Question 1

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

Accepted Answer

When S_T = $150; P = $0; when S_T = $80: P = $40; ($0 - $40)/($150 - $80) = -4/7.

Question 2

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.

Accepted Answer

The answer of Use the Black-Scholes Option Pricing Model for...

Question 3

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

Accepted Answer

The hedge ratio for a put option is the negative of the hedge ratio for a call option. Therefore, if the hedge ratio for the call is 0.60, the hedge ratio for the put would be -0.60. However, the question asks for the absolute value of the hedge ratio for the put, which would be 0.40 (i.e. the same as 1 - 0.60). The correct answer is D.

Question 4

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

Accepted Answer

Higher dividend payout policies lead to a reduction in the underlying stock price, which results in a decrease in the value of the call and an increase in the value of the put. Therefore, higher dividend payout policies have a negative impact on the value of the call and a positive impact on the value of the put.

Question 5

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.

Accepted Answer

The process of constantly updating portfolio hedge ratios in active markets is referred to as dynamic hedging. This involves adjusting the hedge ratio as the delta of the underlying asset changes with market movements. The other options are not applicable in this context – portfolio insurance and gamma hedging deal with different risk management strategies, rebalancing refers to adjusting the mix of assets in a portfolio, and option elasticity is a measure of the sensitivity of an option's price to changes in market factors.

Question 6

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.

Accepted Answer

The buyer of an American call option on a non-dividend paying stock would not have any benefit from exercising the option early since the option would always have time value left. Therefore, they would only exercise the option at expiration if it is in the money. It does not make sense to wait for the stock price to exceed the previous high, nor would they buy an offsetting put whenever the stock price drops below the strike price.

Question 7

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

Accepted Answer

Call hedge ratio = N(d1); Put hedge ratio = N(d1) - 1; 0.7 - 1.0 = -0.3.

Question 8

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.

Accepted Answer

The intrinsic value of the call option is the difference between the current stock price and the strike price, which is $43 - $35 = $8. Therefore, the intrinsic value of the call option is $8. The call premium of $12 is higher than the intrinsic value, so the option has some time value as well.

Question 9

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

Accepted Answer

The answer of A put option is currently selling for...

Question 10

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.

Accepted Answer

Delta-hedging involves adjusting the portfolio's position in the underlying asset in order to keep the delta of the option position neutral. This means that options sellers who are delta-hedging would sell when markets are falling in order to reduce the delta of their overall position, and buy when markets are rising in order to increase the delta of their overall position. Therefore, both options A and B are correct, and the best answer is choice C. Options sellers who are delta-hedging will actively trade their underlying asset to maintain a delta-neutral position, regardless of whether markets are rising or falling.

Question 11

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.

Accepted Answer

Empirical tests have shown that the Black-Scholes model generates values fairly close to the prices at which options trade (option A) but tends to overvalue deep in the money calls and undervalue deep out of the money calls (option B). Additionally, the mispricing that does occur is often attributed to possible early exercise of American options on dividend-paying stocks (option C). Therefore, choices A, B, and C are all partially true, but only choices A and C are fully supported by empirical testing. Thus, the best choice is D, which includes both A and C.

Question 12

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.

Accepted Answer

The intrinsic value of the option is $8 (i.e. $43 - $35), so the time value must be $4 (i.e. the total premium of $12 minus the intrinsic value of $8). Therefore, the correct choice is D.

Question 13

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

Accepted Answer

The dollar change in the value of the portfolio is calculated by considering the change in value of both the shares and the calls. For the shares, a $1 decline in stock price results in a $400 decline (400 shares x $1). For the calls, the hedge ratio of 0.6 means each call loses $0.60 for a $1 decline in stock price, resulting in a $120 decline (200 calls x $0.60). The total change is -$400 - $120 = -$520.

Question 14

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

Accepted Answer

Elasticity is defined as the percentage change in the option price for a 1% change in the price of the underlying asset. We can calculate the elasticity as:
Elasticity = (ΔOption Price / Option Price) / (ΔUnderlying Price / Underlying Price)
We are given that the option has a delta of 0.5, so a 1% increase in the underlying price would result in a 0.5% increase in the option price. We can use this information along with the given data to calculate the elasticity:
ΔOption Price = 0.5 * 12 = 6
Option Price = 12
ΔUnderlying Price = 1% * 43 = 0.43
Underlying Price = 43
Elasticity = (6/12) / (0.43/43) = 1.79
Therefore, the answer is C) 1.79.

Question 15

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

Accepted Answer

Using the put-call parity for American options, the put option value is calculated as: Put = Call + PV(Strike) - Stock Price. Here, Call = $12, PV(Strike) = $35 / (1 + 0.06/2) = $34.48, Stock Price = $43. Thus, Put = $12 + $34.48 - $43 = $3.48, which is closest to $3.00.

Question 16

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.

Accepted Answer

The call price would decrease because the dividend payment would reduce the stock price, making the call option less valuable.

Question 17

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.

Accepted Answer

American put options are more valuable than their European counterparts as they give the holder the right to exercise the option at any time before the expiration date, whereas European puts can only be exercised on the expiration date. This added flexibility of exercising the option earlier increases the value of American put options.

Question 18

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.

Accepted Answer

A put option on the S&P 500 index is designed to protect a portfolio that corresponds to the S&P 500. By purchasing a put option, an investor can protect their portfolio against a decline in the broad market. This would not be the best choice for portfolios consisting of individual stocks or bonds, as the performance of those assets may not directly correspond to the performance of the broader market. Likewise, a put option on the S&P 500 would not be an effective hedge for a portfolio that replicates the Dow, as these two indices are not identical.

Question 19

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.

Accepted Answer

All four variables—interest rates, time to expiration, dividend yield, and stock price volatility—affect the value of options.

Question 20

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

Accepted Answer

The answer of A one dollar decrease in a call...

Quiz 18: Performance Evaluation and Active Portfolio Management

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 _.

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

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

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

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

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

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 ______.

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 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?

Options sellers who are delta-hedging would most likely

Empirical tests of the Black-Scholes option pricing model

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 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?

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?

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?

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

Relative to European puts,otherwise identical American put options

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

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