Management Chapter 13 Since call values are positively related

Solutions for Chapter 13: Questions and Problems

CHAPTER 13

AN INTRODUCTION TO

DERIVATIVE SECURITIES

Answers to Questions

1. Since call values are positively related to stock prices while put values are negatively

related, any action that causes a decline in stock price (e.g., a dividend) will have a

differential impact on calls and puts. Specifically, an impending dividend will boost put

values and depress call values.

Another way to consider the situation is to represent the difference between the

theoretical price of a call option (C) and the theoretical price of a put option (P) as C-P.

2. It is generally true that futures contracts are traded on exchanges whereas forward

contracts are done directly with a financial institution. Consequently, there is a liquid

market for most exchange traded futures whereas there is no guarantee of closing out a

forward position quickly or cheaply. The liquidity of futures comes at a price, though.

Solutions for Chapter 13: Questions and Problems

3. For forwards, calls and puts, what the long position gains, the short position loses, and

vice versa. However, while payoffs to forward positions are symmetric, payoffs to call

and put positions are asymmetric. That is to say, long and short forwards can gain as

much as they can lose, whereas long calls and puts have a gain potential dramatically

4. The important distinction is whether the option is a covered or uncovered position. If the

option is added to a portfolio that already contains the underlying asset (or something

highly correlated), then the option will frequently be a covered position and,

consequently, lower overall risk. For example, selling a call without owning the

5. Call options differ from forward contracts in that calls have unlimited upside potential

and limited downside potential, whereas the gains and losses from a forward contract are

both unlimited. Therefore, since call options do not have the downside potential of

Solutions for Chapter 13: Questions and Problems

6. Since options have nonlinear (kinked) payoffs, broad market movements may have

different relative effects on the value of a portfolio with options depending on whether

the market moves up or down. For example, a portfolio that is put-protected may not

7. A synthetic off-market forward contract with a forward price of $25 could be created

using put-call parity. Buying a call struck at $25 and selling a put struck at $25 assures

8. A long straddle consists of a long call and a long put on the same stock and profits from

dramatic price movement by the stock. A short straddle involves the sale of a call and a

9. A range forward is actually an option strategy that combines a long call and a short put

(or vice versa) through a costless transaction. Because the options will not have the same

striking price, the combination is classified as a range forward as opposed to an actual

forward, created by combining long and short options with the same striking price. It is

fair to view actual forwards as a special case (or zero-cost version) of range forwards.

Solutions for Chapter 13: Questions and Problems

– 95 –

CHAPTER 13

Answers to Problems

l(a).

(i). A long position in a forward with a contract price of $50.

Expiration Date Osprey Long Forward Initial Long

Stock Price (S) (X=$50) Payoff=S-50 Forward Premium Net Profit

25 ($25.00) $0.00 ($25.00)

30 ($20.00) $0.00 ($20.00)

(ii). A long position in a call option with a exercise price of $50 and a front-end

premium expense of $5.20.

Expiration Date Osprey Long Call (X=$50) Initial Long

Stock Price (S) Payoff = max (0,S-50) Call Premium Net Profit

25 $0.00 ($5.20) ($5.20)

30 $0.00 ($5.20) ($5.20)

Solutions for Chapter 13: Questions and Problems

– 96 –

(iii). A short position in a call option with an exercise price of $50 and a front-end

premium receipt of $5.20.

Expiration Date Osprey Short Call (X=$50) Initial Short

Stock Price (S) Payoff = -max (0,S-50) Call Premium Net Profit

25 $0.00 $5.20 $5.20

30 $0.00 $5.20 $5.20

l(b). (i). A long position in a forward with a contract price of $50.

Long Forward

$25.00

$20.00

(ii.) A long position in a call option with an exercise price of $50 and a front-end premium

expense of $5.20:

Long Call

$25.00

Solutions for Chapter 13: Questions and Problems

– 97 –

(iii.) A short position in a call option with an exercise price of $50 and a front-end

premium receipt of $5.20

Short Call

$25.00

$20.00

THE BREAKEVEN POINT FOR THE CALL OPTIONS IS $55.20.

l(c). The long position in a forward with a contract price of $50: The purchaser believes that the

price of Osprey Enterprises stock will be above $50.

2(a). (i). A short position in a forward with a contract price of $50.

Expiration Date Osprey Short Forward Initial Short

Stock Price (S) (X=$50) Payoff= S-50 Forward Premium Net Profit

25 $25.00 $0.00 $25 00

30 $20.00 $0.00 $20.00

Solutions for Chapter 13: Questions and Problems

– 98 –

(ii). A long position in a put option with a exercise price of $50 and a front-end premium

expense of $3.23.

Expiration Date Osprey Long Put (X=$50) Initial Long

Stock Price (S) Payoff= max (0,50-S) Put Premium Net Profit

25 $25.00 ($3.23) $21.77

(iii.) A short position in a put option with an exercise price of $50 and a front-end

premium receipt of $3.23.

Expiration Date Osprey Short Put (X=$50) Initial Short

Stock Price (S) Payoff= -max (0,50-S) Put Premium Net Profit

25 ($25.00) $3.23 ($21.77)

30 ($20.00) $3.23 ($16.77)

2(b). (i). A short position in a forward with a contract price of $50:

Short Forward

$25.00

$20.00

Solutions for Chapter 13: Questions and Problems

– 99 –

(ii). A long position in put option with an exercise price of $50 and front-end premium

expenses of $3.23:

Long Put

$25.00

$20.00

(iii). A short position in a put option with an exercise price of $50 and a front-end

premium receipt of $3.23:

Short Put

$25.00

$20.00

THE BREAKEVEN POINT FOR BOTH PUT OPTIONS IS $46.77.

2(c). A short position in a forward with a contract price of $50: The seller believes the price

of Osprey Enterprises will be below $50.

Solutions for Chapter 13: Questions and Problems

– 100 –

3(a). (i). A short position in a forward option with a exercise price of $50.

Expiration Date Osprey Short Forward (X=$50) Initial Short

Stock Price (S) Payoff =max (0, S-50) Forward Premium Net Profit

25 $25.00 $0.00 $50.00

30 $20.00 $0.00 $50.00

(ii). A long position in a put option with a exercise price of $50 and a front-end

premium expense of $3.23.

Expiration Date Osprey Long Put (X=$50) Initial Long Put

Stock Price (S) Payoff = max (0,50–S) Put Premium Net Profit

25 $25 00 ($3 23) $46.77

30 $20.00 ($3.23) $46.77

premium receipt of $5.20.

Expiration Date Osprey Short Call (X=$50) Initial Short

Stock Price (S) Payoff = -max (0,S-50) Call Premium Net Profit

25 $0.00 $5.20 $30.20

30 $0.00 $5.20 $35.20

Solutions for Chapter 13: Questions and Problems

– 101 –

3(b). (i). A short position in a forward with a contract price of $50:

Short Forward

$80.00

$70.00

(ii). A long position in a put option with an exercise price of $50 and a front-end

premium expense of $3.23:

Long Put

$80.00

$70.00

(iii). A short position in a call option with an exercise price of $50 and a front-end

premium expense of $5.20:

Short Call

$80.00

$70.00

3(c). F0,T = Call – Put + PV(Strike)

$50.00 = 5.20 – 3.23 + PV($50)

$48.03 = PV ($50)

Solutions for Chapter 13: Questions and Problems

– 102 –

4(a). With $13,700 to spend, one could:

(1) Purchase 100 shares of Breener Inc. stock (@ $137 per share); or

(2) Purchase 1370 call options with exercise price of $140

Potential payoff is unlimited in both cases, however the leverage that options provide will

translate into a higher percentage gain than purely purchasing stock. However, leverage

works both ways.

4(b). (1) Stock price increases to $155

a. Stock return = ($155 – $137)/$137 = 13.14%

4(c). Breakeven on this call option is $150. In other words, the writer of the call option will

receive the premium of $10, that is, the maximum amount the seller will receive. If the

seller does not currently own the stock, his/her loss is potentially unlimited.

5(a). Given:

Solutions for Chapter 13: Questions and Problems

– 103 –

(i). Buy one call option

Expiration Date Long Call (X=$40) Initial Long

XYZ Stock Price (S) Payoff = max (0,S-40) Call Premium Net Profit

20 $0.00 ($3.90) ($3.90)

25 $0.00 ($3.90) ($3.90)

$20.00

$15.00

(ii). Short one call option

Expiration Date Short Call (X=$40) Initial Short

XYZ Stock Price (S) Payoff =-max (0,S-40) Call Premium Net Profit

20 $0.00 $3.90 $3.90

25 $0.00 $3.90 $3.90

Solutions for Chapter 13: Questions and Problems

– 104 –

Short Call

$5.00

Both call positions will break even at a stock price of $43.90.

5(b). (i). Buy one put option

Expiration Date Long Put (X=$40) Initial Long

XYZ Stock Price (S) Payoff =max (0,40-S) Put Premium Net Profit

20 $20.00 ($1.45) $18.55

25 $15.00 ($1.45) $13.55

Long Put

$20.00

$15.00

Solutions for Chapter 13: Questions and Problems

– 105 –

(ii). Short one put option

Expiration Date Short Put (X=$40) Initial Short

XYZ Stock Price (S) Payoff =-max (0,40-S) Put Premium Net Profit

20 ($20.00) $1.45 ($18.55)

25 ($15.00) $1.45 ($13.55)

Short Put

$5.00

$0.00

Both put positions will break even at a stock price of $38.55.

5(c). Does Call – Put = S – PV(exercise price)?

Solutions for Chapter 13: Questions and Problems

– 106 –

6(a). To solve this problem, express put call parity in the following form:

C(exercise price) – P(exercise price) – PV(F) + PV(exercise price) = 0

Now we can equate put-call parity for two different options:

C(40) – P(40) – PV(F) + PV(40) = C(50) – P(50) – PV(F) + PV(50)

6(b). To solve this problem, express put call parity in the following form:

C(exercise price) – P(exercise price) – PV(F) + PV(exercise price) = 0

Solve for the share price PV(F) or S = $48/1.03 = $46.60

7. (a). Sum of T-bill, call & put

Payoff

60 T-bill

Call

Solutions for Chapter 13: Questions and Problems

7(b). With a price of $97 for 6 month T-bills, the 6-month risk-free rate is 100/97 -1 = 3.09%

8(a). Expiration Date Long Put (X=$55) Initial Long

Stock Price(S) Payoff = max(0,55-S) Put Premium Net Profit

35 $20.00 ($1.32) $53.68

40 $15.00 ($1.32) $53.68

75 $0.00 ($1.32) $73.68

Long Put

8(b). $80.00

$60.00

Solutions for Chapter 13: Questions and Problems

– 108 –

8(c). Expiration Date Short Call (X=$55) Initial Short

Stock Price(S) Payoff = max(0,S-55) Call Premium Net Profit

35 $0.00 $2.55 $37.55

40 $0.00 $2.55 $42.55

Short Call

8(d). $80.00

$60.00

9(a) Price of ARB Profit on Profit on Net Profit on

Stock at Expiration Initial Cost Call #1 Position Call #2 Position Total Position

40 ($1.72) $0.00 $0.00 ($1.72)

45 ($1.72) $0.00 $0.00 ($1.72)

Solutions for Chapter 13: Questions and Problems

– 109 –

9(b).

$8.00

$4.00

9(c). The user of this position is betting on low volatility (that prices will stay between

breakeven points). The holder has limited liability for substantial price declines and

unlimited liability for substantial price increases.

10. Consider the following put option transactions: (i) long one put #1 (exercise price $35);

(ii) short two puts #2 (exercise price $40), and (iii) long one put #3 (exercise price $45).

SAS Price Value of Value of Value of Cost of Net

(Expiration) Put #1 Put #2 Put #3 Options Profit

20 15.00 -40.00 25.00 (0.83) -0.83

25 10.00 -30.00 20.00 (0.83) -0.83