《金融期货与期权》（英文版） Chapter 4 Hedging Strategies Using Futures

Hedging strategies Using futures Chapter 4 Options, Futures, and other Drerivatives, 5th edition o 2002 by John C. Hull

Options, Futures, and Other Drerivatives, 5th edition © 2002 by John C. Hull 4.1 Hedging Strategies Using Futures Chapter 4

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 price A 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 Drerivatives, 5th edition o 2002 by John C. Hull

Options, Futures, and Other Drerivatives, 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 price • A short futures hedge is appropriate when you know you will sell an asset in the future & want to lock in the price

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 Drerivatives, 5th edition o 2002 by John C. Hull

Options, Futures, and Other Drerivatives, 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

4.4 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 Drerivatives, 5th edition o 2002 by John C. Hull

Options, Futures, and Other Drerivatives, 5th edition © 2002 by John C. Hull 4.4 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

4.5 Convergence of Futures to Spot Futures Price TSpot Price Spot Price Futures Price Time Time (b) Options Futures, and Other Drerivatives, 5th edition@ 2002 by John C. Hull

Options, Futures, and Other Drerivatives, 5th edition © 2002 by John C. Hull 4.5 Convergence of Futures to Spot Time Time (a) (b) Futures Price Futures Price Spot Price Spot Price

4.6 Basis risk Basis is the difference between spot futures Basis risk arises because of the uncertainty about the basis when the hedge is closed out Options, Futures, and other Drerivatives, 5th edition o 2002 by John C. Hull

Options, Futures, and Other Drerivatives, 5th edition © 2002 by John C. Hull 4.6 Basis Risk • Basis is the difference between spot & futures • Basis risk arises because of the uncertainty about the basis when the hedge is closed out

4.7 Long hedge Suppose that f: nitial futures price F 2 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 Drerivatives, 5th edition o 2002 by John C. Hull

Options, Futures, and Other Drerivatives, 5th edition © 2002 by John C. Hull 4.7 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

4.8 Short Hedge Suppose that F1: Initial Futures Price f: Final futures price 2 2 Final asset price entering into a short futures contract You hedge the future sale of an asset by Price Realized=S2+F1-F2=F1+ Basis Options, Futures, and other Drerivatives, 5th edition o 2002 by John C. Hull

Options, Futures, and Other Drerivatives, 5th edition © 2002 by John C. Hull 4.8 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

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 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 There are then 2 components to basis Options Futures, and Other Drerivatives, 5th edition@ 2002 by John C. Hull

Options, Futures, and Other Drerivatives, 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 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. There are then 2 components to basis

4.10 Optimal Hedge Ratio Proportion of the exposure that should optimally be hedged is h S F Where Os is the standard deviation of 8S, the change in the spot price during the hedging period oF is the standard deviation of Sf, the change in the futures price during the hedging period p is the coefficient of correlation between 8S and 8F Options, Futures, and other Drerivatives, 5th edition o 2002 by John C. Hull

Options, Futures, and Other Drerivatives, 5th edition © 2002 by John C. Hull 4.10 Optimal Hedge Ratio Proportion of the exposure that should optimally be hedged is 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. h S F * = r s s