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Explain how companies can hedge risks in their operating costs by using each of the following instruments.
Hypothetical examples are required.
�� Futures and forward contracts
�� Option contracts
�� Swap contracts
�� ing one asset and selling another. What is the hedge ratio and how is it determined?
�� ing one asset and selling another. What is the hedge ratio and how is it determined?
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ANSWER
(I)
A forward contract is a customized contract between two parties to buy or sell an asset at a speci�ed price
on a future date. A forward contract can be used for hedging or speculation, although its non-
standardized nature makes it particularly apt for hedging.
Example of a Forward Contract
Consider the following example of a forward contract. Assume that an agricultural producer has two
million bushels of corn to sell six months from now and is concerned about a potential decline in the price
of corn. It thus enters into a forward contract with its �nancial institution to sell two million bushels of corn
at a price of $4.30 per bushel in six months, with settlement on a cash basis.
In six months, the spot price of corn has three possibilities:
�� It is exactly $4.30 per bushel. In this case, no monies are owed by the producer or �nancial institution to
each other and the contract is closed.
�� It is higher than the contract price, say $5 per bushel. The producer owes the institution $1.4 million, or the
difference between the current spot price and the contracted rate of $4.30.
�� It is lower than the contract price, say $3.50 per bushel. The �nancial institution will pay the producer $1.6
million, or the difference between the contracted rate of $4.30 and the current spot price.
(II)
An options contract is an agreement between a buyer and seller that gives the purchaser of the option the
right to buy or sell a particular asset at a later date at an agreed upon price. Options contracts are often
used in securities, commodities, and real estate transactions.
For example, in a simple call options contract, a trading �rm may expect Company XYZ’s stock price to go
up to $90 in the next month. The trader sees that he can buy an options contract of Company XYZ at $4.50
with a strike price of $75 per share. The trader must pay the cost of the option ($4.50 X 100 shares = $450).
The stock price begins to rise as expected and stabilizes at $100. Prior to the expiry date on the options
contract, the trader executes the call option and buys the 100 shares of Company XYZ at $75, the strike
price on his options contract. He pays $7,500 for the stock. The trader can then sell his new stock on the
market for $10,000, making a $2,050 pro�t ($2,500 minus $450 for the options contract).
(III)
A swap is a derivative contract through which two parties exchange the cash �ows or liabilities from two
different �nancial instruments. Most swaps involve cash �ows based on a notional principal amount such
as a loan or bond, although the instrument can be almost anything. Usually, the principal does not change
hands. Each cash �ow comprises one leg of the swap. One cash �ow is generally �xed, while the other is
variable and based on a benchmark interest rate, �oating currency exchange rate or index price.
In an interest rate swap, the parties exchange cash �ows based on a notional principal amount (this
amount is not actually exchanged) in to hedge against interest rate risk or to speculate. For example,
imagine ABC Co. has just issued $1 million in �ve-year bonds with a variable annual interest rate de�ned as
the London Interbank Offered Rate (LIBOR) plus 1.3% (or 130 basis points). Also, assume that LIBOR is at
2.5% and ABC management is anxious about an interest rate rise.
EXAMPLE
The management team �nds another company, XYZ Inc., that is willing to pay ABC an annual rate of
LIBOR plus 1.3% on a notional principal of $1 million for �ve years. In other words, XYZ will fund ABC’s
interest payments on its latest bond issue. In exchange, ABC pays XYZ a �xed annual rate of 5% on a
Question: Explain how companies can hedge risks in their operating cos
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notional value of $1 million for �ve years. ABC bene�ts from the swap if rates rise signi�cantly over the next
�ve years. XYZ bene�ts if rates fall, stay �at or rise only gradually.
Below are two scenarios for this interest rate swap: LIBOR rises 0.75% per year and LIBOR rises 0.25% per
year.
Scenario 1
If LIBOR rises by 0.75% per year, Company ABC’s total interest payments to its bondholders over the �ve-
year period amount to $225,000. Let’s break down the calculation:
Libor +
1.30%
Variable Interest Paid by XYZ
to ABC
5% Interest Paid by ABC
to XYZ
ABC’s
Gain
XYZ’s
Loss
Year
1
3.80% $38,000 $50,000 -$12,000 $12,000
Year
2
4.55% $45,500 $50,000 -$4,500 $4,500
Year
3
5.30% $53,000 $50,000 $3,000 -$3,000
Year
4
6.05% $60,500 $50,000 $10,500 -$10,500
Year
5
6.80% $68,000 $50,000 $18,000 -$18,000
Total $15,000 ($15,000)
In this scenario, ABC did well because its interest rate was �xed at 5% through the swap. ABC paid $15,000
less than it would have with the variable rate. XYZ’s forecast was incorrect, and the company lost $15,000
through the swap because rates rose faster than it had expected.
Scenario 2
In the second scenario, LIBOR rises by 0.25% per year:
Libor +
1.30%
Variable Interest Paid by XYZ
to ABC
5% Interest Paid by ABC
to XYZ
ABC’s
Gain
XYZ’s
Loss
Year
1
3.80% $38,000 $50,000 ($12,000) $12,000
Year
2
4.05% $40,500 $50,000 ($9,500) $9,500
Year
3
4.30% $43,000 $50,000 ($7,000) $7,000
Year
4
4.55% $45,500 $50,000 ($4,500) $4,500
Year
5
4.80% $48,000 $50,000 ($2,000) $2,000
Total ($35,000) $35,000
In this case, ABC would have been better off by not engaging in the swap because interest rates rose
slowly. XYZ pro�ted $35,000 by engaging in the swap because its forecast was correct.
This example does not account for the other bene�ts ABC might have received by engaging in the swap.
For example, perhaps the company needed another loan, but lenders were unwilling to do that unless the
interest obligations on its other bonds were �xed.
In most cases, the two parties would act through a bank or other intermediary, which would take a cut of
the swap. Whether it is advantageous for two entities to enter into an interest rate swap depends on their
comparative advantage in �xed or �oating-rate lending markets.
(IV)
The hedge ratio compares the value of a position protected through the use of a hedge with the size of
the entire position itself. A hedge ratio may also be a comparison of the value of futures contracts
purchased or sold to the value of the cash commodity being hedged.
Futures contracts are essentially investment vehicles that let the investor lock in a price for a physical asset
at some point in the future.
EXAMPLE
Assume that an airline company fears that the price of jet fuel will rise after the crude oil market has been
trading at depressed levels. The airline company expects to purchase 15 million gallons of jet fuel over the
next year, and wishes to hedge its purchase price. Assume that the correlation between crude oil futures
and the spot price of jet fuel is 0.95, which is a high degree of correlation.
Further assume the standard deviation of crude oil futures and spot jet fuel price is 6% and 3%,
respectively. Therefore, the minimum variance hedge ratio is 0.475, or (0.95 * (3% / 6%)). The NYMEX
Western Texas Intermediate (WTI) crude oil futures contract has a contract size of 1,000 barrels or 42,000
gallons. The optimal number of contracts is calculated to be 170 contracts, or (0.475 * 15 million) / 42,000.
Therefore, the airline company would purchase 170 NYMEX WTI crude oil futures contracts.
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