Chapter 14: Risk Analysis
MULTIPLE CHOICE
1. A subjective definition of probability is:
a.
a weighted average of different peoples’ degrees of certainty of an event’s occurring.
b.
a theoretical probability distribution.
c.
a person’s degree of certainty of an event’s occurring.
d.
an expected value of a particular outcome.
e.
the number of occurrences of an event in a large number of repetitions of an experiment.
2. A frequency definition of probability is:
a.
a weighted average of different peoples’ degrees of certainty of an event’s occurring.
b.
a theoretical probability distribution.
c.
a person’s degree of certainty of an event’s occurring.
d.
an expected value of a particular outcome.
e.
the number of occurrences of an event in a large number of repetitions of an experiment.
3. If a coin were weighted so that heads had three times the chance [P(H)] of coming up as tails [P(T)],
the probability distribution would be given by:
a.
P(H) = 0.67 and P(T) = 0.33.
b.
P(H) = 1 and P(T) = 3.
c.
P(H) = 0.5 and P(T) = 0.5.
d.
P(H) = 0.75 and P(T) = 0.25.
e.
P(H) = 1 and P(T) = 0.33.
4. You pay $3.75 to roll a normal die one time. You get $1 for each dot that turns up. Your expected
profit from this venture is:
a.
–$0.75.
b.
–$0.25.
c.
$0.25.
d.
$3.00.
e.
$3.50.
5. Billy Joe Bob thinks he will win $3 with probability P; otherwise he will win $11. His expected payoff
is:
a.
$3 + $8P.
b.
$11 – $8P.
c.
$7.
d.
$3 + $11P.
e.
$11 – $3P.
6. In a decision tree, a decision fork is represented by a(n):
a.
X.
b.
open circle.
c.
closed circle.
d.
triangle.
e.
square.
7. A company chooses one of four options; then nature decides whether the choice works. If it does not
work, the company has two updating options, each with three possible payoffs. How many decision
forks are on the tree depicting this?
a.
5.
b.
12.
c.
17.
d.
28.
e.
36.
8. Nature gives company A one of three endowments; then company A picks one of two options.
Depending on A’s choice, company B picks one of three options with each one having two possible
payoffs, decided by nature. How many chance forks does the decision tree depicting this have?
a.
4.
b.
9.
c.
19.
d.
28.
e.
36.
9. A game has two players. Player 1 chooses between two options, and then player 2, with the knowledge
of what player 1 chose, chooses between two options. If this were depicted in a decision tree, how
many forks would there be?
a.
2.
b.
3.
c.
7.
d.
12.
e.
24.
10. A decision fork with payoffs given for each branch is assigned a value based on:
a.
the highest-payoff branch.
b.
the lowest-payoff branch.
c.
an average of the highest- and lowest-payoff branches.
d.
an evenly weighted average of all payoff branches.
e.
a probability weighted average of all payoff branches.
11. A chance fork with payoffs given for each branch is assigned a value based on:
a.
the highest-payoff branch.
b.
the lowest-payoff branch.
c.
an average of the highest- and lowest-payoff branches.
d.
an evenly weighted average of all payoff branches.
e.
a probability weighted average of all payoff branches.
12. Expected utility is:
a.
the profit from a given decision.
b.
a probability weighted average of possible profits.
c.
an evenly weighted average of possibility profits.
d.
a probability weighted average of possible utility levels.
e.
the expected profits plus a number that depends on risk.
13. George is indifferent between $100 and a bet with a 0.6 chance of $50 and a 0.4 chance of $200. If
U(50) = a and U(200) = b, then U(100) = :
a.
0.4a + 0.6b.
b.
0.6a + 0.4b.
c.
(a + b) / 2.
d.
a + b.
e.
6a + 4b.
14. Thelma is indifferent between $100 and a bet with a 0.6 chance of no return and a 0.4 chance of $200.
If U(0) = 20 and U(200) = 220, then U(100) = :
a.
88.
b.
94.
c.
100.
d.
110.
e.
132.
15. A person who is risk-neutral has a utility function (with income on the horizontal axis and utility on
the vertical axis) that, as income increases:
a.
is horizontal.
b.
is vertical.
c.
has constant, positive slope.
d.
is curved down.
e.
is curved up.
16. A person who has a utility function (with income on the horizontal axis and utility on the vertical axis)
that is linear is:
a.
risk-averse.
b.
risk loving.
c.
risk-neutral.
d.
irrational.
e.
always sad.
17. A risk-averse person has a utility function that, with income on the horizontal axis and utility on the
vertical axis, as income increases:
a.
is a horizontal line.
b.
is a vertical line.
c.
has constant, positive slope.
d.
is increasing at a decreasing rate.
e.
is increasing at an increasing rate.
18. A person who has a utility function (with income on the horizontal axis and utility on the vertical axis)
that curves up as income increases is:
a.
risk-averse and profit maximizing.
b.
risk-averse and not profit maximizing.
c.
risk loving and profit maximizing.
d.
risk loving and not profit maximizing.
e.
risk-neutral.
19. A risk-loving person has a utility function that, with income on the horizontal axis and utility on the
vertical axis, as income increases:
a.
is horizontal.
b.
is vertical.
c.
has constant, positive slope.
d.
is curved down.
e.
is curved up.
20. Susan is indifferent between $500 for sure and a bet with a 60% chance of $400 and a 40% chance of
$700. Susan is:
a.
risk-averse.
b.
risk loving.
c.
risk-neutral.
d.
a profit maximizer.
e.
irrational.
21. Harold is indifferent between $2,500 for sure and a bet with a 60% chance of $2,400 and a 40%
chance of $2,600. Harold is:
a.
risk-averse.
b.
risk loving.
c.
risk-neutral.
d.
a profit maximizer.
e.
irrational.
22. For constants a and b, 0 < b, b 1, and expected profit E(
), the expected utility function of a person
who is risk-neutral can be written as E(U) = :
a.
a + bE(
).
b.
a – bE(
).
c.
a + b
.
d.
a + [E(
)]b.
e.
a + [E(
)] –b.
23. I. M. Hogg, who is risk-neutral over votes, is running for office with 500,000 sure voters. To add
voters, he wants to choose n, the number of negative campaign ads to run, where 0 n 4. The ads
will backfire with probability n/5 and give him no extra votes. Otherwise, the ads will work and give
him 100,000 + 40,000n extra votes. So n = 0 implies a total of 600,000 votes. He should choose n = :
a.
0.
b.
1.
c.
2.
d.
3.
e.
4.
24. An investor has utility function U = 10 + 5P – 0.02P2. What is the expected utility of the following
investment option?
Probability
Payoff (P)
0.4
10
0.3
20
0.2
30
0.1
40
a.
20.
b.
100.
c.
102.
d.
114.
e.
None of the above.
25. For constants a and b, 0 < b, b 1, and expected profit E(
), the utility function of a person who is
risk-neutral can be written as U = :
a.
a + bE(
).
b.
a – bE(
).
c.
a + b
.
d.
a + [E(
)]b.
e.
a + [E(
)] –b.
26. Fred has a utility function U = 10P 0.5 and also has an investment opportunity that will pay 25 with
probability 0.4 and 100 with probability 0.6. What is the expected utility of this opportunity?
a.
70.
b.
75.
c.
80.
d.
83.7.
e.
None of the above.
27. Joe is risk-neutral with utility U = bR, where b is a positive constant and R is profit from a venture. If a
gamble has a 0.4 chance of R = 1 and a 0.6 chance of R = 2, Joe’s expected utility E(U) is:
a.
b.
b.
1.4b.
c.
1.5b.
d.
1.6b.
e.
2b.
28. Trope Oil Company is considering drilling an exploratory well. The symbol P is the chance of a
successful well, R is the revenue from a successful well, L is the price previously paid for the land, and
C is the cost of drilling. The well will either be successful or dry. A company that is risk-neutral
should drill if:
a.
PR > C.
b.
PR > C + L.
c.
P(R – C) > 0.
d.
P(R – C – L) > 0.
e.
P(R – C) > L.
29. Betty Gamble is willing to pay exactly, but not more than, $20 to get a deal where she has a 1/3 chance
of winning $30 and a 1/6 chance of winning $6 and will win $20 otherwise. Betty is:
a.
risk-averse and profit maximizing.
b.
risk-averse, not profit maximizing.
c.
risk loving and profit maximizing.
d.
risk loving, not profit maximizing.
e.
risk-neutral.
30. Donald Trumpet is indifferent between rates of return satisfying R = 0.10 + 0.01
(
is the standard
deviation). Donald is:
a.
risk-averse and profit maximizing.
b.
risk-averse and not profit maximizing.
c.
risk loving and profit maximizing.
d.
risk loving and not profit maximizing.
e.
risk-neutral.
31. If
is the standard deviation of a project with expected returns R, the coefficient of variation is:
a.
/ R.
b.
2/ R.
c.
R.
d.
2R.
e.
R2
.
32. If xi is defined as xi =
i – E(
i), and pi is the probability of occurrence of any xi, the formula for the
square of the standard deviation can be written as:
a.
xi pi.
b.
xi p2i .
c.
x2i p2i .
d.
x2i pi.
e.
(xi pi)2.
33. Using the coefficient of variation instead of the standard deviation accounts for the:
a.
timing of payoffs.
b.
risk attendance of managers.
c.
riskiness of different projects.
d.
size of different projects.
e.
use of a weighted average of different profits.
34. If you get $10 for heads but lose $10 for tails on the flip of a fair coin, the coefficient of variation is:
a.
undefined.
b.
0.
c.
1.
d.
10.
e.
100.
35. If a payoff is equally likely to be $1, $2, $3, $4, or $5, the coefficient of variation is:
a.
0.
b.
21/2/3.
c.
2/3.
d.
2.
e.
10/3.
36. If a payoff is equally likely to be $1, $2, $3, $4, or $5, the square of the standard deviation is:
a.
0.
b.
2.
c.
4.
d.
10.
e.
100.
37. If
is the standard deviation of a project with expected returns $100 and
2 = 4, the coefficient of
variation is:
a.
1/25.
b.
1/50.
c.
$200.
d.
$400.
e.
$5,000.
38. A project could yield a profit of $1, $2, $3, or $6, with equal probability. Then the variance,
2, is:
a.
1.
b.
3/2.
c.
7/2.
d.
9/2.
e.
14.
39. If an option pays $6 one-quarter of the time and loses $6 three-quarters of the time, then the variance
2 = :
a.
0.
b.
–3.
c.
9.
d.
12.
e.
27.
40. The range of values the standard deviation(s) can take is:
a.
– <
< .
b.
0 <
< .
c.
0 <
< 1.
d.
0 <
< 100.
e.
0 <
< 1,000.
41. If expected profit is R and variance
2 = 0, then:
a.
Ri = 0 for all i.
b.
R – Ri is a positive constant for all i.
c.
R – Ri is a negative constant for all i.
d.
Ri = 0 for all i.
e.
Ri = R for all i.
42. A manager is indifferent between rates of return satisfying i = 0.08 + 0.02
(
is the standard
deviation). The manager’s risk premium for
= 2 is:
a.
0%.
b.
2%.
c.
4%.
d.
8%.
e.
12%.
43. Fred has a utility function U = 10P 0.5 and also has an investment opportunity that will pay 25 with
probability 0.4 and 100 with probability 0.6. What is the certainty equivalent of this opportunity?
a.
64.
b.
70.
c.
80.
d.
83.7.
e.
None of the above.
44. Fred Kruger is indifferent between return rates satisfying R = 0.10 + (–0.01)
, where
measures risk.
Fred is:
a.
risk-averse and profit maximizing.
b.
risk-averse and not profit maximizing.
c.
risk loving and profit maximizing.
d.
risk loving and not profit maximizing.
e.
risk-neutral.