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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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2005 Pearson Education, Inc. Chapter 5 3
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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2005 Pearson Education, Inc. Chapter 5 4
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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2005 Pearson Education, Inc. Chapter 5 5
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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2005 Pearson Education, Inc. Chapter 5 6
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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2005 Pearson Education, Inc. Chapter 5 7
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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2005 Pearson Education, Inc. Chapter 5 8
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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2005 Pearson Education, Inc. Chapter 5 9
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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2005 Pearson Education, Inc. Chapter 5 10
Expected Value An Example
Objective Probability
100 explorations, 25 successes and 75failures
Probability (Pr) of success = 1/4 and theprobability of failure = 3/4
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2005 Pearson Education, Inc. Chapter 5 11
Expected Value An Example
failure)of)(valuePr(failure
success)of)(valuePr(successEV
)($20/share43)($40/share41EV
$25/sharEV
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2005 Pearson Education, Inc. Chapter 5 12
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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2005 Pearson Education, Inc. Chapter 5 13
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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2005 Pearson Education, Inc. Chapter 5 14
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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2005 Pearson Education, Inc. Chapter 5 15
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 $510 if
the company goes out of business (.01probability)
Variability An Example
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2005 Pearson Education, Inc. Chapter 5 16
Variability An Example
Outcome 1 Outcome 2
Prob. Income Prob. Income
Job 1:Commission .5 2000 .5 1000
Job 2:
Fixed Salary .99 1510 .01 510
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2005 Pearson Education, Inc. Chapter 5 17
1500$.5($1000).5($2000))E(X 1
Variability An Example
Income from Possible Sales Job
Job 1 Expected Income
$1500.01($510).99($1510))E(X 2
Job 2 Expected Income
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2005 Pearson Education, Inc. Chapter 5 18
Variability
While the expected values are the same,the variability is not
Greater variability from expected valuessignals greater risk
Variability comes from deviations inpayoffs
Difference between expected payoff andactual payoff
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2005 Pearson Education, Inc. Chapter 5 19
Variability An Example
Deviations from Expected Income ($)
Outcome1 Deviation Outcome2 Deviation
Job1 $2000 $500 $1000 -$500
Job2 1510 10 510 -900
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2005 Pearson Education, Inc. Chapter 5 20
Variability
Average deviations are always zero sowe must adjust for negative numbers
We can measure variability withstandard deviation
The square root of the average of thesquares of the deviations of the payoffs
associated with each outcome from theirexpected value
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2005 Pearson Education, Inc. Chapter 5 21
Variability
Standard deviation is a measure of risk
Measures how variable your payoff will be
More variability means more risk
Individuals generally prefer less variabilityless risk
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2005 Pearson Education, Inc. Chapter 5 22
Variability
The standard deviation is written:
2222
11 )(Pr)(Pr XEXXEX
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2005 Pearson Education, Inc. Chapter 5 23
Standard Deviation Example 1
Deviations from Expected Income ($)
Outcome1 Deviation Outcome2 Deviation
Job1 $2000 $500 $1000 -$500
Job2 1510 10 510 -900
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2005 Pearson Education, Inc. Chapter 5 24
Standard Deviation Example 1
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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2005 Pearson Education, Inc. Chapter 5 25
Standard Deviation Example 1
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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2005 Pearson Education, Inc. Chapter 5 26
Standard Deviation Example 2
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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2005 Pearson Education, Inc. Chapter 5 27
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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2005 Pearson Education, Inc. Chapter 5 28
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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2005 Pearson Education, Inc. Chapter 5 29
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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2005 Pearson Education, Inc. Chapter 5 30
Decision Making Example 2
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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2005 Pearson Education, Inc. Chapter 5 31
Decision Making Example 2
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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2005 Pearson Education, Inc. Chapter 5 32
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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2005 Pearson Education, Inc. Chapter 5 33
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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2005 Pearson Education, Inc. Chapter 5 34
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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2005 Pearson Education, Inc. Chapter 5 36
Risk and Crime Deterrence -Example
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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2005 Pearson Education, Inc. Chapter 5 37
Risk and Crime Deterrence -Example
Enforcement costs are reduced with highfine and low probability
Most effective if drivers dont like to take
risks
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2005 Pearson Education, Inc. Chapter 5 38
Preferences Toward Risk
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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2005 Pearson Education, Inc. Chapter 5 39
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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2005 Pearson Education, Inc. Chapter 5 40
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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2005 Pearson Education, Inc. Chapter 5 41
Preferences Toward Risk
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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2005 Pearson Education, Inc. Chapter 5 42
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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2005 Pearson Education, Inc. Chapter 5 43
Preferences Toward Risk
People differ in their preference towardrisk
People can be risk averse, risk neutral, orrisk loving
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2005 Pearson Education, Inc. Chapter 5 44
Preferences Toward Risk
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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2005 Pearson Education, Inc. Chapter 5 45
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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2005 Pearson Education, Inc. Chapter 5 46
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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2005 Pearson Education, Inc. Chapter 5 47
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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2005 Pearson Education, Inc. Chapter 5 48
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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2005 Pearson Education, Inc. Chapter 5 49
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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2005 Pearson Education, Inc. Chapter 5 50
Preferences Toward Risk
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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2005 Pearson Education, Inc. Chapter 5 51
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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2005 Pearson Education, Inc. Chapter 5 52
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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2005 Pearson Education, Inc. Chapter 5 53
Preferences Toward Risk
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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2005 Pearson Education, Inc. Chapter 5 54
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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2005 Pearson Education, Inc. Chapter 5 55
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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2005 Pearson Education, Inc. Chapter 5 56
Preferences Toward Risk
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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2005 Pearson Education, Inc. Chapter 5 57
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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2005 Pearson Education, Inc. Chapter 5 58
Risk Premium Example
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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2005 Pearson Education, Inc. Chapter 5 59
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
Risk Premium Example
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2005 Pearson Education, Inc. Chapter 5 60
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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2005 Pearson Education, Inc. Chapter 5 61
Risk Aversion and Income
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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2005 Pearson Education, Inc. Chapter 5 62
Risk Aversion and Income
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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2005 Pearson Education, Inc. Chapter 5 63
Risk Aversion and Income
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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2005 Pearson Education, Inc. Chapter 5 64
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
Risk Aversion and Indifference
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2005 Pearson Education, Inc. Chapter 5 65
Risk Aversion and IndifferenceCurves
Standard Deviation of Income
ExpectedIncome Highly Risk Averse: Anincrease in standard
deviation requires alarge increase inincome to maintain
satisfaction.
U1
U2
U3
Risk Aversion and Indifference
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2005 Pearson Education, Inc. Chapter 5 66
Risk Aversion and IndifferenceCurves
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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2005 Pearson Education, Inc. Chapter 5 67
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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2005 Pearson Education, Inc. Chapter 5 68
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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2005 Pearson Education, Inc. Chapter 5 69
Income from Sales ofAppliances
Hot WeatherCold
Weather
Airconditionersales
$30,000 $12,000
Heater sales 12,000 30,000
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2005 Pearson Education, Inc. Chapter 5 70
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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2005 Pearson Education, Inc. Chapter 5 71
Diversification Example
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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2005 Pearson Education, Inc. Chapter 5 72
Diversification Example
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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2005 Pearson Education, Inc. Chapter 5 73
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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2005 Pearson Education, Inc. Chapter 5 74
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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2005 Pearson Education, Inc. Chapter 5 75
The Decision to Insure
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2005 Pearson Education, Inc. Chapter 5 76
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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2005 Pearson Education, Inc. Chapter 5 77
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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2005 Pearson Education, Inc. Chapter 5 78
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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2005 Pearson Education, Inc. Chapter 5 79
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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2005 Pearson Education, Inc. Chapter 5 80
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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2005 Pearson Education, Inc. Chapter 5 81
The Value of Information
The value ofcomplete information
The difference between the expected valueof a choice with complete information and the
expected value when information isincomplete
The Value of Information
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2005 Pearson Education, Inc. Chapter 5 82
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
The Value of Information
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2005 Pearson Education, Inc. Chapter 5 83
The Value of Information Example
Findings
Milk demand is seasonal with the greatestdemand in the spring
Price elasticity of demand is negative andsmall
Income elasticity is positive and large
The Value of Information
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2005 Pearson Education, Inc. Chapter 5 84
The Value of Information Example
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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2005 Pearson Education, Inc. Chapter 5 85
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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2005 Pearson Education, Inc. Chapter 5 86
The Demand for Risky Assets
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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2005 Pearson Education, Inc. Chapter 5 87
The Demand for Risky Assets
Capital Gain
An increase in the value of an asset
Capital loss
A decrease in the value of an asset
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2005 Pearson Education, Inc. Chapter 5 88
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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2005 Pearson Education, Inc. Chapter 5 89
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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2005 Pearson Education, Inc. Chapter 5 90
The Demand for Risky Assets
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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2005 Pearson Education, Inc. Chapter 5 91
The Demand for Risky Assets
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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2005 Pearson Education, Inc. Chapter 5 92
The Demand for Risky Assets
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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2005 Pearson Education, Inc. Chapter 5 93
(1926-1999)
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2005 Pearson Education, Inc. Chapter 5 94
The Demand for Risky Assets
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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2005 Pearson Education, Inc. Chapter 5 95
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
Trade-offs: Risk and Returns
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2005 Pearson Education, Inc. Chapter 5 96
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
Trade-offs: Risk and Returns
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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(
Trade-offs: Risk and Returns
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2005 Pearson Education, Inc. Chapter 5 98
Example
Assume, Rm = 12%, Rf= 4%, and b = 1/2
%8
%)4)(2/11(%)12)(2/1()1(
P
P
fmP
R
RRbbRR
Trade-offs: Risk and Returns
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2005 Pearson Education, Inc. Chapter 5 99
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
Trade-offs: Risk and Returns
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2005 Pearson Education, Inc. Chapter 5 100
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
Trade-offs: Risk and Returns
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2005 Pearson Education, Inc. Chapter 5 101
Example
Expected return on the portfolio, rpincreases as the standard deviation, p ofthat return increases
p
m
fm
fp
fmp
RR
RR
RbbRR
)(
)1(
Trade-offs: Risk and Returns
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2005 Pearson Education, Inc. Chapter 5 102
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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2005 Pearson Education, Inc. Chapter 5 103
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
Choosing Between Risk
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2005 Pearson Education, Inc. Chapter 5 104
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
Choosing Between Risk
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2005 Pearson Education, Inc. Chapter 5 105
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
Choosing Between Risk
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2005 Pearson Education, Inc. Chapter 5 106
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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2005 Pearson Education, Inc. Chapter 5 107
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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2005 Pearson Education, Inc. Chapter 5 108
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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2005 Pearson Education, Inc. Chapter 5 109
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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Behavioral Economics
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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2005 Pearson Education, Inc. Chapter 5 112
Behavioral Economics
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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Behavioral Economics
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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2005 Pearson Education, Inc. Chapter 5 114
Behavioral Economics
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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2005 Pearson Education, Inc. Chapter 5 115
Behavioral Economics
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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2005 Pearson Education, Inc. Chapter 5 116
Behavioral Economics
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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Behavioral Economics
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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Behavioral Economics
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