Chapter 14. Risk and Decision Making
Topics to be Discussed
n Concept of Risk
n Preferences Toward Risk
n Reducing Risk
n The Demand for Risky Assets
Introduction
n How do we choose when certain variables such as income and prices are uncertain (i.e.
making choices with risk)?
Describing Risk
n To measure risk we must know:
1) All of the possible outcomes.
2) The likelihood that each outcome will occur (its probability).
Describing Risk
n 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
n Probability and Expected Value
• Expected value is the weighted average of the payoffs or central tendency.
n 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
n Expected value can be written as:
EV  Pr(success )($40/shar e)  Pr(failure )($20/shar e)
n 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.
n 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
n The standard deviation is written:
  Pr1 X 1  E ( X )2  Pr2 X 2  E ( X )

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Preferences Toward Risk
n Choosing Among Risky Alternatives
• Assume
– Consumption of a single commodity
– Consumer’s know all probabilities
– Payoffs measured in terms of utility
– Utility function given
n 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
n 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.
n 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.
n The certainty equivalent value
- U = SQRT(W)
n The utility of expected value versus the expected utility
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n 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.
n 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
n The risk premium is the amount of money that a risk-averse person would pay to avoid
taking a risk.
n Variability in potential payoffs increase the risk premium.
n 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.
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Reducing Risk
n Three ways consumers attempt to reduce risk are:
1) 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
n 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.
n Examples
– A single coin toss vs. large number of coins
Summary
n Consumers and managers frequently make decisions in which there is uncertainty
about the future.
n Consumers and investors are concerned about the expected value and the variability of
uncertain outcomes.
n Facing uncertain choices, consumers maximize their expected utility, and average of
the utility associated with each outcome, with the associated probabilities serving as
weights.
n A person may be risk averse, risk neutral or risk loving.
n The maximum amount of money that a risk-averse person would pay to avoid risk is
the risk premium.
n Risk can be reduced by diversification, purchasing insurance, and obtaining additional
information.
n 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.
n 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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