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16th Summer School on Risk Finance and Stochastics

Athens, 9-13 September 2019

Optimal Managerial Compensation and Financial Contracts Under Adverse Selection and Moral Hazard

Kostas Koufopoulos

University of York

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Introduction

Idea: Outside investors (financiers) can observe neither the project quality

(Adverse Selection) nor the managers’ actions (Moral Hazard).

Also, the manager’s actions cannot be observed by the entrepreneur.

Both managerial contracts and securities are optimally chosen.

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Implications

The interaction between adverse selection and (effort) moral hazard has

significant effects both on the combinations of securities issued and their pricing.

Firms may issue mispriced securities (adverse selection cost). In the presence of moral hazard, this mispricing may result in the conversion of negative into

positive NPV projects and an improvement in social welfare.

Although managerial contracts are optimally designed, the choice of the

securities issued affects managerial effort incentives and so capital structure matters.

Predictions consistent with well-documented empirical findings.

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Empirical Evidence

Equity issue announcements are associated with stock price drops (e.g.

Asquith and Mullins (1986), Jung et al. (1996) and Masulis and Korwar

(1986)), whereas debt issue announcements have no significant effect on the stock price (e.g. Jung et al. (1996) and Mikkelson and Partch (1986)). That is,

debt is a more favourable signal than equity.

Fama and French (2005) also report that during the period 1973-2002 the number of highly profitable firms declines and the number of unprofitable

firms increases while the proportion of funds raised through equity increases.

Negative correlation between the fraction of funds raised through equity and

the subsequent aggregate returns on equity (Baker and Wurgler (2000)). This

correlation remains statistically significant even after controlling for book-to-market, size, and momentum (Pontiff and Woodgate (2008), McLean, Pontiff

and Watanabe (2009)).

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Existing Models

Most existing models of capital structure consider entrepreneurial firms or take

managerial objectives as exogenously given and ignore the effects of the interaction between managerial compensation and capital structure on the

managers’ choices.

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The Model

One homogeneous (perishable) good.

There are three types of agents: entrepreneurs (Es), managers (Ms), and financiers (Fs).

All agents are risk neutral and consume only at Date 2.

Each E has an indivisible project but no initial wealth (no assets in place). Also, Es cannot lend.

All projects require the same initial investment: I (fixed).

Hence, Es need to raise (at least) I from the capital market.

Each F has a large amount of initial wealth and he can lend at zero interest

rate.

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There are two types of projects: Bad (B) and Good (G).

Proportion of G-type: Proportion of B-type: 1

After his hiring and before his choice of the effort level, the manager learns the type of the project.

The effort level chosen by the M cannot be observed by either the E or the Fs.

There are more managers than projects.

There are two states of nature: Success, Failure.

If a project succeeds, it yields 0iX , with 0 BG XX . In case of failure,

both types of projects yield 0 .

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The probability of success of a project is related to the effort level that each M

chooses privately.

There are two effort levels: Low, High.

If the M chooses the high effort level, he incurs a utility cost C and the

success probability is i

H .

If the M shirks, his utility cost is 0 but the success probability is i

L , where 01 i

L

i

H .

At any identical effort level, both types of projects have the same success

probability, j

B

j

G

j , LHj , .

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When the financing contract is signed, the M knows the type of the project he

runs, but the Fs cannot observe the type of the project (adverse selection) or verify the actions of the Ms (moral hazard).

The Fs, however, know the proportion of each type of project and the nature of the investment and moral hazard “technology”.

There are no taxes, no bankruptcy or financial distress costs.

Es can raise funds by issuing either debt or equity or a combination of these two contracts to Fs. Debt claims are zero-coupon bonds that are senior to

equity.

Financing Contract: The financing contract provides the E with the required

amount of funds, I, in return for a combination of debt and equity ( D , ), 10 , 0D .

D : Face value of debt, : Proportion of equity issued to outside Fs.

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Assumption 1: IXCIX i

i

Li

i

H 0 , GBi , .

Ass. 1 CX i

i

L

i

H )( , GBi , .

That is, the choice of the high effort level by either type leads to an increase in

the net social surplus and so is socially efficient.

Assumption 2: cIX G

HG

G

H , cIX B

HB

B

H

Where LH

Cc

That is, if the securities issued are fairly priced, the M running a G-type project will exert effort whereas that running a B-type project will shirk.

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Managerial Contract: The managerial contract specifies the manager’s

compensation, W , in each state of nature, ),( SF WWM

Manager’s Effort Incentive Constraint

FLSLFHSH WWCWW )1()1(

FLHSLH WCW )()( (1)

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Optimal Managerial Contract (Minimum wage bill)

Given limited liability, the contract that induces the manager to exert effort

while minimizing the wage bill is:

),0(),( *** WWWM SF where cC

WLH

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Debt senior to Managerial Compensation

Given the Es’ limited liability, the manager’s reward in the good state is:

WDXMinS i , (2)

Therefore, the manager will exert effort if:

cWDX i cXD i , GBi ,

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0 D

Figure 1. Effort Incentive Constrains

BICF

GICF

cX G

cX B

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Entrepreneurs’ Objective Function

The manager chooses the financing contract ),( DA to maximize the E’s

expected utility given by:

0),)(1(),,,( WDXMaxWDXU iHi (3)

Financiers’ Objective Function

The expected profit, FP , of an F offering a contract ),( D , given limited liability, is:

IDXMinWDXMaxP iiHF ,0, , GBi , (4)

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Game Structure Stage 1: The E hires the M and the terms of the managerial contract are publicly

known.

Stage 2: Financiers simultaneously offer contracts ),( D . The financiers also

specify whether they are committed or not to the contracts they offer. Each

financier may offer any finite number of contracts.

Stage 3: Ms apply for (at most) one of the contracts offered from one financier.

If an M’s most preferred contract is offered by more than one financiers, he takes each financier’s contract with equal probability. In the light of the contract

chosen, the manager decides whether to work or shirk.

Stage 4: After observing the contracts offered by his rivals and those chosen by

the Ms, the financiers who did not commit to their contract at Stage 1 decide

whether to withdraw or not. If a contract is withdrawn, the Ms who have chosen it go to their endowment.

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Equilibrium

I only consider pure-strategy Bayes-Nash equilibria of the above game.

A pair of contracts ),( BBB DA and ),( GGG DA is an equilibrium if the

following conditions are satisfied (in a pooling equilibrium AAA BG ):

No contract in the equilibrium pair implies negative (expected) profits for the financier.

The entrepreneur’s expected payoff is maximized.

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Types of Equilibria and Provision of Funds: General Results

Proposition 1: A separating equilibrium can exist only if cIX HiH , GBi ,

(moral hazard is not binding). If cIX HiH , for either Bi , or Gi , or

GBi , , then the resulting equilibria must be pooling.

Proposition 2:

a) If cIX HiH , GBi , , then both types of projects receive financing.

b) If cIX HGH , cIX HBH , then funds are offered to both types only if

(a part of) either HPZP or LPZP exists.

c) If cIX HiH , GBi , , there exists a unique pooling equilibrium where no

project is financed.

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BZP 1

GICF

1 GZP

BICF

GIC

BIC

0 WX B HI D 0 HI WX G D

Panel A: B-Type Panel B: G-Type

Figure 2. Effort incentive constraints and zero-profit curves.

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Pure Adverse Selection

Proposition 3: If cIX HiH , BGi , , there exists a pooling equilibrium

where both types issue only debt as well as a continuum of separating equilibria where the G-type issues only debt whereas the B-type issues a combination of

debt and equity. In any equilibrium, the securities issued are fairly priced (See

Figure 3).

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BZP

GZP

0

Figure 3. Equilibria under pure adverse selection.

N HPZP

A D

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Proposition 4. Suppose that that cIX HGH , and cIX HBH .

Then if there exists a unique pooling equilibrium where the managers of both types of projects exert effort and obtain funds by issuing a combination of

debt and equity (See Figure 4).

where )(

)(

BGH

BH

XX

cXI

The equilibrium contract, ),( DA , lies at the intersection of BICF and

HPZP with:

)( BGH

BH

XX

cXI

(5)

cXD B (6)

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A

Gu

A

GZP

0 D

Figure 4. Pooling equilibrium where both debt and (mispriced) equity are

issued

HPZP

BICF

LPZP

.

MA

GICF

cX G

cX B

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Implications

Capital structure is relevant even though managerial contracts are optimally

designed.

Here, in contrast to the pure adverse selection models, the cross-subsidization

is socially beneficial. It converts negative into positive NPV projects and improves social welfare.

Negative correlation between the proportion of funds raised through equity and the subsequent aggregate return on equity (Baker and Wurgler (2000)).

From Eq. (5) it is clear that the higher the proportion of low-profitability firms

(the lower ), the higher (lower) the fraction of funds raised through equity

(debt). Intuitively, as the proportion of good projects falls, the fraction of

equity needed to provide the managers of bad projects with the subsidy necessary to induce them to work increases. This prediction is consistent with

the findings in Fama and French (2005).

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The Social Planner’s Problem

Objective: Maximization of the net social surplus.

This requires the choice of the high effort level by both types.

Since returns are observable and verifiable, the social planner’s problem is:

cIX BHB )(

cIX GHG )(

0)1( BHGH (Feasibility condition)

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Solving for , we obtain:

SP

BGH

BH

XX

cXI

)(

)(

SP : minimum proportion of the G-type in the population of Es consistent with

both types choosing the efficient high effort level.

Question: Can we implement this socially efficient outcome as a competitive equilibrium employing a debt-equity combination under the same conditions as

the social planner?

Answer: Proposition 4.

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Conclusions The interaction between adverse selection and (effort) moral hazard gives rise to

several interesting results:

It makes capital structure relevant even though managerial contracts are

optimally designed.

It provides an explanation of why good firms issue both debt and underpriced equity even though the bankruptcy and other agency costs associated with

debt are zero.

Less information can be socially beneficial. The cross-subsidization, due to hidden information, converts negative into positive NPV projects and

improves social welfare.

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It generates predictions consistent with the following observations:

Negative correlation between leverage and profitability.

Positive correlation between the proportion of low-profitability firms and the fraction of funds raised through equity.

Negative correlation between the proportion of funds raised through equity and subsequent aggregate returns on equity. So, it provides a fully

rational explanation to the empirical findings of Baker and Wurgler

(2000).