Chapter 15 solution

SOLUTIONS MANUAL
CHAPTER 15
PUT AND CALL OPTIONS

PROBLEMS

Exercise (strike) price
1. A stock has an exercise (strike) price of $40.
a. If the stock price goes to $41.50, is the exchange likely to add a new strike price?
b. If the stock price goes to $42.75 is the exchange likely to add a new strike price?

15-1. a) No. For stocks over $25, the normal interval is $5, with a new strike price added at the halfway point or $42.50 (between $40 and $45). b) Yes, the stock price has equaled or exceeded the halfway point of $42.50

Option trading prices
2. Look at the option quotes in Table 15–2 on page 368.
a. What is the closing price of the common stock of SINGLE Systems?
b. What is the highest strike price listed?
c. What is the price of a December 20 call option?
d. What is the price of a January 22.50 put option?

15-2. a) $18.93 b) 25.00 c) 1.10 d) 4.20
Option trading terms
3. Assume a stock is selling for $66.75 with options available at 60, 65, and 70 strike prices. The 65 call option price is at $4.50.
a. What is the intrinsic value of the 65 call?
b. Is the 65 call in the money?
c. What is the speculative premium on the 65 call option?
d. What percentage does the speculative premium represent of common stock price?
e. Are the 60 and 70 call options in the money?

15-3. a) $66.75 − $65 = $1.75 b) Yes $66.75>$65 c) d) $2.75/$66.75 =4.12% e) The 60 call option is because the market price is above the strike price. The 70 is not.
Option trading terms
4. Assume a stock is selling for $48.50 with options available at 40, 50, and 60 strike prices. The 50 call option price is at 2.75.
a. What is the intrinsic value of the 50 call?
b. Is the 50 call in the money?
c. What is the speculative premium on the 50 call option?
d. What percentage of common stock price does the speculative premium represent?
e. Are the 40 and 60 call options in the money?

15-4. a) $48.50−$50 = −$1.50 or zero

b) No $48.50 is less than the strike price $50

c)

d) $4.25/$48.50 = 8.76%

e) The 40 call option is because the market price is above the strike price. The 60 is not.
Option trading terms
5. In the case of Deli USA in Table 15–6 on page 373:
a. What is the intrinsic value of the November 20 call option on October 19?
b. What is the total premium (option price) for the option on that date?
c. What is the speculative premium?

15-5. a) 24.05−20.00 = $4.05

b) 5.50

c)

Option trading terms
6. In the case of American Travel in Table 15–6 on page 373:
a. What is the intrinsic value of the November 32.50 call option on November 2nd?
b. How much is the speculative premium on that date?
c. By what percentage does the stock need to go up by expiration to break even on the call option?
15-6. a) 32.01 – 32.50 = –.49 b)

c) The break-even percent is equal to the speculative premium divided by the stock price. Speculative premium per day
7. Assume on May 1 you are considering a stock with three different expiration dates for the 60 call options. The percentage of the speculative premium for each date is as follows:
May 2.8%
August 6.7
November 10.9
Each contract expires at 11:59 p.m. Eastern time on the Saturday immediately following the third Friday of the expiration month. For purposes of this problem, assume the May option has 21 days to run, the August option has 112 days, and the November option has 203 days.
a. Compute the percentage speculative premium per day for each of the three dates.
b. From the viewpoint of a call option purchaser, which expiration date appears most attractive (all else being equal)?
c. From the viewpoint of a call option writer, which expiration date appears most attractive (all else being equal)?

15-7. a)

% Speculative Premium
Days to Expiration
% Speculative Premium/Day
May
60 2.8% 21
0.1333%/day
August
60
6.7%
112
0.0598%/day
November
60
10.9%
203
0.0537%/day
b) Since the purchaser likes the lowest premium per day, the November 60 should be selected. c) Since the call option writer favors the highest premium per day, the May 60 should be selected.

Leverage strategy
8. Assume New Tech, Inc., is trading at $48 and its November call option is $2.20. If the stock ends up at $60 and the option at $11, what is the leverage factor?

15-8. Call Option Premium Stock Prices
Beginning Ending Beginning Ending $2.20 $11 $48 $60

Naked call options
9. Assume an investor writes a call option for 100 shares at a strike price of 30 for a premium of 5.75. This is a naked option.
a. What would the gain or loss be if the stock closed at 26?
b. What would the break-even point be in terms of the closing price of the stock?

15-9. a) The gain would be 5.75 ($575) because the call would not be exercised below the strike price and the investor who writes the option keeps the premium of $5.75. b) The break-even point is at a stock price of 35.75. This represents the strike price plus the initial premium ($30 + 5.75 = $35.75).

Covered call options
10. Assume you purchase 100 shares of stock at $44 per share and wish to hedge your position by writing a 100-share call option on your holdings. The option has a 40 strike price and a premium of 8.50. If the stock is selling at 38 at the time of expiration, what will be the overall dollar gain or loss on this covered option play? (Consider the change in stock value as well as the gain or loss on the option.) Note that the stock does not pay a cash dividend.

15-10.

Covered call options
11. In problem 10, what would be the overall gain or loss if the stock ended up at
a. $41
b. $25
c. $57
d. $70
[Disregard the stock being called away in parts a, c, and d. Assume you will repurchase the options.]
15-11.

Commission considerations
12. Though commissions are not explicitly considered in problems 9 through 11, might they be significant?

15-12. Commissions tend to be significant in option transactions because of the many transactions that take place, and the relatively large size of the commissions relative to the option prices.

Put options
13. Assume a 40 July put option is purchased for 6.50 on a stock selling at $35 per share. If the stock ends up on expiration at 38.75, what will be the value of the put option?

15-13.

Protecting a short position with options
14. Assume you sell 100 shares of Bowie Corporation short at $72. You also buy a 70 call option for 5.25 to protect against the stock price going up.
a. If the stock ends up at $90, what will be your overall gain or loss?
b. If the stock ends up at $50, what will be your overall gain or loss?
c. If you have an unprotected short sale position (no call option), what is the most you could lose?

15-14.

Net loss ($325)

c) The loss potential is unlimited.

Protecting a short position with options
15. Assume you sell 100 shares of Alston Corporation short at $43. You also buy a 40 call option for $4.80 to protect against the stock price going up.
a. If the stock ends up at $60, what will be your overall gain or loss?
b. If the stock ends up at $20, what will be your overall gain or loss?
c. What is the most you can lose under this short sale–call option plan?
d. If you have an unprotected short sale position (no call option), what is the most you could lose?
e. Under the conditions described in part d, if you had a limit order to buy the stock and close out the position at $54, what is the most you could lose?

15-15. a)

c) The maximum loss is equal to the speculative premium on the call option or $1.80
For example, if the stock goes up to $150, the loss is still only $180 as indicated below:

d) The loss potential is unlimited

e)