There are 2 types of cars (when they come out of the factory)
– good cars and lemons (bad cars). A driver knows whether the car is good or a lemon only after a year of driving. For simplicity, assume that the value of cars is fixed and does not depreciate over time (no time value of money, etc.)
• The fraction of lemons at a dealership is λ.
• Dealers (and Buyers) do not distinguish among good cars versus lemons, but Sellers of used cars know if their car is a lemon (asymmetry of information source).
• Dealers (and Buyers) know that some fraction λ will be lemons (based on past experience).
9-2

•
9-3

Numerical Example:
Suppose the fraction of lemons is 40%, that value of good cars is $2000, the value of lemons is $1000. Sellers of used cars are willing to part from their cars if they receive 80% of car’s value. What is the equilibrium if
1.
Fraction of lemons in the used car market is 40%?
2.
Fraction lemons in the used car market is 50%?
9-4

Key points
• Market quality is endogenous. When sellers have private information about products’ intrinsic worth, they will only bring good products to the market when prices are high.
Buyers understand this, and so must adjust the price they are willing to pay to reflect the quality of the good they expect to buy at that price.
• In equilibrium, goods available at a given price must be worth that price.
• Reducing asymmetries in the market is key for having a market: Consumer Report, checking a car at ICBC before purchase, trip advisor, accreditation, etc.
9-5

A – Assets-in-place
B – New investment projects – requires $100 investment
Assumption: New/Old Shareholders – are risk neutral. Note both A and B provide higher values in the good state.
T=-1 T=0 T=1
Bad state:
A=E(A)=100 Manager takes on
NPV(B)=15 project by raising
$100 from new shareholders
A=50
PV(B)=110
Good state
A=150
PV(B)=120
9-6

A – Assets-in-place
B – New investment projects – requires $100 investment
Assumption: New/Old Shareholders – are risk neutral. Note both A and B provide higher values in the good state.
T=-1 T=0 T=1
Bad state:
A=E(A)=100 Manager know T=1
NPV(B)=15 states and decides whether to take on project by raising
$100 from new shareholders
A=50
PV(B)=110
Good state
A=150
PV(B)=120
9-7

If the firm is endowed with a project that may either be good or bad and the firm insiders know the project type but firm outsiders do not then, ceteris paribus , the firm may reject the good project if outside equity must be issued to finance it.
The current shareholders bear an agency cost due to the asymmetric information if the firm issues equity. If the firm can issue safe debt to finance the good project then it will not be rejected and the current shareholders will not bear an agency cost.
9-8

1.
Note that this is a binomial model – two states in the future, which delivers this intuition.
2.
If the firm had cash S, it would need to raise only I00-S, which would make the new shareholders share in future asset in place smaller – higher chances that new shareholders would be better of also in good state.
3.
The intuition delivered is a pecking order type of story: In order to fund new projects, firms should first use cash, then debt, and only as a last resort use equity. Raising equity is like saying “I am ok with sharing the value of future assets-inplace with new partners”.
4.
Empirical fact – share prices tend to go down with seasoned equity offering.
9-9

• The principal – agent relationship can be thought of as having two parts:
• The task the agent is going to perform is risky, and so there is the question of how much of the risk each party should bear.
• Typically, the principal is assumed to be risk neutral. In this case, the principal doesn’t mind risk, and the agent would prefer to bear no risk at all.
• Incentives: the agent must undertake an action that the principal cannot observe. If the agent receives the same wage regardless of the outcome, he will put forth no effort.
• Obviously, the solution of these two problems is in a tradeoff. If the principal reduces the risk the agent must bear, the agent has less incentive to choose high effort. And, if the agent is given the incentive to choose high effort, he must necessarily bear some risk (as he does not have full control over the performance of the firm).
• So, typically (but not always, as we will soon see), the study of principal-agent problems of this sort (moral hazard) can be thought of as the study of the optimal trade-off between risk sharing and incentives.
9-10

Sometimes models start by assuming that effort is observable and verifiable .
In this case, contracts can be written that specify the effort level that the agent must put forth. The principal’s objective is therefore to specify the wage schedule
(as a function of the observed outcome) and effort level that maximizes its profit subject to the constraint that the agent voluntary choose to enter into the contract with the principal. The case where effort is observable is often referred to as the
“first-best case”. It is first-best because there are no incentive problems; the agent chooses the proper action because the action choice is observable and contractible. If the agent does something else, he will be punished by the courts.
In contrast, the “second-best case” refers to the situation where effort is not observable. In this case, the terms of the contract must be manipulated in order to induce the agent to choose the desired action. This can be modeled by adding additional incentive compatibility constraints (that make the agent take on certain actions) to the problem. Unless the principal implements the lowest cost action in both problems, the solution to the second-best problem will result in lower profits for the principal and will be Pareto inferior to the solution to the firstbest problem.
9-11

Starting points:
1) Shareholders are diversified and do not care about portfolio value, while capital budgeting rules require firm to maximize its own value.
2) There are different types of projects: Cannibalistic projects (mature market projects) and Economy increasing projects (new projects for new markets). The later are typically more risky (e.g., a new Advil versus a cure for cancer).
3) Two firms that affect each other. Shareholders are diversified but managers are given incentives based on performance of the firm they manage (conserve competition in the economy).
4) The firms have cash in place 𝑤 , which is the minimum payment needed for hiring a manager to run the company. The manager is paid this minimum amount plus his effort exertion.
9-12

𝑆 ℎ
𝐸 𝑠𝑖
+ 𝐶𝐸
𝐶𝑖
− 𝐶𝐸
𝐶−𝑖
𝑆 ℎ
𝐸 𝑠−𝑖
+ 𝐶𝐸
𝐶−𝑖
− 𝐶𝐸
𝐶𝑖
0.5
0.5
0.5
0.5
𝑆 𝑙
𝐸 𝑠𝑖
+ 𝐶𝐸
𝐶𝑖
− 𝐶𝐸
𝐶−𝑖
𝑆 𝑙
𝐸 𝑠−𝑖
+ 𝐶𝐸
𝐶−𝑖
− 𝐶𝐸
𝐶𝑖
Subscript i and ( -i ) represent two competing firms
𝑆 ℎ
, 𝑆 𝑙
- the payoff per unit of effort from economy increasing effort in the high and low state.
C – payoff per unit of cannibalistic effort
𝐸 𝑠𝑖
, 𝐸 𝑠−𝑖
, 𝐸 𝑐𝑖
, 𝐸 𝑐−𝑖 are chosen by managers
9-13

1.
Shareholders are homogenous and perfectly diversified so they maximize the expected payoff at t=1 minus the cost of the managers’ wages.
2.
Managers get the binding participation constraint, which equals the sum of a fixed wage 𝑤 plus the cost of effort.
3.
Since effort is observable, it is “like” shareholders choosing managerial effort
(projects).
9-14

1 − 𝑏
𝑆 ℎ
𝐸 𝑠𝑖
+ 𝐶𝐸
𝐶𝑖
− 𝐶𝐸
𝐶−𝑖
1 − 𝑏
𝑆 ℎ
𝐸 𝑠−𝑖
+ 𝐶𝐸
𝐶−𝑖
− 𝐶𝐸
𝐶𝑖 𝑏 𝑏
𝑆 𝑙
𝐸 𝑠𝑖
+ 𝐶𝐸
𝐶𝑖
− 𝐶𝐸
𝐶−𝑖
𝑆 𝑙
𝐸 𝑠−𝑖
+ 𝐶𝐸 𝒔. 𝒕
𝑽 𝒑
= 𝒎𝒂𝒙
𝑬 𝒄𝒊
,𝑬 𝒔𝒊 𝒊=𝟏,𝟐 𝝁
𝟏
+ 𝝁
𝟐 𝒘
𝟎𝒊
𝟏
𝟐
𝑬
𝟐 𝒄𝒊
+ 𝑬
𝟐 𝒔𝒊
, 𝒊 = 𝟏, 𝟐
𝟎𝟏
− 𝒘
𝟎𝟐
𝐶−𝑖
− 𝐶𝐸
𝐶𝑖
9-15

Since effort is not observable, we provide managers with incentives in the form of receiving a share 𝛼 𝑖 share is like providing stock compensation.
in the firm. This 𝑤 − 𝑤
01
− 𝑤
02 𝑠. 𝑡
𝑉 𝑒
= max 𝛼 𝑖
,𝑖=1,2
(1 − 𝛼
1
)𝜇
1
+ (1 − 𝛼
2
)𝜇
2
𝐸 𝑐𝑖
, 𝐸 𝑤
0𝑖 𝑠𝑖
1
2
𝐸
2 𝑐𝑖
+ 𝐸
2 𝑠𝑖
∈ arg max 𝛼 𝑖 𝜇 𝑖
−
1
2
− 𝛼 𝑖 𝜇 𝑖
,
𝐸
2 𝑐𝑖
+ 𝐸
2 𝑠𝑖
, 𝑖 = 1,2 𝑖 = 1,2
9-16

The incentive 𝛼 𝑖 and portfolio value 𝑉 𝑒 are 𝛼
1 𝑠 2
= 𝑐 2 + 𝑠 2
𝑉 𝑒
= 𝑠 4 𝑐 2 + 𝑠 2
9-17

𝑆 ℎ
𝐸 𝑠𝑖
+ 𝐶𝐸
𝐶𝑖
− 𝐶𝐸
𝐶−𝑖
𝑆 ℎ
𝐸 𝑠−𝑖
+ 𝐶𝐸
𝐶−𝑖
− 𝐶𝐸
𝐶𝑖
1 − 𝑏 1 − 𝑏 𝑏 𝑏
𝑆 𝑙
𝐸 𝑠𝑖
+ 𝐶𝐸
𝐶𝑖
− 𝐶𝐸
𝐶−𝑖
𝑆 𝑙
𝐸 𝑠−𝑖
+ 𝐶𝐸
1. Shareholders of firm i issue stock option grants with an exercise price equal to
𝑆 𝑙
𝐸 𝑠𝑖
+ 𝐶𝐸
𝐶𝑖
− 𝐶𝐸
𝐶−𝑖
≤ 𝐾 𝑖
< 𝑆 ℎ
𝐸 𝑠𝑖
+ 𝐶𝐸
𝐶𝑖
− 𝐶𝐸
𝐶−𝑖
2. Shareholders also set the option grant incentive, which is the percentage of cash flow 𝛽 𝑖 above the exercise price that the manger receives if the high payoff is realized.
𝐶−𝑖
− 𝐶𝐸
𝐶𝑖
9-18

𝑆 ℎ
𝐸 𝑠𝑖
+ 𝐶𝐸
𝐶𝑖
− 𝐶𝐸
𝐶−𝑖
𝑆 ℎ
𝐸 𝑠−𝑖
+ 𝐶𝐸
𝐶−𝑖
− 𝐶𝐸
𝐶𝑖
1 − 𝑏 1 − 𝑏 𝑏 𝑏
𝑆 𝑙
𝐸 𝑠𝑖
+ 𝐶𝐸
𝐶𝑖
− 𝐶𝐸
𝐶−𝑖
𝑆 𝑙
𝐸 𝑠−𝑖
+ 𝐶𝐸
𝐶−𝑖
− 𝐶𝐸
2 𝑠. 𝑡
𝐸 𝑐𝑖
𝑉 𝑜𝑝
, 𝐸 𝑤 𝑠𝑖
= max 𝛽 𝑖
,𝑖=1,2
0𝑖 𝑖=1
1
𝐸
2
2 𝑐𝑖
∈ arg max 𝛽 𝑖
1 − 𝑏 𝜇 ℎ𝑖
+ 𝐸 2 𝑠𝑖
− 𝛽
(1 − 𝑏) 𝜇 𝑙𝑖
− 𝛽 𝑖 𝑖 𝜇 𝑙𝑖
− 𝐾
(1 − 𝑏) 𝜇 𝑙𝑖
− 𝐾 𝑖
−
1
2
𝐸 𝑖
+ 𝑏𝜇
− 𝐾
2 𝑐𝑖 𝑖
+ 𝐸
,
2 𝑠𝑖 𝑙𝑖 𝑖 = 1,2
, 𝑤 − 𝑤
0𝑖 𝑖 = 1,2
9-19
𝐶𝑖

Option compared to stock grants contribute to a higher portfolio value to diversified shareholders as long as the firms have some cannibalistic ability. That is, as long as c>0 , we have 𝑉 𝑜𝑝
> 𝑉 𝑒
9-20

1.
Shareholders do not care about the value of a particular firm, but rather the value of their portfolio. Therefore, they always prefer new cash flows to the economy, rather than cannibalistic (stealing cash flow) activity.
2.
Both projects (economy increasing and cannibalistic) are good for competition, but diversified shareholders prefer economy increasing projects.
3.
Options are usually perceived as promoting reckless behavior of promoting risk, but that is fine from the point of shareholders if it reduces cannibalism.
9-21

1.
There is a big difference between diversified shareholders and non-diversified shareholders. Nondiversified shareholders care about the value of only the firm they own and would be ok with cannibalism. What are the implications for institutional owners versus Bill
Gates?
2.
Note that cannibalism is a prisoner dilemma situation.
Each firm would be better off without it, but if the shareholders are not diversified, they can not commit not to take on cannibalistic projects.
3.
Options are usually perceived as promoting reckless behavior of promoting risk, but from a portfolio since that is fine, do we really care about the survival of firms, or do we want innovative products?
9-22

What would be the implications for debt? Relative performance evaluation?
See paper
9-23

Assume that shareholders that hold the S&P 500 Index are thinking of setting a compensation package for the managers of COKE and Pepsi. Assume that these are the only two companies that are in the business of soft-drinks. The two companies are basically the same and can either engage in a respective new project (e.g., new soft drink for dogs (in the case of Coke) and a new drink that improves memory of old people (in the case of Pepsi). Alternatively, they can simply steal business from the competitor . Assume that the new projects of both firms will generate a cash flow of either $1M per unit of effort, or 0 with a probability of 0.9 and 0.1 respectively. Stealing business is completely safe and generates $100k per unit of effort. Based on Kraus and
Rubin (2010) What will be the market value of the two firms if the managers are compensated with shares, what if they are compensated with option grants?
9-24

Use the same model as in Kraus and Rubin (2010) to show what would the optimal stock compensation of managers be if shareholders were not diversified (i.e., would want to maximize only the value of one firm).
What is the intuition of the result, and how is it related to the traditional agency-conflict (i.e., by traditional we mean the regular principal-agent problem with a risk-averse manager)?
9-25

How does the introduction of options affects an economy with short sales constraints?
Starting points:
1.
Risk averse investors that maximize their expected utility.
2.
Key: some investors are pessimistic on the market. With the introduction of options they can bet against it (prior to that, they simply did not trade).
9-26

𝑋 𝑜
𝑋 𝑜
− optimistic investor choice of risky asset
− optimistic investor endowment
9-27

When short sale constraint is binding… 𝜋 𝑝
<
𝑃 − 𝐵
𝐴 − 𝐵
9-28

𝐿𝑒𝑡 , 𝑇 =
𝐴 1 − 𝜋 𝑜
𝑋 𝑜
2 1 − 𝑋 𝑜
𝐴𝐵
𝐹 =
+ 𝐵 1 − 𝜋 𝑜
𝑋 𝑜
1 − 𝑋 𝑜
Then the unique equilibrium in the short-sale constrained economy is:
𝑇 − 𝑇 2 − 𝐹
9-29

The price of the stock in a constrained economy P is a concave function (second derivative is negative) of the two possible payoffs, A and B.
𝑃 = 𝑇 − 𝑇 2 − 𝐹
𝑇 =
𝐴 1 − 𝜋 𝑜
𝑋 𝑜
+ 𝐵 1 − 𝜋
𝐹 =
2 1 − 𝑋 𝑜
𝐴𝐵
1 − 𝑋 𝑜 𝑜
𝑋 𝑜
9-30

Important steps in the derivation:
𝜕𝑇
𝜕𝑥
2
>
2𝑇
𝜕𝑇
𝜕𝑥
−
𝜕𝐹
𝜕𝑥
4(𝑇 2 − 𝐹)
2
> 0
𝜕 2 𝑃
=
𝜕𝑥 2
−
𝜕𝑇
𝜕𝑥
2
+
2𝑇
𝜕𝑇
𝜕𝑥
−
𝜕𝐹
𝜕𝑥
4(𝑇 2 − 𝐹)
2
𝑇 2 − 𝐹
9-31

𝑃𝑋 𝑜 𝜋 𝑜
(𝐴 − 𝑃)
+ 𝑋 𝑜
(𝐴 − 𝑃)
+
(1 − 𝜋 𝑜
)(𝐵 − 𝑃)
𝑃𝑋 𝑜
+ 𝑋 𝑜
(𝐵 − 𝑃)
= 0
𝑃𝑋 𝑝 𝜋 𝑝
(𝐴 − 𝑃)
+ 𝑋 𝑝
(𝐴 − 𝑃)
+
(1 − 𝜋 𝑝
)(𝐵 − 𝑃)
𝑃𝑋 𝑝
+ 𝑋 𝑝
(𝐵 − 𝑃)
= 0
Note that in equilibrium 𝑋 𝑜
𝑋 𝑝
= 1
+
9-32

The price in the unconstrained economy is lower than the price in a constrained economy.
𝐴𝐵
𝑃 =
𝐴 1 − 𝜋 𝑝
𝑋 𝑝
−𝜋 𝑜
𝑋 𝑜
+ 𝐵(𝜋 𝑝
𝑋 𝑝
+𝜋 𝑜
𝑋 𝑜
)
9-33

The price in an unconstrained economy is a concave function of the two possible payoffs, A and
B.
𝐴𝐵
𝑃 =
𝐴 1 − 𝜋 𝑝
𝑋 𝑝
−𝜋 𝑜
𝑋 𝑜
+ 𝐵(𝜋 𝑝
𝑋 𝑝
+𝜋 𝑜
𝑋 𝑜
)
9-34

The price as a function of the future A and B values is more concave in a constrained world than in the unconstrained world.
9-35

9-36

9-37

• The introduction of options in Israel (August 1993) effectively eliminated the short sale constraints
• During that time, the Oslo agreements between the Israeli and Palestinians were signed (September 13, 1993). A can be successful implementation of the peace process, while B is a failure (note A and B are in systematic terms as this is an Index).
• One can also say, since a long string of previous peace efforts had failed, the effect of successful outcome was much more uncertain since the long-run economic effect of peace were unclear.
• A-B is large, greater variability of A than in B. Prediction – increase in volatility due to reduced constraints.
9-38