Chapter 15: Decisions Under Risk and Uncertainty
Chapter 15:
DECISIONS UNDER RISK AND UNCERTAINTY
Essential Concepts
1. Conditions of risk occur when a manager must make a decision for which the outcome is not known
2. In order to measure the risk associated with a decision, the manager can examine several
3. In order to measure the risk associated with a decision, several statistical characteristics of the
probability distribution can be employed:
a. The expected value (or mean) of a probability distribution is
b. The variance (a measure of absolute risk) of a probability distribution measures the dispersion of
the outcomes about the mean or expected outcome. The variance is calculated as
d. When the expected values of outcomes differ substantially, managers should measure the
riskiness of a decision relative to its expected value using the coefficient of variation (a measure
of relative risk):
4. While no single decision rule guarantees that profits will actually be maximized, there are a number
of decision rules that managers can use to help them make decisions under risk. Decision rules do not
eliminate the risk surrounding a decision, they just provide a method of systematically including risk
in the process of decision making. The three rules presented in this chapter are (1) the expected value
rule, (2) the mean-variance rules, and (3) the coefficient of variation rule. These three rules are
summarized below:
Summary of Decision Rules Under Conditions of Risk
Expected value rule
Choose the decision with the highest expected value.
Mean-variance rules
Given two risky decisions A and B:
5. Which rule is best?
When a decision is to be made repeatedly, with identical probabilities each time, the expected
value rule provides managers with the most reliable rule for maximizing (expected) profit. The
6. The actual decisions made by a manager depend upon the manager’s willingness to accept risk. To
allow for different attitudes toward risk-taking in decision making, modern decision theory treats
7. Expected utility theory postulates that managers make risky decisions in a way that maximizes the
expected utility of the profit outcomes, where the expected utility of a risky decision is the sum of the
probability-weighted utilities of each possible profit outcome:
8. A manager’s attitude toward risk is determined by the manager’s marginal utility of profit:
profit ( )/MU U
p p
=D D
Chapter 15: Decisions Under Risk and Uncertainty
9. A manager’s attitude toward risky decisions can be related to his or her marginal utility of profit.
Someone who experiences diminishing (increasing) marginal utility for profit will be a risk averse
(risk loving) decision maker. Someone whose marginal utility of profit is constant is risk neutral.
10. If a manager maximizes expected utility for profit, the decisions can differ from decisions reached
11. In the case of uncertainty, decision science can provide very little guidance to managers beyond
offering them some simple decision rules to aid them in their analysis of uncertain situations. Four
basic rules for decision making under uncertainty are summarized in the following table.
Summary of Decision Rules Under Conditions of Uncertainty
Maximax rule
Identify the best outcome for each possible decision and
choose the decision with the maximum payoff.
Maximin rule
Identify the worst outcome for each decision and choose
the decision associated with the maximum worst payoff.
chooses the decision with the minimum worst potential
Answers to Applied Problems
1. a. Maximax rule: operate plants in US, Mexico, Canada
c. The potential regret matrix is
OINC Passes
OINC Fails
OINC Stalls
US only
10 million
0
2 million
US, Mexico, Canada
5 million
0
5 million
3 million
2.5 million
Chapter 15: Decisions Under Risk and Uncertainty
Maximum potential regrets are:
US only
10 million
US, Mexico, Canada
18/3 = 6.0 million
2. Maximin rule
3. A portfolio manager needs to pick “winning portfolios” rather than individual stocks that are
“winners”. The performance of a portfolio reflects interactions among stocks as well as the
4. a. E(profit of option A) = 0.3(800,000) + 0.7(1,200,000)
= 240,000 + 840,000
= 1,080,000
E(profit of option B) = 0.3(1,000,000) + 0.7(875,000)
= 300,000 + 612,500
d. VarA = 0.7(1,200,000 1,080,000)2 + 0.3(800,000 1,080,000)2 = 33,600,000,000
σA = 183,303
VarB = .7(875,000 912,500)2 + .3(1,000,000 912,500)2 = 3,281,250,000
σB = 57,282
Based on the coefficient of variation rule, option B would be chosen.
5. a. Maximax rule Option A
6. a. E(Profit)US = $4.9 million
E(Profit)US,Mexico = $6.35 million
E(Profit)US,Mexico,Canada = $9.4 million