo-market timing: companies issue more
equity at higher stock market levels
Then IPOs cluster at ex post peaks
Ernst Maug PhD Course in Corporate Finance
Idea
The argument in �ve steps:
1 More companies are taken public when stock market values are
higher than when they are lower.
2 If stock prices decline, then the number of IPOs goes down
subsequently.
3 Then the ex post peak of the stock market also becomes the
ex post peak of IPO activity.
4 Event studies weight returns by the number of IPOs at the
beginning of the period, hence they give more weight to these
ex post peaks followed by negative returns.
5 Event study returns are lower than calendar returns.
Ernst Maug PhD Course in Corporate Finance
Example
Two periods
In each period, the excess return on the stock market is either
+10% or -10%.
The current level of the IPO price is equal to 100.
IPO activity depends on the price level
if P<95: no IPOsif 95<P<105: 1 IPOif P>105: 3 IPOs
With two periods and two states there are four equally likely
scenarios.
Ernst Maug PhD Course in Corporate Finance
Two-period model: Calculations
Period 0 Period 1 Total X Return
Scen. Price # X Ret Price # X Ret IPOs Cal. Event
1 100 1 0.10 110 3 0.10 4 0.10 0.10
2 100 1 0.10 110 3 -0.10 4 0.00 -0.05
3 100 1 -0.10 90 0 0.10 1 0.00 -0.10
4 100 1 -0.10 90 0 -0.10 1 -0.10 -0.10
Avg. 0.00 0.00 -0.04
Consider scenario 2:
Calendar day return = (XRet0 + XRet1) /2 = (0.10− 0.10) /2 = 0.00
Event day return = (1× XRet0 + 3× XRet2) /4
= (1× 0.10 + 3×−0.10) /4 = −0.05.
Ernst Maug PhD Course in Corporate Finance
A general restatement
CAARs in long-term event studies are calculated as:
CAAR =t=T∑t=1
1
N
[i=N∑i=1
(ri ,t − rm,t)
].
Here:
r = returnt = event month (usually runs from 1 to 36 or 60)i = stock of IPO �rm (runs from 1 to number of IPOs)m = market or matching stock
Ernst Maug PhD Course in Corporate Finance
Why average CAR-estimates are biased
Standard assumption: N is �xed.
Assumption here: N is a random variable
E (CAAR) = E
(1
N
)E
(t=T∑t=1
i=N∑i=1
(ri ,t − rm,t)
)
+ Cov
(1
N,
t=T∑t=1
i=N∑i=1
(ri ,t − rm,t)
).
N is positively correlated with returns
Covariance in second line is negative (correlation with 1/N)
Estimate of CAAR is biased downward
Ernst Maug PhD Course in Corporate Finance
How big is this e�ect?
Need to calibrate magnitude of this e�ect and compare it to
returns from statistical studies
Research design:
1 Measure empirical sensitivity of number of IPOs to value ofstock market and to value of �rms that recently went public
2 Simulate economy with realistic parameters for returns to themarket, IPO-portfolio, and issuance activity
3 Calibrate model so that markets in the simulated economy aree�cient and no real market timing is possible
4 Measure e�ect of pseudo market timing using usualbuy-and-hold returns (BHAR)
Ernst Maug PhD Course in Corporate Finance
Step 1: Measure sensitivity of IPOs to returns
Research design:
Construct IPO-index from �rms that went public in 60 monthsprior, calculate returnIndex value is 100 in February 1973, subsequently index valueis IPO-Index(t)=IPO-Index(t-1)*(1+mean return to IPO �rms)Regress IPO activity from 1973 to 1997 on IPO-index, stockmarket index, and time
#IPOs = −1.974− 0.144t − 0.057Markett(−11.66)
+ 0.153IPOt(19.43)
.
The R-squared of this regression is 77.8%.
Ernst Maug PhD Course in Corporate Finance
Steps 2-4: Run Monte Carlo simulations
Step 2: Estimate statistics of returns
Mean monthly return is 1.12% with standard deviation of4.52%Regress return to IPO-portfolio on market return: is 1.31 timeshigher with residual variance of 4.27%
Step 3: Calibrate economy and run 5,000 times
Generate returns from normal distribution with parameters asestimated in step 2 for market returnsFor IPO-portfolio, use slope coe�cient and variance ofdisturbance term from regression, but use intercept to equateexpected IPO returns with expected market returnsGenerate returns for 300 months (25 years)
Step 4: Calculate BHARs, average across 5,000 runs
Ernst Maug PhD Course in Corporate Finance
Simulated excess returns and wealth relatives
BHARs
1-12 1-24 1-36 1-60
Median -5.29% -10.97% -17.06% -31.75%
Mean -5.26% -10.18% -15.18% -26.50%
Std. error 0.10% 0.19% 0.29% 0.55%
t-statistic -54.77 -54.35 -52.74 -47.94
Percent<0 81.80% 82.10% 82.70% 82.80%
Wealth relatives
1-36 1-60
Median 85.29% 77.81%
Mean 86.43% 80.82%
Std. error 0.20% 0.29%
Ernst Maug PhD Course in Corporate Finance
Comparison to other theories
Behav. Inad. Psd.
market risk market
timing adj. timing
1 Underperformance after o�erings " " "
2 Poor operating perf. after o�erings " "
3 Underperf.: Other countries, other times ? ? "
4 O�ering clustering at market peaks " "
5 Perf. is worse in event-time " "
6 Perf. is worst after heavy issuance " "
7 Perf. is poor after debt issues ? "
8 Managers do not appear to pro�t "
Ernst Maug PhD Course in Corporate Finance
Conclusions
It is better to measure returns in calendar time, not in event
time, to account for the endogeneity (dependence on stock
market valuation) of the event itself.
Benchmark against index that not only has the same expected
return under the null, but is also highly correlated with the
event itself.
More detailed discussion of econometric issues: Baker,
Taliaferro, Wurgler, JF 2006; Viswanathan & Wei, RFS 2008.
Ernst Maug PhD Course in Corporate Finance