Chapter 17 Problems-
1. A three-month call option is the right to buy stock at $20. Currently the stock is selling for $22 and the call is selling for S5. You are considering buying 100 shares of the stock ($2,200) or one call option ($500).
a) If the price of the stock rises to $29 within three months, what would be the profits or losses on each position? What would be the percentage gains or losses?
b) If the price of the stock declines to $18 within three months, what would be the profits or losses on each position? What would be the percentage gains or losses?
c) If the price of the stock remained stable at $22, what would be the percentage gains or losses at the expiration of the call option?
d) If you compare purchasing the stock to purchasing the call, why do the percentage gains and losses differ?
2. A particular call is the option to buy stock at $25. It expires in six months and currently sells for $4 when the price of the stock is $26.
a) What is the intrinsic value of the call? What is the time premium paid for the call?
b) What will the value of this call be after six months if the price of the stock is $20? $25? $30? $40?
c) If the price of the stock rises to $40 at the expiration date of the call, what is the percentage increase in the value of the call? Does this example illustrate favorable leverage?
d) If an individual buys the stock and sells this call, what is the cash outflow (i.e., net cost) and what will the profit on the position he after six months if the price of the stock is $10? $15? $20? $25? $26? $30? $40?
e) If an individual sells this call naked, what will the profit or loss be on the position after six months if the price of the stock is $20? $26? $40?
3. What are the intrinsic values and time premiums paid for the following options?
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Option
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Price of the Option
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Price of the stock
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Calls: XYZ, Inc., 30
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$7.00
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$34
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XYZ, Inc., 35
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2.50
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34
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Puts: XYZ, Inc., 30
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1.25
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34
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XYZ, Inc., 35
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4.25
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34
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If the stock sells for $31 at the expiration date of the preceding options, what are the profits and losses for the writers and the buyers of these options?
4. The price of a stock is $51. You can buy a six-month call at $50 for $5 or a six-month put at $50 for $2.
a) What is the intrinsic value of the call?
b) What is the intrinsic value of the put?
c) What is the time premium paid for the call?
d) What is the time premium paid for the put?
e) If the price of the stock falls, what happens to the value of the put?
f) What is the maximum you could lose by selling the call covered?
g) What is the maximum possible profit if you sell the stock short?
After six months, the price of the stock is $58.
h) What is the value of the call?
i) What is the profit or loss from buying the put?
j) If you had sold the stock short six months earlier, what would your profit or loss be?
k) If you had sold the call covered, what would your profit or loss be?
Book: Mayo, Investments: An Introduction (with Stock-Trak Coupon), 12th ed., South-Western College Pub, ISBN 9781305638419.