Ross et al.: Fundamentals
of Corporate Finance, Sixth
Edition, Alternate EditionVIII. Topics in Corporate
Finance- Risk Management: An
Introduction to Financial
Engineering
(^814) © The McGraw−Hill
Companies, 2002
The Payoff Profile
The payoff profileis the key to understanding how forward contracts and other con-
tracts that we discuss later are used to hedge financial risks. In general, a payoff profile
is a plot showing the gains and losses on a contract that result from unexpected price
changes. For example, suppose we were examining a forward contract on oil. Based on
our discussion, the buyer of the forward contract is obligated to accept delivery of a
specified quantity of oil at a future date and pay a set price. Part A of Figure 23.7 shows
the resulting payoff profile on the forward contract from the buyer’s perspective.
What Figure 23.7 shows is that, as oil prices increase, the buyer of the forward con-
tract benefits by having locked in a lower-than-market price. If oil prices decrease, then
the buyer loses because that buyer ends up paying a higher-than-market price. For the
seller of the forward contract, things are simply reversed. The payoff profile of the seller
is illustrated in Part B of Figure 23.7.
Hedging with Forwards
To illustrate how forward contracts can be used to hedge, we consider the case of a pub-
lic utility that uses oil to generate power. The prices that our utility can charge are regu-
lated and cannot be changed rapidly. As a result, sudden increases in oil prices are a
source of financial risk.^2 The utility’s risk profile is illustrated in Figure 23.8.
If we compare the risk profile in Figure 23.8 to the buyer’s payoff profile on a for-
ward contract shown in Figure 23.7, we see what the utility needs to do. The payoff pro-
file for the buyer of a forward contract on oil is exactly the opposite of the utility’s risk
profile with respect to oil. If the utility buys a forward contract, its exposure to unex-
pected changes in oil prices will be eliminated. This result is shown in Figure 23.9.
Our public utility example illustrates the fundamental approach to managing finan-
cial risk. We first identify the firm’s exposure to financial risk using a risk profile. We
then try to find a financial arrangement, such as a forward contract, that has an offset-
ting payoff profile.
A Caveat Figure 23.9 shows that the utility’s net exposure to oil price fluctuations is
zero. If oil prices rise, then the gains on the forward contract will offset the damage from
increased costs. However, if oil prices decline, the benefit from lower costs will be off-
set by losses on the forward contract.
For example, in January of 2000, America Online (AOL) announced that it would
buy Time Warner, forming the company we now know as AOL Time Warner. Following
the announcement, stock in Time Warner soared to more than $90 per share. Time
Warner Vice Chairman (and well-known media mogul) Ted Turner had previously en-
tered into a hedging arrangement under which he locked in a maximum possible price
of $30 per share on 4 million shares of stock he owned. As a result, he missed out on
$240 million in gains—good thing he owned over 100 million shares in all, up more
than $2.8 billion on the day!
This example illustrates an important thing to remember about hedging with forward
contracts. Price fluctuations can be good or bad, depending on which way they go. If we
hedge with forward contracts, we do eliminate the risk associated with an adverse price
change. However, we also eliminate the potential gain from a favorable move. You
might wonder if we couldn’t somehow just hedge against unfavorable moves. We can,
and we describe how in a subsequent section.
788 PART EIGHT Topics in Corporate Finance
(^2) Actually, many utilities are allowed to automatically pass on oil price increases.
payoff profile
A plot showing the gains
and losses that will
occur on a contract as
the result of unexpected
price changes.