282 Gitman/Joehnk/Smart • Fundamentals of Investing, Eleventh Edition
(b) If the market looks like it is heading down, sell all of the options and make money on the puts,
5. Answers will vary according to student choices.
◼ Solutions to Problems
1. Fundamental value = ($19 − $18) 100 = $100
5. A call option purchased for $600 with a $60 strike price can later be sold (or exercised) when the
underlying stock has a $75 price; given this, it will generate the following:
=−
= − −
= − =
− −
=
==
= =
Profit Value at expiration Purchase price
[($75 $60) 100] $600
$1,500 $600 $900
[($75 $60) 100] $600
HPR $600
$900 150%
$600
Annualized rate of return 150% (12/6) 300%
6. Cost of ETF puts = 1,000 $1.20 = $1,200
7. You would lose the cost of the puts, which would expire worthless
284 Gitman/Joehnk/Smart • Fundamentals of Investing, Eleventh Edition
If the stock price goes up to $90, Myles would make additional capital gains on the stock. Net of
the cost of the put, he made $23,400 on the entire transaction. He made an additional profit of
Even though out-of-the-money options are inexpensive, using those options to create a put hedge will
Profit:
600 shares of stock ($70 − $48.50)
$12,900
Value of six puts (6 100 $0)
0
Cost of six puts (6 100 $1)
−600
Total profit $12,300
Myles’s profit dropped from $15,900 to $12,300, for a net loss of $3,600 on the put hedge. This loss
is due to $3,000 of unprotected capital gains and the $600 cost of the put.
10. (a) (i) Market value of Chang’s portfolio $735,000
(ii) Current level of S&P 500 Index 1,470
(b) SCENARIO I: Market drops by 15%
Hedging using the six-month put with a strike price of 1,450
Current value of Chang’s portfolio
$735,000
Chang’s portfolio value after the 15% drop
$624,750
Chang’s loss in the portfolio
−$110,250
Chang’s gain using the put option [(1,450 − 1,249.5) 100] 5
$100,250
Less: Chang’s cost of the put option
$ 13,000
Chang’s net gain from the put option
$ 87,250
Chang’s total gain/loss
−$ 23,000
Chapter 14 Options: Puts and Calls 285
Hedging using the six-month put with a strike price of 1,390
Current Value of Chang’s Portfolio
$735,000
Chang’s Portfolio value after the 15% drop
$624,750
Chang’s Loss in the Portfolio
−$110,250
Chang’s gain using the Put Option [(1,390 − 1,249.5) 100] 5
$ 70,250
Less: Chang’s Cost of the Put Option
$ 2,250
Chang’s Net Gain from the Put Option
$ 68,000
Chang’s Total Gain/Loss
−$ 42,250
SCENARIO II: Market drops by 5%
Hedging using the six-month put with a strike price of 1,450
Current Value of Chang’s Portfolio
$735,000
Chang’s Portfolio value after the 5% drop
$698,250
Chang’s Loss in the Portfolio
−$ 36,750
Chang’s gain using the Put Option [(1,450 − 1,396.5) 100] 5
$ 26,750
Less: Chang’s Cost of the Put Option
$ 13,000
Chang’s Net Gain from the Put Option
$ 13,750
Chang’s Total Gain/Loss
−$ 23,000
Hedging using the six-month put with a strike price of 1,390
Current Value of Chang’s Portfolio
$735,000
Chang’s Portfolio value after the 5% drop
$698,250
Chang’s Loss in the Portfolio
−$ 36,750
Chang’s gain using the Put Option [(1,390 − 1,415.5) 100] 5
$ 0
Less: Chang’s Cost of the Put Option
$ 2,250
Chang does not exercise this Option
Chang’s Net Loss from the Put Option
−$ 2,250
Chang’s Total Gain/Loss
−$ 39,000
SCENARIO III: Market goes up 10%
Hedging using the six-month put with a strike price of 1,450
Current Value of Chang’s Portfolio
$735,000
Chang’s Portfolio value after the 10% increase
$808,500
Chang’s Gain in the Portfolio
$ 73,500
Chang’s gain using the Put Option [(1,450 − 1,617)] 100] 5
$ 0
Less: Chang’s Cost of the Put Option
$ 13,000
Chang’s Net Loss from the Put Option
−$ 13,000
Chapter 14 Options: Puts and Calls 287
©2011 Pearson Education, Inc. Publishing as Prentice Hall
Chang would be better off with the DJIA put option (strike price = 144) rather than the S&P 500
put option. This is because the DJIA puts provide a little more payoff when the market drops and
cost slightly less than the S&P 500 puts (compare $12,250 for the DJIA puts to $13,000 for
S&P 500 puts).
Chapter 14 Options: Puts and Calls 289
If the market goes up by 750 points:
Profit from 100 call option = 750 100
=
$75,000
Profit from 100 put options
=
$ 0
Gross profit from the straddle (ignoring transaction costs)
=
$75,000
Cost of straddle
=
−$43,000
Net profit (loss)
=
($32,000)
If the market stays at 11,200 points:
Profit from 100 call option
=
$ 0
Profit from 100 put options
=
$ 0
Gross profit from the straddle (ignoring transaction costs)
=
$ 0
Cost of straddle
=
−$ 43,000
Profit (loss)
=
($ 43,000)
(b) SHORT STRADDLE (you are the writer)
Profit of one July 112 call option = $2.65 100
=
$ 265
Profit of 100 July 112 call options = $265 100
=
$26,500
Profit of one July 112 put option = $1.65 100
=
$ 165
Profit of 100 Dec 93 put options = $165 100
=
$16,500
Profit from the short straddle = $26,500 + $16,500
=
$43,000
If the market falls by 750 points:
Loss from 100 call options
=
$ 0
Loss from 100 put options = 750 100
=
−$75,000
Total loss from the straddle
=
−$75,000
Sale of straddle
=
+43,000
Net profit (loss)
=
($32,000)
If the market goes up 750 points:
Loss from 100 call options = 750 100
=
−$75,000
Loss from 100 put options
=
0
Total loss from the straddle
=
−$75,000
Sale of straddle
=
+43,000
Net profit (loss)
=
($32,000)
If the market stays at 11,200 points:
Gain from 100 call options
=
$26,500
Gain from 100 put options
=
$16,500
Total gain from the straddle
=
$43,000
(c) Option straddles are extremely risky investment strategies; hence, an investor using this strategy
must completely understand the risk involved in the above. For larger movements in the market,
Chapter 14 Options: Puts and Calls 291
(c) Let’s examine this question on profitability in two different ways to show the benefits of leverage
with options. First, consider 100-share investments using each of the four vehicles and assuming
Hector is correct about the price appreciation, and the other figures in question 2 are correct.
Investment Vehicles
Per Share
Common Stock
$50 Call
$60 Call
Investment
$57.50
$ 8.00
$ 5.00
Dividends
1.20
0
0
Price in six months
80.00
30.00
20.00
Capital gain
22.50
22.00
15.00
Profits
23.70
22.00
15.00
Times 100 shares = Total profits
$2,370
$2,200
$1,500
Dollar profits are highest for the common stock. However, recall that HPR is highest for the $60 call
Investments
Totals
Common Stock
$50 Call
$60 Call
Investment
$5,750
$5,750
$ 5,750
Dividends
120
0
0
Value in six months
8,000
21,563
23,000
Capital gain
2,250
15,813
17,250
Total profits
$ 2,370
$15,813
$17,250
With equal dollar investment, the $60 call options would have the largest profit (in both dollar and
percentage terms); therefore, if Hector wants to maximize profits, he would invest in the $60 calls.
Case 14.2 Luke’s Quandary—To Hedge or Not to Hedge
This case illustrates a basic option strategy, hedging. Students review the hedging process, then analyze
the costs and benefits of a specific hedging situation.
292 Gitman/Joehnk/Smart • Fundamentals of Investing, Eleventh Edition
(a) Luke has an unrealized capital gain of 300 ($75 − $40) = $10,500, and he naturally wants to protect
the gain. One way to do this is to sell the stock and realize the actual gain. To do so in these
(b) If Luke purchases the three puts, the minimum before-tax profit he can realize is:
Current market value of the stock = $75 300 $22,500
*Note: Since the put is an out-of-the-money option, its purchase price is made up exclusively of
investment premium and as such is a sunk cost.
(c) If Luke purchases three options and the stock price goes to $100, the market value of his investments
at the expiration date of the option would be:
*Note: The puts will be worthless upon expiration; Luke will lose the cost of the puts.
Stock:
Value of stock = 300 $50 $15,000
Chapter 14 Options: Puts and Calls 293
tax treatment of long-term capital gains, the remainder of his profit, $5,850 from the puts, will be
subject to the short-term capital gains tax rate.
(d) Since Luke is uncertain about the market, he should seriously consider the use of puts to hedge the
profit he has already made on his investment. If he is wrong and the stock price continues to go up,
there is really no limit to the amount of profit he can make. On the other hand, if the stock price falls,
◼ Answer to Chapter Opening Problem
(a) (36.72 − 30.21) 2 million = $13 million.
◼ Outside Project
Chapter 14 What Is Investment Premium and How Does It Change?
Puts and calls have value because they allow the holder to buy or sell stocks at a fixed price. This “real”
value, however, is only part of the total premium for an in-the-money option, and it does not explain any
of the premium for an out-of-the-money option (where the real value is zero). Investment premium is the
amount by which the price of the option exceeds its real value. The size of the investment premium is a
function of several factors. The purpose of this project is to help you get a feeling for two of these factors:
the length of time to expiration and the amount of leverage in the option. What you should observe is that
investment premiums tend to increase as the expiration date extends farther into the future, and that they
are greatest when the strike price is nearest the current market price of the underlying security.
For simplicity, look at common stock puts and calls. In a current newspaper, The Wall Street Journal or
Barron’s, find the listing for the puts and calls of an actively traded company (in essence, pick just ONE
company with a lot of puts and calls written on it). One thing to make sure of is that there are a number of
options traded at most (or all) of the different strike prices. Also, the puts and calls at most (or all) of the
expiration dates should have prices given—if not, that means there’s no trading activity in those options.
See if you can organize the data into a schedule on a single sheet of paper so you can easily see what is
happening. One suggestion is to list strike prices down the page and expiration months across the top,
much like the newspaper listing; be sure to make one schedule for the puts and another for the calls
(i.e., don’t mix the puts and calls on one schedule). Now calculate the real values for each put and call—
use the formulas given in the text. Next, calculate the investment premium (in dollars) for each option.
Take a few minutes to study your schedule of investment premiums; how do they behave relative to the
length of time to expiration and the amount of leverage potential in the options? Do puts and calls
294 Gitman/Joehnk/Smart • Fundamentals of Investing, Eleventh Edition
behave the same? Comment on your findings. Briefly note how you might use such insights when
putting together an investment position in options.