Deck 16: Uncertainty

Question 1

Assume the following.In location A yearly temperatures range from -30°F to 100°F and in location B yearly temperatures range from 55°F to 75°F.In both locations the average yearly temperature equals 65°F.We can conclude that

A)temperature in location A has a higher variance.
B)temperature in location B has a higher standard deviation.
C)temperature in location A has a lower standard deviation.
D)temperatures in both locations have the same standard deviation but different variances.

Answer 1

temperature in location A has a higher variance.

Question 2

Although he is very poor,Al plays the million-dollar lottery every day because he is certain that one day he will win.Al makes this calculation based upon

A)the frequency of past outcomes.
B)subjective probability.
C)knowledge of all possible outcomes.
D)tossing a coin.

Answer 2

subjective probability.

Question 3

Lisa runs a local flower shop,if it rains on Valentine's Day and she opens the shop,she will lose $200.If it does not rain on Valentine's Day,she will earn $500 dollars as profits.The chance of rain is 30%,the standard deviation of the profits Lisa could earn on Valentine's Day is

A)198.17.
B)135.61.
C)432.43.
D)290.

Answer 3

198.17.

Question 4

Expected value represents the average of all outcomes if one were to undertake the risky event many times over and over again.

Question 5

Expected value represents

A)the actual payment one expects to receive.
B)the average of all payments one would receive if one undertook the risky event many times.
C)the payment one receives if he or she makes the correct decision.
D)the payment that is most likely to occur.

Question 6

If there are 10,000 people in your age bracket,and 10 of them died last year,an insurance company believes that the probability of someone in that age bracket dying this year would be

A)0.
B).001.
C).0001.
D)1,000.

Question 7

If a payout is certain to occur,then the variance of that payout equals

A)zero.
B)one.
C)the expected value.
D)the expected value squared.

Question 8

In a small town,it snowed 10 times on Christmas Eve during 25 years.What is the frequency of snowing on Christmas Eve in that small town?

A)10
B)25
C)2.5
D)0.4

Question 9

All else held constant,as the variance of a payoff increases,the

A)expected value of the payoff increases.
B)risk of the payoff increases.
C)expected value of the payoff decreases.
D)risk of the payoff decreases.

Question 10

On any given day we know a salesman can earn $0 with a 40% probability,$100 with a 20% probability or $300 with 40% probability.His expected earnings equal

A)$0.
B)$140.
C)$300.
D)It cannot be determined from the available information.

Question 11

Sarah buys little stuffed animals for $5 each.They come in different varieties.If the producer stops making (retires)a certain variety,a stuffed animal of that variety will be worth $100;otherwise it is worth $0.There is 50% chance that any variety will be retired.What is the value to Sarah of knowing ahead of time whether a variety will be retired?

A)$50
B)$5
C)$2.50
D)$0

Question 12

Your friend Dimitre tells you that he thinks that his favorite basketball team has a 70% chance of winning the next game.This is an example of

A)an objective probability.
B)a subjective probability.
C)a risk-averse statement.
D)Friedman-Savage preferences.

Question 13

On any given day,a salesman can earn $0 with a 40% probability,$100 with a 40% probability,or $300 with a 20% probability.His expected earnings equal

A)$0.
B)$100 because that is the most likely outcome.
C)$100 because that is what he will earn on average.
D)$200 because that is what he will earn on average.

Question 14

On any given day,a salesman can earn $0 with a 30% probability,$100 with a 20% probability,or $300 with a 50% probability.His expected earnings equal

A)$0.
B)$100.
C)$150.
D)$170.

Question 15

Sarah buys little stuffed animals for $5 each.They come in different varieties.If the producer stops making (retires)a certain variety,a stuffed animal of that variety will be worth $100;otherwise it is worth $0.There is 50% chance that any variety will be retired.When Sarah buys her next stuffed animal,the expected profit is

A)$50.
B)$47.50.
C)$45.
D)$0.

Question 16

Lisa runs a local flower shop.If it rains on Valentine's Day and she opens the shop,she will lose $200.If it does not rain on Valentine's Day,she will earn $500 dollars as profits.What is Lisa's expected profit on Valentine's Day if she only knows that there is a 30% chance of rain that day?

A)$350
B)$290
C)$200
D)$150

Question 17

You draw colored balls out of a bag.You draw a red ball 30% of the time and a blue ball 70% of the time.For each draw,the blue outcome and the red outcome are

A)mutually exclusive.
B)exhaustive.
C)Both A and B.
D)None of the above.

Question 18

Lisa runs a local flower shop,if it rains on Valentine's Day and she opens the shop,she will lose $200.If it does not rain on Valentine's Day,she will earn $500 dollars as profits.The chance of rain is 30%,what is Lisa's gain from perfect information about weather conditions on the forthcoming Valentine's Day?

A)50
B)60
C)90
D)150

Question 19

A lottery game pays $500 with .001 probability and $0 otherwise.The variance of the payout is

A)15.8.
B)249.50.
C)249.75.
D)499.

Question 20

People in a certain group have a 0.3% chance of dying this year.If a person in this group buys a life insurance policy for $3,300 that pays $1,000,000 to her family if she dies this year and $0 otherwise,what is the expected value of a policy to the insurance company?

A)$0
B)$300
C)$3,000
D)$3,300

Question 21

The above figure shows Bob's utility function.He currently has $100 of wealth,but there is a 50% chance that it could all be stolen.If Bob could keep $50 with certainty,his utility would be

A)a.
B)b.
C)c.
D)d.

Question 22

The above figure shows Bob's utility function.He currently has $100 of wealth,but there is a 50% chance that it could all be stolen.Over and above the price of fair insurance,what is the risk premium Bob would pay to eliminate the chance of theft?

A)$0
B)$20
C)$30
D)$50

Question 23

The above figure shows Bob's utility function.He currently has $100 of wealth,but there is a 50% chance that it could all be stolen.Bob will buy theft insurance to cover the full $100

A)as long as it does not cost more than $25.
B)as long as it does not cost more than $50.
C)as long as it does not cost more than $70.
D)at any price.

Question 24

If a person is entertained by gambling,then

A)she is not risk averse.
B)she does not understand the concept of a fair game.
C)she may gamble even if it is an unfair game.
D)she will definitely not buy automobile insurance.

Question 25

If a person is risk neutral,then she

A)is indifferent about playing a fair game.
B)will pay a premium to avoid a fair game.
C)has a horizontal utility function.
D)has zero marginal utility of wealth.

Question 26

The above figure shows Bob's utility function.He currently has $100 of wealth,but there is a 50% chance that it could all be stolen.What is the most Bob would pay for insurance that would replace his $100 should it be stolen?

A)$30
B)$50
C)$70
D)$75

Question 27

Sarah buys little stuffed animals for $5 each.They come in different varieties.If the producer stops making (retires)a certain variety,a stuffed animal of that variety will be worth $100;otherwise it is worth $0.There is 25% chance that any variety will be retired.For the purchase of an individual animal,what is the value to Sarah of knowing ahead of time whether or not that variety will be retired?

Question 28

The above figure shows Bob's utility function.He currently has $100 of wealth,but there is a 50% chance that it could all be stolen.Bob's expected utility is

A)a.
B)b.
C)c.
D)d.

Question 29

For a given expected value,the smaller the standard deviation of the expected value,the larger the risk.

Question 30

The above figure shows Bob's utility function.He currently has $100 of wealth,but there is a 50% chance that it could all be stolen.The midpoint of the chord that runs from zero and intersects the utility function where wealth is 100,represents Bob's

A)risk premium.
B)expected utility of receiving $50 with certainty.
C)expected utility of receiving $0 50% of the time and $100 50% of the time.
D)risk neutrality.

Question 31

Explain why the variance of an investment is a useful measure of the risk associated with it.

Question 32

The above figure shows Bob's utility function.He currently has $100 of wealth,but there is a 50% chance that it could all be stolen.To reduce the chance of theft to zero,Bob is willing to pay

A)$20.
B)$50.
C)$70.
D)$80.

Question 33

The above figure shows Bob's utility function.He currently has $100 of wealth,but there is a 50% chance that it could all be stolen.Bob's expected wealth is

A)$0.
B)$50.
C)$75.
D)$100.

Question 34

The above figure shows Bob's utility function.He currently has $100 of wealth,but there is a 50% chance that it could all be stolen.Living with this risk gives Bob the same expected utility as if there was no chance of theft and his wealth was

A)$0.
B)$20.
C)$30.
D)$50.

Question 35

For a risk-neutral person,the expected utility associated with various levels of wealth

A)is above the person's utility function.
B)is below the person's utility function.
C)is equal to the person's utility function.
D)does not exist.

Question 36

On any given day,a salesman can earn $0 with a 20% probability,$100 with a 40% probability,or $300 with a 20% probability.Calculate the expected value and variance of his earnings,and interpret.

Question 37

A risk-preferring person is willing to pay

A)a risk premium.
B)a fee to make a fair bet.
C)to obtain decreasing marginal utility.
D)None of the above.

Question 38

The above figure shows Bob's utility function.He currently has $100 of wealth,but there is a 50% chance that it could all be stolen.Bob is

A)risk averse.
B)risk neutral.
C)risk loving.
D)risk premium.

Question 39

The above figure shows Bob's utility function.He currently has $100 of wealth,but there is a 50% chance that it could all be stolen.Bob is risk averse because

A)his utility function is concave.
B)he has diminishing marginal utility of wealth.
C)he is willing to pay a premium to avoid a risky situation.
D)All of the above.

Question 40

The above figure shows Bob's utility function.He currently has $100 of wealth,but there is a 50% chance that it could all be stolen.Bob is risk averse because

A)his utility function is convex.
B)he has negative marginal utility of wealth.
C)he is willing to pay a premium to avoid a risky situation.
D)All of the above.

Question 41

If a person is risk averse,then she has negative marginal utility of wealth.

Question 42

Describe how the risk premium for a person with a convex utility function is determined.

Question 43

Bob invests $50 in an investment that has a 50% chance of being worth $100 and a 50% chance of being worth $0.From this information we can conclude that Bob is NOT

A)risk loving.
B)risk neutral.
C)risk averse.
D)rational.

Question 44

Johnny owns a house that would cost $100,000 to replace should it ever be destroyed by fire.There is a 0.1% chance that the house could be destroyed during the course of a year.Johnny's utility function is U = W^0.5.How much would fair insurance cost that completely replaces the house if destroyed by fire? Assuming that Johnny has no other wealth,how much would Johnny be willing to pay for such an insurance policy? Why the difference?

Question 45

The Friedman-Savage utility function can explain why

A)people buy automobile insurance.
B)somebody becomes addicted to gambling.
C)people become more risk averse as their wealth increases.
D)people place small bets to have a chance at winning a large amount.

Question 46

For the utility function U = W^a,what values of "a" correspond to being risk averse,risk neutral,and risk loving?

Question 47

John derives more utility from having $1,000 than from having $100.From this,we can conclude that John

A)is risk averse.
B)is risk loving.
C)is risk neutral.
D)has a positive marginal utility of wealth.

Question 48

If Ann's utility function is U = W^0.5,and she invests in a business which can yield $6,400 with probability 1/5,and $3600 with probability 4/5,then her expected wealth is

A)$1280.
B)$2880.
C)$4160.
D)$5840.

Question 49

What type of risk behavior does the person exhibit who is willing to pay $5 for the chance to bet $60 on a game where 20% of the time the bet returns $100,and 80% of the time returns $50? Explain.

Question 50

If Ann's utility function is U = 3W^0.5,and she invests in a business which can yield $6,400 with probability 1/5,and $3600 with probability 4/5,then her Arrow-Pratt measure of risk aversion is

A)0.5/w.
B)1/w.
C)1.5w.
D)3/w.

Question 51

A fair game is a game in which the chances are 50-50 that you win or lose.

Question 52

The Arrow-Pratt measure of risk aversion is

A)negative if a person is risk averse.
B)greater than one if a person is risk averse.
C)negative if a person is risk loving.
D)None of the above.

Question 53

John's utility from an additional dollar increases more when he has $1,000 than when he has $10,000.From this,we can conclude that John

A)is risk averse.
B)is risk loving.
C)is risk neutral.
D)has a negative marginal utility of wealth.

Question 54

Catherine is risk averse.When faced with a choice between a gamble and a certain level of wealth,she will

A)always prefer the gamble.
B)always prefer the certain level of wealth.
C)prefer the gamble if the expected utility from it is higher than the utility from the certain level of wealth.
D)prefer the certain level of wealth if the expected utility from the gamble is higher than the utility of the certain level of wealth.

Question 55

If Ann's utility function is U = W^0.5,and she invests in a business which can yield $6,400 with probability 1/5,and $3600 with probability 4/5,then her risk premium to avoid bearing this risk is

A)$36.
B)$41.6.
C)$64.
D)$100.

Question 56

If Ann's utility function is U = W^0.5,and she invests in a business which can yield $6,400 with probability 1/5,and $3600 with probability 4/5,then her expected utility is

A)80.
B)76.
C)64.
D)60.

Question 57

If a person willingly plays an unfair game that is not in his favor,he is risk loving.

Question 58

Bob invests $25 in an investment that has a 50% chance of being worth $100 and a 50% chance of being worth $0.From this information we can conclude that Bob is

A)risk loving.
B)risk neutral.
C)risk averse.
D)Any one of the three above.

Question 59

Which of the following games involving the roll of a single die is a fair bet?

A)Bet $1 and receive $1 if 3 or 4 comes up.
B)Bet $1 and receive $1 if 3,4,or 5 comes up.
C)Bet $1 and receive $4 if six comes up.
D)None of the bets is a fair bet.

Question 60

Bob invests $75 in an investment that has a 50% chance of being worth $100 and a 50% chance of being worth $0.From this information we can conclude that Bob is

A)risk loving.
B)risk neutral.
C)risk averse.
D)irrational.

Question 61

Stephan has the utility function U(w)= 3
,where w is his wealth.Initially,Stephan has
w = $100.Would Stephan pay $5 to take the following gamble: With probability 0.03 he wins $25;otherwise,he wins nothing.

Question 62

Bob's utility function is shown in the above Figure.He currently has $100 worth of property,but there is a 50% chance that all of it will be stolen.An insurance company offers to reimburse Bob for his loss if the money is stolen.What is the most that Bob would pay for such a policy? Explain.

Question 63

Many people do not fully insure against risk because

A)they are risk averse.
B)the insurance companies are all crooks.
C)the insurance offered is less than fair.
D)the insurance offered is more than fair.

Question 64

An individual has an initial wealth of $35,000 and might incur a loss of $10,000 with probability p.Insurance is available that charges $gK to purchase $K of coverage.What value of g will make the insurance actuarially fair? If she is risk averse and insurance is fair,what is the optimal amount of coverage?

Question 65

Derive the Arrow-Pratt measure of risk aversion for the following utility functions.Which represents the greatest level of risk aversion according to the measure?
a.U(X)=
b.U(X)= -e^-x
c.U(X)= 1 - 1/X

Question 66

Cindy's attitudes towards risk are summarized by the utility function U(w)=
.Cindy has an initial wealth of $100.There is a 10% chance that her home will sustain flood damage next year costing her $40 in repairs.What is the most she will pay to for a full $40 of flood insurance?

Question 67

Steven currently has wealth of $10,000.He is risk averse about losing any of his wealth,but risk loving about adding to his wealth.Draw his utility function.

Question 68

A deductible is an amount of a claim not covered by insurance.A deductible is a fixed portion of the accident cost that the insured person must pay in order to make a claim to their insurer (this is similar to a co-pay in which you must pay a portion of the medical costs in the case you get sick).For example,if I break my arm,I have to pay a $50 deductible to the insurance company in order to get them to cover the rest of my medical costs from the accident.
Rosa has a 10% chance of getting sick in the next year.If she gets sick,her medical bills will amount to $500.She has a wealth of $1,000.Suppose she has the utility function U(X)= X^0.5 where x is her net wealth at the end of the year.
Suppose Rosa can purchase insurance.The insurance company provides two plans for Rosa to select from,both providing $500 of coverage in the case that Rosa gets hurt.Plan A has zero deductibles (good!)but charges a high premium (bad!).Specifically,Plan A charges $55 for $500 of coverage.Plan B has a deductible of $K,where K < 500,but charges a premium of just $(55 - .11K).
a.Suppose K = $100.Will Rosa purchase insurance and if so,which plan? Show this mathematically.
b.If Rosa can choose the deductible,K,what amount of deductible will she choose?
c.Suppose Rosa knows her chance of getting sick is really just 5%.How will this affect the deductible she chooses? You only need to provide intuition (in words)for this part,not explicit computation.

Question 69

Bob has an initial wealth of $1200 but faces a 50% chance of losing $800 to doctors' bills in the coming year.Insurance is available at a rate of 60¢ per $1 of coverage.This means that if Bob purchases $X in coverage,it costs 6X¢ and pays $X towards Bob's doctors' bills.If Bob's utility function is U(w)= 2
,how much insurance (X)will Bob purchase?

Question 70

If two events are perfectly positively correlated,then

A)diversification is not necessary since there is no risk.
B)diversification eliminates all risk.
C)diversification does not reduce risk at all.
D)diversification only cuts the risk in half.

Question 71

In terms of the stock market,systematic risk refers to the fact that

A)some stocks have higher returns than others.
B)some stocks' returns have a higher variance than others.
C)all stock prices are correlated with the health of the economy.
D)most stock prices are perfectly negatively correlated.

Question 72

The ability of diversification to reduce risk

A)is greater the more negatively correlated the two events are.
B)is greater the more positively correlated the two events are.
C)is greater the more uncorrelated the two events are.
D)is greater the more risk averse the individual is.

Question 73

If fair insurance is offered to a risk-averse person,she will

A)buy enough insurance to eliminate all risk.
B)not buy any insurance because it is overpriced.
C)not buy any insurance since the marginal utility of the amount of the payment is positive.
D)buy enough insurance to cover about half of the possible loss.

Question 74

Buying a diversified mutual stock fund allows you to

A)completely avoid all types of risk.
B)avoid only random,unsystematic risk.
C)avoid only systematic risk.
D)avoid risk only when all the stock prices are perfectly correlated.

Question 75

Searching the Internet for information to help select a product that is more reliable is most likely to be done by a

A)risk-averse person.
B)risk-neutral person.
C)risk-preferring person.
D)This cannot be determined with the information provided.

Question 76

A person is betting a coin will come up heads or tails.The coin always lands on one of these two outcomes.This person can bet to

A)eliminate only the systematic risk.
B)eliminate only the random risk.
C)eliminate all risk.
D)All of the above.

Question 77

Sarah has the utility function U(x)= 1 - 1/x,where x is the present value of her lifetime income.Sarah is trying to select a career.If she goes into teaching,she will make x=5 with certainty.If she pursues acting,she will make x=400 if successful or x=2 if unsuccessful (and therefore ends up waiting tables).The chance of succeeding in acting is 1% if she pursues acting.
a.Determine which career Sarah will choose.Is she choosing the career with the higher expected value? Explain.
b.An acting career expert charges 0.01 to determine if a person will succeed at acting.By going to an expert,Sarah can choose the best career according to her skills.Assuming that the expert is able to correctly determine if Sarah will be a successful actor,will she pay for this service?

Question 78

For each of the following statements,state whether the statement is true,false,or uncertain and explain why.
i.A risk neutral person is indifferent to a gamble and the expected value of the gamble.
ii.A risk-averse person will never accept a gamble.
iii.A risk-loving person will accept any gamble.

Question 79

Which of the following helps to reduce risk?

A)abstain from risk taking
B)obtain more information
C)diversify
D)All of the above.

Question 80

Which of the following losses to an individual would an insurance company NOT cover?

A)The person's automobile is stolen.
B)Fire destroys the person's home.
C)The person's father dies.
D)The person's country is invaded.