Value at

date T

A

Cash flow from

The “hedge”D

operations

long forward

G – S T

S T – K

Cash flow from operations

plus a long forward = G – K

G – K
		S T
	K

	B
C

a cash inflow of G˜

S, and the forward contract, which at maturity has a cash inflow

T

˜K,eliminates the oil price risk. This is illustrated in Exhibit 22.2 by the hori-

of S

T

zontal line (with the height of G K,which is the sum of cash flow from operations

(line AB) and the cash flow from the forward (line CD). In this case, the firm can

comfortably acquire oil in the spot market at date T,and it knows that the price it pays,

˜

S, will be hedged by the gains or losses on the forward contract, as Example 22.3

T

indicates.⁴

Example 22.3:Hedging Oil Price Risk with a Maturity-Matched

Forward Contract

Assume that Metallgesellschaft has an obligation to deliver 1.25 million barrels of oil one

year out at a fixed price of $25 per barrel.How can it hedge this obligation in the forward

market and eliminate its exposure to crude oil prices?

Answer:The cash needed to acquire the oil to meet this obligation is uncertain.

Metallgesellschaft can eliminate the variability in its profit arising from this uncertainty by

acquiring 1.25 million barrels of oil for forward delivery one year from now.If the date 0

⁴It is also possible to view a forward contract as simply locking in a price for oil needed for

operations in the future. Obviously, this eliminates oil price risk. In many instances, however, the

commodity delivered in the forward market is not precisely suited for the oil refiner’s operations.

Delivery might be at an inconvenient location or the oil might not be the right grade for the refiner’s

operations. In these cases, the cash flow algebra used above tells us that if a slightly different product

exists in the spot market, the forward contract described above will do a good job of hedging its price

risk. The oil received as a result of the maturation of the forward contract may be sold to a third party.

The oil needed for future operations, which may be slightly different in quality, delivery location, and so

forth, can be bought in the spot market from a fourth party at approximately the same price. In this case,

the position in the forward contract still hedges oil price risk, albeit imperfectly. Further discussion of

this topic is covered under cross-hedging in Section 22.9.

Grinblatt1573Titman: Financial	VI. Risk Management	22. The Practice of Hedging	© The McGraw1573Hill
Markets and Corporate			Companies, 2002
Strategy, Second Edition

Chapter 22

The Practice of Hedging

781

forward price is less than $25 per barrel, Metallgesellschaft will profit with certainty.If the

forward price is greater than $25 per barrel, it will lose money with certainty.In either case,

its profit (or loss) from operations and hedging will be known at date 0.

The Information in Forward Prices.In addition to being useful hedging instru-

ments, forward prices provide critical information about profitability. Regardless of

Metallgesellschaft’s opinion about the spot oil price one year from now, the company

loses money, in a present value sense, if it charges its customers less than the forward

oil price and makes money if it charges its customers more than that oil price.

During the Persian Gulf War of 1990–91, when spot oil prices were close to $40

a barrel, several financial intermediaries began to introduce oil-linked bonds. One set

of these bonds, which had a maturity of about 2 years, carried a relatively high rate of

interest and paid principal equal to the minimum of (1) four times the price of oil at

maturity and (2) $100. The bonds were selling at approximately $100 each. Many

investors looked at these bonds and found them attractive because of their high inter-

est rate and the belief that, at $40 a barrel, it was virtually a sure thing that the bond

would pay off $100 in principal in two years. However, to understand the risk of not

getting back the $100 principal on these bonds, it was important that investors look at

the two-year forward price for oil(which was about $23 a barrel) rather than the $40

spot price. Four times the two-year forward price equals $92, which indicates that the

return of $100 in principal was much less of a sure thing.

Using Forward Contracts to Hedge Currency Obligations

The last subsection illustrated how to use forward contracts to hedge commodity price

risk, in that case, oil. Corporations and financial institutions also commonly use for-

ward contracts to hedge currency risk. Corporations generally enter into currency for-

ward contracts with their commercial banker. Such contracts are customized for the

amount and required maturity date and can be purchased in almost all major curren-

cies. Maturities can range from a few days to several years (long-dated forwards),

although the average maturity is one year.

Because forward contracts are fairly simple and can be customized, they are the

hedging tool most commonly used by corporate foreign exchange managers. Example

22.4 illustrates a typical foreign exchange hedge with currency forwards.

Example 22.4:Hedging Currency Risk with a Currency Forward Contract

Assume that Disney wants to hedge the currency risk associated with the expected losses

of Euro-Disneyland (outside Paris) over the next year.The expected loss is 1 billion French

francs.How can Disney accomplish this, assuming that the current French franc/U.S.dollar

spot rate is FFr 5 per US$ and the forward rate for currency exchanged six months from

now is FFr 5.15/US$?

Answer:To approximate the 1 billion French franc loss spread evenly over the entire year,

assume that the entire loss occurs in six months.Thus, if Disney agrees to buy FFr 1 billion

six months from now, it will have to pay US$1 billion/5.15 or approximately US$194.2 mil-

lion.The US$194.2 million is the locked-in loss.If the dollar depreciates to FFr 4 per US$

six months from now, the FFr 1 billion loss becomes US$250 million, but this is offset by a

gain of US$55.8 million on the forward contract:

1billion

US$ US$194.2 millionUS$55.8 million

4

Grinblatt1575Titman: Financial	VI. Risk Management	22. The Practice of Hedging	© The McGraw1575Hill
Markets and Corporate			Companies, 2002
Strategy, Second Edition

782Part VIRisk Management

Currency forward rates are determined by the ratios of the gross interest rates in

the two countries. Specifically, we know from Chapter 7 that in the absence of arbi-

trage, the forward currency rate F(for example, FFrUS$) is related to the current

0

exchange rate (or spot rate) Sby the covered interest parity equation

0

F1r^T

⁰foreign

S1r

0domestic

where

T years to forward settlement

r annually compounded zero-coupon bond yield for a maturity of T

Because forward rates are determined by the relative interest rates in the two countries,

it should not be surprising that currency hedges also can be executed with positions in

domestic and foreign debt instruments. Amoney market hedge, for example, involves

borrowing one currency on a short-term basis and converting it to another currency

immediately. In the absence of transaction costs and arbitrage, a money market hedge

is exactly like a forward contract. Also, like a forward contract, it eliminates the uncer-

tainty associated with exchange rate changes.⁵

Example 22.5:Hedging with a Money Market Hedge

How can Disney (see Example 22.4) use a money market hedge to ensure that the expected

FFr 1 billion loss from Euro-Disneyland over the next year will not grow larger in U.S.dollars

as a consequence of a depreciating dollar? Assume as before that the current spot rate is

FFr 5 per US$.To be consistent with the six-month forward rate of FFr 5.15 per US$, it is

necessary to assume that six-month dollar LIBOR is 6 percent per annum, while six-month

French franc LIBOR is 12.114 percent per annum, and six months is 182 days.

Answer:The money market hedge requires the following three steps:

1.	Borrow U.S.dollars in the LIBOR market today for six months.
2.	Exchange the U.S.dollars for French francs.
3.	Invest the French francs for six months in French franc LIBOR deposits.

In six months, the maturing US$ LIBOR loan will require repayment in dollars, while the

maturing FFr LIBOR investment will provide the necessary French francs that the U.S.com-

pany wanted to purchase.Hence, if the dollars borrowed in step 1 is

FFr 1 billion

US$188.46 million

182

51.12114FFr/US$

360

exactly 1 billion FFr will be received in six months and the Eurodollar loan in step 1 will

require payment of

182

US$194.2 millionUS$188.46 million1.06

360

Note that the US$194.2 million payout in six months is the same amount locked

in as a loss with the forward rate because the interest rates chosen were consistent with

the covered interest parity relation.

⁵The equivalence of hedging with forward contracts and a money market hedge is known as the

covered interest parity relation. See Chapter 7 for more detail.

Grinblatt1577Titman: Financial	VI. Risk Management	22. The Practice of Hedging	© The McGraw1577Hill
Markets and Corporate			Companies, 2002
Strategy, Second Edition

Chapter 22

The Practice of Hedging

783