Introduction to Corporate Finance

ParT 2: ValuaTION, rISk aNd reTurN

Again, the seller’s perspective is just the opposite of the buyer’s. The seller earns a maximum net gain

of $7 if the option expires worthless, because the share price exceeds $75 on the expiration date, and the

seller faces a maximum net loss of $68 if the company goes bankrupt and its shares become worthless.

example

Jennifer sells a put option on Albany Lighting Systems

(ALS) shares to Murray. The option’s strike price is $65,

and it expires in one month. Murray pays Jennifer a

premium of $5 for the option. One month later, ALS

sells for $45 per share. Murray purchases a share of

ALS in the open market for $45 and immediately

exercises his option to sell it to Jennifer for $65

(or Jennifer and Murray could agree to settle their

contract by having Jennifer pay Murray $20). The

payoff on Murray’s option is $20, or $15 on a net basis.

Jennifer loses $20 on the deal, or just $15, taking into

account the $5 premium she received up-front.

We must now clarify an important point. Thus far, all our discussions about options payoffs have

assumed that each option buyer or seller had what traders refer to as a naked option position. A naked call

option, for example, occurs when an investor buys or sells an option on a share without already owning the

underlying share. Similarly, when a trader buys or sells a put option without owning the underlying shares,

the trader creates a naked put position. Buying or selling naked options is an act of pure speculation.

Investors who buy naked calls believe that the share price will rise. Investors who sell naked calls believe

the opposite. Similarly, buyers of naked puts expect the share price to fall, and sellers take the opposite view.

But many options trades do not involve this kind of speculation. Investors who own particular shares

may purchase put options on those shares, not because they expect share prices to decline, but because

they want protection in the event that they do. Executives who own shares of their companies’ shares

may sell call options, not because they think that the share’s future gains are limited, but because they

are willing to give up potential profits on their shares in exchange for current income. To understand this

proposition, we need to examine payoff diagrams for portfolios of options and other securities.

8-2c PaYOFFS FOr POrTFOlIOS OF OPTIONS aNd OTHer

SeCurITIeS

Experienced options traders know that by combining different types of options, they can construct

a wide range of portfolios with unusual payoff structures. Think about what happens if an investor

simultaneously buys a call option and a put option on the same underlying shares and with the same

exercise price. We’ve seen before that the call option pays off handsomely if the share price rises, whereas

the put option is most profitable if the share price falls. By combining both into one portfolio, an investor

has a position that can make money whether the share price rises or falls.

Suppose that Cybil cannot decide whether the shares of Internet Phones Company (IPC) will rise

or fall from their current value of $30. Suppose Cybil decides to purchase a call option and a put option

on IPC shares, both having a strike price of $30 and an expiration date of 20 April. Cybil pays premiums

of $4.50 for the call and $3.50 for the put, for a total cost of $8. Figure 8.3 illustrates Cybil’s position.

The payoff of her portfolio equals $0 if IPC’s share price is $30 on 20 April, and if that occurs, Cybil will

experience a net loss of $8. But if the share price is higher or lower than $30 on 20 April, at least one of

Cybil’s options will be in the money. On a net basis, Cybil makes a profit if the IPC share price either

falls below $22 or rises above $38, but she does not have to take a view on which outcome is more likely.

naked option position
To buy or to sell an option,
without a simultaneous
position in the underlying
asset