Uncertainty Risk

8/3/2019 Uncertainty Risk

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Decision Making Under Uncertaintyand Asymmetric information

Expected Utility

Insurance Premium

Risk Return Analysis

Asymmetric information

Moral Hazard (Hidden action)

Adverse Selection (Hidden information)

http://cepa.newschool.edu/het/home.htm


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Utility Function for Risk Averse Individual

Wealth

( )WU ln=

WL WH

Utility

0

1

( )11

( ) HL WWEW 11 1 +=

( ) ( ) ( )HL WWEU ln1ln 11 +=

Expected utility

Expected wealth

EWCEW

ln(CEW)

InsurancePremium

ln(WH)

ln(WL)


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Utility Function for Risk Averse Individual

Wealth

( )WU ln=

WL WH

Utility

0

1 ( )11

( )( )( ) 0

1

1

1

'

''2

>=

== WW

W

WU

WUWr

Pratt(1964) Measure of risk aversion:


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WeU =

WHWL

Utility Function for Risk Loving Individual

0

Utility

( )11 1

( )( )

( )0

'

''2


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WaU .=

WHWL

Utility Function for Risk Neutral Individual

0

Utility

( )11 1

( )( )( )

00

'

''===

aWU

WUWr


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Wealth

Utility

Uncertainty and Expected Utility

010000 20000

( )WU ln=UH

UL

UEW

UCE

RiskPremium


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Wealth

Utility

Uncertainty and Expected Utility and Insurance Payment

010000 20000

( )WU ln=

5.01 = ( ) 5.01 1 =

EW=15000

9.903

9.616

9.201

9.557

14143

Risk premium15000-14143

= 857

Insurance

payment


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Preference of an Investor Toward Risks Returns

0p

Standard deviation of return to a portfolio

pR

R

eturnona

portfolio

Treasury Bill Stocks

BR

STR

( ) fmp RbbRR += 1

Risks

mRMarketreturn

fR risk freereturn

10


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Optimal Portfolio

0p


pR

Expec

ted

Retur

nonaportfolio

BR

STR

p

m

mf

fp

RR

RR

+=

m

pb

=U1

U2

Not feasibleM

E

Optimal point


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111 2

1R

2R

p

m

mf

fp

RRRR

+=

Expec

ted

Retur

nonaportfolio


U2

U1

Choices of Risk Averse vs Risk Lover in a Financial Market

Risk averse investor.

Risk loving investor.


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Asymmetric information

Equilibrium is affected when someeconomic agents have more information

than others. Market of used cars

Plums: good cars

Lemons: bad cars

Seller knows his quality of cars but buyersdoes not

Market for good cars disappear becauseof existence of bad cars in the market


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Akerlofs Model of Asymmetric Information

SHSL

DL

DH

DM

250 500

10

7.5

DL

DM

500 750

5

7.5

Markets for good carsMarkets for bad carsP

P

Q Q

5

200

Sellers know exactly quality of cars but buyers do not.

Demand for high quality car falls and that for low quality rise, ultimately allLow quality cars remain in the market.


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Signalling for high quality

Warranty and Guarantee

Providing warranty less costly for highquality carsThey last long.

warranty is costly for low quality cars asthey frequently break down.

Principal agent problem


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Adverse Selection (hidden information) Problem

Uncertainty about the quality of good low quality items crowd out high quality items;

Theft insurance; health insurance; risky vs. gentle borrowers in the financialmarket.

Healthy people are less likely to buy health

insurance, people from safe area are less likely to buy

theft insurance

honest borrowers less likely to borrow athigher interest rates.


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Moral hazard (hidden action):

People who have theft insurance are likely

to have easy to break locks in their bicycle(car) and most likely to claim insurances.

Probability of event is affected by theaction of the person

Remedy: deductible amount; to ensurethat some customers take care in security.


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Impacts of Asymmetric information

Equilibrium if inefficient relative to full

information Government can improve the market by

setting high standards Signalling: Warranty


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Education as a signal of quality of workers:

Type 1 is less productive than type 2

worker but an employer cannot distinguish

off-hand.

The marginal productivity of type 1 is less

than that of type 2, 11 aa

Uncertainty Risk

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