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TA B L E 14.1
ST ST
Payoff to protective Stock
X ST
put strategy Put 0
X ST
Total




F I G U R E 14.7
Payoff
Value of a protective
put position at
expiration

A: Stock




ST
X


Payoff




B: Put
X




ST
X

Payoff and profit

Payoff


C: Protective Profit
put

X


ST
X

X “ (S0 + P)
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




506 Part FIVE Derivative Markets




F I G U R E 14.8 Stock
Profits
Protective put versus
stock investment Protective put
portfolio




ST
S0 = X
“P




“S0




Figure 14.8 makes it clear that the protective put offers some insurance against stock price
declines in that it limits losses. As we shall see in the next chapter, protective put strategies are
the conceptual basis for the portfolio insurance industry. The cost of the protection is that, in
the case of stock price increases, your profit is reduced by the cost of the put, which turned out
to be unneeded.
This example also shows that despite the common perception that “derivatives mean risk,”
derivative securities can be used effectively for risk management. In fact, such risk manage-
risk management
ment is becoming accepted as part of the fiduciary responsibility of financial managers. Indeed,
Strategies to limit the
in a recent court case, Brane v. Roth, a company™s board of directors was successfully sued for
risk of a portfolio.
failing to use derivatives to hedge the price risk of grain held in storage. Such hedging might
have been accomplished using protective puts. Some observers believe that this case will soon
lead to a broad legal obligation for firms to use derivatives and other techniques to manage risk.

Covered calls A covered call position is the purchase of a share of stock with the si-
covered call
multaneous sale of a call on that stock. The position is “covered” because the potential obli-
Writing a call on an
gation to deliver the stock is covered by the stock held in the portfolio. Writing an option
asset together with
without an offsetting stock position is called by contrast naked option writing. The payoff to
buying the asset.
a covered call, presented in Table 14.2, equals the stock value minus the payoff of the call. The
call payoff is subtracted because the covered call position involves issuing a call to another in-
vestor who can choose to exercise it to profit at your expense.
The solid line in Figure 14.9C illustrates the payoff pattern. You see that the total position is
worth ST when the stock price at time T is below X and rises to a maximum of X when ST exceeds
X. In essence, the sale of the call option means the call writer has sold the claim to any stock
value above X in return for the initial premium (the call price). Therefore, at expiration, the po-
sition is worth at most X. The dashed line of Figure 14.9C is the net profit to the covered call.
Writing covered call options has been a popular investment strategy among institutional in-
vestors. Consider the managers of a fund invested largely in stocks. They might find it
appealing to write calls on some or all of the stock in order to boost income by the premiums
collected. Although they thereby forfeit potential capital gains should the stock price rise
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




507
14 Options Markets


ST X ST X
TA B L E 14.2
ST ST
Payoff to a covered Payoff of stock
X)
call Payoff of call 0 (ST
ST X
Total




F I G U R E 14.9
Payoff
Value of a covered
call position at
expiration
A: Stock




ST
X

Payoff




ST
X


B: Written call




Payoff and profit




C: Covered call

Payoff
X


Profit

ST
X

(S0 C)




above the exercise price, if they view X as the price at which they plan to sell the stock any-
way, then the call may be viewed as enforcing a kind of “sell discipline.” The written call
guarantees the stock sale will occur as planned.
Bodie’Kane’Marcus: V. Derivative Markets 14. Options Markets © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




508 Part FIVE Derivative Markets


Assume a pension fund holds 1,000 shares of GXX stock, with a current price of $130 per
share. Suppose management intends to sell all 1,000 shares if the share price hits $140,
14.4 EXAMPLE and a call expiring in 90 days with an exercise price of $140 currently sells for $5. By writ-
ing 10 GXX call contracts (100 shares each) the fund can pick up $5,000 in extra income.
Covered Call
The fund would lose its share of profits from any movement of GXX stock above $140 per
share, but given that it would have sold its shares at $140, it would not have realized those
profits anyway.



Straddle A long straddle is established by buying both a call and a put on a stock, each with
straddle
the same exercise price, X, and the same expiration date, T. Straddles are useful strategies for in-
A combination of a
vestors who believe a stock will move a lot in price but are uncertain about the direction of the
call and a put, each
move. For example, suppose you believe an important court case that will make or break a com-
with the same
exercise price and pany is about to be settled, and the market is not yet aware of the situation. The stock will either
expiration date. double in value if the case is settled favorably or will drop by half if the settlement goes against
the company. The straddle position will do well regardless of the outcome because its value is
highest when the stock price makes extreme upward or downward moves from X.
The worst-case scenario for a straddle is no movement in the stock price. If ST equals X,
both the call and the put expire worthless, and the investor™s outlay for the purchase of both
options is lost. Straddle positions basically are bets on volatility. An investor who establishes
a straddle must view the stock as more volatile than the market does. Conversely, investors
who write straddles”selling both a call and a put”must believe the market is less volatile.
They accept the option premiums now, hoping the stock price will not change much before op-
tion expiration.
The payoff to a straddle is presented in Table 14.3. The solid line of Figure 14.10C illus-
trates this payoff. Notice the portfolio payoff is always positive, except at the one point where
the portfolio has zero value, ST X. You might wonder why all investors don™t pursue such a
no-lose strategy. The straddle requires that both the put and call be purchased. The value of the
portfolio at expiration, while never negative, still must exceed the initial cash outlay for a
straddle investor to clear a profit.
The dashed line of Figure 14.10C is the profit to the straddle. The profit line lies below the
payoff line by the cost of purchasing the straddle, P C. It is clear from the diagram that the
straddle position generates a loss unless the stock price deviates substantially from X. The stock
price must depart from X by the total amount expended to purchase the call and the put in or-
der for the purchaser of the straddle to clear a profit.
Strips and straps are variations of straddles. A strip is two puts and one call on a security
with the same exercise price and maturity date. A strap is two calls and one put.


>
3. Graph the profit and payoff diagrams for strips and straps.
Concept
CHECK
Spreads A spread is a combination of two or more call options (or two or more puts) on
the same stock with differing exercise prices or times to maturity. Some options are bought,
spread while others are sold, or written. A vertical or money spread involves the purchase of one
option and the simultaneous sale of another with a different exercise price. A horizontal or
A combination of two
time spread refers to the sale and purchase of options with differing expiration dates.
or more call options
or put options on the Consider a money spread in which one call option is bought at an exercise price X1, while
same asset with another call with identical expiration date, but higher exercise price, X2, is written. The payoff
differing exercise
to this position will be the difference in the value of the call held and the value of the call writ-
prices or times to
ten, as in Table 14.4.

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