<<

. 123
( 193 .)



>>

of plunging. Most of these naked puts seem to have who put 50 to 70 H.B. Shaine clients into stock-index
been options on the Standard & Poor™s 100 stock index, options, says he told clients that the strategy™s risk was
which are traded on the CBOE. When stocks crashed, “moderate barring a nuclear attack or a crash like
many traders with unhedged positions got margin calls 1929.” It wasn™t speculative. The market could go up
or down, but not substantially up or down. If the crash
for several times their original investment.
had only been as bad as ™29, he adds, “we would have
made it.”
THE ˜PUT™ STRATEGY
The losses were especially sharp in “naked, out-of-the- SOURCE: Abridged from The Wall Street Journal, December 2, 1987.
money puts.” A seller of puts agrees to buy stock or Reprinted by permission of The Wall Street Journal, © 1987 Dow
stock-index contracts at a set price before the put Jones & Company, Inc. All Rights Reserved Worldwide.




could fall in price. Suppose a six-month maturity call option with exercise price of $70 sells
for $10, and the semiannual interest rate is 2%. Consider the following three strategies for in-
vesting a sum of $7,000. Remember that Microsoft does not pay any dividends.
Strategy A: Purchase 100 shares of Microsoft
Strategy B: Purchase 700 call options on Microsoft with exercise price $70. (This would
require 7 contracts, each for 100 shares.)
Strategy C: Purchase 100 call options for $1,000. Invest the remaining $6,000 in six-
month T-bills, to earn 2% interest.
Let us trace the possible values of these three portfolios when the options expire in six
months as a function of Microsoft stock price at that time.
501
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




502 Part FIVE Derivative Markets


Microsoft Price

Portfolio $65 $70 $75 $80 $85 $90
A: 100 shares stock $6,500 $7,000 $7,500 $8,000 $ 8,500 $ 9,000
B: 700 call options 0 0 3,500 7,000 10,500 14,000
C: 100 calls plus
$6,000 in T-bills 6,120 6,120 6,620 7,120 7,620 8,120


Portfolio A will be worth 100 times the share value of Microsoft. Portfolio B is worthless
unless Microsoft sells for more than the exercise price of the call. Once that point is reached,
the portfolio is worth 700 times the excess of the stock price over the exercise price. Finally,
portfolio C is worth $6,120 from the investment in T-bills ($6,000 1.02 $6,120) plus any
profits from the 100 call options. Remember that each of these portfolios involves the same
$7,000 initial investment. The rates of return on these three portfolios are as follows:

Microsoft Price

Portfolio $65 $70 $75 $80 $85 $90
A: 100 shares stock 7.1% 0.0% 7.1% 14.3% 21.4% 28.6%
B: 700 call options 100.0 100.0 50.0 0.0 50.0 100.0
C: 100 calls plus
$6,000 in T-bills 12.6 12.6 5.4 1.7 8.9 16.0


These rates of return are graphed in Figure 14.6.
Comparing the returns of portfolios B and C to those of the simple investment in Microsoft
stock represented by portfolio A, we see that options offer two interesting features. First, an
option offers leverage. Compare the returns of portfolios B and A. When Microsoft stock fares
poorly, ending anywhere below $70, the value of portfolio B falls precipitously to zero”a rate
of return of negative 100%. Conversely, modest increases in the rate of return on the stock re-
sult in disproportionate increases in the option rate of return. For example, a 5.9% increase in
the stock price from $85 to $90 would increase the rate of return on the call from 50% to




F I G U R E 14.6 100
B: All options
Rate of return to three
80
strategies
60
Rate of return (%)




A: All stock
40
C: Calls plus bills
20
0
90 Stock price
70 75 80 85
65
20
40
60
80
100
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




EXCE L Applications www.mhhe.com/bkm


> Options, Stock, and Lending


An Excel model based on the Microsoft example discussed in the text is shown below. The model
allows you to use any variety of options, stock, and lending or borrowing with a set investment
amount and demonstrates the investment flexibility of options.
You can learn more about this spreadsheet model by using the interactive version available on
our website at www.mhhe.com/bkm.
A B C D E F G H I J K
1 Chapter 14 Microsoft Example
2 Comparison of Options, Equity and Combined Bills and Options
3
4 Basic Data for Spreadsheet
5 Current Stock Price $70
6 Options Price $10
7 Exercise Price $70 Ending Stock Price
8 T-Bill Rate Annual 2%
9 Ending Stock Price $80
10 Ending Value Per Option $10 Option 65 70 75 80 85 90
11 Investment Amount $7,000 Total Ending Value $7,000 0 0 3500 7000 10500 14000
12
13 Options Only Strategy
14 Options Purchased 700
15 Ending Value per Option $10 Stock 65 70 75 80 85 90
16 Total Ending Value $7,000 Total Ending Value $8,000 6500 7000 7500 8000 8500 9000
17 Total Profit $0
18 Return on Investment 0.00%
19
20 Stock Only Strategy Bills & Option 65 70 75 80 85 90
21 Shares Purchased 100 Total Ending Value $7,120 6120 6120 6620 7120 7620 8120
22 Total Ending Value $8,000
23 Total Profit $1,000
24 Return on Investment 14.29%
25 Addit. Combinations 65 70 75 80 85 90
26 Bills and Options Strategy Total Ending Value $7,424 3,824 4,024 5,724 7,424 9,124 10,824
27 Number of Options Purchased 100
28 Investment in Options $1,000
29 Investment in Bills $6,000
30 Ending Value of the Options $1,000 Option 65 70 75 80 85 90
31 Ending Value on the Bills $6,120 Return 0.00% -100.00% -100.00% -50.00% 0.00% 50.00% 100.00%
32 Total Ending Value $7,120
33 Total Profit $120
34 Return on Investment 1.71%
35 Stock 65 70 75 80 85 90
36 Additional Combinations: Return 14.29% -7.14% 0.00% 7.14% 14.29% 21.43% 28.57%
37 Bills, Options and Stock
38 Total Investment Amount $7,000
39 Options Purchased 300
40 Options Investment $3,000 Bill & Option 65 70 75 80 85 90
41 Stock Purchased 40 Return 1.71% -12.57% -12.57% -5.43% 1.71% 8.86% 16.00%
42 Stock Investment $2,800
43 Bill Investment $1,200
44 Ending Value of the Options $3,000
45 Ending Value of the Stock $3,200 Addit. Combinations 65 70 75 80 85 90
46 Ending Value of the Bills 1224 Return 6.06% -45.37% -42.51% -18.23% 6.06% 30.34% 54.63%
47 Total Ending Value $7,424
48 Total Profit $424
49 Return on Investment 6.06%
50
51 Average Returns for Sample Returns
52 Options -16.67%
53 Stock 10.71%
54 Bill & Options -0.67%
55 Additional Combinations -2.51%
56
57 St. Deviation for Sample Returns
58 Options 81.65%
59 Stock 13.36%
60 Bill & Options 11.66%
61 Additional Combinations 40.25%




100%. In this sense, calls are a levered investment on the stock. Their values respond more
than proportionately to changes in the stock value.
Figure 14.6 vividly illustrates this point. For stock prices above $70, the slope of the all-
option portfolio is far steeper than that of the all-stock portfolio, reflecting its greater propor-
tional sensitivity to the value of the underlying security. The leverage factor is the reason that
investors (illegally) exploiting inside information commonly choose options as their invest-
ment vehicle.
The potential insurance value of options is the second interesting feature, as portfolio C
shows. The T-bill plus option portfolio cannot be worth less than $6,120 after six months, as
the option can always be left to expire worthless. The worst possible rate of return on portfo-
lio C is 12.6%, compared to a (theoretically) worst possible rate of return of Microsoft stock
of 100% if the company were to go bankrupt. Of course, this insurance comes at a price:
503
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




504 Part FIVE Derivative Markets


When Microsoft does well, portfolio C does not perform as well as portfolio A, the all-stock
portfolio. For stock prices above $70, portfolio C underperforms portfolio A by about 12.6
percentage points.
This simple example makes an important point. While options can be used by speculators
as effectively leveraged stock positions, as in portfolio B, they also can be used by investors
who desire to tailor their risk exposures in creative ways, as in portfolio C. For example, the
call plus T-bills strategy of portfolio C provides a rate of return profile quite unlike that of the
stock alone. The absolute limitation on downside risk is a novel and attractive feature of this
strategy. In the next section we will discuss several option strategies that provide other novel
risk profiles that might be attractive to hedgers and other investors.


Option Strategies
An unlimited variety of payoff patterns can be achieved by combining puts and calls with var-
ious exercise prices. Below we explain the motivation and structure of some of the more pop-
ular ones.

Protective put Imagine you would like to invest in a stock, but you are unwilling to bear
potential losses beyond some given level. Investing in the stock alone seems risky to you be-
cause in principle you could lose all the money you invest. You might consider instead in-
vesting in stock and purchasing a put option on the stock.
Table 14.1 shows the total value of your portfolio at option expiration. Whatever happens
to the stock price, you are guaranteed a payoff equal to the put option™s exercise price because
the put gives you the right to sell the share for the exercise price even if the stock price is be-
low that value.


Suppose the strike price is X $55 and the stock is selling for $52 at option expiration. Then
the value of your total portfolio is $55: The stock is worth $52 and the value of the expiring
14.3 EXAMPLE put option is
Protective Put X ST $55 $52 $3
Another way to look at it is that you are holding the stock and a put contract giving you the
right to sell the stock for $55. If S $55, you can still sell the stock for $55 by exercising the
put. On the other hand, if the stock price is above $55, say $59, then the right to sell a share
at $55 is worthless. You allow the put to expire unexercised, ending up with a share of stock
worth ST $59.



Figure 14.7 illustrates the payoff and profit to this protective put strategy. The solid line in
protective put
Figure 14.7C is the total payoff. The dashed line is displaced downward by the cost of estab-
An asset combined
lishing the position, S0 P. Notice that potential losses are limited.
with a put option that
It is instructive to compare the profit on the protective put strategy with that of the stock in-
guarantees minimum
proceeds equal to the vestment. For simplicity, consider an at-the-money protective put, so that X S0. Figure 14.8
put™s exercise price. compares the profits for the two strategies. The profit on the stock is zero if the stock price re-
mains unchanged, and ST S0. It rises or falls by $1 for every dollar swing in the ultimate
stock price. The profit on the protective put is negative and equal to the cost of the put if ST is
below S0. The profit on the protective put increases one for one with increases in the stock
price once the stock price exceeds X.
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




505
14 Options Markets


ST X ST X

<<

. 123
( 193 .)



>>