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Hedging Strategies Using Futures Chapter 3 Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.1 Hedging issues Hedging vs speculating – hedging to reducing particular risk Perfect hedge – complete elimination of risk Issues in hedging strategies Short or long hedge? Size of the hedge? Which futures contract to be used? Hedge-and-forget strategy vs dynamic hedging Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.2 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 Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.3 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 Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.4 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 Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.5 Convergence of Futures to Spot (Hedge initiated at time t1 and closed out at time t2) Futures Price Spot Price Time t1 t2 Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.6 Basis Risk Basis is the difference between spot price & futures price Basis risk arises because of the uncertainty about the basis when the hedge is closed out Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.7 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 Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 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 Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.9 A Short Hedge May 15: An oil producer will have 1 million barrels of crude oil to sell on August 15. Quotes: Spot price of crude oil: $60 per barrel August futures price: $59 per barrel May 15: The producer sells 1,000 August contracts on crude oil August 15: Closes out futures position Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.10 Short hedge – cont. Suppose the spot price on August 15 is $55 per barrel. Producers gain on futures contract = $59 - $55 = $4 Total amount realized = 55 + 4 = $59 Note that the futures price equals spot price on Aug 15, due to convergence Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.11 Long Hedge Jan 15: A copper fabricator will require 100,000 pounds of copper on May 15. Quotes Jan 15: Spot price = 340 cents per pound May futures = 320 cents per pound Jan 15:The producer takes a long position on copper futures May 15: Closes out the futures position Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.12 Long hedge – cont. Suppose the copper price on May 15 is 325 cents per pound. Gain on futures = $3.25 – 3.20 = $.05/lbs Total = .05 x 100,000 = $5000 Total price paid = $3.25 - .05 = $3.20/lbs OR: S2 – F2 + F1 OR: S2 - (F2 – F1) =F1+ (S2 - F2) OR: F1+ basis Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.13 Basis risk in a short hedge March 1: US exported expects to receive ¥50 million at the end of July. September futures on ¥ is currently @ ¢0.7800/ ¥. Strategy: Short four September contracts on Yen; close out position end of July. Suppose end of July: Spot price = ¢0.7200/ ¥ September futures = ¢0.7250/ ¥. Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.14 Basis risk in a short hedge – cont. There are two ways of arriving at the net exchange rate after hedging: S2 - (F2 – F1) = F1+ (S2 - F2) (1) Spot price in July - gain on futures 0.7200 - (.7250 - .7800) = .7750 (2) Futures price in March + Basis in July .7800 + (.7200 - .7250) = .7800 - .0050 = .7750 Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.15 Basis risk in a long hedge Jun 8: A company will need 20,00 barrels of crude oil in October or November. The current December oil futures price is $68 per barrel. Strategy: long 20 December contracts @ $68/bbl. Close out position when ready to buy. Suppose the company is ready to purchase oil on November 10. At the time: Spot price = $75/bbl December futures @ $72 Basis = 75 – 72 = $3 Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.16 Basis risk in a long hedge There are two ways of arriving at the net cost of crude after hedging: S2 - (F2 – F1) = F1+ (S2 - F2) (1) Spot price in Nov. - gain on futures 75 - (72 - 68) = 75 - 4 = $71 (2) Futures price in March + Basis in July 68 + (75 - 72) = 68 + 3 = $71 Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.17 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: Choice of the asset underlying futures Choice of the delivery month Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.18 Optimal Hedge Ratio Proportion of the exposure that should optimally be hedged is s hr S 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. Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.19 Optimal Number of Contracts QA = Size of position being hedged (units) QF: Size of one futures contract (units) N* : Optimal number of futures contracts * * QA N h QF Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.20 Trailing the hedge In futures contract adjustment must be made to the optimal number of contracts for the daily settlement: * * VA N h VF Where VA and VF is the dollar value of the position and of one futures contract. Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.21 Stock Index Futures CBT: DJIA based on 30 blue chip companies; price weighted index; valued @ $10 x index CBT: Mini-DJIA , valued @ $5 x index CME: S&P500 index, market capitalization weighted index; valued@ $250 x index CME: Mini S&P500, valued @ $50 x index CME: Nasdaq 100; valued @ $100 x index CME: Mini-Nasdaq 100; valued @ $20 x index NYBOT: Russell 1000; valued @ $500 x index Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.22 Hedging Using Index Futures (Page 62) To hedge the risk in a portfolio the number of contracts that should be shorted is P b F where P is the value of the portfolio, b is its beta, and F is the current value of one futures (=futures price times contract size) Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.23 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.) Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.24 Example S&P 500 index = 1,000 Futures price of S&P 500 is 1,010 Size of portfolio is $5,050,000 Risk-free interest rate =4% per annum Dividend yield on index = 1% per annum Beta of portfolio is 1.5 What position in futures contracts on the S&P 500 is necessary to hedge the portfolio? Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.25 No of contracts needed One contract is on $250 times the index F = 250 x 1010 = 252,500 Number of futures contracts to short: P 5,050,000 b 1.5 30 F 252,500 Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.26 Gain/Loss Suppose the index turns out to be 900 in three months, and the futures price is 902. Gain from short futures position: 30 x (1010 -902) x 250 = $810,000 Loss on the index = 10% Considering dividend yield loss on net loss on the index would be 10% - 1%/4 = 9.75% Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.27 Value of the portfolio According to CAPM, the expected return on the portfolio is: E[rp] = rf + β(rm –rf) When market index return is -9.75% E[rp] = 1 + 1.5(-9.75 – 1) = -15.125% Or the expected value of the portfolio is: 5,050,000 x (1 – 15.125%) = $4,286,187 Total value of the portfolio include gain on the short hedge: 4,286,187 + 810,000 = $5,096,187 close to the original value Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.28 Changing Beta What position is necessary to reduce the beta of the portfolio to 0.75? P 5,050,000 ( b b ) (1.5 0.75) 15 F 252,500 What position is necessary to increase the beta of the portfolio to 2.0? 5,050,000 * P ( b b ) (1.5 2.0) 10 F 252,500 * i.e., 10 long contracts Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.29 Rolling The Hedge Forward 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 Fundamentals of Futures and Options Markets, 6th Edition, Copyright © John C. Hull 2007 3.30