Problems
1. Writing Call Options. A call option on Illinois stock specifies an exercise price of $38. Today’s price
of the stock is $40. The premium on the call option is $5. Assume the option will not be exercised
until maturity, if at all. Complete the following table:
Assumed Stock Price at the Time Net Profit or Loss per Share to Be Earned
the Call Option Is About to Expire by the Writer (Seller) of the Call Option
$37
$39
$41
$43
$45
$48
ANSWER:
Assumed Stock Price at the Time Net Profit or Loss per Share to Be Earned
the Call Option Is About to Expire by the Writer (Seller) of the Call Option
$37 $5
2. Purchasing Call Options. A call option on Michigan stock specifies an exercise price of $55. Today
the stock’s price is $54 per share. The premium on the call option is $3. Assume the option will not be
exercised until maturity, if at all. Complete the following table for a speculator who purchases the call
option:
Assumed Stock Price at the Time Net Profit or Loss per Share
the Call Option Is About to Expire to Be Earned by the Speculator
$50
$52
$54
$56
$58
$60
$62
ANSWER:
Assumed Stock Price at the Time Net Profit or Loss per Share
the Call Option Is About to Expire to Be Earned by the Speculator
$50 –$3
3. Purchasing Put Options. A put option on Iowa stock specifies an exercise price of $71. Today the
stock’s price is $68. The premium on the put option is $8. Assume the option will not be exercised
until maturity, if at all. Complete the following table for a speculator who purchases the put option
(and currently does not own the stock):
Assumed Stock Price at the Time Net Profit or Loss per Share
the Put Option Is About to Expire to Be Earned by the Speculator
$60
$64
$68
$70
$72
$74
$76
ANSWER:
Assumed Stock Price at the Time Net Profit or Loss per Share
the Put Option Is About to Expire to Be Earned by the Speculator
$60 $3
$64 –$1
4. Writing Put Options. A put option on Indiana stock specifies an exercise price of $23. Today the
stock’s price is $24. The premium on the put option is $3. Assume the option will not be exercised
until maturity, if at all. Complete the following table:
Assumed Stock Price at the Time Net Profit or Loss per Share to Be Earned
the Put Option Is About to Expire by the Writer (Seller) of the Put Option
$20
$21
$22
$23
$24
$25
$26
ANSWER:
Assumed Stock Price at the Time Net Profit or Loss per Share to Be Earned
the Put Option Is About to Expire by the Writer (Seller) of the Put Option
$20 $0
$21 $1
5. Covered Call Strategy.
a. Evanston Insurance Inc. has purchased shares of Stock E at $50 per share. It will sell the stock in
six months. It considers using a strategy of covered call writing to partially hedge its position in
this stock. The exercise price is $53, the expiration date is six months, and the premium on the
call option is $2. Complete the following table.
Profit or Loss per Share Profit or Loss per Share
Possible Price of Stock E If a Covered Call Strategy If a Covered Call Strategy
in 6 Months Is Used Is Not Used
$47
$50
$52
$55
$57
$60
ANSWER:
Profit or Loss per Share Profit or Loss per Share
Possible Price of Stock E If a Covered Call Strategy If a Covered Call Strategy
in 6 Months Is Used Is Not Used
$47 –$1 –$3
$50 $2 $0
b. Assume that each of the six stock prices in the table’s first column has an equal probability of
occurring. Compare the probability distribution of the profits (or losses) per share when using
covered call writing versus not using it. Would you recommend covered call writing in this
example? Explain.
ANSWER: There is a 50 percent chance that covered call writing will result in an additional $2 per
6. Put Options on Futures. Purdue Savings and Loan Association purchased a put option on Treasury
bond futures with a September delivery date and an exercise price of 91-16. Assume the put option
has a premium of 1-32. Assume that the price of the Treasury bond futures decreases to 88-16. Should
Purdue exercise the option or let the option expire? What is Purdue’s net gain or loss after accounting
for the premium paid on the option?
ANSWER: Purdue should purchase a T-bond futures contract at 88-16 and exercise its put option to
7. Call Options on Futures. Wisconsin Inc. purchased a call option on Treasury bond futures at a
premium of 2-00. The exercise price is 92-08. If the price of the Treasury bond futures rises to 93-08,
should Wisconsin Inc. exercise the call option or let it expire? What is Wisconsin’s net gain or loss
after accounting for the premium paid on the option?
ANSWER: Wisconsin Inc. should exercise its call option in order to purchase Treasury bond futures
8. Call Options on Futures. DePaul Insurance Company purchased a call option on an S&P 500 futures
contract. The option premium is quoted as $6. The exercise price is $1,430. Assume the index on the
futures contract becomes $1,440. Should DePaul exercise the call option or let it expire? What is the
net gain or loss to DePaul after accounting for the premium paid for the option?
ANSWER: DePaul should exercise its call option by purchasing the S&P 500 futures index for
9. Covered Call Strategy. Coral Inc. has purchased shares of stock M at $28 per share. It will sell the
stock in six months. It considers using a strategy of covered call writing to partially hedge its position
in this stock. The exercise price is $32, the expiration date is six months, and the premium on the call
option is $2.50. Complete the following table:
Possible Price of Stock M Profit or Loss per Share If a
in 6 Months Covered Call Strategy Is Used
$25
$28
$33
$36
ANSWER:
Possible Price of Stock M Profit or Loss per Share If a
in 6 Months Covered Call Strategy Is Used
10. Hedging with Bond Futures. Smart Savings Bank desired to hedge its interest rate risk. It was
considering two possibilities: (1) sell Treasury bond futures at a price of 94-00, or (2) purchase a put
option on Treasury bond futures. At the time, the price of Treasury bond futures was 95-00. The face
value of Treasury bond futures was $100,000. The put option premium was 2-00, and the exercise
price was 94-00. Just before the option expired, the Treasury bond futures price was 91-00, and Smart
Savings Bank would have exercised the put option at that time, if at all. This is also the time when it
would offset its futures position, if it had sold futures. Determine the net gain to Smart Savings Bank
if it had sold Treasury bond futures versus if it had purchased a put option on Treasury bond futures.
Which alternative would have been more favorable, based on the situation that occurred?
ANSWER:
Results from Selling T-Bond Futures:
Results from Purchasing a Put Option on T-Bond Futures:
The results from selling the T-Bond futures were more favorable than the results from purchasing a
put option on T-bond futures.
Flow of Funds Exercise
Hedging With Options Contracts
Carson Company would like to acquire Vinnet Inc., a publicly traded firm in the same industry. Vinnet’s
stock price is currently much lower than the prices of other firms in the industry, because it is inefficiently
managed. Carson believes that it could restructure Vinnet’s operations and improve its performance. It is
about to contact Vinnet to determine whether Vinnet will agree to an acquisition. Carson is somewhat
concerned that investors may learn of its plans and buy Vinnet stock in anticipation that Carson will need
to pay a high premium (perhaps a 30 percent premium above the prevailing stock price) in order to
complete the acquisition. Carson decides to call a bank about its risk, as the bank has a brokerage
subsidiary that can help it hedge with stock options.
a. How can Carson use stock options to reduce its exposure to this risk? Are there any limitations to
this strategy, given that Carson will ultimately have to buy most or all of the Vinnet stock?
Carson would not be able to buy call options on all of the stock. In addition, by purchasing a
b. Describe the maximum possible loss that may be directly incurred by Carson as a result of
engaging in this strategy.
c. Explain the results of the strategy you offered in the previous question if Vinnet plans to avoid the
acquisition attempt by Carson.
Carson would still have the call options. It may be able to profit from the strategy if it can sell the