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Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013
Hedging Strategies UsingFutures
Chapter 3
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Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013
Long & Short Hedges
A long futures hedge is appropriate whenyou know you will purchase an asset in
the future and want to lock in the priceA short futures hedge is appropriatewhen you know you will sell an asset inthe future & want to lock in the price
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Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013
Arguments in Favor of Hedging
Companies should focus on the mainbusiness they are in and take steps to
minimize risks arising from interestrates, exchange rates, and othermarket variables
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Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013
Arguments against Hedging
Shareholders are usually well diversifiedand can make their own hedging decisions
It may increase risk to hedge whencompetitors do not
Explaining a situation where there is a loss
on the hedge and a gain on the underlyingcan be difficult
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Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013
Convergence of Futures to Spot(Hedge initiated at time t1and closed out at time t2;
Figure 3.1, page 56)
Time
Spot
Price
Futures
Price
t1 t2
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Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013
Basis Risk
Basis is the difference betweenspot & futures
Basis risk arises because ofthe uncertainty about the basiswhen the hedge is closed out
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Long Hedge for Purchase of an Asset
Define
F1: Futures price at time hedge is set up
F2: Futures price at time asset is purchased
S2 : Asset price at time of purchaseb2 : Basis at time of purchase
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Cost of asset S2
Gain on Futures F2F1
Net amount paid S2 (F2F1) =F1+ b2
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Short Hedge for Sale of an Asset
Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013 8
Define
F1: Futures price at time hedge is set up
F2: Futures price at time asset is soldS2 : Asset price at time of sale
b2 : Basis at time of sale
Price of asset S2
Gain on Futures F1F2
Net amount received S2 + (F1F2) =F1+ b2
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Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013
Choice of Contract
Choose a delivery month that is as closeas possible to, but later than, the end ofthe life of the hedge
When there is no futures contract onthe asset being hedged, choose thecontract whose futures price is most highlycorrelated with the asset price. There arethen 2 components to basis
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Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013
Optimal Hedge Ratio
Proportion of the exposure that should optimally behedged is
where
sSis the standard deviation of DS, the change in the
spot price during the hedging period,
sF
is the standard deviation of DF, the change in the
futures price during the hedging period
ris the coefficient of correlation between DSand DF.
F
Sh
=
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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)
Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013 11
Optimal number of contracts ifno tailing adjustment
F
A
Q
Qh*=
Optimal number of contractsafter tailing adjustment to allowor daily settlement of futures
F
A
V
Vh*=
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Example (Page 62)
Airline will purchase 2 million gallons of jetfuel in one month and hedges using heatingoil futures
From historical data sF=0.0313, sS= 0.0263,
and r= 0.928
Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013 12
7777003130026309280 ....* ==h
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Example continued
The size of one heating oil contract is 42,000 gallonsThe spot price is 1.94 and the futures price is 1.99(both dollars per gallon) so that
Optimal number of contracts assuming no dailysettlement
Optimal number of contracts after tailing
Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013 13
033700042000000277770 .,,,. ==
103658083000880377770 .,,,. ==
580830004299100088030000002941
,,.
,,,,.
==
==
F
A
V
V
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Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013
Hedging Using Index Futures(Page 65)
To hedge the risk in a portfolio thenumber of contracts that should beshorted is
where VAis the current value of the
portfolio, b is its beta, and VFis thecurrent value of one futures(=futures price times contract size)
F
A
VV
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Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013
Example
Futures price of S&P 500 is 1,000
Size of portfolio is $5 million
Beta of portfolio is 1.5One contract is on $250 times the index
What position in futures contracts on theS&P 500 is necessary to hedge theportfolio?
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Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013
Changing Beta
What position is necessary to reduce thebeta of the portfolio to 0.75?
What position is necessary to increase thebeta of the portfolio to 2.0?
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Why Hedge Equity Returns
May want to be out of the market for a while.Hedging avoids the costs of selling andrepurchasing the portfolio
Suppose stocks in your portfolio have anaverage beta of 1.0, but you feel they have beenchosen well and will outperform the market inboth good and bad times. Hedging ensuresthat the return you earn is the risk-free returnplus the excess return of your portfolio over themarket.
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Stack and Roll (page 69-70)
We can roll futures contracts forward tohedge future exposures
Initially we enter into futures contracts to
hedge exposures up to a time horizonJust before maturity we close them out anreplace them with new contract reflect thenew exposure
etc
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Liquidity Issues (See Business Snapshot 3.2)
In any hedging situation there is a dangerthat losses will be realized on the hedge whilethe gains on the underlying exposure areunrealized
This can create liquidity problems
One example is Metallgesellschaft which soldlong term fixed-price contracts on heating oil
and gasoline and hedged using stack and rollThe price of oil fell.....
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Stock Picking
If you think you can pick stocks that willoutperform the market, futures contractcan be used to hedge the market risk
If you are right, you will make moneywhether the market goes up or down
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Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013
Rolling The Hedge Forward
We can use a series of futurescontracts to increase the life of a
hedgeEach time we switch from 1 futurescontract to another we incur a type of
basis risk
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