Chapter 3 on SEO Seminar Factors

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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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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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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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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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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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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

Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013 7

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


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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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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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)


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


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


033700042000000277770 .,,,. ==

103658083000880377770 .,,,. ==

580830004299100088030000002941

,,.

,,,,.

==

==

F

A

V

V


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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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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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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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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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