Steven Landsburg, University of Rochester Chapter 18 Risk and Uncertainty Copyright ©2005 by Thomson South-Western, a part of the Thomson Corporation.

Steven Landsburg,

University of Rochester

Chapter 18Risk and Uncertainty

Copyright ©2005 by Thomson South-Western, a part of the Thomson Corporation. All rights reserved.

Landsburg, Price Theory and Applications, 6th edition 2

Introduction

• State of the world

• Individual choice about transferal of wealth– Determining equilibrium prices– Examples of markets where transfers exist

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Attitudes Toward Risk

• Basket of outcomes– Indifference curves represent individual’s

preferences

• Ex ante– Determined before state of world known

• Ex post– Determined after state of world known

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Characterizing Baskets

• Expected values– Average value over all states of world with

each state weighted by its probability– Law of large numbers

• Repeat gamble many times• Average outcome is expected value

• Riskiness– Risk-free

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Opportunities

• Budget line and prices

• Fair odds– Odds that reflect true probabilities of various

states of world– Expected value of betting same as expected

value of not betting

• Individual offered fair odds– Budget line coincides with expected value line

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Preferences

• Consumer’s optimum– Frequent gambler

• Diversify• Risk-neutral

– Indifference curves identical to iso-expected value lines– Indifferent about amount bets whether fair or unfair odds

• Risk-averse• Risk-preferring

– Gambling at favorable odds• Risk attitude

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EXHIBIT 18.4 Risk Neutrality

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EXHIBIT 18.5 Risk Aversion

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EXHIBIT 18.8 Gambling at Favorable Odds

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Risk and Society

• Societies’ desire for risk neutrality in some instances

• Individual entrepreneurial endeavors promote risk aversion– Underinvest in risky projects– Corporations good buffer

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Market for Insurance

• Facilitate transfer of risk from one party to another

• Diversification

• Imperfect information– Moral hazard– Adverse selection

• Uninsurable risks

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EXHIBIT 18.9 Adverse Selection

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Futures Markets

• Futures contract– Deliver specified good at specified future date

at specified price

• Futures market– Market for futures contracts

• Spot market– Market for goods for immediate delivery

• Spot price– Price in spot market

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Speculation

• Speculator– Attempts to earn profits in futures market– Predicts future changes in supply or demand

• Speculation and welfare– Guess future correctly

• Earn profit• Increase social welfare

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Market for Risky Assets

• Returns– Assets valued not for uses in consumption but

for potential increase to owners’ wealth

• Expected returns– Expected present value of those returns

• Standard deviation– Measure of risk– Spread in possible outcomes

• Investors

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Portfolios

• Combination of risky assets– Standard deviation of portfolio at most equal

to average standard deviation of individual stocks

– Expected return to portfolio exactly equal to average expected returns of individual stocks

• Efficient set and portfolios

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EXHIBIT 18.13 The Efficient Set

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Investor’s Choice

• Capital asset pricing model– Model assumes investor cares only about

expected return and risk– Risk measured by standard deviation

• Risk-free asset– Market line and portfolios

• Rational investor– Hold portfolio combines risk-free asset with

market portfolio in some proportions

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EXHIBIT 18.14 The Investor’s Choice

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Constructing a Market Portfolio

• Portfolios consists of all risky assets in economy– Held in proportion to their existing quantities

• Mutual funds

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Rational Expectations

• Setting prices in face of uncertain demand

• Market for uncertain demand– Rational expectations

• Expectations held by market participants• Fulfill expectations on average

• Making wrong predictions– Econometricians

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EXHIBIT 18.18Rational Expectations

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EXHIBIT 18.19Lumberjacks’ Income and the Price of Lettuce