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Hedging Strategies Using Futures Chapter 3 Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005 3.1 Hedging with futures Perfect hedge completely eliminates the risk – it is rare Most commonly we construct a hedge so that they perform as close to perfect hedge as possible When is a short futures appropriate, and when a long one, which contract should be used and in what size? Hedge and forget vs. dynamic hedging Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005 3.2 Basic principles Hedging has an objective to neutralize the risk as far as possible. If a company knows it will gain 10.000 for each cent in increase in the price of an asset over the next 3 mo and loose 10.000 for each cent in price decrease? Hedge: short futures that leads to loss of 10.000 for each cent in price increase and a gain of 10.000 for each cent in price decrease. Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005 3.3 Long & Short Hedges A short futures hedge (just described) is appropriate when you own an asset (or will own it) and know you will sell it in the future & want to lock in the price A long futures hedge is appropriate when you know you will purchase an asset in the future and want to lock in the price Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005 3.4 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 6th Edition, Copyright © John C. Hull 2005 3.5 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 6th Edition, Copyright © John C. Hull 2005 3.6 Convergence of Futures to Spot (Hedge initiated at time t1 and closed out at time t2) Futures Price Spot Price Time t1 t2 Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005 3.7 Basis Risk Basis is the difference between spot of asset to be hedged & futures price of contract used Basis risk arises because of the uncertainty about the basis when the hedge is closed out Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005 3.8 Short Hedge Suppose that F1 : Initial Futures Price F2 : Final Futures Price S2 : Final Asset Price You hedge the future sale of an asset by entering into a short futures contract Price Realized=S2+ (F1 – F2) = F1 + Basis Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005 3.9 Long Hedge Suppose that F1 : Initial Futures Price F2 : Final Futures Price S2 : Final Asset Price You hedge the future purchase of an asset by entering into a long futures contract Cost of Asset=S2 – (F2 – F1) = F1 + Basis Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005 3.10 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 6th Edition, Copyright © John C. Hull 2005 3.11 Optimal Hedge Ratio Proportion of the exposure that should optimally be hedged is sS r sF where 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 period r is the coefficient of correlation between DS and DF. Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005 3.12 Hedging Using Index Futures (Page 63) To hedge the risk in a portfolio the number of contracts that should be shorted is P b A where 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 6th Edition, Copyright © John C. Hull 2005 3.13 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 6th Edition, Copyright © John C. Hull 2005 3.14 Example Value of S&P 500 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 6th Edition, Copyright © John C. Hull 2005 3.15 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 6th Edition, Copyright © John C. Hull 2005 3.16 Hedging Price of an Individual Stock Similar to hedging a portfolio Does not work as well because only the systematic risk is hedged The unsystematic risk that is unique to the stock is not hedged Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005 3.17 Why Hedge Equity Returns May want to be out of the market for a while. Hedging avoids the costs of selling and repurchasing the portfolio Suppose 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. Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005 3.18 Rolling The Hedge Forward (page 6768) We can use a series of futures contracts to increase the life of a hedge Each time we switch from 1 futures contract to another we incur a type of basis risk Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005 3.19