1 chapter 1 primary market making--- underwriting theory
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1
Chapter 1
Primary Market Making---
Underwriting Theory
2
A. Investment Bank Reputation Theory
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(A) Assumptions
1. Two period model, t=0, t=1. Three risk neutral agents: entrepreneurs, investment banks, and investors, risk-free rate=0
2. Firms are of two types f=G or f=B. Investment bank valuation of firm of two types: e=G or e=B.
r: prob. of good evaluation to a bad firm.
r [p,1], p>0. prob(e=G f=G)=1; Prob(e=G f=B)=r∣ ∣3. Investment banks are of two types, I=H or I=N
α0 : Prob. of no cost type investment bank
4. Evaluation cost C(r), Cr <0, C(1)=0. Investment banking fee k surplus value, k (0,1)
4
(B) Model
1. Firm valuation
}
)1(
1
)1({)(
0
0
0
000
HN rrV
5
2. Investment Bank Objective(1) High-cost type Investment Bank
(2) No-Cost type Investment Bank
)()( 1111HSH rcuvk
Revenue Cost
)(])1([)1(
][
][)()(
111010
10
100000
HBHGH
H
HHH
rckuvrvr
kEwhere
Ercuvk
][)(
)(
10000
111
HH
SH
Euvk
uvk
6
3. The Entrepreneur’s Objective
Proceed from direct sale:
Proceed from investment Bank sale:
Choice of firm type f at t:
)}({ ttt uvkv tu
},{, Rumm ft
ft
tttt
ttttft
uuvkvifR
uuvkvifUm
)(
)(
7
4. Equilibrium• Proposition I : In equilibrium,
(1) Investment Bank Choices:
Both high cost and no cost investment banks market only the equity of firms that obtain good evaluation by the above evaluation standard.
(2) Entrepreneur choices:
1;
;**
**
10
10
HH
NN
rpr
prr
BeifRmm
Geifummmm
BB
BGBG
**
****
10
1100
8
(3) Investor beliefs along the equilibrium path,
at t=0,
t=1,
Investor beliefs off the equilibrium path: at either date, investors set Prob(I=N)=0, in response to out-of-equilibrium choices by investment banks. They set Prob(f=G)=0 in response to out-of-equilibrium choices by entrepreneurs.
0
})1(
1
)1({)(,
)(
0
0
0
0
0000
0
RmGfprob
rrVUmGeGfprob
NIprob
f
HNf
0
})1(
1
)1({)(,
1
1
1
1
1111
1
1
RmGfprob
rrVUmGeGfprob
BSNIprob
andGSNIprob
f
H
S
N
SSSf
B
G
9
• Proposition II:
The equilibrium evaluation standard set by the high-cost type represents a unique interior solution
if the magnitude of the marginal cost of changing the evaluation standard, is a constant that satisfies the parametric restriction:
*
0Hr
)1(*
0 pr H rC
]})1()[1(}{)1()]1([{
)1()1()1(
0000
00222
ppp
pkc
c
10
• Proposition III: (Effect of a change in reputation) (i) For low reputation values , the high-cost investment bank’s eval
uation standard is stricter as its reputation is greater, ie. is decreasing in
(ii) For tending to 1, the high-cost investment bank’s evaluation standard becomes less strict as its reputation is greater, ie. is increasing in
0*
0Hr
0
0*
0Hr
0
Reputation Smile0
*
0Hr
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• Proposition IV: (Comparative Statics)
(i) The high-cost investment bank’s time 0 evaluation
standard is stricter as the fraction k of the surplus value
charge as a fee increase.
(ii) The high-cost investment bank’s time 0 evaluation
standard is less strict as the marginal cost, c, of setting
a stricter standard increases.
(iii) For low reputation values, small, and >1/2, the
variance of the true value of firms marketed by the
high-cost type at time 0 is decreasing in its reputation.
0
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(C) Implications
1. Investment banks and information asymmetry:• Investment banks with greater reputation capital are more
effective in reducing the impact of information asymmetry in the equity market.
• The extent of under-pricing is a decreasing function of the reputation of the investment bank underwriting the IPO.
2. Reputation and equity value uncertainty:• The greater the reputation of the investment bank, the lower is
the variance of possible firm value of the firms it markets.
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3. Reputation and underwriter compensation:Underwriters with greater reputation capital charge larger fees and therefore have higher gross incomes than their less prestigious rivals.
4. Reputation and equity offer proceeds:The proceed, net of underwriting fees, accruing to issuing firms are increasing in underwriting reputation.
5. Reputation and underwriter choice:Firms prefer to use the services of the most prestigious investment bank that agrees to market their equity, even when the amount charged as fees is larger for more prestigious investment banks.
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6. Underwritter vs. Non-underwritter offerings:
Firms that face an asymmetrically informed equity market prefer to make underwritter equity offering rather than market the equity directly.
15
B. Strategic Venture Investing Theory
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(A) Assumptions
1. Risk neutral with no discounting.
2. An entrepreneur E starts a venture I , with no wealth, approaching independent venture capitalist V, or strategic investor S.
3. Two state, success and failure, p , (1-p)
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(B) Model
• Case I, E+V
• Case II, E+S
)0(1
)']1,0[(
00
ablenontranferu
sharessvbeuSuccess
uuFailure
vE
vvv
vE
su
successinassetsSuSuSuccess
ufailureinassetsSuuFailure
E
SS
ESS
1
)'(
0)'(
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• Let
: net impact of strategic actions between new venture and asset of strategy investor.
then, if >0, S has a complementary asset
if <0, S has a substitute asset.
• Let
• V financing:
V is active investor (hold a board seat)
SS uu
Base prob. of success
2
2
1)(, iiiiii cpPq
Increase prob. of success
SSvSVS
vvvvVv
SvvVE
IquU
IcqU
qU
)(
)(
)1(
19
• S financing:
IcquU
qU
SSSSSS
SSSE
)()(
)1(
20
1. Optimal choice of investorsDefine
Suppose S and V are equally able,
(i) if Pure S financing.
(ii) if Pure V-financing.
(iii) if mix financing, where V is active and S is passive
)()(
)(
111
*00
VE
SE
vv
uufrom
from
01 010
0 Sq
vqMvq
10
0
financingMixedMv *qq
financingVPure
v *qq
financingSPure
S
21
2. Comparative Statics
(i) 10 ,
0
)( 2* q
)( 1* q
)( 2Sq)( 1Sq
vq
)( 20 )( 10 1
financingVPure financingSPure
financingVPureof
rangeincreased
22
(ii) 10 , I*q
)( 2IqS
)( 1IqS
)( 2Iqv
)( 1Iqv
)( 10 I )( 20 I1
0
financingMixedof
rangeIncreased financingVPure financingSPure
23
(iii) 10 ,)( SS porP
financingVPure
financingSPureof
rangeincreased financingSPure
1
0 0 )( 2
1 SP
)( 2*SS Pq
)( 1**SSv Pqq
)( 2SS Pq
)( 1SS Pq
vq
24
(IV) 10 ,)( vv porP
)( 2*vv Pq
)( 1**vvS Pqq
Sq
)( 2vv Pq
)( 1vv Pq
)( 20 vP )( 1
0 vP)( 1
1 vP )( 21 vP
financingVPureof
rangeincreased
financingSPure
0
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