Introduction to Corporate Finance

ParT 2: ValuaTION, rISk aNd reTurN

The red line in Figure 8.1 shows a payoff diagram for the option buyer, or the long position. This picture is a

classic in finance, known as the hockey-stick diagram. It shows that the option, at worst, will be worth $0, and

at best, the option’s value is unlimited. The blue line in the figure represents the investor’s net payoff. The net

payoff line appears $8 lower than the solid line, reflecting the $8 premium the investor paid to acquire the

option. On a net basis, the holder of the call option makes a profit when the price of the shares exceeds $83.^7

Figure 8.1 also shows the call’s payoff from the seller’s perspective, or the short position. Options

are a zero-sum game, meaning that profits on the long position represent losses on the short side, and

vice-versa. In this part of the figure, the red line illustrates that the seller’s payoff equals $0 when the

share price is below $75. It decreases as the share price rises above $75. The incentive for the seller

to engage in this transaction is the $8 premium, as shown by the blue line. If the option expires out of

7 Notice that when the share price is above $75 but below $83, it still makes sense for the investor to exercise his option, or to sell it, because

it reduces the investor’s losses. For example, if the share price at expiration equals $80, the option payoff is $5, reducing the net loss to –$3.

The careful reader may notice that we are committing a major sin, for finance professors anyway, by comparing the $8 premium paid up-front

to the payoff received three months later. At this point, ignoring the time value of money in the graphs is relatively harmless, but rest assured,

we take that into account later when we determine the price of an option.

net payoff
The difference between
the payoff received when
the option expires and the
premium paid to acquire the
option

FIGure 8.1 PAYOFF OF A CALL OPTION WITH X = $75

The top graph illustrates, from the option buyer’s perspective,

how a call option’s payoff varies as the underlying share price

changes. The red line illustrates that the call option’s payoff is

$0 if the share price is $75 or less on the expiration date, but the

option’s payoff rises dollar for dollar with the share price as the

share price rises above $75. The blue line illustrates the option’s

net payoff after taking into account the $8 premium that the buyer

paid to acquire the option. The breakeven point occurs when the

share price is $83 ($75 + $8). At higher prices, the buyer earns

a profit, and at lower prices, the buyer loses money. The buyer’s

maximum loss is $8, and the maximum gain is unlimited.

The lower graph illustrates the seller’s perspective. The red line

illustrates that the call option’s payoff is $0 if the share price is

$75 or less on the expiration date, but the option’s payoff falls

dollar for dollar with the share price as the share price rises

above $75. The blue line illustrates the option’s net payoff after

taking into account the $8 premium that the seller received from

the buyer. The breakeven point occurs when the share price

is $83. At lower prices, the seller earns a profit, and at higher

prices, the seller loses money. The seller’s maximum profit is $8,

and the maximum loss is unlimited.

8

Call payoff ($)

Share price on expiration date ($)

option premium

25 50 75 100 125 150

83

0

–25

–50

–75

Payoff

Net payoff

Share price on expiration date ($)

option premium 100 125 150

25 50

–8 83

Call payoff ($)

0

25

50

75

Payoff

Net payoff

75