Ch05_Pindyck

7/28/2019 Ch05_Pindyck

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Chapter 5

Uncertainty and ConsumerBehavior


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2005 Pearson Education, Inc. Chapter 5 2

Topics to be Discussed

Describing Risk

Preferences Toward Risk

Reducing Risk

The Demand for Risky Assets


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Introduction

Choice with certainty is reasonablystraightforward

How do we make choices when certainvariables such as income and prices areuncertain (making choices with risk)?


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Describing Risk

To measure risk we must know:

1. All of the possible outcomes

2. The probability or likelihood that eachoutcome will occur


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Describing Risk

Interpreting Probability

1. Objective Interpretation

Based on the observed frequency of pastevents

2. Subjective Interpretation

Based on perception that an outcome willoccur


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Interpreting Probability

Subjective Probability

Different information or different abilities toprocess the same information can influencethe subjective probability

Based on judgment or experience


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Describing Risk

With an interpretation of probability,must determine 2 measures to helpdescribe and compare risky choices

1. Expected value

2. Variability


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Describing Risk

Expected Value

The weighted average of the payoffs orvalues resulting from all possible outcomes

Expected value measures the central tendency;the payoff or value expected on average


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Expected Value An Example

Investment in offshore drillingexploration:

Two outcomes are possibleSuccess the stock price increases from

$30 to $40/share

Failure the stock price falls from $30 to

$20/share


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Objective Probability

100 explorations, 25 successes and 75failures

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


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failure)of)(valuePr(failure

success)of)(valuePr(successEV

)($20/share43)($40/share41EV

$25/sharEV


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Expected Value

In general, for n possible outcomes:

Possible outcomes having payoffs X1, X2, ,Xn

Probabilities of each outcome is given by Pr1,Pr2, , Prn

nn2211 XPr...XPrXPrE(X)


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Describing Risk

Variability

The extent to which possible outcomes of anuncertain event may differ

How much variation exists in the possiblechoice


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Variability An Example

Suppose you are choosing between twopart-time sales jobs that have the sameexpected income ($1,500)

The first job is based entirely oncommission

The second is a salaried position


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There are two equally likely outcomes inthe first job: $2,000 for a good sales joband $1,000 for a modestly successfulone

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

the company goes out of business (.01probability)



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Outcome 1 Outcome 2

Prob. Income Prob. Income

Job 1:Commission .5 2000 .5 1000

Job 2:

Fixed Salary .99 1510 .01 510


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1500$.5($1000).5($2000))E(X 1


Income from Possible Sales Job

Job 1 Expected Income

$1500.01($510).99($1510))E(X 2

Job 2 Expected Income


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Variability

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

Greater variability from expected valuessignals greater risk

Variability comes from deviations inpayoffs

Difference between expected payoff andactual payoff


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Deviations from Expected Income ($)

Outcome1 Deviation Outcome2 Deviation

Job1 $2000 $500 $1000 -$500

Job2 1510 10 510 -900


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Variability

Average deviations are always zero sowe must adjust for negative numbers

We can measure variability withstandard deviation

The square root of the average of thesquares of the deviations of the payoffs

associated with each outcome from theirexpected value


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Variability

Standard deviation is a measure of risk

Measures how variable your payoff will be

More variability means more risk

Individuals generally prefer less variabilityless risk


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Variability

The standard deviation is written:

2222

11 )(Pr)(Pr XEXXEX


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Standard Deviation Example 1

Deviations from Expected Income ($)

Outcome1 Deviation Outcome2 Deviation

Job1 $2000 $500 $1000 -$500

Job2 1510 10 510 -900


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Standard deviations of the two jobs are:

500000,250

)000,250($5.0)000,250($5.0

1

1

50.99900,9

)100,980($01.0)100($99.0

2

2

2222

11 )(Pr)(Pr XEXXEX


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Job 1 has a larger standard deviation andtherefore it is the riskier alternative

The standard deviation also can be usedwhen there are many outcomes insteadof only two


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

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


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Outcome Probabilities - Two Jobs

Income

0.1

$1000 $1500 $2000

0.2

Job 1

Job2

Job 1 has greaterspread: greater

standard deviationand greater risk

than Job 2.

Probability


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Decision Making Example 1

What if the outcome probabilities of twojobs have unequal probability ofoutcomes?

Job 1: greater spread and standard deviation

Peaked distribution: extreme payoffs are lesslikely that those in the middle of the

distributionYou will choose job 2 again


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Unequal Probability Outcomes

Job 1

Job 2

The distribution of payoffsassociated with Job 1 has agreater spread and standard

deviation than those with Job 2.

Income

0.1

$1000 $1500 $2000

0.2

Probability


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Suppose we add $100 to each payoff inJob 1 which makes the expected payoff =$1600

Job 1: expected income $1,600 and astandard deviation of $500

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


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Which job should be chosen?

Depends on the individual

Some may be willing to take risk with higherexpected income

Some will prefer less risk even with lowerexpected income


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Risk and Crime Deterrence

Attitudes toward risk affect willingness tobreak the law

Suppose a city wants to deter peoplefrom double parking

Monetary fines may be better than jailtime


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Risk and Crime Deterrence

Costs of apprehending criminals are notzero, therefore

Fines must be higher than the costs tosociety

Probability of apprehension is actually lessthan one


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Risk and Crime Deterrence -Example

Assumptions:

1. Double-parking saves a person $5 in termsof time spent searching for a parking space

2. The driver is risk neutral

3. Cost of apprehension is zero


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The same deterrence effect is obtainedby either

A $50 fine with a 0.1 probability of beingcaught resulting in an expected penalty of $5

or

A $500 fine with a 0.01 probability of being

caught resulting in an expected penalty of $5


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Enforcement costs are reduced with highfine and low probability

Most effective if drivers dont like to take

risks


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Can expand evaluation of riskyalternative by considering utility that isobtained by risk

A consumer gets utility from income

Payoff measured in terms of utility


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Preferences Toward Risk -Example

A person is earning $15,000 andreceiving 13.5 units of utility from the job

She is considering a new, but risky job

0.50 chance of $30,000

0.50 chance of $10,000


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Preferences Toward Risk -Example

Utility at $30,000 is 18

Utility at $10,000 is 10

Must compare utility from the risky jobwith current utility of 13.5

To evaluate the new job, we mustcalculate the expected utility of the risky

job


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The expected utility of the risky option isthe sum of the utilities associated with allher possible incomes weighted by the

probability that each income will occur

E(u) = (Prob. of Utility 1) *(Utility 1)

+ (Prob. of Utility 2)*(Utility 2)


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Preferences Toward Risk Example

The expected is:

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 thanthe current utility of 13.5 and therefore

preferred


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People differ in their preference towardrisk

People can be risk averse, risk neutral, orrisk loving


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Risk Averse

A person who prefers a certain given incometo a risky income with the same expected

valueThe person has a diminishing marginal utility

of income

Most common attitude towards risk

Ex: Market for insurance


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Risk Averse - Example

A person can have a $20,000 job with100% probability and receive a utilitylevel of 16

The person could have a job with a 0.5chance of earning $30,000 and a 0.5chance of earning $10,000


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Risk Averse Example

Expected Income of Risky Job

E(I) = (0.5)($30,000) + (0.5)($10,000)

E(I) = $20,000

Expected Utility of Risky Job

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

E(u) = 14


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Risk Averse Example

Expected income from both jobs is thesame risk averse may choose current

job

Expected utility is greater for certain job

Would keep certain job

Risk averse persons losses (decreased

utility) are more important than riskygains


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Risk Averse

Can see risk averse choices graphically

Risky job has expected income =$20,000 with expected utility = 14

Point F

Certain job has expected income =$20,000 with utility = 16

Point D


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Income($1,000)

Utility

The consumer is riskaverse because she wouldprefer a certain income of

$20,000 to an uncertainexpected income =

$20,000

E

10

10 20

14

16

18

0 16 30

A

C

D

Risk Averse Utility Function

F


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A person is said to be risk neutral if theyshow no preference between a certainincome, and an uncertain income with

the same expected value

Constant marginal utility of income


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Risk Neutral

Expected value for risky option is thesame as utility for certain outcome

E(I) = (0.5)($10,000) + (0.5)($30,000)

= $20,000

E(u) = (0.5)(6) + (0.5)(18) = 12

This is the same as the certain income of$20,000 with utility of 12


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Income($1,000)10 20

Utility

0 30

6

A

E

C12

18

The consumer is riskneutral and is indifferent

between certain eventsand uncertain events

with the sameexpected income.

Risk Neutral


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A person is said to be risk loving if theyshow a preference toward an uncertainincome over a certain income with the

same expected valueExamples: Gambling, some criminal activities

Increasing marginal utility of income


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Risk Loving

Expected value for risky option point F

E(I) = (0.5)($10,000) + (0.5)($30,000)

= $20,000

E(u) = (0.5)(3) + (0.5)(18) = 10.5

Certain income is $20,000 with utility of 8 point C

Risky alternative is preferred


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Income($1,000)

Utility

0 10 20 30

The consumer is riskloving because she

would prefer the gambleto a certain income.

Risk Loving

3A

E

C8

18

F10.5


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The risk premium is the maximumamount of money that a risk-averseperson would pay to avoid taking a risk

The risk premium depends on the riskyalternatives the person faces


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Risk Premium Example

From the previous example

A person has a .5 probability of earning$30,000 and a .5 probability of earning

$10,000The expected income is $20,000 with

expected utility of 14


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Point F shows the risky scenario theutility of 14 can also be obtained withcertain income of $16,000

This person would be willing to pay up to$4000 (20 16) to avoid the risk ofuncertain income

Can show this graphically by drawing a

straight line between the two points lineCF


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Income($1,000)

Utility

0 10 16

Here, the riskpremium is $4,000because a certainincome of $16,000gives the person

the same expectedutility as the

uncertain incomewith expected value

of $20,000.

10

18

30 40

20

14

A

CE

G

20

Risk Premium

F



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Risk Aversion and Income

Variability in potential payoffs increasesthe 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).


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Example (cont.):

The expected income is still $20,000, but theexpected utility falls to 10

E(u) = (0.5)u($0) + (0.5)u($40,000)= 0 + .5(20) = 10

The certain income of $20,000 has utility of16

If person must take new job, their utility willfall by 6


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Example (cont.):

They can get 10 units of utility by taking acertain job paying $10,000

The risk premium, therefore, is $10,000 (i.e.they would be willing to give up $10,000 ofthe $20,000 and have the same E(u) as therisky job


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The greater the variability, the more theperson would be willing to pay to avoidthe risk, and the larger the risk premium

Risk Aversion and Indifference


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Risk Aversion and IndifferenceCurves

Can describe a persons risk aversionusing indifference curves that relateexpected income to variability of income

(standard deviation)Since risk is undesirable, greater risk

requires greater expected income tomake the person equally well off

Indifference curves are therefore upwardsloping



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Standard Deviation of Income

ExpectedIncome Highly Risk Averse: Anincrease in standard

deviation requires alarge increase inincome to maintain

satisfaction.

U1

U2

U3



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Standard Deviation of Income

ExpectedIncome Slightly Risk Averse:A large increase in standard

deviation requires only asmall increase in incometo maintain satisfaction.

U1

U2

U3


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Reducing Risk

Consumers are generally risk averseand therefore want to reduce risk

Three ways consumers attempt toreduce risk are:

1. Diversification

2. Insurance

3. Obtaining more information


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Reducing Risk

Diversification

Reducing risk by allocating resources to avariety of activities whose outcomes are not

closely relatedExample:

Suppose a firm has a choice of selling airconditioners, heaters, or both

The probability of it being hot or cold is 0.5

How does a firm decide what to sell?

Income from Sales of


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Income from Sales ofAppliances

Hot WeatherCold

Weather

Airconditionersales

$30,000 $12,000

Heater sales 12,000 30,000


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Diversification Example

If the firm sells only heaters or airconditioners 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


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If the firm divides their time evenly betweenappliances, their air conditioning and heatingsales would be half their original values

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

If it were cold, their expected income would be

$6,000 from air conditioners and $15,000 fromheaters, or $21,000


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

Better off diversifying to minimize risk

Firms can reduce risk by diversifyingamong a variety of activities that are notclosely related

Reducing Risk The Stock


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Reducing Risk The StockMarket

If invest all money in one stock, then takeon a lot of risk

If that stock loses value, you lose all your

investment value

Can spread risk out by investing in manydifferent stocks or investments

Ex: Mutual funds


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Reducing Risk Insurance

Risk averse are willing to pay to avoidrisk

If the cost of insurance equals theexpected loss, risk averse people will buyenough insurance to recover fully from apotential financial loss


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The Decision to Insure


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Reducing Risk Insurance

For the risk averse consumer, guaranteeof same income regardless of outcomehas higher utility than facing the

probability of riskExpected utility with insurance is higher

than without


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The Law of Large Numbers

Insurance companies know that althoughsingle events are random and largelyunpredictable, the average outcome of

many similar events can be predictedWhen insurance companies sell many

policies, they face relatively little risk


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Reducing Risk Actuarially Fair

Insurance companies can be sure totalpremiums paid will equal total moneypaid out

Companies set the premiums so moneyreceived will be enough to pay expectedlosses


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Reducing Risk Actuarially Fair

Some events with very little probability ofoccurrence such as floods andearthquakes are no longer insured

privatelyCannot calculate true expected values and

expected losses

Governments have had to create insurancefor these types of events

Ex: National Flood Insurance Program


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The Value of Information

Risk often exists because we dont know

all the information surrounding a decision

Because of this, information is valuableand people are willing to pay for it


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The value ofcomplete information

The difference between the expected valueof a choice with complete information and the

expected value when information isincomplete



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The Value of Information Example

Per capita milk consumption has fallenover the years

The milk producers engaged in marketresearch to develop new sales strategiesto encourage the consumption of milk



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Findings

Milk demand is seasonal with the greatestdemand in the spring

Price elasticity of demand is negative andsmall

Income elasticity is positive and large



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Milk advertising increases sales most inthe spring

Allocating advertising based on this

information in New York increased profitsby 9% or $14 million

The cost of the information was relatively

low, while the value was substantial(increased profits)


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Demand for Risky Assets

Most individuals are risk averse and yetchoose to invest money in assets thatcarry some risk

Why do they do this?

How do they decide how much risk to bear?

Must examine the demand for risky

assets


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Assets

Something that provides a flow of money orservices to its owner

Ex: homes, savings accounts, rental property,shares of stock

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


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Capital Gain

An increase in the value of an asset

Capital loss

A decrease in the value of an asset


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Risky and Riskless Assets

Risky Asset

Provides an uncertain flow of money orservices to its owner

ExamplesApartment rent, capital gains, corporate bonds,

stock prices

Dont know with certainty what will happen to

the value of a stock


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Risky and Riskless Assets

Riskless Asset

Provides a flow of money or services that isknown with certainty

Examples Short-term government bonds, short-term

certificates of deposit


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People hold assets because of themonetary flows provided

To compare assets, one must consider

the monetary flow relative to the assetsprice (value)

Return on an assetThe total monetary flow of an asset,

including capital gains or losses, as a fractionof its price


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Individuals hope to have an asset thathas returns larger than the rate ofinflation

Want to have greater purchasing power

Real Return of an Asset (inflationadjusted)

The simple (or nominal) return less the rateof inflation


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Since returns are not known withcertainty, investors often make decisionsbased on expected returns

Expected ReturnReturn that an asset should earn on average

In the end, the actual return could be higher

or lower than the expected return

Investments Risk and Return


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(1926-1999)


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The higher the return, the greater the risk

Investors will choose lower returninvestments in order to reduce risk

A risk-averse investor must balance riskrelative to return

Must study the trade-off between return and

risk

Trade-offs: Risk and Returns


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Example

An investor is choosing between T-Billsand stocks:

1. T-bills riskless

2. Stocks risky

Investor can choose only T-bills, onlystocks, or some combination of both



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Example

Rf= risk-free return on T-bill

Expected return equals actual return on ariskless asset

Rm = the expected return on stocks rm = the actual returns on stock

Assume Rm > Rfor no risk averse

investor would buy the stocks



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Example

How do we determine the allocation offunds between the two choices?b = fraction of funds placed in stocks

(1-b) = fraction of funds placed in T-billsExpected return on portfolio is weighted

average of expected return on the twoassets

fmP RbbRR )1(



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Example

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

%8

%)4)(2/11(%)12)(2/1()1(

P

P

fmP

R

RRbbRR



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Example

How risky is the portfolio?

As stated before, one measure of risk isstandard deviation

Standard deviation of the risky asset, mStandard deviation of risky portfolio, p

Can show that:

mp b



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Example

We still need to figure out the allocationbetween the investment choices

A type of budget line can be constructed

describing the trade-off between risk andexpected return



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Example

Expected return on the portfolio, rpincreases as the standard deviation, p ofthat return increases

p

m

fm

fp

fmp

RR

RR

RbbRR

)(

)1(



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Example

The slope of the line is called the priceof risk

Tells how much extra risk an investor must

incur to enjoy a higher expected return

mfm )/R(RSlope

Choosing Between Risk


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and Return

If all funds are invested in T-bills (b=0),expected return is Rf

If all funds are invested in stocks (b=1),

expected return is Rm but with standarddeviation ofm Funds may be invested between the

assets with expected return between Rf

and Rm, with standard deviation betweenm and 0



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and Return

We can draw indifference curvesshowing combinations of risk and returnthat leave an investor equally satisfied

Comparing the payoffs and risk betweenthe two investment choices and thepreferences of the investor, the optimalportfolio choice can be determined

Investor wants to maximize utility withinthe affordable options



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and Return

pReturn,of

DeviatioStandard

ExpectedReturn,Rp

U2is the optimal choice since it gives the highestreturn for a given risk and is still affordable

Rf

Budget Line

m

Rm

R*

U2

U1

U3



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and Return

Different investors have different attitudestoward risk

If we consider a very risk averse investor (A)

Portfolio will contain mostly T-bills and less in stock,with return slightly larger than Rf

If we consider a riskier investor (B)

Portfolio will contain mostly stock and less T-bills, witha higher return Rb but with higher standard deviation

The Choices of Two Different


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Investors

ExpectedReturn,Rp

pReturn,of

DeviatioStandard

Given the same

budget line,investorA

chooses lowreturn/low risk,while investorB

chooses highreturn/high risk.

UA

RA

A

UB

R

f

Budget line

m

Rm

RB

B


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Investing in the Stock Market

In 1990s many people began investing in

the stock market for the first time

Percent of US families who had directly or

indirectly invested in the stock market 1989 = 32%

1998 = 49%

Percent with share of wealth in stock market

1989 = 26%

1998 = 54%


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Investing in the Stock Market

Why were stock market investmentsincreasing during the 90s?

Ease of online trading

Significant increase in stock prices duringlate 90s

Employers shifting to self-directed retirementplans

Publicity for do it yourself investing


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Behavioral Economics

Sometimes individuals behaviorcontradicts basic assumptions ofconsumer choice

More information about human behaviormight lead to better understanding

This is the objective ofbehavioraleconomics Improving understanding of consumer choice by

incorporating more realistic and detailedassumptions regarding human behavior


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There are a number of examples ofconsumer choice contradictions

You take at trip and stop at a restaurant that

you will most likely never stop at again. Youstill think it fair to leave a 15% tip rewardingthe good service.

You choose to buy a lottery ticket even

though the expected value is less than theprice of the ticket


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Reference PointsEconomists assume that consumers place a

unique value on the goods/servicespurchased

Psychologists have found that perceivedvalue can depend on circumstances You are able to buy a ticket to the sold out Cher

concert for the published price of $125. You find

out you can sell the ticket for $500 but youchoose not to, even though you would neverhave paid more than $250 for the ticket.


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Reference Points (cont.)The point from which an individual makes a

consumption decision

From the example, owning the Cher ticket isthe reference point Individuals dislike losing things they own

They value items more when they own themthan when they do not

Losses are valued more than gains Utility loss from selling the ticket is greater than

original utility gain from purchasing it


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Experimental Economics

Students were divided into two groups

Group one was given a mug with a market

value of $5.00Group two received nothing

Students with mugs were asked how muchthey would take to sell the mug back

Lowest price for mugs, on average, was $7.00

B h i l E i


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Experimental Economics (cont.)

Group without mugs was asked minimumamount of cash they would except in lieu of

the mugOn average willing to accept $3.50 instead of

getting the mug

Group one had reference point of owning the

mugGroup two had reference point of no mug

B h i l E i


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FairnessIndividuals often make choices because they

think they are fair and appropriate Charitable giving, tipping in restaurants

Some consumers will go out of their way topunish a store they think is unfair in theirpricing

Manager might offer higher than market

wages to make for happier workingenvironment or more productive worker

B h i l E i


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The Laws of Probability

Individuals dont always evaluate uncertain

events according to the laws of probability

Individuals also dont always maximizeexpected utility

Law of small numbers

Overstate probability of an event when faced

with little information Ex: overstate likelihood they will win the lottery

B h i l E i


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Theory up to now has explained muchbut not all of consumer choice

Although not all of consumer decisions

can be explained by the theory up to thispoint, it helps us understand much of it

Behavioral economics is a developingfield to help explain and elaborate on

situations not well explained by the basicconsumer model

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Ch05_Pindyck