Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,4.1,Hedging Strategies Using Futures,Chapter 4,Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,4.2,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 priceA short futures hedge is appropriate when you know you will sell an asset in the future & want to lock in the price,Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,4.3,Arguments 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,Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,4.4,Arguments against Hedging,Shareholders 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,Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,4.5,Convergence of Futures to Spot,Time,Time,(a),(b),FuturesPrice,FuturesPrice,Spot Price,Spot Price,Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,4.6,Basis Risk,Basis is the difference between spot & futuresBasis risk arises because of the uncertainty about the basis when the hedge is closed out,Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,4.7,Long Hedge,Suppose thatF1 : Initial Futures PriceF2 : Final Futures PriceS2 : Final Asset PriceYou hedge the future purchase of an asset by entering into a long futures contractCost of Asset=S2 (F2 F1) = F1 + Basis,Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,4.8,Short Hedge,Suppose thatF1 : Initial Futures PriceF2 : Final Futures PriceS2 : Final Asset PriceYou hedge the future sale of an asset by entering into a short futures contractPrice Realized=S2+ (F1 F2) = F1 + Basis,Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,4.9,Choice of Contract,Choose 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,Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,4.10,Optimal Hedge Ratio,Proportion 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.,Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,4.11,Hedging Using Index Futures(Page 82),To hedge the risk in a portfolio the number of contracts that should be shorted iswhere P is the value of the portfolio, b is its beta, and A is the value of the assets underlying one futures contract,Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,4.12,Reasons for Hedging an Equity Portfolio,Desire to be out of the market for a short period of time. (Hedging may be cheaper than selling the portfolio and buying it back.)Desire to hedge systematic risk (Appropriate when you feel that you have picked stocks that will outpeform the market.),Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,4.13,Example,Value of S&P 500 is 1,000Value of Portfolio is $5 millionBeta of portfolio is 1.5What position in futures contracts on the S&P 500 is necessary to hedge the portfolio?,Options, Futures, and Other Derivatives, 5th edition 2002 by John C. Hull,4.14,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, 5th edition 2002 by John C. Hull,4.15,Rolling The Hedge Forward,We 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,