Deck 14: Risk Analysis

Question 1

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.

Answer 1

A

Question 2

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.

Answer 2

A

Question 3

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.

Answer 3

B

Question 4

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.

Question 5

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.

Question 6

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.

Question 7

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.

Question 8

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.

Question 9

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.

Question 10

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.

Question 11

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.

Question 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.

Question 13

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.

Question 14

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.

Question 15

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.

Question 16

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.

Question 17

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.

Question 18

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.

Question 19

In a decision tree,a decision fork is represented by a(n):

A) X.
B) open circle.
C) closed circle.
D) triangle.
E) square.

Question 20

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.

Question 21

The range of values the standard deviation(s)can take is:

A) - $\infty$ < $\sigma$ < $\infty$ .
B) 0 < $\sigma$ < $\infty$ .
C) 0 < $\sigma$ < 1.
D) 0 < $\sigma$ < 100.
E) 0 < $\sigma$ < 1,000.

Question 22

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.

Question 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.

Question 24

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.

Question 25

If x_i is defined as x_i = $\pi$ _i - E( $\pi$ _i),and p_i is the probability of occurrence of any x_i,the formula for the square of the standard deviation can be written as:

A) $\Sigma$ x_i p_i.
B) $\Sigma$ x_i p²_i .
C) $\Sigma$ x²_i p²_i .
D) $\Sigma$ x²_i p_i.
E) $\Sigma$ (x_i p_i)².

Question 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.

Question 27

An investor has utility function U = 10 + 5P - 0.02P².What is the expected utility of the following investment option?

A) 20.
B) 100.
C) 102.
D) 114.
E) None of the above.

Question 28

If $\sigma$ is the standard deviation of a project with expected returns R,the coefficient of variation is:

A) $\sigma$ / R.
B) $\sigma$ ²/ R.
C) $\sigma$ R.
D) $\sigma$ ²R.
E) R² $\sigma$ .

Question 29

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.

Question 30

A project could yield a profit of $1,$2,$3,or $6,with equal probability.Then the variance $\sigma$ ²,is:

A) 1.
B) 3/2.
C) 7/2.
D) 9/2.
E) 14.

Question 31

If a payoff is equally likely to be $1,$2,$3,$4,or $5,the coefficient of variation is:

A) 0.
B) 2^1/2/3.
C) 2/3.
D) 2.
E) 10/3.

Question 32

If $\sigma$ is the standard deviation of a project with expected returns $100 and $\sigma$ ² = 4,the coefficient of variation is:

A) 1/25.
B) 1/50.
C) $200.
D) $400.
E) $5,000.

Question 33

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.

Question 34

For constants a and b,0 < b,b $\neq$ 1,and expected profit E( $\pi$ ),the utility function of a person who is risk-neutral can be written as U = :

A) a + bE( $\pi$ ).
B) a - bE( $\pi$ ).
C) a + b $\pi$ .
D) a + [E(b ^$\pi$ )].
E) a + [E( $\pi$ )] ^-b.

Question 35

For constants a and b,0 < b,b $\neq$ 1,and expected profit E( $\pi$ ),the expected utility function of a person who is risk-neutral can be written as E(U)= :

A) a + bE( $\pi$ ).
B) a - bE( $\pi$ ).
C) a + b ^$\pi$ .
D) a + [E( $\pi$ )]^b.
E) a + [E( $\pi$ )] ^-b.

Question 36

If an option pays $6 one-quarter of the time and loses $6 three-quarters of the time,then the variance $\sigma$ ² = :

A) 0.
B) -3.
C) 9.
D) 12.
E) 27.

Question 37

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.

Question 38

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.

Question 39

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.

Question 40

Donald Trumpet is indifferent between rates of return satisfying R = 0.10 + 0.01 $\sigma$ ( $\sigma$ 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.

Question 41

Fred Kruger is indifferent between return rates satisfying R = 0.10 + (-0.01) $\sigma$ ,where $\sigma$ 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.

Question 42

A manager is indifferent between rates of return satisfying i = 0.08 + 0.02 $\sigma$ ( $\sigma$ is the standard deviation).The manager's risk premium for $\sigma$ = 2 is:

A) 0%.
B) 2%.
C) 4%.
D) 8%.
E) 12%.

Question 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.

Question 44

If expected profit is R and variance $\sigma$ ² = 0,then:

A) R_i = 0 for all i
B) R - R_i is a positive constant for all i.
C) R - R_i is a negative constant for all i.
D) R_i = 0 for all i.
E) R_i = R for all i.