Chapter 3

CHOICE UNDER UNCERTAINTY

Chapter outline

1. Describing Risk2. Preference toward risk3. Reducing Risk4. The Demand for Risk Assets5. Behavioral Economics

Uncertainty and Consumer behaviorTo examine the ways that people can compare andchoose among risky alternatives, we take the followingsteps:1. In order to compare the risk of alternative choices, we

need to quantify risk2. We will examine people’s preference toward risk3. We will se how people can sometimes reduce or

eliminate risk.4. In some situations, people must choose the amount of

risk they wish to bear.

In the final section of this chapter, we offer an overview of the flouring field of behavioral economics

3.1 DESCRIBING RISK To measure risk, must know:

All possible outcomes Probability/likelihood each outcome will occur

Interpreting Probability1. Objective interpretation: based on observed frequency o

r past events2. Subjective interpretation: based on perception that outc

ome will occur. Two measures help describe ans compare risky c

hoices:1. Expected Value2. Variability

3.1.1 Expected Value Expected Value

Probability- weight average of payoffs or values resulting from all possible outcomes

For n possible outcomes: Payoffs Probabilities of each outcomes:

The EV measures the central tendency- the payoff or value that we would expected on the average

1 2, ,..., nV V V1 2P ,P ..., Pn

1

1n

i

Pi

1

.n

i

EV PiVi

3.1.1 Expected Value

E.g. two outcomes possible: Success- stock price increase $30 to

$40/share => V1 = $40 Failure- Stock price fall $30 to

$20/share=> V2 = $20 100 trials: 25 successes and 75

failures=> P1 = 0.25 and P2 = 0.75 EV =?

3.1.2 Variability

Extent to which possible outcomes of an uncertain event may differ

How much variation exists in possible choice

Table 1 Income from Sales jobs

Outcome 1 Outcome 2 Expected Income ($)Proba

bilityIncome

($)Probab

ilityIncome

($)

Job1: Commission

0.5 2000 0.5 1000 1500

Job2: Fixed Salary

0.99 1510 0.01 510 1500

3.1.2 Variability Greater variability from expected values

signals greater risk Variability comes from deviations in

payoffs Deviation: difference between expected

payoff and actual payoff (V-E(V))

22( ) ( ) .i

Var X Vi EV Pi

3.1.2 Variability Standard Deviation

Squared root of average of squares of deviations of payoffs associated with each outcome from expected value

Greater standard deviation signals greater risk

n

i

EVViPi1

2)(

3.1.2 VariabilityTable 2 Deviation from Expected Income ($)

Outcome 1 Deviation Outcome 2 Deviation

Job 1 2000 500 1000 - 500

Job 2 1510 10 510 - 990

Table 3 Calculating Variance ($) and Standard Deviation

Outcome 1

Deviation Squared

Probability

Outcome 2

Deviation

Squared

Probability

Variance Standard Deviation

Job 1 2000 500 0.5 1000 250,000 0.5 250,000 500

Job 2 1510 10 0.99 510 980,100 0.01 9900 99.5

3.1.3 Decision Making Suppose add $100 to each payoff in job 1

which makes expected income = $1,600 Job 1: EI = $1,600 and standard deviation $500 Job 2: EI = $1,510 and standard deviation $99.5

Which job should be chosen? Depends on individual

Some willing to take risk with higher expected income

Some prefer less risk even with lower expected income

3.2 PREFERENCES TOWARD RISK

Different Preferences Risk Averse

Condition of preferring a certain income to a risky income with the same expected value

Risk Neutral Condition of being indifferent between a certain

income and un uncertain income with the same expected value

Risk Loving Condition of preferring a risky income to a

certain income with the same expected value

Expected Utility EU of risky option is sum of utilities associated

with all possible incomes weighted by probability of each

E.g. Risky job with 50% chance of $10,000 (utility 10) and 50% chance of $30,000 (utility 18) EI =? EU=?

1

Pr .n

i ii

EU U

3.2.1 Risk Averse

Consumer is risk averse because he would prefer certain income of $20,000 to uncertain expected income = $20,000

10

EU=14

20EI

10

Income

Utility

18

30

A

B

EF

16I*

Risk Premium

Maximum amount that risk-averse person would pay to avoid risk

3.2.2 Risk Neutral

10 20 30

6

12

18

Utility

Income

3.2.3 Risk Loving

10 20EI

U(EI)=8

3

Income

Utility

18

30

A

B

E

25I*

3.3 REDUCING RISK

Consumers generally risk averse and want to reduce risk

3.3.1 Diversification Practice of reducing risk by allocating

resources to a variety of activities whose outcomes are not closely related.

Table 4 Income form Sales of Appliances ($)

Hot weather Cold weather

Air conditioner sales

30,000 12,000

Heater Sales 12,000 30,000

3.3.2 Insurance If cost of insurance equals expected

loss, risk averse people buy enough insurance to recover fully from potential loss

If risk averse, guarantee of same income regardless of outcome has utility than facing risk

Expected utility with insurance higher than without

3.3.3 Value of information

Risk often exists because don’t know all information surrounding decision

Information is valuable and peole willing to pay for it

Value of complete information Difference between expected value of choice wi

th complete information and expected value with incomplete information.

3.4 DEMAND FOR RISKY ASSETS

3.4.1 Risky and risk less assets Risky assets

Provides uncertain flow of money or services to its owner

E.g.: Risk less assets

Provides flow of money or service that is known with certainty

E.g.:

3.4.1 Risky and risk less assets Return on assets

Total money flow of an assets, including capital gain or losses, as a fraction of its price

Real return: Simple (or nominal) return on an assets less the rate of inflation

Expected Return Return that asset should earn on average Actual return could be higher or lower Risk averse investor balances risk relative to

return.

3.4.2 The investor’s choice

Trade-off: Risk and Return Investor is dividing her funds between two asse

ts- Treasury bills and stocks. To receive higher return, she must incur some risk

Rf: risk-free return on bill Rm: expected return on stocks rm: actual return on stocks Assume Rm>Rf

Trade-off: Risk and Return How determine allocation of funds?

b: fraction of funds placed in stocls (1-b): fraction of funds placed in T-bills

Expected Return on the investment porfolio:

(1 )p m fR bR b R

Trade-off: Risk and Return How risky is porfolio?

Standard deviation of stocks: Standard deviation of portfolio:

Budget line describing trade-off between risk and expected return

Price of risk: extra risk that an investor must incur to enjoy a higher expected return

m.p mm

( )m fp f p

m

R RR R

m f

m

R R

Choosing between risk and return

σ*

Rp

　 σp

U1U2U3

R*

Budget line

3.5 BEHAVIOURAL ECONOMICS Objectives:

Improving understanding of consumer choice by incorporating more realistic, detailed assumptions regarding human behavior

Developing field to explain situations not well explained by basic consumer model

Fairness People often make choices that they

think are fair

Behavioral economics Reference points

Economists assume consumers place unique value on goods/services purchased

Psychologists found that perceived value depend on circumstances

Law of Probability Individual don’t always evaluate uncertain

events according to law of probability Don’t always maximize expected utility Law of small numbers