Chapter 5 Choice Under Uncertainty. Chapter 5Slide 2 Topics to be Discussed Describing Risk Preferences Toward Risk Reducing Risk The Demand for Risky.

Chapter 5

Choice Under Uncertainty


Chapter 5 Slide 2

Topics to be Discussed

Describing Risk

Preferences Toward Risk

Reducing Risk

The Demand for Risky Assets

Chapter 5 Slide 3

Introduction

Choice with certainty is reasonably straightforward.

How do we choose when certain variables such as income and prices are uncertain (i.e. making choices with risk)?

Chapter 5 Slide 4

Describing Risk

To measure risk we must know:

1) All of the possible outcomes.

2) The likelihood that each outcome will occur (its probability).

Chapter 5 Slide 5

Describing Risk

Interpreting ProbabilityThe likelihood that a given outcome will

occur

Chapter 5 Slide 6

Describing Risk

Interpreting ProbabilityObjective Interpretation

Based on the observed frequency of past events

Chapter 5 Slide 7

Describing Risk

Interpreting ProbabilitySubjective

Based on perception or experience with or without an observed frequency

Different information or different abilities to process the same information can influence the subjective probability

Chapter 5 Slide 8

Describing Risk

Expected ValueThe weighted average of the payoffs or

values resulting from all possible outcomes.The probabilities of each outcome are

used as weightsExpected value measures the central

tendency; the payoff or value expected on average

Chapter 5 Slide 9

Describing Risk

An ExampleInvestment in offshore drilling exploration:

Two outcomes are possibleSuccess -- the stock price increase from

$30 to $40/shareFailure -- the stock price falls from $30

to $20/share

Chapter 5 Slide 10

Describing Risk

An ExampleObjective Probability

100 explorations, 25 successes and 75 failures

Probability (Pr) of success = 1/4 and the probability of failure = 3/4

Chapter 5 Slide 11

Describing Risk

An Example:

e))($20/sharPr(failuree))($40/sharPr(success EV

)($20/share43)($40/share41 EV

$25/share EV

Expected Value (EV)Expected Value (EV)

Chapter 5 Slide 12

Describing Risk

Given:

Two possible outcomes having payoffs X1 and X2

Probabilities of each outcome is given by Pr1 & Pr2

Chapter 5 Slide 13

Describing Risk

Generally, expected value is written as:

nn2211 XPr...XPrXPr E(X)

Chapter 5 Slide 14

Describing Risk

Variability

The extent to which possible outcomes of an uncertain even may differ

Chapter 5 Slide 15

Describing Risk

A ScenarioSuppose you are choosing between two

part-time sales jobs that have the same expected income ($1,500)

The first job is based entirely on commission.

The second is a salaried position.

VariabilityVariability

Chapter 5 Slide 16

Describing Risk

A ScenarioThere are two equally likely outcomes in the

first job--$2,000 for a good sales job and $1,000 for a modestly successful one.

The second pays $1,510 most of the time (.99 probability), but you will earn $510 if the company goes out of business (.01 probability).


Chapter 5 Slide 17

Income from Sales Jobs

Job 1: Commission .5 2000 .5 1000 1500

Job 2: Fixed salary .99 1510 .01 510 1500

ExpectedProbability Income ($) Probability Income ($) Income

Outcome 1 Outcome 2

Describing Risk

Chapter 5 Slide 18

1500$ .5($1000).5($2000))E(X1

Job 1 Expected Income

$1500.01($510).99($1510) )E(X2

Job 2 Expected Income

Income from Sales Jobs

Describing Risk

Chapter 5 Slide 19

While the expected values are the same, the variability is not.

Greater variability from expected values signals greater risk.

Deviation

Difference between expected payoff and actual payoff

Describing Risk

Chapter 5 Slide 20

Deviations from Expected Income ($)

Job 1 $2,000 $500 $1,000 -$500

Job 2 1,510 10 510 -900

Outcome 1 Deviation Outcome 2 Deviation

Describing Risk

Chapter 5 Slide 21

Adjusting for negative numbers

The standard deviation measures the square root of the average of the squares of the deviations of the payoffs associated with each outcome from their expected value.


Describing Risk

Chapter 5 Slide 22

Describing Risk

The standard deviation is written:

222

211 )(Pr)(Pr XEXXEX


Chapter 5 Slide 23

Calculating Variance ($)

Job 1 $2,000 $250,000 $1,000 $250,000 $250,000 $500.00

Job 2 1,510 100 510 980,100 9,900 99.50

Deviation Deviation Deviation Standard Outcome 1 Squared Outcome 2 Squared Squared Deviation

Describing Risk

Chapter 5 Slide 24

Describing Risk

The standard deviations of the two jobs are:

50.99

900,9$

00).01($980,1.99($100)

500

000,250$

0.5($250,000).5($250,00

2

2

2

1

1

1

*Greater Risk

Chapter 5 Slide 25

Describing Risk

The standard deviation can be used when there are many outcomes instead of only two.

Chapter 5 Slide 26

Describing Risk

Job 1 is a job in which the income ranges from $1000 to $2000 in increments of $100 that are all equally likely.

ExampleExample

Chapter 5 Slide 27

Describing Risk

Job 2 is a job in which the income ranges from $1300 to $1700 in increments of $100 that, also, are all equally likely.

ExampleExample

Chapter 5 Slide 28

Outcome Probabilities for Two Jobs

Income

0.1

$1000 $1500 $2000

0.2

Job 1

Job 2

Job 1 has greater spread: greater

standard deviationand greater risk

than Job 2.

Probability

Chapter 5 Slide 29

Describing Risk

Outcome Probabilities of Two Jobs (unequal probability of outcomes)

Job 1: greater spread & standard deviation

Peaked distribution: extreme payoffs are less likely

Chapter 5 Slide 30

Describing Risk

Decision Making

A risk avoider would choose Job 2: same expected income as Job 1 with less risk.

Suppose we add $100 to each payoff in Job 1 which makes the expected payoff = $1600.

Chapter 5 Slide 31

Unequal Probability Outcomes

Job 1

Job 2

The distribution of payoffsassociated with Job 1 has a greater spread and standard

deviation than those with Job 2.

Income

0.1

$1000 $1500 $2000

0.2

Probability

Chapter 5 Slide 32

Income from Sales Jobs--Modified ($)

Recall: The standard deviation is the square root of the deviation squared.

Job 1 $2,100 $250,000 $1,100 $250,000 $1,600 $500

Job 2 1510 100 510 980,100 1,500 99.50

Deviation Deviation Expected Standard Outcome 1 Squared Outcome 2 Squared Income Deviation

Chapter 5 Slide 33

Describing Risk

Job 1: expected income $1,600 and a standard deviation of $500.

Job 2: expected income of $1,500 and a standard deviation of $99.50

Which job?Greater value or less risk?

Decision MakingDecision Making

Chapter 5 Slide 34

Suppose a city wants to deter people from double parking.

The alternatives …...

Describing Risk

ExampleExample

Chapter 5 Slide 35

Assumptions:

1) Double-parking saves a person $5 in terms of time spent searching for a

parking space.

2) The driver is risk neutral.

3) Cost of apprehension is zero.

ExampleExample

Describing Risk

Chapter 5 Slide 36

A fine of $5.01 would deter the driver from double parking.Benefit of double parking ($5) is less than

the cost ($5.01) equals a net benefit that is less than 0.

ExampleExample

Describing Risk

Chapter 5 Slide 37

Increasing the fine can reduce enforcement cost:A $50 fine with a .1 probability of being

caught results in an expected penalty of $5.

A $500 fine with a .01 probability of being caught results in an expected penalty of $5.

ExampleExample

Describing Risk

Chapter 5 Slide 38

The more risk averse drivers are, the lower the fine needs to be in order to be effective.

ExampleExample

Describing Risk

Chapter 5 Slide 39


Choosing Among Risky AlternativesAssume

Consumption of a single commodityThe consumer knows all probabilitiesPayoffs measured in terms of utilityUtility function given

Chapter 5 Slide 40


A person is earning $15,000 and receiving 13 units of utility from the job.

She is considering a new, but risky job.

ExampleExample

Chapter 5 Slide 41


She has a .50 chance of increasing her income to $30,000 and a .50 chance of decreasing her income to $10,000.

She will evaluate the position by calculating the expected value (utility) of the resulting income.

ExampleExample

Chapter 5 Slide 42


The expected utility of the new position is the sum of the utilities associated with all her possible incomes weighted by the probability that each income will occur.

ExampleExample

Chapter 5 Slide 43


The expected utility can be written:E(u) = (1/2)u($10,000) + (1/2)u($30,000)

= 0.5(10) + 0.5(18)

= 14

E(u) of new job is 14 which is greater than the current utility of 13 and therefore preferred.

ExampleExample

Chapter 5 Slide 44


Different Preferences Toward RiskPeople can be risk averse, risk neutral, or

risk loving.

Chapter 5 Slide 45


Different Preferences Toward RiskRisk Averse: A person who prefers a certain

given income to a risky income with the same expected value.

A person is considered risk averse if they have a diminishing marginal utility of income

The use of insurance demonstrates risk aversive behavior.

Chapter 5 Slide 46


A ScenarioA person can have a $20,000 job with

100% probability and receive a utility level of 16.

The person could have a job with a .5 chance of earning $30,000 and a .5 chance of earning $10,000.

Risk AverseRisk Averse

Chapter 5 Slide 47


Expected Income = (0.5)($30,000) +

(0.5)

($10,000) =

$20,000


Chapter 5 Slide 48


Expected income from both jobs is the same -- risk averse may choose current job


Chapter 5 Slide 49


The expected utility from the new job is found:

E(u) = (1/2)u ($10,000) + (1/2)u($30,000)

E(u) = (0.5)(10) + (0.5)(18) = 14

E(u) of Job 1 is 16 which is greater than

the E(u) of Job 2 which is 14.


Chapter 5 Slide 50


This individual would keep their present job since it provides them with more utility than the risky job.

They are said to be risk averse.


Chapter 5 Slide 51

Income ($1,000)

Utility The consumer is riskaverse because she

would prefer a certainincome of $20,000 to a

gamble with a .5 probabilityof $10,000 and a .5

probability of $30,000.

E

10

10 15 20

1314

16

18

0 16 30

AB

C

D



Chapter 5 Slide 52


A person is said to be risk neutral if they show no preference between a certain income, and an uncertain one with the same expected value.

Risk NeutralRisk Neutral

Chapter 5 Slide 53

Income ($1,000)10 20

Utility

0 30

6A

E

C

12

18

The consumer is riskneutral and is indifferentbetween certain eventsand uncertain events

with the same expected income.


Risk NeutralRisk Neutral

Chapter 5 Slide 54


A person is said to be risk loving if they show a preference toward an uncertain income over a certain income with the same expected value.Examples: Gambling, some criminal

activity

Risk LovingRisk Loving

Chapter 5 Slide 55

Income ($1,000)

Utility

0

3

10 20 30

A

E

C8

18The consumer is riskloving because she

would prefer the gamble to a certain income.


Risk LovingRisk Loving

Chapter 5 Slide 56


The risk premium is the amount of money that a risk-averse person would pay to avoid taking a risk.

Risk PremiumRisk Premium

Chapter 5 Slide 57


A ScenarioThe person has a .5 probability of earning

$30,000 and a .5 probability of earning $10,000 (expected income = $20,000).

The expected utility of these two outcomes can be found:

E(u) = .5(18) + .5(10) = 14


Chapter 5 Slide 58


Question

How much would the person pay to avoid risk?


Chapter 5 Slide 59

Income ($1,000)

Utility

0 10 16

Here , the risk premiumis $4,000 because a

certain income of $16,000gives the person the same

expected utility as the uncertain income thathas an expected value

of $20,000.

10

18

30 40

20

14

A

CE

G

20

F

Risk Premium



Chapter 5 Slide 60


Variability in potential payoffs increase the risk premium.

Example:A job has a .5 probability of paying $40,000

(utility of 20) and a .5 chance of paying 0 (utility of 0).

Risk Aversion and IncomeRisk Aversion and Income

Chapter 5 Slide 61


Example:The expected income is still $20,000, but

the expected utility falls to 10.

Expected utility = .5u($) + .5u($40,000)

= 0 + .5(20) = 10


Chapter 5 Slide 62


Example:The certain income of $20,000 has a utility

of 16.

If the person is required to take the new position, their utility will fall by 6.


Chapter 5 Slide 63


Example:The risk premium is $10,000 (i.e. they

would be willing to give up $10,000 of the $20,000 and have the same E(u) as the risky job.


Chapter 5 Slide 64


Therefore, it can be said that the greater the variability, the greater the risk premium.


Chapter 5 Slide 65


Combinations of expected income & standard deviation of income that yield the same utility

Indifference CurveIndifference Curve

Chapter 5 Slide 66

Risk Aversion andIndifference Curves

Standard Deviation of Income

ExpectedIncome

Highly Risk Averse:Anincrease in standarddeviation requires a large increase in income to maintainsatisfaction.

U1

U2

U3

Chapter 5 Slide 67

Risk Aversion andIndifference Curves

Standard Deviation of Income

ExpectedIncome

Slightly Risk Averse:A large increase in standarddeviation requires only a small increase in incometo maintain satisfaction.

U1

U2

U3

Chapter 5 Slide 68

Business Executivesand the Choice of Risk

Study of 464 executives found that:20% were risk neutral

40% were risk takers

20% were risk adverse

20% did not respond

ExampleExample

Chapter 5 Slide 69

Those who liked risky situations did so when losses were involved.

When risks involved gains the same, executives opted for less risky situations.

ExampleExample


Chapter 5 Slide 70

The executives made substantial efforts to reduce or eliminate risk by delaying decisions and collecting more information.

ExampleExample


Chapter 5 Slide 71

Reducing Risk

Three ways consumers attempt to reduce risk are:

1) Diversification

2) Insurance

3) Obtaining more information

Chapter 5 Slide 72

Reducing Risk

Diversification Suppose a firm has a choice of selling air

conditioners, heaters, or both.

The probability of it being hot or cold is 0.5.

The firm would probably be better off by diversification.

Chapter 5 Slide 73

Income from Sales of Appliances

Air conditioner sales $30,000 $12,000

Heater sales 12,000 30,000

* 0.5 probability of hot or cold weather

Hot Weather Cold Weather

Chapter 5 Slide 74

Reducing Risk

If the firms sells only heaters or air conditioners their income will be either $12,000 or $30,000.

Their expected income would be:1/2($12,000) + 1/2($30,000) = $21,000

DiversificationDiversification

Chapter 5 Slide 75

Reducing Risk

If the firm divides their time evenly between appliances their air conditioning and heating sales would be half their original values.


Chapter 5 Slide 76

Reducing Risk

If it were hot, their expected income would be $15,000 from air conditioners and $6,000 from heaters, or $21,000.

If it were cold, their expected income would be $6,000 from air conditioners and $15,000 from heaters, or $21,000.


Chapter 5 Slide 77

Reducing Risk

With diversification, expected income is $21,000 with no risk.


Chapter 5 Slide 78

Reducing Risk

Firms can reduce risk by diversifying among a variety of activities that are not closely related.


Chapter 5 Slide 79

Reducing Risk

Discussion Questions

How can diversification reduce the risk of investing in the stock market?

Can diversification eliminate the risk of investing in the stock market?

The Stock MarketThe Stock Market

Chapter 5 Slide 80

Reducing Risk

Risk averse are willing to pay to avoid risk.

If the cost of insurance equals the expected loss, risk averse people will buy enough insurance to recover fully from a potential financial loss.

InsuranceInsurance

Chapter 5 Slide 81

The Decision to Insure

No $40,000 $50,000 $49,000 $9,055

Yes 49,000 49,000 49,000 0

Insurance Burglary No Burglary Expected Standard(Pr = .1) (Pr = .9) Wealth Deviation

Chapter 5 Slide 82

Reducing Risk

While the expected wealth is the same, the expected utility with insurance is greater because the marginal utility in the event of the loss is greater than if no loss occurs.

Purchases of insurance transfers wealth and increases expected utility.

InsuranceInsurance

Chapter 5 Slide 83

Reducing Risk

Although single events are random and largely unpredictable, the average outcome of many similar events can be predicted.

The Law of Large NumbersThe Law of Large Numbers

Chapter 5 Slide 84

Reducing Risk

ExamplesA single coin toss vs. large number of

coins

Whom will have a car wreck vs. the number of wrecks for a large group of drivers

The Law of Large NumbersThe Law of Large Numbers

Chapter 5 Slide 85

Reducing Risk

Assume:

10% chance of a $10,000 loss from a home burglary

Expected loss = .10 x $10,000 = $1,000 with a high risk (10% chance of a $10,000 loss)

100 people face the same risk

Actuarial FairnessActuarial Fairness

Chapter 5 Slide 86

Reducing Risk

Then:

$1,000 premium generates a $100,000 fund to cover losses

Actual Fairness

When the insurance premium = expected payout

Actuarial FairnessActuarial Fairness

Chapter 5 Slide 87

The Value of Title InsuranceWhen Buying a House

A Scenario:

Price of a house is $200,000

5% chance that the seller does not own the house

ExampleExample

Chapter 5 Slide 88


Risk neutral buyer would pay:

ExampleExample

000,190]0[05.]000,200[95(.

Chapter 5 Slide 89


Risk averse buyer would pay much less

By reducing risk, title insurance increases the value of the house by an amount far greater than the premium.

ExampleExample

Chapter 5 Slide 90

Reducing Risk

Value of Complete Information

The difference between the expected value of a choice with complete information and the expected value when information is incomplete.

The Value of InformationThe Value of Information

Chapter 5 Slide 91

Reducing Risk

Suppose a store manager must determine how many fall suits to order:100 suits cost $180/suit

50 suits cost $200/suit

The price of the suits is $300


Chapter 5 Slide 92

Reducing Risk

Suppose a store manager must determine how many fall suits to order:Unsold suits can be returned for half cost.

The probability of selling each quantity is .50.


Chapter 5 Slide 93

The Decision to Insure

1. Buy 50 suits $5,000 $5,000 $5,000

2. Buy 100 suits 1,500 12,000 6,750

ExpectedSale of 50 Sale of 100 Profit

Chapter 5 Slide 94

Reducing Risk

With incomplete information:

Risk Neutral: Buy 100 suits

Risk Averse: Buy 50 suits

Chapter 5 Slide 95

Reducing Risk

The expected value with complete information is $8,500.8,500 = .5(5,000) + .5(12,000)

The expected value with uncertainty (buy 100 suits) is $6,750.


Chapter 5 Slide 96

Reducing Risk

The value of complete information is $1,750, or the difference between the two (the amount the store owner would be willing to pay for a marketing study).


Chapter 5 Slide 97

Per capita milk consumption has fallen over the years

The milk producers engaged in market research to develop new sales strategies to encourage the consumption of milk.

Reducing Risk

The Value of Information: ExampleThe Value of Information: Example

Chapter 5 Slide 98

FindingsMilk demand is seasonal with the greatest

demand in the spring

Ep is negative and small

EI is positive and large

Reducing Risk


Chapter 5 Slide 99

Milk advertising increases sales most in the spring.

Allocating advertising based on this information in New York increased sales by $4,046,557 and profits by 9%.

The cost of the information was relatively low, while the value was substantial.

Reducing Risk


Chapter 5 Slide 100

Assets

Something that provides a flow of money or services to its owner.

The flow of money or services can be explicit (dividends) or implicit (capital gain).


Chapter 5 Slide 101

Capital Gain

An increase in the value of an asset, while a decrease is a capital loss.


Chapter 5 Slide 102


Risky Asset

Provides an uncertain flow of money or services to its owner.

Examplesapartment rent, capital gains, corporate

bonds, stock prices

Risky & Riskless AssetsRisky & Riskless Assets

Chapter 5 Slide 103


Riskless Asset

Provides a flow of money or services that is known with certainty.

Examplesshort-term government bonds, short-

term certificates of deposit

Risky & Riskless AssetsRisky & Riskless Assets

Chapter 5 Slide 104


Asset ReturnsReturn on an Asset

The total monetary flow of an asset as a fraction of its price.

Real Return of an AssetThe simple (or nominal) return less the

rate of inflation.

Chapter 5 Slide 105


Asset Returns

Price Purchase

FlowMonetary Return Asset

%10$1,000

$100/yr.

Price Bond

Flow Return Asset

Chapter 5 Slide 106


Expected Return

Return that an asset should earn on average

Expected vs. Actual ReturnsExpected vs. Actual Returns

Chapter 5 Slide 107


Actual Return

Return that an asset earns


Chapter 5 Slide 108

Investments--Risk and Return (1926-1999)

Common stocks (S&P 500) 9.5 20.2

Long-term corporate bonds 2.7 8.3

U.S. Treasury bills 0.6 3.2

RiskReal Rate of (standardReturn (%) deviation,%)

Chapter 5 Slide 109


Higher returns are associated with greater risk.

The risk-averse investor must balance risk relative to return


Chapter 5 Slide 110


An investor is choosing between T-Bills and stocks:T-bills (riskless) versus Stocks (risky)

Rf = the return on risk free T-bills

Expected return equals actual return when there is no risk

The Trade-Off Between Risk and ReturnThe Trade-Off Between Risk and Return

Chapter 5 Slide 111


An investor is choosing between T-Bills and stocks:

Rm = the expected return on stocks

rm = the actual returns on stock


Chapter 5 Slide 112


At the time of the investment decision, we know the set of possible outcomes and the likelihood of each, but we do not know what particular outcome will occur.


Chapter 5 Slide 113


The risky asset will have a higher expected return than the risk free asset (Rm > Rf).

Otherwise, risk-averse investors would buy only T-bills.


Chapter 5 Slide 114


How to allocate savings:

b = fraction of savings in the stock market

1 - b = fraction in T-bills

The Investment PortfolioThe Investment Portfolio

Chapter 5 Slide 115


Expected Return:

Rp: weighted average of the expected return on the two assets

Rp = bRm + (1-b)Rf


Chapter 5 Slide 116


Expected Return:

If Rm = 12%, Rf = 4%, and b = 1/2

Rp = 1/2(.12) + 1/2(.04) = 8%


Chapter 5 Slide 117


Question

How risky is their portfolio?


Chapter 5 Slide 118


Risk (standard deviation) of the portfolio is the fraction of the portfolio invested in the risky asset times the standard deviation of that asset:

mp b


Chapter 5 Slide 119


Determining b:

fmp RbbRR )1(

)( fmfp RRbRR

The Investor’s Choice ProblemThe Investor’s Choice Problem

Chapter 5 Slide 120


Determining b:

pm

fmfp

RRRR

)(

mpb /

The Investor’s Choice ProblemThe Investor’s Choice Problem

Chapter 5 Slide 121


Observations

1) The final equation

is a budget line describing the trade- off between risk and expected return .

Risk and the Budget LineRisk and the Budget Line

pm

fmfp

)R(RRR

)( p)p(R

Chapter 5 Slide 122


Observations:

2) Is an equation for a straight line:

3)

constants are and ,R ,R mfm

mfm )/R(R Slope


pm

fmfp

)R(RRR

Chapter 5 Slide 123


Observations

3) Expected return, RP, increases as risk increases.

4) The slope is the price of risk or the risk-return trade-off.


Chapter 5 Slide 124

Choosing BetweenRisk and Return

0 p Return, of

Deviation Standard

ExpectedReturn,Rp

U2 is the optimal choice of those

obtainable, since it gives the highest

return for agiven risk and istangent to the

budget line.

Rf

Budget Line

m

Rm

R*

U2U1

U3

Chapter 5 Slide 125

Rf

Budget line

The Choices ofTwo Different Investors

0

ExpectedReturn,Rp

p Return, of

Deviation Standard

Given the same budgetline, investor A chooses

low return-low risk, while investor B

chooses high return-high risk.

UA

RA

A

UB

RB

m

Rm

B

Chapter 5 Slide 126

Rf

Budget line

Buying Stocks on Margin

0

ExpectedReturn,Rp

UA

RA

A

UA: High risk aversion --Stock & T-bill portfolio

p Return, of

Deviation Standard

UB

RB

m

Rm

B

UA: Low risk aversion --The investor would invest more than 100% of their wealth by borrowing or buying on the margin.

Chapter 5 Slide 127

Investing in the Stock Market

ObservationsPercent of American families who had

directly or indirectly invested in the stock market

1989 = 32%1995 = 41%

Chapter 5 Slide 128


ObservationsShare of wealth in the stock market

1989 = 26%1995 = 40%

Chapter 5 Slide 129


ObservationsParticipation in the stock market by age

Less than 35 1989 = 23% 1995 = 29%

More than 35 Small increase

Chapter 5 Slide 130


What Do You Think?Why are more people investing in the stock

market?

Chapter 5 Slide 131

Summary

Consumers and managers frequently make decisions in which there is uncertainty about the future.

Consumers and investors are concerned about the expected value and the variability of uncertain outcomes.

Chapter 5 Slide 132

Summary

Facing uncertain choices, consumers maximize their expected utility, and average of the utility associated with each outcome, with the associated probabilities serving as weights.

A person may be risk averse, risk neutral or risk loving.

Chapter 5 Slide 133

Summary

The maximum amount of money that a risk-averse person would pay to avoid risk is the risk premium.

Risk can be reduced by diversification, purchasing insurance, and obtaining additional information.

Chapter 5 Slide 134

Summary

The law of large numbers enables insurance companies to provide actuarially fair insurance for which the premium paid equals the expected value of the loss being insured against.

Consumer theory can be applied to decisions to invest in risky assets.

End of Chapter 5



Chapter 5 Choice Under Uncertainty. Chapter 5Slide 2 Topics to be Discussed Describing Risk Preferences Toward Risk Reducing Risk The Demand for Risky.

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