Deck 18: Performance Evaluation and Active Portfolio Management

Question 1

Other things equal,the price of a stock call option is positively correlated with the following factors except

A) the stock price.
B) the time to expiration.
C) the stock volatility.
D) the exercise price.
E) none of these.

Answer 1

D

Question 2

A stock option has an intrinsic value of zero if the option is

A) at the money.
B) out of the money.
C) in the money.
D) a and c.
E) a and b.

Answer 2

E

Question 3

Delta neutral

A) is the volatility level for the stock that the option price implies.
B) is the continued updating of the hedge ratio as time passes.
C) is the percentage change in the stock call option price divided by the percentage change in the stock price.
D) means the portfolio has no tendency to change value as the underlying portfolio value changes.
E) is the volatility level for the stock that the option price implies and is the percentage change in the stock call option price divided by the percentage change in the stock price.

Answer 3

D

Question 4

A hedge ratio for a call option is ________ and a hedge ratio for a put option is __________.

A) negative,positive
B) negative,negative
C) positive,negative
D) positive,positive
E) zero,zero

Question 5

The elasticity of a stock call option is always

A) greater than one.
B) smaller than one.
C) negative.
D) infinite.
E) none of these.

Question 6

The percentage change in the stock call option price divided by the percentage change in the stock price is called

A) the elasticity of the option.
B) the delta of the option.
C) the theta of the option.
D) the gamma of the option.
E) none of these.

Question 7

All the inputs in the Black-Scholes Option Pricing Model are directly observable except

A) the price of the underlying security.
B) the risk free rate of interest.
C) the time to expiration.
D) the variance of returns of the underlying asset return.
E) none of these.

Question 8

A hedge ratio for a call is always

A) equal to one.
B) greater than one.
C) between zero and one
D) between minus one and zero.
E) of no restricted value

Question 9

Other things equal,the price of a stock put option is positively correlated with the following factors except

A) the stock price.
B) the time to expiration.
C) the stock volatility.
D) the exercise price.
E) None of these is correct

Question 10

Portfolio A consists of 400 shares of stock and 400 calls on that stock.Portfolio B consists of 500 shares of stock.The call delta is 0.5.Which portfolio has a higher dollar exposure to a change in stock price?

A) Portfolio B
B) Portfolio A
C) The two portfolios have the same exposure
D) A if the stock price increases and B if it decreases.
E) B if the stock price decreases and A if it increases.

Question 11

The gamma of an option is

A) the volatility level for the stock that the option price implies.
B) the continued updating of the hedge ratio as time passes.
C) the percentage change in the stock call option price divided by the percentage change in the stock price.
D) the sensitivity of the delta to the stock price.
E) the volatility level for the stock that the option price implies and the percentage change in the stock call option price divided by the percentage change in the stock price.

Question 12

A hedge ratio of 0.70 implies that a hedged portfolio should consist of

A) long 0.70 calls for each short stock.
B) short 0.70 calls for each long stock.
C) long 0.70 shares for each short call.
D) long 0.70 shares for each long call.
E) none of these.

Question 13

If the stock price increases,the price of a put option on that stock __________ and that of a call option _________.

A) decreases,increases
B) decreases,decreases
C) increases,decreases
D) increases,increases
E) does not change,does not change

Question 14

A hedge ratio for a put is always

A) equal to one.
B) greater than one.
C) between zero and one.
D) between minus one and zero.
E) of no restricted value.

Question 15

Before expiration the time value of an in the money stock option is always

A) equal to zero.
B) positive.
C) negative.
D) equal to the stock price minus the exercise price.
E) none of these.

Question 16

Delta is defined as

A) the change in the value of an option for a dollar change in the price of the underlying asset.
B) the change in the value of the underlying asset for a dollar change in the call price.
C) the percentage change in the value of an option for a one percent change in the value of the underlying asset.
D) the change in the volatility of the underlying stock price.
E) none of these.

Question 17

The price of a stock put option is __________ correlated with the stock price and __________ correlated with the striking price.

A) positively,positively
B) negatively,positively
C) negatively,negatively
D) positively,negatively
E) not,not

Question 18

Prior to expiration

A) the intrinsic value of a call option is greater than its actual value.
B) the intrinsic value of a call option is always positive.
C) the actual value of call option is greater than the intrinsic value.
D) the intrinsic value of a call option is always greater than its time value.
E) none of these.

Question 19

The dollar change in the value of a stock call option is always

A) lower than the dollar change in the value of the stock.
B) higher than the dollar change in the value of the stock.
C) negatively correlated with the change in the value of the stock.
D) b and c.
E) a and c.

Question 20

The elasticity of a stock put option is always

A) positive.
B) smaller than one.
C) negative
D) infinite
E) none of these.

Question 21

Use the two-state put option value in this problem.S_O= $100;X = $120;the two possibilities for S_Tare $150 and $80.The range of P across the two states is _________;the hedge ratio is _______.

A) $0 and $40;-4/7
B) $0 and $50;+4/7
C) $0 and $40;+4/7
D) $0 and $50;-4/7
E) $20 and $40;+1/2

Question 22

Use the Black-Scholes Option Pricing Model for the following problem.Given: S_O= $70;X = $70;T = 70 days;r = 0.06 annually (0.0001648 daily);σ = 0.020506 (daily).No dividends will be paid before option expires.The value of the call option is

A) $10.16.
B) $5.16.
C) $0.00.
D) $2.16.
E) none of these.

Question 23

If the hedge ratio for a stock call is 0.60,the hedge ratio for a put with the same expiration date and exercise price as the call would be

A) 0.60
B) 0.40
C) -0.60
D) -0.40
E) -.17

Question 24

Higher dividend payout policies have a __________ impact on the value of the call and a __________ impact on the value of the put.

A) negative,negative
B) positive,positive
C) positive,negative
D) negative,positive
E) zero,zero

Question 25

Since deltas change as stock values change,portfolio hedge ratios must be constantly updated in active markets.This process is referred to as

A) portfolio insurance.
B) rebalancing.
C) option elasticity.
D) gamma hedging.
E) dynamic hedging.

Question 26

An American call option buyer on a non-dividend paying stock will

A) always exercise the call as soon as it is in the money.
B) only exercise the call when the stock price exceeds the previous high
C) never exercise the call early.
D) buy an offsetting put whenever the stock price drops below the strike price.
E) none of these.

Question 27

If the hedge ratio for a stock call is 0.70,the hedge ratio for a put with the same expiration date and exercise price as the call would be ______.

A) 0.70
B) 0.30
C) -0.70
D) -0.30
E) -.17

Question 28

An American-style call option with six months to maturity has a strike price of $35.The underlying stock now sells for $43.The call premium is $12.What is the intrinsic value of the call?

A) $12
B) $8
C) $0
D) $23
E) none of these.

Question 29

A put option is currently selling for $6 with an exercise price of $50.If the hedge ratio for the put is -0.30 and the stock is currently selling for $46,what is the elasticity of the put?

A) 2.76
B) 2.30
C) -7.67
D) -2.76
E) -2.30

Question 30

Options sellers who are delta-hedging would most likely

A) sell when markets are falling
B) buy when markets are rising
C) both a and b.
D) sell whether markets are falling or rising.
E) buy whether markets are falling or rising.

Question 31

Empirical tests of the Black-Scholes option pricing model

A) show that the model generates values fairly close to the prices at which options trade.
B) show that the model tends to overvalue deep in the money calls and undervalue deep out of the money calls.
C) indicate that the mispricing that does occur is due to the possible early exercise of American options on dividend-paying stocks.
D) a and c.
E) a,b,and c.

Question 32

An American-style call option with six months to maturity has a strike price of $35.The underlying stock now sells for $43.The call premium is $12.What is the time value of the call?

A) $8
B) $12
C) $0
D) $4
E) cannot be determined without more information.

Question 33

A portfolio consists of 400 shares of stock and 200 calls on that stock.If the hedge ratio for the call is 0.6,what would be the dollar change in the value of the portfolio in response to a one dollar decline in the stock price?

A) +$700
B) +$500
C) -$580
D) -$520
E) none of these

Question 34

An American-style call option with six months to maturity has a strike price of $35.The underlying stock now sells for $43.The call premium is $12.If the option has delta of .5,what is its elasticity?

A) 4.17
B) 2.32
C) 1.79
D) 0.5
E) 1.5

Question 35

An American-style call option with six months to maturity has a strike price of $35.The underlying stock now sells for $43.The call premium is $12.If the risk-free rate is 6%,what should be the value of a put option on the same stock with the same strike price and expiration date?

A) $3.00
B) $2.02
C) $12.00
D) $5.25
E) $8.00

Question 36

An American-style call option with six months to maturity has a strike price of $35.The underlying stock now sells for $43.The call premium is $12.If the company unexpectedly announces it will pay its first-ever dividend 3 months from today,you would expect that

A) the call price would increase.
B) the call price would decrease.
C) the call price would not change.
D) the put price would decrease.
E) the put price would not change.

Question 37

Relative to European puts,otherwise identical American put options

A) are less valuable.
B) are more valuable.
C) are equal in value.
D) will always be exercised earlier.
E) none of these.

Question 38

A put option on the S&P 500 index will best protect ________

A) a portfolio of 100 shares of IBM stock.
B) a portfolio of 50 bonds.
C) a portfolio that corresponds to the S&P 500.
D) a portfolio of 50 shares of AT&T and 50 shares of Xerox stocks.
E) a portfolio that replicates the Dow.

Question 39

Which one of the following variables influence the value of options?
I)Level of interest rates.
II)Time to expiration of the option.
III)Dividend yield of underlying stock.
IV)Stock price volatility.

A) I and IV only.
B) II and III only.
C) I,II,and IV only.
D) I,II,III,and IV.
E) I,II and III only.

Question 40

A one dollar decrease in a call option's exercise price would result in a(n)__________ in the call option's value of __________ one dollar.

A) increase,more than
B) decrease,more than
C) decrease,less than
D) increase,less than
E) increase,exactly

Question 41

The time value of an option is
I)he difference between the option's price and the value it would have if it were expiring immediately.
II)the same as the present value of the option's expected future cash flows.
III)the difference between the option's price and its expected future value.
IV)different from the usual time value of money concept.

A) I
B) I and II
C) II and III
D) II
E) I and IV

Question 42

You are evaluating a stock that is currently selling for $30 per share.Over the investment period you think that the stock price might get as low as $25 or as high as $40.There is a call option available on the stock with an exercise price of $35.Answer the following questions about hedging your position in the stock.Assume that you will hold one share.
What is the hedge ratio?
How much would you borrow to purchase the stock?
What is the amount of your net investment in the stock?
Complete the table below to show the value of your stock portfolio at the end of the holding period.

Question 43

The Black-Scholes formula assumes that
I)the risk-free interest rate is constant over the life of the option.
II)the stock price volatility is constant over the life of the option.
III)the expected rate of return on the stock is constant over the life of the option.
IV)there will be no sudden extreme jumps in stock prices.

A) I and II
B) I and III
C) II and II
D) I,II and IV
E) I,II,III,and IV

Question 44

As the underlying stock's price increased,the call option valuation function's slope approaches

A) zero.
B) one.
C) two times the value of the stock.
D) one-half time s the value of the stock.
E) infinity

Question 45

The intrinsic value of an at-the-money put option is equal to

A) the stock price minus the exercise price.
B) the put premium.
C) zero.
D) the exercise price minus the stock price.
E) None of these is correct

Question 46

In the table below,list the six variables that influence the value of an American call option in column one.In column two,indicate whether an increase in the value of each would cause an increase or a decrease in the value of the call.Assume all other variables remain constant in each case.In column three,give a brief explanation of why this relationship exists.

Question 47

The hedge ratio of an option is also called the option's

A) alpha
B) beta
C) sigma
D) delta
E) rho

Question 48

Which of the variables affecting option pricing is not directly observable? If this variable is estimated to be higher or lower than the variable actually is how is the option valuation affected?

Question 49

Relative to non-dividend-paying European calls,otherwise identical American call options

A) are less valuable.
B) are more valuable.
C) are equal in value.
D) will always be exercised earlier.
E) none of these.

Question 50

In volatile markets,dynamic hedging may be difficult to implement because

A) prices move too quickly for effective rebalancing.
B) as volatility increases,historical deltas are too low.
C) price quotes may be delayed so that correct hedge ratios cannot be computed.
D) volatile markets may cause trading halts.
E) all of these.

Question 51

Vega is defined as

A) the change in the value of an option for a dollar change in the price of the underlying asset.
B) the change in the value of the underlying asset for a dollar change in the call price.
C) the percentage change in the value of an option for a one percent change in the value of the underlying asset.
D) the change in the volatility of the underlying stock price.
E) the sensitivity of an option's price to changes in volatility.

Question 52

Rubinstein (1994)observed that the performance of the Black-Scholes model had deteriorated in recent years,and he attributed this to

A) investor fears of another market crash.
B) higher than normal dividend payouts.
C) early exercise of American call options.
D) decreases in transaction costs.
E) none of these.

Question 53

Dollar movements in option prices are ________ than dollar movements in the stock price,and rate of return volatility of options is ________ than stock return volatility.

A) less,less
B) greater,greater
C) less,greater
D) greater,less
E) There is no particular pattern.

Question 54

What is an option hedge ratio? How does the hedge ratio for a call differ from that of a put (or are the two equivalent)? Explain.

Question 55

Which Excel formula is used to execute the Black-Scholes option pricing model?

A) NORMAL
B) ABNORMAL
C) NORMSDIST
D) DIST
E) NORMALDIST

Question 56

You purchased a call option for a premium of $4.The call has an exercise price of $29 and is expiring today.The current stock price is $31.What would be your best course of action?

A) Exercise the call because the stock price is greater than the exercise price.
B) Do not exercise the call because the stock price is greater than the exercise price.
C) Do not exercise the call because the difference between the exercise price and the stock price is not enough to cover the amount of the premium.
D) Exercise the call to get a positive net return on the investment.
E) Do not exercise the call to avoid a negative net return on the investment.

Question 57

Discuss the relationship between option prices and time to expiration,volatility of the underlying stocks,and the exercise price.