Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013Hedging Strategies Using FuturesChapter 3*

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

Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013Long & Short HedgesA long futures hedge is appropriate when you know you will purchase an asset in the future and want to lock in the priceA short futures hedge is appropriate when you know you will sell an asset in the future & want to lock in the price*

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

Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013Arguments in Favor of Hedging

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

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

Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013Arguments against HedgingShareholders are usually well diversified and can make their own hedging decisionsIt may increase risk to hedge when competitors do notExplaining a situation where there is a loss on the hedge and a gain on the underlying can be difficult*

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

Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013Convergence of Futures to Spot(Hedge initiated at time t1 and closed out at time t2; Figure 3.1, page 56) TimeSpot PriceFuturesPricet1t2*

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

Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013Basis RiskBasis is the difference between spot & futuresBasis risk arises because of the uncertainty about the basis when the hedge is closed out*

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

Long Hedge for Purchase of an Asset DefineF1 : Futures price at time hedge is set upF2 : Futures price at time asset is purchasedS2 : 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*

Cost of assetS2Gain on FuturesF2 F1 Net amount paidS2 (F2 F1) =F1 + b2

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

Short Hedge for Sale of an Asset Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013*DefineF1 : Futures price at time hedge is set upF2 : Futures price at time asset is soldS2 : Asset price at time of saleb2 : Basis at time of sale

Price of assetS2Gain on FuturesF1 F2 Net amount receivedS2 + (F1 F2) =F1 + b2

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

Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013Choice of ContractChoose a delivery month that is as close as possible to, but later than, the end of the life of the hedgeWhen there is no futures contract on the asset being hedged, choose the contract whose futures price is most highly correlated with the asset price. There are then 2 components to basis

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

Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013Optimal Hedge RatioProportion of the exposure that should optimally be hedged iswhere sS is 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 periodr is the coefficient of correlation between DS and DF.*

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

Optimal Number of ContractsFundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013*Optimal number of contracts if no tailing adjustment

Optimal number of contracts after tailing adjustment to allow or daily settlement of futures

QA Size of position being hedged (units)QFSize of one futures contract (units)VAValue of position being hedged (=spot price time QA)VFValue of one futures contract (=futures price times QF)

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

Example (Page 62)Airline will purchase 2 million gallons of jet fuel in one month and hedges using heating oil futuresFrom 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*

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

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 daily settlement Optimal number of contracts after tailing

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

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

Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013Hedging Using Index Futures(Page 65)To hedge the risk in a portfolio the number of contracts that should be shorted is

where VA is the current value of the portfolio, b is its beta, and VF is the current value of one futures (=futures price times contract size)*

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

Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013ExampleFutures price of S&P 500 is 1,000Size of portfolio is $5 millionBeta of portfolio is 1.5One contract is on $250 times the index

What position in futures contracts on the S&P 500 is necessary to hedge the portfolio?

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

Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013Changing BetaWhat 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?*

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

Why Hedge Equity ReturnsMay want to be out of the market for a while. Hedging avoids the costs of selling and repurchasing the portfolioSuppose 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.Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013*

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

Stack and Roll (page 69-70)We can roll futures contracts forward to hedge future exposuresInitially we enter into futures contracts to hedge exposures up to a time horizonJust before maturity we close them out an replace them with new contract reflect the new exposureetc

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

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

Liquidity Issues (See Business Snapshot 3.2)In any hedging situation there is a danger that losses will be realized on the hedge while the gains on the underlying exposure are unrealizedThis can create liquidity problemsOne example is Metallgesellschaft which sold long term fixed-price contracts on heating oil and gasoline and hedged using stack and rollThe price of oil fell.....Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013*

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

Stock PickingIf you think you can pick stocks that will outperform the market, futures contract can be used to hedge the market riskIf you are right, you will make money whether the market goes up or downFundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013*

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

Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013Rolling The Hedge ForwardWe can use a series of futures contracts to increase the life of a hedgeEach time we switch from 1 futures contract to another we incur a type of basis risk*

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

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