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Chapter 1. Primary Market Making--- Underwriting Theory. Investment Bank Reputation Theory. (A) Assumptions. Two period model, t=0, t=1. Three risk neutral agents: entrepreneurs, investment banks, and investors, risk-free rate=0

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chapter 1

Chapter 1

Primary Market Making---

Underwriting Theory

a assumptions
(A) Assumptions
  • Two period model, t=0, t=1. Three risk neutral agents: entrepreneurs, investment banks, and investors, risk-free rate=0
  • 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

  • Investment banks are of two types, I=H or I=N

α0 : Prob. of no cost type investment bank

  • Evaluation cost C(r), Cr <0, C(1)=0. Investment banking fee k surplus value, k (0,1)
b model
(B) Model
  • Firm valuation



2. Investment Bank Objective

(1) High-cost type Investment Bank

(2) No-Cost type Investment Bank

3. The Entrepreneur’s Objective

Proceed from direct sale:

Proceed from investment Bank sale:

Choice of firm type f at t:

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:

(3) Investor beliefs along the equilibrium path,

at t=0,


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.

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:


Reputation Smile

  • Proposition III: (Effect of a change in reputation)

(i) For low reputation values , the high-cost investment bank’s evaluation 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

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.

c implications
(C) Implications
  • 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.
  • 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.
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.

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.

a assumptions16
(A) Assumptions
  • Risk neutral with no discounting.
  • An entrepreneur E starts a venture I , with no wealth, approaching independent venture capitalist V, or strategic investor S.
  • Two state, success and failure, p , (1-p)
b model17
(B) Model
  • Case I, E+V
  • Case II, E+S

Base prob. of success

Increase prob. of success

  • 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)

Optimal choice of investors


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