Solving Incentive Problems
Two Basic Incentive Problems
• Adverse Selection - fixed price insurance - bad risks.
• Moral Hazard - change behavior after insurance purchase.
• Both problems arise because of asymmetric information parties to financial contracts do not have the same
information so one has an incentive to shortchange
the other.
• Financial innovations and financial intermediaries often
help solve or reduce the severity of these problems.
• Example: Banks monitor developers after making loan.
Adverse Selection
Akerlof (1970) - Market for Lemons
• Most economic models assume buyers and sellers have
perfect or equal information.
• Asymmetric information is a market failure.
• Unsolved asymmetric information problem leads to fewer
beneficial trades and lower overall economic welfare.
• Question: Why are most used cars lemons?
Asymmetric information - people more often want to
sell the bad ones; the good ones are kept so that the average
sales price will reflect poor quality - good ones won’t receive
higher price because their owners have no way of credibly
supporting claims of good quality.
Related Question: Why does the value of a new car drop
suddenly after purchase from a dealer?
• Some claim dealers charge for the joy of owning a new car.
• More likely, after driving the car for a time, the owner
learns about whether it is a lemon - owner has
asymmetric information. If it is a lemon, she is more
likely to try to sell it. If I buy new from a dealer, the
chance I will get a lemon is smaller. I should be
willing to pay extra for the lower probability.
• This simple issue underlies many problems in finance and
financial institutions and special financial products
are often used to solve them.
Health Insurance
• Example: Suppose it is your job to set a price for health
insurance for people over 65. How do you do it?
• Older people use more services so we set a high price.
• But at the high price, those in good health may not buy.
• Those with very poor health will buy - a bargain.
• If you raise the premiums, more of the better risk leave,
raising premiums again and again breaks down the market.
• Result: insurers don’t get to sell a useful product and the
elderly don’t get the insurance they want.
Potential Solution to Health
Insurance Problem
• Mandatory, government required health insurance.
• Group insurance - working people are more likely to be
healthy and health quality in the group more random.
• Different levels of coverage and prices - self-selection.
• Specialized health information gathering companies.
• Testing - remove the asymmetry between the insured and
the insurer.
• HMO’s - advertise using only healthy people.
- offer benefits like health club that only the healthy
will value.
- subtle tactics - top floor administration,
application, offices - discourages the sick.
Other Financial Examples
1. Real estate agents - help resolve the information
asymmetry between buyer and seller by passing
information between them after screening for
truthfulness.
2. Local banks - help solve the lemons problem in lending.
• Suppose you set a fixed loan rate. Only the high-risk
firms would apply. Furthermore, the best risks can raise
funds from operations to fund their investments.
• Local banks know the risks and collateral value of local
firms and can reduce informational asymmetry by
continually monitoring the borrowing firm.
Moral Hazard
Leland and Pyle (1977) - Signaling
• Even local lenders with access to information on borrowers
may still encounter asymmetric information problems
after a loan is made.
• Moral hazard problem - after a loan is made, borrowers
have incentives to alter their projects in ways that are
hard to observer but make them riskier. The riskier
project has a bigger potential payoff but more chance
for failure (loan default), the costs of which are born
by the lender.
• Solution - borrowers signal the quality of a project by the
amount of their own capital they put into it.
• The lending market will offer lower interest rates for
projects with larger owner equity. This separates projects by
quality and allows lenders to offer a range of interest rates.
• Question: Is this how the home mortgage market works?
• Question: Since many mortgage lenders hold mortgages for
a short time before selling the loans through GNMA
guaranteed trusts, and they charge the same rate for each
conventional loan, how strong are lenders’ incentives to
accurately judge the default risk of each borrower?
• Question: Given your answer to the question above, do you
predict higher or lower default rates in the future?
• Question: Are higher default rates an inefficient result?
•Note: Electricity market deregulation – more brownouts.
Alternative Methods of Loan
Disposition
Type
Who Holds Title?
Who Monitors and
Bears Default Loss
------------------------------------------------------------------------Loan Sale
Purchaser
Purchaser
Syndication
Joint
Lead Lender
Participation Originator
Lead Lender
Securitization Conduit
Third-party guarantor
Principal-Agent Problems Moral Hazards
Jensen and Meckling (1976)
• An agency relationship arises when a principal (owner)
hires and agent (manager) to run her business or
make decisions in her place.
• Agency Problem: Since the principal can not continuously
observe the agent or perfectly measure his
performance, the agent may not work as hard as the
principal would or may make decisions that benefit
him at the principal’s expense.
• This problem is very general - applies to almost any
economic interaction including owners-managers,
managers-subordinates, customers- suppliers etc.
• Jensen and Meckling focus on the agency problem between
owners and managers - the separation of ownership
from control of business decisions.
• A business run by a 100 percent owner will have a higher
value than one run by a professional manager - all
else equal.
• All else is not equal, however. Allowing tradable ownership
shares improves liquidity, diversification through
pooling and management specialization. Hence, there
is a conflict between the benefits professional
management and agency costs associated with
separate ownership.
• Financial firms try to limit agency costs.
General Solutions to Agency
Problems
1. Management incentive compensation - options, bonuses.
2. Monitoring - auditors, boards of directors.
3. Bonding - deferred management compensation.
4. Debt - more debt puts pressure on managers to work hard
to make debt payments - more common when project
risk cannot be manipulated and where monitoring is
costly.
5. Competition among managers for jobs and firms for
customers.
6. Mergers and acquisitions - investment bankers job is to
look for poorly-managed firm and arrange for wellmanaged firm to buy them and fire poor managers.
Agency Problems in
Corporate Finance
Problem: A firm wants to issue equity to finance new
investment projects but cannot credibly tell investors
that the investment will be profitable.
Investors fear adverse selection where firms tend to
finance very profitable investments with retained
earnings and sell shares externally to finance less
attractive investments. Investors-offer low price.
Financial Solution: Convertible Debt - acts as insurance.
The investor may accept convertible debt because if
the investment is a poor one she has a more secure
claim on the firm’s assets and if it is good then the
debt will be converted to equity and the firm has the
equity financing it wanted in the first place.
Alternative Solutions
Alternative 1: The firm can sell equity (or debt) that has a put
feature. If the investment is good, investors maintain
their equity position. If the investment is bad,
investors get their funds back assuming the firm is
not bankrupt.
Question: Any potential problems with this solution relative
to convertible debt?
Alternative 2: Collateralized debt. The firm can sell debt
collateralized by its other projects that are easier to
value and are not as risky. These funds can finance
the new project at a reasonable cost.
Potential Problem: Firm bears all the risk itself.
Macro Effects of Incentive
Problems
Steps in Explaining the Business Cycle
1. Profits fall in the short-term due to interest rate increases
or cost inflation.
2. With internal cash-flow reduced, firms must issue more
external financing to fund their investments.
3. But investors require higher returns (offer lower prices) for
these securities because of adverse selection.
4. Fewer projects will have positive NPVs at the higher
required returns.
5. Fewer projects are undertaken and economic growth falls.
Corporate risk management smooths cash flows and helps
avoid having to raise funds externally - Some insurance
companies are considering offering Earnings Insurance.
Agency Costs in Financial
Firms
Due to the highly liquid nature of financial firms’ assets an
liabilities, there is more potential for managers to manipulate
risk and commit fraud/theft.
Agency Solutions for Financial Firms
1. Risk-based reserve requirements.
2. Transparent organization and financial reporting.
3. Assets placed with a separate depository/custodian.
4. Separate decision-makers from ratification, accounting and
reporting systems (e.g. billing agents from payments).
5. Management hierarchy levels that review major decision
(e.g., boards of directors).
6. Mutual monitoring - agents compete for promotions.
7. Redeemable shares - removes assets from management.
Solutions to Asymmetric
Information
1. Gathering information - expert dealers, licensing.
2. Stratify the market so that people self-select into quality
bins.
3. Bonding - putting up funds to insure performance.
4. Brand name or reputation - a type of bonding.
5. Collateral - also similar to bonding.
6. Guarantees - purchased from financial institutions or given
by governments.
7. Signaling information that can’t be costlessly copied.
Call Option
Definition: The right to purchase 100 shares of a security at
a specified exercise price (Strike) during a specific period.
EXAMPLE:
A January 60 call on Microsoft (at 7 1/2)
This means the call is good until the third Friday of January
and gives the holder the right to purchase the stock from the
writer at $60 / share for 100 shares.
cost is $7.50 / share x 100 shares = $750 premium or
option contract price.
Put Option
Definition: The right to sell 100 shares of a security at a
specified exercise price during a specific period.
EXAMPLE:
A January 60 put on Microsoft (at 14 1/4)
This means the put is good until the third Friday of January
and gives the holder the right to sell the stock to the writer
for $60 / share for 100 shares.
cost $14.25 / share x 100 shares = $1425 premium.
Microsoft stock price was 53 at the time.
Variables Affecting Options
Values
1. Time until expiration.
2. Stock return variance.
3. Stock Price.
4. Exercise price.
5. Risk-free rate.
For our discussion of incentive problems, the return variance
and the exercise price are the two variables that agents can
manipulate in the situations we will discuss.
Black-Scholes Model - Nearly
Exact Option Pricing Model
C0 = P0N(d1) - E e-rt N(d2)
where Price of Stock = P0
Exercise price = E
Risk free rate = r
Time until expiration in years = t
Normal distribution function = N( )
Exponential function (base of natural log) = e
Note: Here the hedge ratio is represented by N(d1) and
N(d2) where:
d1 
d2 
ln( P0 / E )  (r .5s 2 )t
s t
ln( P0 / E )  (r .5s 2 )t
s t
 d1  s t
where Standard deviation of stocks return = s
Natural log function = ln
TO GET THE VALUE OF
THE CALL, C0
EXAMPLE: ASSUME
Price of Stock
Exercise price
Risk free rate
time period 3 mo.
Std Dev of stock return
P0 = 36
E = 40
r = .05
t = .25
s = .50
•Substitute into d1 and d2.
ln(36 / 40)  [.05  .5(.50) ].25
d 
 .25
.50 .25
2
1
d  .25  .50 .25  .50
2
•Substitute d1, d2 and other variables in the main equation
C0 = 36N(-.25) - 40e-.05(.25)N(-.50)
•Look up in the normal table for d to get N(d).
here N(d1) = N(-.25) = .4013
and N(d2) = N(-.50) =.3085
•Substitute in the main equation
C0  36(.4013)  40e .05(.25) (.3085)  2.26
Use Put-Call Parity Formula
to Get Put Price
T0 = PUT PRICE
T0  C0  P0  Ee rt
EXAMPLE - use info above - you need the call price
T0  2.26  36  40e .05(.25)
= 2.26 - 36 + 39.5 = 5.76
Application of Option Pricing
to Incentive Problems
1. Whenever financial firms or government agencies
explicitly or implicitly guarantee (insure) a financial
transaction, they bear a implicit cost and confer an explicit
benefit. The cost can be estimated as the value of a put option
and this value (an a profit markup) can be charged as an
insurance “premium.”
2. Guarantees create the potential for adverse selection and
moral hazard which are often accentuated if the firm or
agency fails to charge the appropriate premium.
3. Example: The government often declares disaster areas
after a hurricane or flood and provides funds to help people
rebuild their homes. Result: many people refuse to purchase
disaster insurance and those that do find very high premiums.
Example: Risky Loans
1. Risky loans involve a risk-free loan and an implicit (or
sometimes explicit) loan guarantee.
Risky Loan Value = Risk-free Loan Value - Loan Guarantee Premium
2. Consider a borrower’s alternatives.
• Borrower needs $100 and goes to a bank offering loans
to businesses of its risk at 25% - $25 annual interest. The
bank offers to lend to the U.S. government at 10%.
• Borrower purchases a guarantee from an insurance
company for a $15 annual premium and returns to the
bank which offers to lend at 10% - $10 annual interest.
• Loan rate = 25% = 10% (risk-free rate) + 15% (risk
premium)
List of Other Examples
1. Product warrantees/guarantees.
2. Bank deposit insurance.
3. Crop insurance.
4. Price support programs - sugar, milk etc.
5. Student, small business and mortgage loan guarantees.
6. Parent companies often guarantee the debt of their
subsidiaries - a large problem in Japan, Korea, etc.
7. Swaps entered into directly with counter-parties.
8. Marketing schemes - “satisfaction guaranteed or your
money back.
9. Pension Fund guarantees.
Using Black-Scholes to get the
Value of Loan Guarantees
Problem: Suppose you are an insurance company and a firm
wants you to insure its $200 million loan from Fleet
Financial. The firm is putting up $40 million equity along
with the $200 million loan to buy the Civic Center. The
firm’s stock has a return standard deviation of 0.50. If the
risk-free rate is 10 percent, what should be the annual
guarantee premium?
1. Get d1 and d2.
ln( 240 / 200)  [.10  .5(.50) ]1
d 
 0.815
.50 1
2
1
d  0.815  .50 1  0.315
2
2. Get the normal probabilities.
N(.815)  N(.80) =0.7881 and N(.315)  N(.30) = 0.6179
3. Get the Call Price.
C  240(.7881)  200e
.10 ( 1 )
0
(.6179)  77.32
4. Get the Put Price.
T  77.32  240  200e
0
.10 ( 1 )
 18.29
We should charge at least $18.29 million for the guarantee.
If it is a 10 year loan and we wished to charge for a 10 year
guarantee up front, use 10 instead of 1 in the model above.
Using Black-Scholes to get the
Value of Pension Guarantees
Problem: Your firm has a defined-benefit pension plan
committing it to pay benefits with a present value of $100
million. The fund backing the plan, however, has $120
million in it now (over-funded by $20 million). Your plan is
guaranteed by the Pension Benefits Guarantee Corporation
(PBGC). Assume the firm’s stock has a return standard
deviation of 0.30, and the risk-free rate is 10 percent, what
should be the annual guarantee premium?
ln(120 / 100)  [.10  .5(.30) ]1
d 
 1.09
.30 1
2
1
d  1.09  .30 1  0.79
2
Get the normal probabilities.
N(1.09)  N(1.10) =0.8643 and N(.79)  N(.80) = 0.7881
Get the Call Price.
C  120(.8643)  100e
.10 ( 1 )
0
(.7881)  32.41
Get the Put Price.
T  32.41  120  100e
0
.10 ( 1 )
 2.89
PBGC should charge at least $2.89 million for the guarantee.
Problems with PBGC
Guarantee Premiums
• Premiums are not set with an options model but using
various ad hoc rules. Before 1994, the premiums were
relatively low and had fixed maximums, leading to
significant PBGC losses.
• Firms can still opt out (in) of the PBGC insurance by
switching from a fixed benefit (contribution) to a fixed
contribution (benefit) plan or by contracting an insurance
company to assume its obligations. The over-funded plans
tend to opt out while deadbeats opt in - adverse selection and
free rider problems. Social Security System solves these
problems by making participation mandatory.
• When an over-funded plan is extinguished, the excess
assets go to the firm’s shareholders - used in takeovers.
• PBGC does not determine how benefits or contributions are
calculated. A firm’s pension contribution depends upon its
own assumptions on the expected return on fund assets, the
work-life and retirement life of its covered workers, and the
return on the assets supporting retirees’ annuities (FASB).
Pension contributions and the determination of a fund’s
under- or over-funding can be manipulated - 1991, Chrysler
reported $3.7 billion under-fund - PBGC estimate was $7.7.
• Payout is flexible so retirees may choose lump-sum payouts
instead of annuities which reduces the assets backing the
benefits or the remaining unretired workers - LTV executives
change payout rules just before retiring - PBGC lost $230 m.
• PBGC cannot restrict the risk of fund assets. The assets in
the pension fund may be low risk or quite risky.
Problem: Now suppose everything is the same as above
except that your pension fund is invested in your firm’s stock
(an internet company) and its value just fell by 33 percent.
This means that the fund backing the plan has only $80
million in it now (under-funded by $20 million). What
happens to the value of PBGC’s guarantee?
ln(80 / 100)  [.10  .5(.30) ]1
d 
 0.26
.30 1
2
1
d  0.26  .30 1  0.56
2
Get the normal probabilities.
N(-.26)  N(-.25) =0.4013 and N(-.56)  N(-.55) = 0.2912
Get the Call Price.
C  80(.4013)  100e
.10 ( 1 )
0
(.2912)  5.75
Get the Put Price.
T  5.75  80  100e
0
.10 ( 1 )
 16.23
PBGC should charge at least $16.23 mm for the guarantee.
Question: Why the big premium change? Any other ways for
the firm to boost the value of its PBGC guarantee?