chapter04_12ed.pptx.pptx

Walter Nicholson
1
Amherst College
Christopher Snyder
Dartmouth College
PowerPoint Slide Presentation | Philip Heap, James Madison University
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

CHAPTER
2
4
Uncertainty

• We now want to introduce uncertainty into economic choices.
• Three issues to address:
1. How does uncertainty affect people’s decisions?
2. Why do people generally dislike risk?
3. What can people do to reduce or avoid risk?
Ch. 4 • 3
Chapter Preview

Probability and Expected Value
Ch. 4 • 4
• Probability:
– The relative frequency with which an event occurs.
– What is the probability of flipping a heads; rolling a 5 on a die?
• Expected value the average outcome from an uncertain gamble.
• Fair gamble is a gamble with an expected value of zero.

Probability and Expected Value
Ch. 4 • 5
1 2
• Let P = ½ and P = ½ be the probability that event 1 and 2 occur.
If event 1 occurs you win X1 = $10, and if event 2 occurs you lose
X2 = -$1. What is the expected value of the gamble?
– Expected value = P X + P X
1 1 2 2
– ½ x $10 + ½ x -$1 = $4.50
• How much would you be willing to pay for the right to play this
gamble?

Risk Aversion
Ch. 4 • 6
• Would you take the previous gamble if you had to pay $4.50 to
participate?
• Risk aversion is the tendency of people to refuse to accept fair
gambles.
• Do you care about the gamble’s monetary payoff or the utility
associated with the gamble’s prizes?
• People tend to be risk averse due to diminishing marginal utility
of income.

Diminishing Marginal Utility of Income
Utility
Income
($1,000’s)
50
20 35
What happens to utility as income increases?
Ch. 4 • 7
As income rises, utility rises but at a diminishing rate.

Utility
Income
($1,000’s)
50
20
U3 is the utility from $35,000
Would you take a fair gamble
with a 50:50 chance of
winning or losing $5,000?
U3
30 35 40
U2
Ch. 4 • 8
Don’t take gamble: can get a
sure U3 or an expected U2

Utility
Income
($1,000’s)
50
20
U3
What about a fair gamble
with a 50:50 chance of
winning or losing $15,000
30 35 40
Don’t take gamble: can get a
sure U3 or an expected U1
Ch. 4 • 9
U1

Willingness to Pay to Avoid Risk
Utility
Income
($1,000’s)
50
20
U3
How much would you be
willing to pay to avoid the first
gamble?
U2 To get U you would need
2
$33,000.
30 33 35 40
Ch. 4 • 10
So you would pay $2,000 to
avoid the gamble.

Degrees of Risk Aversion
Ch. 4 • 11
• What does the shape of the utility curve tell you about the degree
of risk aversion?
• The steeper the curve, the more risk averse the individual.
• What if the utility curve is linear?
• The person is risk neutral. A risk neutral person would always be
willing to accept a fair gamble.
• For small gambles a risk averse person may be “nearly” risk
neutral.

How T
o Reduce Risk and Uncertainty
Ch. 4 • 12
• Four methods:
– Insurance
– Diversification
– Flexibility
– Information

Reducing Risk w/ Insurance
• Suppose you make $35,000 per year. There is a 50% chance you
will incur medical bills of $15,000.
Utility
Income
($1,000’s)
20 35
Without insurance your expected utility is U1
Ch. 4 • 13
U1
27.5

• Fair insurance: insurance for which the premium is equal to the
expected value of the loss.
Utility
Income
($1,000’s)
20 35
U1
Ch. 4 • 14
27.5
U2
The premium would be
$7,500 (35 – 27.5).
2
A policy that costs $7,500
would allow the person to
obtain a certain utility of U .
But an insurance company
would never offer fair
insurance. Why?

• How much would this person be willing to pay for insurance?
Utility
Income
($1,000’s)
20 35
U1
Ch. 4 • 15
27.5
U2
Therefore, they would be willing
to pay up to $11,000 to get
insurance.
With no insurance, they get an
1
expected utility of U .
24
They can get a certain utility, U1
with $24,000 income.

Ch. 4 • 16
• In general:
– Risk averse people will buy insurance against risky outcomes
as long as the premiums do not exceed the expected value by
too much.
• There are uninsurable risks.
– Some risks may be unique or difficult to evaluate
– Problem of adverse selection
– Problem of moral hazard

Reducing Risk w/ Diversification
Ch. 4 • 17
• What is diversification? How does it allow you to spread risk?
• Suppose You have $35,000 to invest $15,000 in Company A
and/or B. One share in each company costs $1.
• At the end of the year there is a 50:50 chance that the share price
will rise to $2 and a 50:50 chance it will fall to $0.
• What is the expected value of your income if you put all your
money in one company?
– $35k since you have a 50:50 chance of winning/losing $15k

Ch. 4 • 18
• Now suppose you put half of your money in each company.
Final Income Company B
Company A
• There is a 25% probability that each outcome occurs.
• Like before, your expected value is $35,000
• What’s the difference?
Poor Good
Poor $20,000 $35,000
Good $35,000 $50,000

Utility
Income
($1,000’s)
50
20 35
•
Ch. 4 • 19
The difference is your expected utility
U1
You get U if you invest in
1
only one company.
But you can get U2 if you
invest in both companies.
U2
So by diversifying you can
increase your utility.

Reducing Risk w/ Flexibility
Ch. 4 • 20
• Diversification works if you are able to allocate small amounts of
some large quantity among a number of different choices.
• What if decisions are “all-or-nothing”?
• Flexibility.
– Keeps the decision maker from being tied to one course of
action. Provides different options depending on the
circumstances.

Ch. 4 • 21
• Suppose you can buy one of three coats.
• At equal prices, the 2-in-1 coat is clearly better since it provides
more options.
COAT BITTER COLD MILD
PARKA 100 50
WINDBREAKER 50 100
2-in-1 100 100

Ch. 4 • 22
• Option contract – a financial contract offering the right, not the
obligation, to buy or sell an asset over a specified period of time.
• Attributes of options
– Specification of underlying transaction
– Definition of period during which option may be exercised
– Price of option
• Value of an option is influenced by:
– The value of the underlying transaction.
– The duration of the option.

Reducing Risk w/ Information
Ch. 4 • 23
• Why is information valuable? What are the costs and benefits?
• 2-in-1 coat expensive. Parka and windbreaker sell for same price.
• If knew for certain that it will be bitter cold you buy a Parka and
gain 25 utils.
• In more extreme case the gain would be 75 utils.
PARKA 100 (150) 50 (0)
WINDBREAKER 50 (0) 100 (150)

Ch. 4 • 24
• Would a risk neutral person gain from additional information?
• Assume the payoffs in the table represent $ values rather than utils.
• The risk neutral person would gain either $25 or $75 from a perfect
forecast.
• Need to compare the benefits and costs of the information.
PARKA 100 (150) 50 (0)
WINDBREAKER 50 (0) 100 (150)

Ch. 4 • 25
• What determines the amount of information someone will acquire?
• Costs: partly determined by skills and or experiences.
• Preferences: do you care about getting a good deal; do you like to
bargain.
• Since costs and preferences are likely to differ the level of
information people acquire will differ.
• Is procrastination a virtue or a curse?

Pricing of Risk in Financial Assets
Ch. 4 • 26
• Investors care about expected return and risk when deciding what
financial assets to buy.
– Holding expected return constant, assets with less risk are
preferred to assets with more risk.
– Holding risk constant, assets with greater expected return are
preferred to assets with lower expected return.
– Investors need to be compensated for taking on more risk by
getting a greater expected return.

Return
Risk
B
A
Risk-free asset
C
Ch. 4 • 27
AC is the market line
It shows different assets that can
be created by mixing the risk-free
asset A and different risky assets.
Note that any asset on AC
provides the greatest expected
return for a given amount of risk.
Risky assets

Return
Risk
B
A
Risk-free asset
C
Different investors will choose an
asset on the market line depending
on their risk tolerance.
UL
UH
UM
Note that the flatter the
indifference curve the higher the
degree of risk tolerance.
Ch. 4 • 28
How do different investors decide
which asset on AC they buy?

Two State Model
Ch. 4 • 29
• Want to develop a model that will tie everything we’ve discussed
together.
• Assume there are two possible outcomes or states of the world.
• In each state, the individual’s consumption is either C or C .
1 2
• There are four possible choices (gambles): A, B, D and F.
• Want to see how an individual decides which gamble to choose.

Two State Model
C2
C1
CA1
CA2
B
D
F
A
EU1
EU2
EU3
Ch. 4 • 30
Certainty line:
C1=C2
Which gamble will the person
choose?
The individual will choose gamble B
since it lies on the highest expected
utility curve.

Two State Model and Risk Aversion
C2
A
B
EU3
EU2
EU1
C1
Risk aversion is captured by the convexity of the
indifference curves
Ch. 4 • 31
Faced with a choice between gambles A, B and D,
an individual would prefer D
D provides a balance in consumption: “averages
are preferred to extremes”
D

Two State Model and Risk Aversion
C2
What do these two indifference curves tell you?
EU1 is an indifference curve for a risk averse
person.
EU2 is an indifference curve for a risk neutral
person.
EU1
EU2
C1
Ch. 4 • 32

Two State Model and Insurance
C2
C1
A
CA1
CA2
D
EU3
EU2
EU1
Suppose an accident can occur in state 2
but not state 1
CD1
Ch. 4 • 33
CD2
A is the situation with no insurance
With fair insurance a person can move to
point D: pay CA - CD to get CD – CA
1 1 2 2

Two State Model and Insurance
C2
C1
A
CA1
CA2
D
EU3
EU2
EU1
CD1
CD2
Even if only partial insurance is available,
the person is better off with insurance
than without.
C1=C2
The person can move from A to B.
B
Like before the amount they pay in C1 <
2
the amount the gain in C .
Ch. 4 • 34

Two State Model and Diversification
C2
C1
A1
A2
B
EU2
EU1
By investing in a mix of both assets the investor
Ch. 4 • 35
can attain any point on a line between A and A
1 2
An investor can put all their money in asset A1 or
all their money in asset A2
If they are indifferent, A1 and A2 lie on the same
EU curve.
So by diversifying they can receive greater
expected utility.

Summary
Ch. 4 • 36
• When individuals face uncertain situations they consider their
expected utility.
• If individuals have diminishing marginal utility for income, they
are risk averse and will refuse fair gambles.
• Insurance allows risk averse individuals to avoid participating in
fair gambles.
• Risk may also be reduced with diversification, buying options, or
acquiring better information.

Summary
Ch. 4 • 37
• Individuals will compare expected return and risk when deciding
what financial assets to buy.

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