Chapter 14
Chapter 14. Risk and Decision Making
Topics to be Discussed
Concept of Risk
Preferences Toward Risk
Reducing Risk
The Demand for Risky Assets
Introduction
How do we choose when certain variables such as income and prices are uncertain (i.e. making choices with risk)?
Describing Risk
To measure risk we must know:
1) All of the possible outcomes.
The likelihood that each outcome will occur (its probability).
Describing Risk
Measuring Probability
Objective
Based on the observed frequency of past events
100 explorations, 25 successes and 75 failures
Probability (Pr) of success = 1/4 and the probability of failure = ¾
Subjective
Based on perception or experience with or without an observed frequency
Different information or different abilities to process the same information can influence the subjective probability
Probability and Expected Value
Expected value is the weighted average of the payoffs or central tendency.
For Example
Investment in offshore drilling exploration:
Two outcomes are possible
Success--stock prices increase from $30 to $40/share
Failure--stock prices fall from $30 to $20/share
Expected value can be written as:
[pic]
The standard deviation measures the square root of the average of the squares of the deviations of the payoffs associated with each outcome from their expected value.
The coefficient of variation is defined as the standard deviation over the expected value. It is a measure of risk per dollar of return
Describing Risk
The standard deviation is written:
[pic]
Preferences Toward Risk
Choosing Among Risky Alternatives
Assume
Consumption of a single commodity
Consumer’s know all probabilities
Payoffs measured in terms of utility
Utility function given
Example
A person is earning $15,000 and receiving 13 units of utility from the job.
She is considering a new, but risky job.
She has a .50 chance of increasing her income to $30,000 and a .50 chance of decreasing her income to $10,000.
She will evaluate the position by calculating the expected value (utility) of the resulting income
Example
The expected utility of the new position is the sum of the utilities associated with all her possible incomes weighted by the probability that each income will occur.
The expected utility of new job can be written:
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 than the current utility of 13 and therefore preferred.
The certainty equivalent value
- U = SQRT(W)
The utility of expected value versus the expected utility
[pic]
Different Preferences Toward Risk
People can be risk averse, risk loving, or risk neutral.
A person who prefers a certain given income to a risky job with the same expected income is risk averse.
Different Preferences Toward Risk
A person is considered risk averse if they have a diminishing marginal utility of income
The use of insurance demonstrates risk aversive behavior.
A person is said to be risk neutral if they show no preference between a certain income, and an uncertain one with the same expected value.
A person is said to be risk loving if they show a preference toward an uncertain income over a certain income with the same expected value.
Examples: Gambling, some criminal activity
Preferences Toward Risk
The risk premium is the amount of money that a risk-averse person would pay to avoid taking a risk.
Variability in potential payoffs increase the 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).
The expected income is still $20,000, but the expected utility falls to 10.
Reducing Risk
Three ways consumers attempt to reduce risk are:
Diversification
Suppose a firm has a choice of selling air conditioners, heaters, or both.
The probability of it being hot or cold is .50.
The firm would probably be better off by diversification.
2) Insurance
3) Obtaining more information
The law of large numbers tells us that while individual events are random and unpredictable, the average outcome of many similar events can be predicted.
Examples
A single coin toss vs. large number of coins
Summary
Consumers and managers frequently make decisions in which there is uncertainty about the future.
Consumers and investors are concerned about the expected value and the variability of uncertain outcomes.
Facing uncertain choices, consumers maximize their expected utility, and average of the utility associated with each outcome, with the associated probabilities serving as weights.
A person may be risk averse, risk neutral or risk loving.
The maximum amount of money that a risk-averse person would pay to avoid risk is the risk premium.
Risk can be reduced by diversification, purchasing insurance, and obtaining additional information.
The law of large numbers enables insurance companies to provide actuarially fair insurance for which the premium paid equals the expected value of the loss being insured against.
Consumer theory can be applied to decisions to invest in risky assets.
SKIP Page 486 (from Adjusting the Discount Rate) – 495
SKIP Problems : 15.16.17.18.19.20.21.22.23.24
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