Chapter Sixteen
Option Overwriting
KEY POINTS
Option overwriting is an increasingly popular portfolio activity by both individual and
institutional investors. This is the option activity with which stockbrokers and other
investment professionals are most familiar.
The writing of covered calls is an extremely important strategy that should be understood
by everyone involved in the market. Writing puts is less common but is very appropriate
for many investors.
Many portfolio managers prefer index options to individual equity options. Margin
considerations make this activity potentially involved, but also potentially very rich.
Options can also be written to buy stock at a price lower than the currently prevailing
price, or to sell stock at a higher than current price. In both cases the difference stems
from time value of money implications.
TEACHING CONSIDERATIONS
Having discussed principles of options and options pricing, the main point of this chapter
is to show how they are most commonly integrated into investment portfolios. Covered
calls are widely used, are very useful, and, with index options, are potentially more
sophisticated managerial tools than most people initially realize.
Go through an extended example showing how the margin rules provide different levels
of income from call writing depending on the collateral used.
The notion of improving on the market should be discussed in detail. Be sure, however,
to stress that this strategy does not in any way imply market inefficiency. Capturing the
time value involves a time value of money tradeoff.
ANSWERS TO QUESTIONS
1. Declining prices make put overwriting dangerous. Precipitous declines can be
disastrous to put writers, as some people discovered during the crash of 1987.
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Option Overwriting
2. The tradeoff is simple: the lower the striking price of a call, the higher its premium,
but the greater the likelihood of it being exercised. An option writer would earn
more premium by writing the APR 70, but would also have a higher risk of exercise.
3. An in-the-money put stands a greater chance of exercise than an out-of-the-money
put. The stock price must advance further with an in-the-money put before it ceases
to have intrinsic value.
4. Covered calls can be used in any portfolio that contains common stock. Writing
covered calls is attractive during periods of declining market prices or when market
prices are flat.
5. The portfolio manager need not worry about individual equity positions being called
away if index options are written. Also, the manager does not need to keep track of
many different positions; it is much easier to follow a single index such as the S&P
100.
6. This would be very reasonable and is often done. Both writing calls and buying puts
are bearish strategies, and there is no reason they cannot be done simultaneously.
7. With covered calls, the maximum loss is known and limited. With naked calls,
however, potential losses are theoretically unlimited. An unlimited loss would put
the charitable organization out of business.
8. Student response.
9. As stated in the text, the term “short put”" is somewhat ambiguous. For margin
purposes, a put is covered if the put writer has on deposit cash or cash equivalents
whose market value equals 100% of the strike price.
10. This makes sense to me. If the short put is exercised, the put writer must buy shares,
conceivably at a loss. But the short stock position would hedge this loss entirely.
The shares purchased could immediately be delivered against the short position.
11. With a fiduciary put, the exercise price is escrowed. In the event of exercise, the put
writer already has the funds to buy the stock. Non-fiduciary puts do not offer this
protection.
12. You cannot say that writing index puts is always preferable to writing individual
equity calls. Sometimes company-specific events make it appropriate to write
individual equity calls, sometimes a portfolio is too small to permit the writing of
even a single covered index call, and sometimes regulatory policy precludes the use
of index options.
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Option Overwriting
13. Student response.
14. If the plan is to buy stock, the option writer wants a high likelihood that the options
will be exercised. The more the option is in-the-money, the greater the likelihood of
exercise. So presumably the in-the-money put is preferred.
15. At expiration someone holds the valuable put. Whoever holds it when the music
stops is going to exercise it. Otherwise they would be throwing money away.
ANSWERS TO PROBLEMS
1.
9
61
70
61
2. Gain on stock: 400 x (77 3/8 - 70) = $2,950
Options expire worthless: gain = 2 x 2 1/2 x 100 = $500 Total gain = $3,450
3.
6 1/8
80
73 7/8
73 7/8
4.
5
62 ½
65
125
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Chapter Sixteen
Option Overwriting
5. a. You paid $27,000; income received was $3,000, and the capital gain was also
$3,000. Therefore,
HPR 
b.
30,000 - 27,000  3,000
 22.2%
27,000
3000
30000

 27000  0
60
(1  R )
(1  R ) 78
This gives a daily R of 0.00263. To annualize, multiply by 365:
.00263 x 365 = 96.0%
6. a. Maximum number of calls =
$10 million
 316 contracts
$100 x 315.66
316 contracts x $ 1 1/8 x 100 = $35,550
b. .15 x 315.66 x 100 x N
Plus
N x 1 1/8 x 100
Minus
(320.00 – 315.66) x 100 x N
=
4734.9 N
=
112.5 N
=
Total
(434.0 N)
4413.4 N
10 million = 4413.4 N
N = 2265
c. 50% of cash level: 2265 x .50 = 1132
7. You received 50 x 1 1/8 x 100 = 5625
At expiration you must pay (320.00 - 334.96) x 50 x 100 = $74,800
8.
25 3/4
20 3/4
120
109 5/8
5/8
125
219 1/4
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Chapter Sixteen
Option Overwriting
9. Presumably the stock will be used for collateral in a margin account. Stock counts
half the value of cash for margin purposes. You can then solve for N, the maximum
number of contracts that can be written:
N {[626.01 x 15% x 100]-[(626.01-600 x 100]+[37.50 x 100]} =.5 x $5 million
N = 237 contracts
237 contracts x $37.50 x 100 = $888,750
10. The market rose
660.00  626.01
 5.43%%
626.01
The portfolio should rise by 1.15 x 5.43% = 6.24%, or
$124,800
Gain on the 650 calls: 2 x 100 x ($27.5 – 10.0) =
Gain on the 600 puts: 2 x 100 x (22.5 - 0) =
total
3,500
4,500
$132,800
11. N{[626.01 x 15% x 100]-[(626.01-610) x 100]+[23.50 x 100]}= .5 x $5 million
N = 246 contracts
246 contracts x 23.50 x 100 = $578,100
12. N{[626.01 x 15% x 100]-[(680 – 626.01) x 100]+[7 x 100]} = .5 x $5 million
N = 532 contracts
532 contracts x $7 x 100 = $372,400
110