steven landsburg, university of rochester chapter 18 risk and uncertainty copyright ©2005 by...

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

Landsburg, Price Theory and Applications, 6th edition 3

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

Landsburg, Price Theory and Applications, 6th edition 4

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

Landsburg, Price Theory and Applications, 6th edition 5

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

Landsburg, Price Theory and Applications, 6th edition 6

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

Landsburg, Price Theory and Applications, 6th edition 7

EXHIBIT 18.4 Risk Neutrality

Landsburg, Price Theory and Applications, 6th edition 8

EXHIBIT 18.5 Risk Aversion

Landsburg, Price Theory and Applications, 6th edition 9

EXHIBIT 18.8 Gambling at Favorable Odds

Landsburg, Price Theory and Applications, 6th edition 10

Risk and Society

• Societies’ desire for risk neutrality in some instances

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

Landsburg, Price Theory and Applications, 6th edition 11

Market for Insurance

• Facilitate transfer of risk from one party to another

• Diversification

• Imperfect information– Moral hazard– Adverse selection

• Uninsurable risks

Landsburg, Price Theory and Applications, 6th edition 12

EXHIBIT 18.9 Adverse Selection

Landsburg, Price Theory and Applications, 6th edition 13

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

Landsburg, Price Theory and Applications, 6th edition 14

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

Landsburg, Price Theory and Applications, 6th edition 15

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

Landsburg, Price Theory and Applications, 6th edition 16

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

Landsburg, Price Theory and Applications, 6th edition 17

EXHIBIT 18.13 The Efficient Set

Landsburg, Price Theory and Applications, 6th edition 18

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

Landsburg, Price Theory and Applications, 6th edition 19

EXHIBIT 18.14 The Investor’s Choice

Landsburg, Price Theory and Applications, 6th edition 20

Constructing a Market Portfolio

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

• Mutual funds

Landsburg, Price Theory and Applications, 6th edition 21

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

Landsburg, Price Theory and Applications, 6th edition 22

EXHIBIT 18.18Rational Expectations

Landsburg, Price Theory and Applications, 6th edition 23

EXHIBIT 18.19Lumberjacks’ Income and the Price of Lettuce