### Lecture9x

```Theories in corporate finance and
financial markets
The Akerlof model
(Nobel Prize Winner in Economic 2001)
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
The Akerlof model (Nobel Prize Winner)
•
9-3
The Akerlof model (Nobel Prize Winner)
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
The Akerlof model (Nobel Prize Winner)
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.
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
9-5
Financial Market Asymmetry
Myers and Majluf (JFE, 1984)
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
A=E(A)=100
NPV(B)=15
T=0
Manager takes on
project by raising
\$100 from new
shareholders
T=1
Good
state
A=50
A=150
PV(B)=110
PV(B)=120
9-6
Financial Market Asymmetry
Myers and Majluf (JFE, 1984)
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
A=E(A)=100
NPV(B)=15
T=0
Manager know T=1
states and decides
whether to take on
project by raising
\$100 from new
shareholders
T=1
Good
state
A=50
A=150
PV(B)=110
PV(B)=120
9-7
The 1984 Myers-Majluf Theorem.
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
The 1984 Myers-Majluf Theorem.
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-in-place with new partners”.
4. Empirical fact – share prices tend to go down with
seasoned equity offering.
9-9
Principal– Agent Problems
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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
Principal– Agent Problems
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
Kraus and Rubin (JFI, 2010)
Setting contracts when shareholders are
diversified and firm affect each other
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 , 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
The payoffs for firm i and (-i) at t=1
ℎ  +  − −
ℎ − + − −
0.5
0.5
0.5
0.5
+  − −
− + − −
Subscript i and (-i) represent two competing firms
ℎ , - the payoff per unit of effort from economy increasing effort
in the high and low state.
C – payoff per unit of cannibalistic effort
, − ,  , − are chosen by managers
9-13
Maximization problem (observable effort)
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
plus the cost of effort.
3. Since effort is observable, it is “like”
shareholders choosing managerial effort
(projects).
9-14
The payoffs for firm i and (-i) at t=1
ℎ  +  − −
ℎ − + − −
1−
1−

+  − −
=
.

, =,
≥  +

− + − −
+  +  −  −
+  ,  = ,
9-15
Non - observable effort – stock compensation
Since effort is not observable, we provide managers with
incentives in the form of receiving a share  in the firm. This
share is like providing stock compensation.
= max (1 − 1 )1 + (1 − 2 )2 + 2 − 01 − 02
.
,=1,2
1 2
2
0 ≥  +  +
−   ,
2
1 2
2
,  ∈ arg max   −  +
2
= 1,2
,
= 1,2
9-16
Proposition 2
The incentive  and portfolio value  are
2
1 = 2
+ 2
4
= 2
+ 2
9-17
Non - observable effort – option
compensation
ℎ  +  − −
ℎ − + − −
1−
1−

+  − −
− + − −
1. Shareholders of firm i issue stock option grants with an
exercise price equal to
+  − − ≤  < ℎ  +  − −
2. Shareholders also set the option grant incentive, which is
the percentage of cash flow  above the exercise price that
the manger receives if the high payoff is realized.
9-18
Non - observable effort – option
compensation
ℎ  +  − −
ℎ − + − −
1−
1−

+  − −
− + − −
2
= max
,=1,2
.
1 −  ℎ −   −
+  +  − 0
=1
1
2
+
2
2
+
−  (1 − )  −  ,  = 1,2
1 2
2
,  ∈ arg max  (1 − )  −  −  +
,
= 1,2
2
0 ≥
9-19
Proposition 4
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  >
9-20
What did we learn? What are the
implications?
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
What did we learn? What are the
implications?
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 did we learn? What are the
implications?
What would be the implications for debt? Relative
performance evaluation?
See paper
9-23
Practice questions 1 (homework)
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
Practice questions 2 (homework)
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
regular principal-agent problem with a risk-averse manager)?
9-25
Kraus and Rubin (2003)
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
9-26
− optimistic investor choice of risky asset
− optimistic investor endowment
9-27
When short sale constraint is binding…
−
<
−
9-28
Solving for the price in a short sale
constrained economy:
1 −   +  1 −
,
=
2 1 −

=
1 −
Then the unique equilibrium in the short-sale
constrained economy is:
− 2 −
9-29
Proposition 1
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.
=  − 2 −
1 −   +  1 −
=
2 1 −

=
1 −
9-30
Proposition 1
Important steps in the derivation:

2
2
2
−
=

2
−

>
4( 2 − )

2
2
>0

2
−

+
4( 2 − )
2
2 −
9-31
Relaxing the short sale constraint
( − )
(1 −  )( − )
+
=0
+  ( − )  +  ( − )
( − )
(1 −  )( − )
+
=0
+  ( − )  +  ( − )
Note that in equilibrium  +
= 1
9-32
Proposition 2
The price in the unconstrained economy is lower
than the price in a constrained economy.
=

1 −   −  + (  +  )
9-33
Proposition 3
The price in an unconstrained economy is a
concave function of the two possible payoffs, A and
B.
=

1 −   −  + (  +  )
9-34
Proposition 4
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
Varying A – B constant
9-36
Varying B – A constant
9-37
Empirical experiment
• 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
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