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Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,5/15/2011,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,#,Chapter 3,Hedging Strategies Using Futures,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,1,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,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,2,Arguments in Favor of Hedging,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,3,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,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,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,4,Basis Risk,Basis is usually defined as the spot price minus the futures price,Basis risk arises because of the uncertainty about the basis when the hedge is closed out,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,5,Long Hedge for Purchase of an Asset,Define,F,1,:,Futures price at time hedge is set up,F,2,:,Futures price at time asset is purchased,S,2,:,Asset price at time of purchase,b,2,:Basis at time of purchase,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,6,Cost of asset,S,2,Gain on Futures,F,2,F,1,Net,amount paid,S,2,(,F,2,F,1,),=,F,1,+,b,2,Short Hedge for Sale of an Asset,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,7,Define,F,1,:,Futures price at time hedge is set up,F,2,:,Futures price at time asset is sold,S,2,:,Asset price at time of sale,b,2,:Basis at time of sale,Price,of asset,S,2,Gain on Futures,F,1,F,2,Net amount,received,S,2,+,(,F,1,F,2,),=,F,1,+,b,2,Choice of Contract,Choose a delivery month that is as close as possible to,but later than,the end of the life of the hedge,When there is no futures contract on the asset being hedged,choose the contract whose futures price is most highly correlated with the asset price.This is known as cross hedging.,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,8,Optimal Hedge Ratio,(page 57),Proportion of the exposure that should optimally be hedged is,where,s,S,is the standard deviation of,D,S,the change in the spot price during the hedging period,s,F,is the standard deviation of,D,F,the change in the futures price during the hedging period,r,is the coefficient of correlation between,D,S,and,D,F,.,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,9,Optimal Number of Contracts,Q,A,Size of position being hedged(units),Q,F,Size of one futures contract (units),V,A,Value of position being hedged(=spot price time,Q,A,),V,F,Value of one futures contract (=futures price times,Q,F,),Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,10,Optimal number of contracts if no tailing adjustment,Optimal number of contracts after tailing adjustment to allow or daily settlement of futures,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,s,F,=0.0313,s,S,=0.0263,and,r,=0.928,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,11,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,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,12,Hedging Using Index Futures,(Page 61),To hedge the risk in a portfolio the number of contracts that should be shorted is,where,V,A,is the value of the portfolio,b,is its beta,and,V,F,is the value of one futures contract,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,13,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?,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,14,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?,Options,Futures,and Other Derivatives,8th Edition,Copyright John C.Hull 2012,15,Why Hedge Equity Returns,May want to be out of the market for a while.Hedging avoids the
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