Chapter 13 Risk Analysis
MULTIPLE CHOICE
1. 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
2. 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
3. If a coin were weighted so heads had 3 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 1 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. 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
7. 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
8. 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
9. 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
10. 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
11. Two people alternate choosing either to quit or to continue a process at various stages
numbered 1 to 4. If a person quits at stage n, that person gets $(n + 1), the opponent gets $(n
− 1), and no other payoffs are possible. If neither player ever quits, they reach stage 5, and
each gets $4. Player 1 can choose to quit or continue at stages 1 and 3; player 2 can choose
at stages 2 and 4. Both players care only for their own payoffs and expect their opponent to
do the same. No coordinating of strategies is allowed. Backward induction predicts the stage
at which the game stops will be stage number:
a.
1
b.
2
c.
3
d.
4
e.
5
12. Two people alternate choosing either to quit or to continue a process at various stages
numbered 1 to 1,001. If a person quits at stage n, that person gets $(n + 1), the opponent gets
$(n − 1), and no other payoffs are possible. If neither player ever quits, they reach stage
1,001, and each gets $1,000. Player 1 can choose to quit or continue at odd-numbered
stages; player 2 can choose at even-numbered stages. Both players care only for their own
payoffs and expect their opponent to do the same. No coordinating of strategies is allowed.
Backward induction predicts the average payoff to the two players will be:
a.
$1
b.
$200
c.
$500
d.
$750
e.
$1,000
13. In a decision tree, a decision fork is represented by a(n):
a.
X
b.
open circle
c.
closed circle
d.
triangle
e.
square
14. 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
15. 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
16. 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
17. 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
18. A diamond miner has p chance of finding diamonds with R revenue if the miner finds
diamonds; otherwise the miner gets zero. The mine costs C; the expected value of perfect
information is:
a.
0
b.
C
c.
p(R − C)
d.
(1 − p)C
e.
(1 − p)(R − C)
19. Exploring a new coal mine costs $100,000 and has a 40 percent chance of finding $500,000
of coal and a 60 percent chance of finding $100,000 of coal. The expected value of perfect
information is:
a.
$0
b.
$100,000
c.
$150,000
d.
$200,000
e.
$300,000
20. Susan is indifferent between $500 for sure and a bet with a 60 percent chance of $400 and a
40 percent 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 percent chance of $2,400
and a 40 percent chance of $2,600. Harold is:
a.
risk-averse
b.
risk loving
c.
risk-neutral
d.
a profit maximizer
e.
irrational
22. 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
23. 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
24. 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
25. 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
26. 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
27. 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
28. 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
29. 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
30. 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
31. 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
32. 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
33. 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
34. 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
35. 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
36. 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
37. The range of values the standard deviation(s) can take is:
a.
− <
<
b.
0 <
<
c.
0 <
< 1
d.
0 <
< 100
e.
0 <
< 1,000
38. 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
39. 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
40. 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
41. 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
42. 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
43. 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 percent
b.
2 percent
c.
4 percent
d.
8 percent
e.
12 percent
44. 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
45. An investor has utility function U = 10 + 5P − 0.02P2. What is the expected utility of the
following investment option:
40
0.1
30
0.2
20
0.3
10
0.4
Payoff (P)
Probability
a.
30
b.
110
c.
140
d.
142
e.
none of the above
46. A sensitivity analysis is designed to:
a.
measure a manager’s risk sensitivity
b.
identify key factors affecting outcome probabilities
c.
predict how those outside a firm will act
d.
combine factor frequency distributions to get a payoff distribution
e.
check the manager’s arithmetic
47. 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
48. 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
49. 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
50. 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