CHAPTER 24



MULTIPLE CHOICE PROBLEMS

USE THE FOLLOWING INFORMATION FOR THE NEXT SIX PROBLEMS

62,500 GERMAN MARK EUROPEAN STYLE

CALLS PUTS

69 DEC $0.038

66.5 DEC $0.032

(d) 1 How much must an investor pay for the German Mark call option?

a) $380.00

b) $3,800.00

c) $62.50

d) $2,375.00

e) $625.00

(c) 2 How much must an investor pay for the German Mark put option?

a) $3,800.00

b) $6,250.00

c) $2,000.00

d) $3,200.00

e) $3.20

(c) 3 If the spot rate at expiration is 75.1 and the call option was purchased, what is the dollar gain or loss?

a) $0

b) $3750.00 gain

c) $1375.00 gain

d) $3750.00 loss

e) $1375.00 loss

(b) 4 If the spot rate at expiration is 72.3 and the call option was purchased, what is the dollar gain or loss?

a) $123.00 gain

b) $312.50 loss

c) $312.50 gain

d) $2,375.00 gain

e) $0, the option expires worthless.

(a) 5 If the spot rate at expiration is 65.3 and the put option was purchased, what is the dollar gain or loss?

a) $1,250.00 loss

b) $1,250.00 gain

c) $750.00 gain

d) $750.00 loss

e) $2,000.00 loss

(d) 6 If the spot rate at expiration is 61.4 and the put option was purchased, what is the dollar gain or loss?

a) $0, the option expires worthless.

b) $2,000.00 loss

c) $2,000.00 gain

d) $1,187.50 gain

e) $1,187.50 loss

USE THE FOLLOWING INFORMATION FOR THE NEXT TEN PROBLEMS

XYZ CORP

EXERCISE NYSE

DATE PRICE PRICE CLOSE

CALLS OCT 85 16 3/4 101 11/16

OCT 90 12 101 11/16

OCT 95 7 5/8 101 11/16

PUTS OCT 85 1/8 101 11/16

OCT 90 3/8 101 11/16

OCT 95 13/16 101 11/16

(a) 7 If you establish a long straddle using the options with an 85 exercise price, what is your dollar gain or loss if at expiration XYZ is still trading at 101 11/16?

a) $18.75 loss

b) $18.75 gain

c) $1,668.75 gain

d) $1,668.75 loss

e) $1,687.50 loss

(d) 8 If you establish a long strap using the options with an 85 exercise price, what is your dollar gain or loss if at expiration XYZ is still trading at 101 11/16?

a) $1,687.50 loss

b) $3,362.50 loss

c) $3,675.50 gain

d) $13.00 gain

e) $13.00 loss

(e) 9 If you establish a long strip using the options with an 85 exercise price, what is your dollar gain or loss if at expiration XYZ is still trading at 101 11/16?

a) $1,668.75 gain

b) $1,700.00 gain

c) $1,700.00 loss

d) $31.25 gain

e) $31.25 loss

(a) 10 If you establish a long straddle using the options with an 90 exercise price, what is your dollar gain or loss if at expiration XYZ is still trading at 101 11/16?

a) $68.75 loss

b) $68.75 gain

c) $37.50 loss

d) $1,200.00 loss

e) $1,200.00 gain

(c) 11 If you establish a long strap using the options with an 90 exercise price, what is your dollar gain or loss if at expiration XYZ is still trading at 101 11/16?

a) $37.50 loss

b) $37.50 gain

c) $100.00 loss

d) $100.00 gain

e) $2,437.50 loss

(b) 12 If you establish a long strip using the options with an 90 exercise price, what is your dollar gain or loss if at expiration XYZ is still trading at 101 11/16?

a) $106.25 gain

b) $106.25 loss

c) $1,275.00 loss

d) $1,275.00 gain

e) $75.00 loss

(d) 13 If you establish a long straddle using the options with an 95 exercise price, what is your dollar gain or loss if at expiration XYZ is still trading at 101 11/16?

a) $668.75 gain

b) $668.75 loss

c) $94.56 gain

d) $94.56 loss

e) $81.25 loss

(d) 14 If you establish a long strap using the options with an 95 exercise price, what is your dollar gain or loss if at expiration XYZ is still trading at 101 11/16?

a) $81.25 loss

b) $1,606.25 gain

c) $1,606.25 loss

d) $268.75 loss

e) $268.75 gain

(a) 15 If you establish a long strip using the options with a 95 exercise price, what is your dollar gain or loss if at expiration XYZ is still trading at 101 11/16?

a) $256.25 loss

b) $256.25 gain

c) $925.00 loss

d) $668.75 gain

e) $668.75 loss

(b) 16 If XYZ were trading at $90/share and you formed a bull money spread, what is your profit if XYZ is trading at $110 at expiration?

a) $912.50 loss

b) $87.50 gain

c) $87.50 loss

d) $1,000.00 gain

e) $1,000.00 loss

THE following INFORMATION IS FOR THE NEXT TWO PROBLEMS

A stock currently trades for $120 per share. Options on the stock are available with a strike price of $125. The options expire in 30 days. The risk free rate is 3% over this time period, and the expected volatility is 0.35.

(d) 17 Use the Black-Scholes option pricing model to calculate the price of a call option.

a) $5.935

b) $4.935

c) $3.935

d) $2.935

e) None of the above

(a) 18 Calculate the price of the put option.

a) $7.623

b) $8.623

c) $9.623

d) $10.623

e) None of the above

(a) 19 Assume that you have just sold a stock for a loss at a price of $75, for tax purposes. You still wish to maintain exposure to the sold stock. Suppose that you buy a call with a strike price of $70 and a price of $6.75. Calculate the effective price paid to repurchase the stock if the price after 35 days is $65.

a) $71.75

b) $76.75

c) $58.25

d) $81.75

e) None of the above

(d) 20 Assume that you have just sold a stock for a loss at a price of $75, for tax purposes. You still wish to maintain exposure to the sold stock. Suppose that you buy a call with a strike price of $70 and a price of $6.75. Calculate the effective price paid to repurchase the stock if the price after 35 days is $80.

a) $81.75

b) $73.25

c) $86.75

d) $76.75

e) None of the above

(d) 21 Assume that you have just sold a stock for a loss at a price of $75, for tax purposes. You still wish to maintain exposure to the sold stock. Suppose that you sell a put with a strike price of $80 and a price of $7.25. Calculate the effective price paid to repurchase the stock if the price after 35 days is $70.

a) $77.75

b) $87.25

c) $82.25

d) $72.75

e) None of the above

(a) 22 Assume that you have just sold a stock for a loss at a price of $75, for tax purposes. You still wish to maintain exposure to the sold stock. Suppose that you sell a put with a strike price of $80 and a price of $7.25. Calculate the effective price paid to repurchase the stock if the price after 35 days is $85.

a) $77.75

b) $87.25

c) $82.25

d) $72.75

e) None of the above.

USE THE FOLLOWING INFORMATION FOR THE NEXT 12 QUESTIONS

Consider the following information on put and call options for Citigroup

Strike Price Put Price Call Price

$32.50 $2.85 $1.65

(b) 23 Calculate the net value of a protective put position at a stock price at expiration of $20, and a stock price at expiration of $45.

a) $6.35, $18.85

b) $29.65, $42.15

c) $21.65, $34.15

d) $8, $8

e) -$8, -$8

(b) 24 A protective put is an appropriate strategy if

a) An investor wishes to generate additional income.

b) An investor wished to insure against a decline in share values.

c) An investor expected share prices to be volatile.

d) An investor expected share prices to remain in a trading range.

e) An investor expected share prices to be volatile, but was inclined to be bullish.

(c) 25 Calculate the net value of a covered call position at a stock price at expiration of $20, and a stock price at expiration of $45.

a) $6.35, $18.85

b) $29.65, $42.15

c) $21.65, $34.15

d) $8, $8

e) -$8, -$8

(a) 26 A covered call is an appropriate strategy if

a) An investor wishes to generate additional income.

b) An investor wished to insure against a decline in share values.

c) An investor expected share prices to be volatile.

d) An investor expected share prices to remain in a trading range.

e) An investor expected share prices to be volatile, but was inclined to be bullish.

(d) 27 Calculate the payoffs of a long straddle at a stock price at expiration of $20 and a stock price at expiration of $45.

a) $6.35, $18.85

b) $29.65, $42.15

c) $21.65, $34.15

d) $8, $8

e) -$8, -$8

(c) 28 A long straddle is an appropriate strategy if

a) An investor wishes to generate additional income.

b) An investor wished to insure against a decline in share values.

c) An investor expected share prices to be volatile.

d) An investor expected share prices to remain in a trading range.

e) An investor expected share prices to be volatile, but was inclined to be bullish.

(e) 29 Calculate the payoffs of a short straddle at a stock price at expiration of $20 and a stock price at expiration of $45.

a) $6.35, $18.85

b) $29.65, $42.15

c) $21.65, $34.15

d) $8, $8

e) -$8, -$8

(d) 30 A short straddle is an appropriate strategy if

a) An investor wishes to generate additional income.

b) An investor wished to insure against a decline in share values.

c) An investor expected share prices to be volatile.

d) An investor expected share prices to remain in a trading range.

e) An investor expected share prices to be volatile, but was inclined to be bullish.

(a) 31 Calculate the payoffs of a long strap at a stock price at expiration of $20 and a stock price at expiration of $45.

a) $6.35, $18.85

b) $29.65, $42.15

c) $21.65, $34.15

d) $8, $8

e) -$8, -$8

(e) 32 A long strap is an appropriate strategy if

a) An investor wishes to generate additional income.

b) An investor wished to insure against a decline in share values.

c) An investor expected share prices to be volatile.

d) An investor expected share prices to remain in a trading range.

e) An investor expected share prices to be volatile, but was inclined to be bullish.

CHAPTER 23

ANSWERS TO PROBLEMS

1 ($/DM)(.038)(62,500 DM) = $2,375.00

2 ($/DM)(.032)(62,500 DM) = $2,000.00

3 Cost = $2,375.00

Payoff = (.751 - .690)(62,500) = $3,750.00

Net gain = $3750.00 - $2,375.00 = $1,375.00

4 Cost = $2,375.00

Payoff = (.723 - .690)(62,500) = $2,062.50

Loss = $2,062.50 - $2,375.00 = -$312.50

5 Cost = $2,000.00

Payoff = (.665 - .653)(62,500) = $750.00

Loss = $750.00 - $2,000.00 = -$1,250.00

6 Cost = $2,000.00

Payoff = (.665 - .614)(62,500) = $3,187.50

Gain = $3,187.50 - $2,000.00 = $1,187.50

7 Long straddle: purchase one OCT 85 put and one OCT 85 call

Cost of one call = 16 3/4(100) = $1,675.00

Cost of one put = 1/8(100) = $12.50

Total cost = $1,687.50

Payoff on one call = 100(101 11/16 - 85) = $1,668.75

Payoff on one put = 0, expires out of the money

Net gain/loss = $1,668.75 - $1,687.50 = $18.75 loss

8 Long strap: purchase two OCT 85 calls and one OCT 85 put

Cost of 2 calls = 2(16.75(100) = $3,350.00

Cost of one put = 1/8(100) = $12.50

Total cost = $3,362.50

Payoff on 2 calls = 2(100)(101 11/16 - 85) = $3,375.00

Payoff on one put = 0, expires out of the money

Net gain/loss = $3,375.50 - $3,362.50 = $13.00 gain

9 Long strip: purchase one OCT 85 call and two OCT 85 puts

Cost of one call = 16 3/4(100) = $1,675.00

Cost of two puts = 2(1/8)(100) = $25.00

Total cost = $1,700.00

Payoff on one call = 100(101 11/16 - 85) = $1,668.75

Payoff on two puts = 0, expires out of the money

Net gain/loss = $1,668.75 - $1,700.00 = $31.25 loss

10 Long straddle: purchase one OCT 90 put and one OCT 90 call

Cost of one call = 12(100) = $1,200.00

Cost of one put = 3/8(100) = $37.50

Total cost = $1,237.50

Payoff on one call = 100(101 11/16 - 90) = $1,168.75

Payoff on one put = 0, expires out of the money

Net gain/loss = $1,168.75 - $1,237.50 = $68.75 loss

11 Long strap: purchase two OCT 90 calls and one OCT 90 put

Cost of 2 calls = 2(12.00(100) = $2,400.00

Cost of one put = 3/8(100) = $37.50

Total cost = $2,437.50

Payoff on 2 calls = 2(100)(101 11/16 - 90) = $2,337.50

Payoff on one put = 0, expires out of the money

Net gain/loss = $2,337.50 - $2,437.50 = $100.00 loss

12 Long strip: purchase one 90 call and two OCT 90 puts

Cost of one call = 12(100) = $1,200.00

Cost of two puts = 2(3/8)(100) = $75.00

Total cost = $1,275.00

Payoff on one call = 100(101 11/16 - 90) = $1,168.75

Payoff on two puts = 0, expires out of the money

Net gain/loss = $1,168.75 - $1,275.00 = $106.25 loss

13 Long straddle: purchase one OCT 95 put and one OCT 95 call

Cost of one call = 7 5/8(100) = $762.50

Cost of one put = 13/16(100) = $81.25

Total cost = $763.31

Payoff on one call = 100(101 11/16 - 95) = $668.75

Payoff on one put = 0, expires out of the money

Net gain/loss = $668.75 - $763.31 = $94.56 loss

14 Long strap: purchase two OCT 95 calls and one OCT 95 put

Cost of 2 calls = 2(7 5/8)(100) = $1,525.00

Cost of one put = 13/16(100) = $81.25

Total cost = $1,606.25

Payoff on 2 calls = 2(100)(101 11/16 - 95) = $1,337.50

Payoff on one put = 0, expires out of the money

Net gain/loss = $1,337.50 - $1,606.25 = $268.75 loss

15 Long strip: purchase one 95 call and two OCT 95 puts

Cost of one call = 7 5/8(100) = $762.50

Cost of two puts = 2(13/16)(100) = $162.50

Total cost = $925.00

Payoff on one call = 100(101 11/16 - 95) = $668.75

Payoff on two puts = 0, expires out of the money

Net gain/loss = $668.75 - $925.00 = $256.25 loss

16 Bull money spread = buy the in-the-money call, i.e., OCT 85 and sell the out-of-the-money call, i.e., OCT 95

Cost of buying OCT 85 call = 100(16 3/4) = $1,675.00

Proceeds from selling OCT 95 call = 100(7 5/8) = $762.50

Net cost $912.50

Payoff on OCT 85 call = 100(110 - 85) = $2,500.00

Payoff on OCT 95 call = 100(110 - 95) = ($1,500.00)

Net payoff = $2,500.00 - 1,500.00 = $1,000.00

Total gain/loss = $1,000.00 - 912.50 = $87.50 gain

17 Price using the B-S option pricing model

d1 = ln(120/125) + [(.03 + 5(.352))(.0833)]/(.35(.0833.5))

= -0.3288

d2 = -0.3288 - (.35(.0833.5)) = -0.4298

N(d1) = 0.3712

N(d2) = 0.3337

Call price = Pc = 120[0.3712 – 125(e-.03(.0833))(0.3337]

= $2.935

18 Put price = 2.935 + 125(e-.03(.0833)) – 120 = $7.623

19 The effective price is 65 + 6.75 = $71.75

The option expires worthless so your effective price is

the current price plus the option premium.

20 The effective price is 70 + 6.75 = $76.75

The option is exercised so your effective price is

the strike price plus the option premium.

21 The effective price is 80 – 7.25 = $72.75

The option is exercised so your effective price is

the strike price less the option premium.

22 The effective price is 85 – 7.25 = $77.75

The option expires worthless so your effective price is

the current price less the option premium.

23 At S = 20

Net value of protective put = (32.5 – 20) – 2.85 + 20 = 29.65

At S = 45

Net value of protective put = – 2.85 + 45 = 42.15

24 This strategy is appropriate if an investor wished to insure against a decline in share values.

25 At S = 20

Net value of covered call = 1.65 + 20 = 21.65

At S = 45

Net value of covered call = -(45 – 32.5) + 1.65 + 45 = 34.15

26 This strategy is appropriate if an investor wished to generate additional income.

27 At S = 20

Net payoff on a long straddle = (32.5 – 20) -1.65 – 2.85 = 8

At S = 45

Net payoff on a long straddle = (45 - 32.5) -1.65 – 2.85 = 8

28 This strategy is appropriate if an investor expected share prices to be volatile.

29 At S = 20

Net payoff on a short straddle = -(32.5 – 20) + 1.65 + 2.85 = -8

At S = 45

Net payoff on a long straddle = -(45 - 32.5) + 1.65 + 2.85 = -8

30 This strategy is appropriate if an investor expected share prices to remain in a trading range.

31 At S = 20

Net payoff on a long strap = (32.5 – 20) – (2)(1.65) – 2.85 = 6.35

At S = 45

Net payoff on a long straddle = (2)(45 - 32.5) – (2)(1.65) – 2.85 = 18.85

32 This strategy is appropriate if an investor expected share prices to be volatile.

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