This document discusses various hedging strategies using futures contracts. It describes long and short hedges to lock in future purchase or sale prices of assets. Arguments in favor of hedging include reducing risks from market variables, while arguments against include shareholders already being diversified and increased risk if competitors do not hedge. Examples illustrate how futures hedging works for both long and short hedges. The document also discusses cross hedging using different but correlated assets, calculating optimal hedge ratios, and hedging equity portfolios using stock index futures.

1. Chapter 3
Hedging Strategies Using
Futures
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2. Long & Short Hedges
A long futures hedge is appropriate when
you know you will purchase an asset in
the future and want to lock in the price
A short futures hedge is appropriate
when you know you will sell an asset in
the future and want to lock in the price
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3. Arguments in Favor of Hedging
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Companies should focus on the main
business they are in and take steps to
minimize risks arising from interest rates,
exchange rates, and other market variables

4. Arguments against Hedging
Shareholders are usually well diversified and
can make their own hedging decisions
It may increase risk to hedge when
competitors do not
Explaining a situation where there is a loss on
the hedge and a gain on the underlying can
be difficult
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5. Short Hedge for Sale of an Asset
A short hedge is appropriate when the hedger
already owns an asset an expects to sell it at
some time in the future.
Eg: It is May 15. An oil producer has
negotiated a contract to sell 1 million barrels
of crude oil in August 15. Quotes:
Spot price : $60 per barrel
August oil futures price:$59 per barrel
1contract = 1000 barrels
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6. Illustration
The oil producer can hedge with the following
transactions:
May 15: Short 1000 August futures contracts
on crude oil
August 15: Close out futures position
Suppose spot price on August 15 proves to be $55.
- Gain in futures: $59-55 = $4 per barrel or $4million.
- Sales in spot market = $ 55m
- Net = $55+ $4 = $59million
-Effective price = $ 59 million/1 million barrels = $59/b
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7. What if price of oil on August 15 proves
to be $65 per barrel?
Calculate gain/loss in futures position;
What is the net outcomes?
What is the effective price?
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8. Long Hedge for Purchase of an Asset
A long hedge is appropriate when a company
knows it will have to purchase a certain asset
in the future and wants to lock in a price now.
Eg: A copper fabricator knows it will need
100,000 pounds of copper on May 15. The
spot price of copper is 340 cents/pound and
the May futures price is 320 cents/pound.
Each contract is for the delivery of 25,000
pound of copper.
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9. Illustration
The copper fabricator can hedge with the following
transactions:
now: Take a long position in 4 May futures
contracts on copper
May 15: Close out the position.
Suppose that the price of copper on May 15 is 325
cents.
-Gain in futures: (3.25-3.20)*100,000= $5000
- Buying cost in spot: $ 325,000
- Net outcomes: ($325,000) + 5000= (320,000)
- Effective price: 320 cents per pound
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10. What if price of copper on May 15
proves to be 305 cents per pound?
Calculate gain/loss in futures position;
What is the net outcomes?
What is the effective price?
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11. Cross hedging
Occurs when 2 assets are different.
Hedge ratio is the ratio of the size of the
position taken in futures contracts to the size
of the exposure.
Hedge ratio=1 if underlying asset in futures
contract is the same as the asset being
hedge
When cross hedging is used, setting the
hedge ratio equal to 1 is not always optimal.
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12. Optimal Hedge Ratio (page 57)
Proportion of the exposure that should optimally be
hedged is
where
σS is the standard deviation of ∆S, the change in the
spot price during the hedging period,
σF is the standard deviation of ∆F, the change in the
futures price during the hedging period
ρ is the coefficient of correlation between ∆S and ∆F.
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F
S
h
σ
σ
ρ=*

13. Optimal Number of Contracts
QA Size of position being hedged (units)
QF Size of one futures contract (units)
VA Value of position being hedged (=spot price time QA)
VF Value of one futures contract (=futures price times QF)
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Optimal number of contracts if
no tailing adjustment
F
A
Q
Qh*
=
Optimal number of contracts
after tailing adjustment to allow
or daily settlement of futures
F
A
V
Vh*
=

14. Example (Pages 59-60)
Airline will purchase 2 million gallons of jet
fuel in one month and hedges using heating
oil futures
From historical data σF =0.0313, σS =0.0263,
and ρ= 0.928
14
77770
03130
02630
9280 .
.
.
.*
=×=h

15. Example continued
The size of one heating oil contract is 42,000 gallons
The spot price is 1.94 and the futures price is 1.99
(both dollars per gallon) so that
Optimal number of contracts assuming no daily
settlement
Optimal number of contracts after tailing
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033700042000000277770 .,,,. =×=
103658083000880377770 .,,,. =×=
5808300042991
00088030000002941
,,.
,,,,.
=×=
=×=
F
A
V
V

16. Hedging Using Index Futures
(Page 61)
To hedge the risk in a portfolio the
number of contracts that should be
shorted is
where VA is the value of the portfolio, β is
its beta, and VF is the value of one
futures contract
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F
A
V
V
β

17. Example
S&P 500 futures price is 1,000
Value of Portfolio is $5 million
Beta of portfolio is 1.5
What position in futures contracts on the S&P
500 is necessary to hedge the portfolio?
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18. Changing Beta
What position is necessary to reduce
the beta of the portfolio to 0.75?
What position is necessary to increase
the beta of the portfolio to 2.0?
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19. Why Hedge Equity Returns
May want to be out of the market for a while.
Hedging avoids the costs of selling and
repurchasing the portfolio
Suppose stocks in your portfolio have an
average beta of 1.0, but you feel they have
been chosen well and will outperform the
market in both good and bad times. Hedging
ensures that the return you earn is the risk-
free return plus the excess return of your
portfolio over the market.
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