Deck 16: Time, Risk and Options

Question 1

According to the Black-Scholes formula, the price of a European call option depends on its strike price, the current price of the underlying asset, the volatility of the underlying's price, the time to expiration, and the interest rate.

Answer 1

True

Question 2

The present value of $200 to be received after 5years at 10 percent interest is $112.2.

Answer 2

False

Question 3

Unanticipated increase in inflation transfers wealth from the borrower, who pays the pre-decided rate of interest to the lender.

Answer 3

False

Question 4

The longer the annuity on a sum of money the lower will be its present value.

Question 5

For a risk-averse person, an indifference curve representing the different combinations of variance of return and expected return will be downward sloping and convex to the variance of return axis.

Question 6

A loan used as an investment turns out to be profitable if the sale price of its output covers the _____ of all other inputs and interest on the funds loaned.

A)internal costs
B)marginal cost
C)opportunity cost
D)average cost

Question 7

Given two investments P and Q, with the former having a mean 0.7 and variance 0.17 and the latter having a mean 0.7 and a variance 0.03, a risk-preferrer will be indifferent between the two.

Question 8

Rational individuals prefer to consume goods during the current year rather than in the future because of:

A)positive time preference.
B)positive consumption preference.
C)high expected rate of inflation.
D)high market rate of interest.

Question 9

Conditional probability of event A given that event B has already occurred is represented as the ratio between Pr[A and B] and Pr[B].

Question 10

The Bayes' theorem states that the conditional probability of event B given event A depends on the conditional probability of event A given event B and the independent probability of event B.

Question 11

Which of the following is true of the present value of an investment?

A)The higher the rate of interest the higher will be the present value of an investment.
B)Present value of an investment is an increasing function of the time period of investment.
C)The longer the time period of investment the lower will be its present value.
D)Present value falls less than proportionately with the length of the delay in payment.

Question 12

The utility function with respect to wealth is negatively sloped for a risk averse person.

Question 13

Options do not eliminate the risks but they give people choices about which risks they will hold and help to price those risks they might wish to assign to others.

Question 14

A tycoon purchasing a loss making company will install new management teams only as long as the marginal value of the additional information these teams generate is worth the cost of installing them.

Question 15

Suppose a six-sided dice is rolled twice.The probability of getting a five during the second roll will depend on the outcome of the first roll.

Question 16

Assume that Jane has limited wealth to invest in two assets both of which promise her returns worth $3,000 after two years.The first is a bank deposit assuring an interest of 10 percent per annum and the second is a private bond with an interest rate of 8 percent per annum.Which of the two would require a low initial investment and of what amount?

A)The bond requiring an initial investment worth $2,564.
B)The bank deposit requiring an initial investment worth $2,479.
C)The bond requiring an initial investment worth $2,479.
D)The bank deposit requiring an initial investment worth $2,564.

Question 17

A probability distribution with a smaller percentage of its observations beyond a certain distance from the mean will have a higher variance.

Question 18

Assume that Rudolf withdraws $600 from his bank account which was earning him 10 percent interest per annum to buy a high-end digital camera.The bank interest forgone by him will be the opportunity cost of this purchase.

Question 19

Calculate the discounted value of $2,875 to be received from a bank a year later at an interest of 15 percent per annum.

A)$2,625
B)$2,075
C)$2,015
D)$2,500

Question 20

If an individual invests $20 in a bank deposit promising an interest of 12 percent per annum, compounded annually, he will receive $40 after 8 years.

Question 21

The nominal interest rate on a loan with an annual inflation rate of π and a real interest rate i is represented as:

A)i+π÷iπ
B)i+π×iπ
C)i+π+iπ
D)i+π-iπ

Question 22

A risky borrower can pay a lower interest rate if:

A)she invests the amount in a profitable business.
B)she can assure the lender of a low inflation rate.
C)she makes a promise to repay within a short interval.
D)she can arrange for a collateral.

Question 23

Individuals in favor of privatization of Social Security believe that it would allow people to:

A)evade the exorbitant rates of Social Security taxes.
B)substitute purchases of stocks and other financial assets for a portion of their Social Security taxes.
C)lower their medical bill by taking extra precaution and care for their health.
D)experience a lower inflation in healthcare services.

Question 24

A builder is planning to construct to a departmental store with an investment worth $1,200.He receives proposals from two retailers interested to lease space in it assuring him future cash flows worth $1,000 at the end of the first year and $700 at the end of two years.If the building lasts only for two years and the discount rate is 15 percent, what would be the net present value of this project?

A)$300.50
B)$257.63
C)$198.67
D)$118.38

Question 25

If A and B are two sets such that set A is a subset of B, and "Pr" represents the probability, then Pr(A and B) will be:

A)Pr[A].
B)Pr[B].
C)Pr[A-B].
D)Pr[A+B].

Question 26

Suppose Annie expects an annual return of $520 from an investment worth $500.What should be the rate of interest charged by her to a risky borrower who is likely to repay the principal and interest with a probability of 0.7?

A)45 percent
B)48.6 percent
C)20.33 percent
D)53.4 percent

Question 27

Two events A and B in a sample space are considered _____ if the probability that A will happen is the same regardless of whether or not B has happened.

A)conditional
B)correlated
C)independent
D)exclusive

Question 28

A _____ is a combination of an annuity that consists of coupon payments and a terminal payment of the par value.

A)share
B)bond
C)perpetuity
D)debenture

Question 29

Assume that the interest rate on a federally insured deposit declines from 15 percent per annum to 10 percent.If an individual holding a U.S.Treasury bill worth $2,500 plans to sell it after this drop in interest rate, he would realize (approximately) a:

A)capital gain worth $99.
B)capital loss worth $100.
C)capital gain worth $100.
D)capital loss worth $99.

Question 30

Assume that a lender had lent $2,500 at the rate of 12 percent per annum for a year, expecting an inflation rate of 3 percent.However, at the end of the year rate of inflation increased to 5 percent.The purchasing power of the lender:

A)will decline by $51.78
B)will appreciate by $51.78
C)will decline by $211.54
D)will appreciate by $211.54

Question 31

If A and B are two disjoint sets, and "Pr" represents the probability, then Pr[A and B] will be:

A)negative.
B)infinity.
C)unity.
D)zero.

Question 32

What is the difference between the present value of $550 to be received after 3 years and after 5 years from now at an annual interest of 15 percent?

A)$73.49
B)$61.60
C)$250.02
D)$88.11

Question 33

Calculate the annual return earned by a lender on a sum of $800 lent out at 8 percent interest, if prices inflate at the rate of 5 percent per annum.

A)$909.03
B)$808.50
C)$800.67
D)$907.20

Question 34

In the figure given below A and B are two sets, such that Pr[A and B]=1/3, Pr[A]=2/4, Pr[B]=3/4.
Figure 16-1

Refer to Figure 16-1.The conditional probability Pr[A/B] will be:

A)4/9.
B)2/9.
C)4/6.
D)2/6.

Question 35

If A and B are two disjoint sets, and "Pr" represents the probability, then Pr[A or B] will be:

A)unity.
B)zero.
C)Pr[A]+Pr[B].
D)Pr[A]-Pr[B].

Question 36

A(n) _____ is a set of equal annual payments received by an investor from the investment.

A)perpetuity
B)annuity
C)interest
D)capital value

Question 37

Which of the following is true of a "vanilla" bond?

A)It realizes capital gains in multiples of $1,000.
B)It provides a fluctuating stream of interest income every year.
C)It assures a return higher than the market rate of interest.
D)It has a par value payable after a certain number of years from its issuance.

Question 38

What is the maximum amount an investor should be willing to pay for a two-year $200 annuity, if the best alternative investment earns 20 percent per annum?

A)$305.56
B)$166.67
C)$138.89
D)$268.79

Question 39

In the figure given below A and B are two sets, such that Pr[A and B]=1/3, Pr[A]=2/4, Pr[B]=3/4.
Figure 16-1

Refer to Figure 16-1.Pr[A or B] will be:

A)5/6.
B)11/12.
C)1/6.
D)3/4.

Question 40

Which of the following alternatives signify the difference between the present value of a $150 perpetuity and 2-year $150 annuity, both discounted at 15 percent per annum.

A)The perpetuity would require an initial investment worth $100 while the annuity would require an initial investment worth $244.07.
B)The perpetuity would require an initial investment worth $1,500 while the annuity would require an initial investment worth $115.07.
C)The perpetuity would require an initial investment worth $1,000 while the annuity would require an initial investment worth $244.07.
D)The perpetuity would require an initial investment worth $100 while the annuity would require an initial investment worth $115.07.

Question 41

According to the Black-Scholes formula:

A)the value of an in-the-money option will equal the difference between the stock's current price and the strike price.
B)the payoff from an average option is either a multiple or a power of the difference between the strike price and the price they are exercised at.
C)the holder of a basket option has the right to buy or sell the underlying at the highest price it has attained over the life of the option.
D)the price of a call or put option varies with the price of the underlying asset.

Question 42

A derivative is any financial instrument whose value depends on the:

A)extent of asset diversification.
B)expected rate of inflation.
C)purchasing power of the people.
D)value of an underlying asset.

Question 43

The variance of a distribution increases more than proportionately with the spread of the distribution because:

A)variance is a squared quantity.
B)variance always lies at the center of the distribution.
C)variance is half the value of mean.
D)variance is closer to the maximum values.

Question 44

If two investments, X and Y, have the same expected return an individual investor would prefer:

A)the one with a higher standard deviation.
B)the one with a higher mean.
C)the one with a lower correlation coefficient.
D)the one with a lower variance.

Question 45

The _____ shows all of the combinations of risk and return that leaves an investor equally well off from holding either a low-risk or a high-risk investment.

A)indifference curve
B)expectation
C)standard deviation
D)correlation coefficient

Question 46

Assume that A and B are two events in the sample space such that Pr[A/B] is 2/3, Pr[B] is 1/4, and Pr[A] is 1/6.Applying the Bayesian reasoning calculate the probability Pr[B/A].

A)Pr[B/A]=0
B)Pr[B/A]=0.75
C)Pr[B/A]=1
D)Pr[B/A]=0.5

Question 47

A _____ is a function that takes on a defined value for every point in the sample space.

A)discrete variable
B)random variable
C)dependent variable
D)continuous variable

Question 48

The _____ measures the degree of association between two independent variables in an a distribution.

A)expectation
B)standard deviation
C)correlation coefficient
D)variance

Question 49

Which of the following options can be exercised upon expiration at a price equal to the average price of the underlying over its life span?

A)Average options
B)Lookback options
C)Barrier options
D)Basket options

Question 50

Diversification of a portfolio leads to:

A)a negative correlation between the investments.
B)a lower mean of returns.
C)a lower variance of returns.
D)a higher standard deviation of returns.

Question 51

Jeff holds $50,000 wealth which has a utility of 7.07 utils (assuming utility is the square root of wealth in thousand dollars).He considers investing this in a gamble which has a 0.6 probability of increasing his total wealth to $100,000 and 0.4 probability of decreasing it to $30,000.What will be Jeff's expected utility from the gamble?

A)15 utils
B)8.19 utils
C)3.2 utils
D)12.12 utils

Question 52

Which of the following is a characteristic of a real option?

A)The call option on a stock exercised if some average of the prices of its components passes a critical level.
B)The right to postpone construction on the basis of net present value calculation.
C)The put option on a stock that need to be paid for (at a predetermined price) if they are actually exercised.
D)The right to sell an option at the strike price.

Question 53

Which of the following is true of an option?

A)It is based on market volatility and thus assures a high profit to risk preferring individuals.
B)It provides the holder the right (but does not obliges him/her) to buy or sell a certain quantity of an underlying asset before its expiration.
C)The greater the volatility of the underlier's price the less likely that the option will go "in the money" before it expires.
D)Options help individuals to minimize their business risks by transferring it to others for a fixed time interval.

Question 54

A situation in which an individual has no information about probabilities and the underlying distributions of the possible outcomes of an investment choice is called:

A)a prior distribution.
B)updating.
C)risk tolerance.
D)pure uncertainty.

Question 55

Which of the following strategies are adopted by a business tycoon when the first new management of the purchased company fails?

A)He tries a second management team.
B)He tries to train and motivate the existing management team.
C)He sells off part of the company in the market.
D)He tries to reduce the cost of production by lowering output.

Question 56

If events A and B are independent, then Pr[A and B] will be:

A)Pr[A]÷Pr[B].
B)Pr[A]-Pr[B].
C)Pr[A]+Pr[B].
D)Pr[A]×Pr[B].

Question 57

The value of a real option varies with all of the following, EXCEPT:

A)the range of outcomes.
B)the rate of interest.
C)the rate of unemployment.
D)the delay in resolving uncertainty.

Question 58

Which of the following properties can be associated with an indifference curve of a risk-averse investor?

A)Indifference curve for a risk-averse investor is a vertical line parallel to the variance axis.
B)Two indifference curves can intersect at the equilibrium combination of risk and return.
C)An indifference curve closer to the expected return axis gives a better utility than the one farther away.
D)Indifference curve for a risk-averse investor is always downward sloping.

Question 59

If the market price of an option just before its expiration is $33 while its strike price is $29, arbitrage will determine a price for it that:

A)leaves an investor indifferent between buying the stock outright or buying an option and then exercising it.
B)encourages the investor to buy the stock outright and sell it when the option expires.
C)encourages the investor to buy an option and exercise it only after its expiration.
D)encourages the investor to buy the stock outright and rewrite an option later.

Question 60

If the writer of an option, holds shares of the stock or an actual quantity of the commodity when she writes the call option on it, her position is said to be:

A)protected.
B)exposed.
C)covered.
D)naked.

Question 61

Explain graphically how the prices of a call and a put option calculated from the Black-Scholes formula vary with the price of an underlying stock.

Question 62

Why are interest rates considered to be the opportunity cost of investments?

Question 63

Mention some applications of real options.

Question 64

Briefly describe the different conditions which affect the value of a real option.

Question 65

Why are present value calculations used in real options?

Question 66

Why are interest rates adjusted for inflation?

Question 67

Derive the Black-Scholes formula to represent the relationship between the price of an option and the price of its underlying stock.

Question 68

Derive the optimum portfolio of an investor seeking only to minimize the variance of returns.

Question 69

When do financial options prove to be beneficial?

Question 70

Suppose Player X's probability of winning a gamble is 0.8 while that of Player Y is 0.5.Which of the two will be willing to pay for a test and why?

Question 71

How is the writer of an option affected by changes in its stock price?

Question 72

How is the optimal degree of diversification of a portfolio determined?

Question 73

Point out the relevance of the Bayes' theorem.