Ch03HullOFOD9thEdition.pptx

Chapter 3 Hedging Strategies Using Futures Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 1 Using futures for hedging Purpose of using futures contract for hedging The ultimate aim for futures market transactions, in this context, is to reduce risk. These risks s...

Chapter 3 Hedging Strategies Using Futures Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 1 Using futures for hedging Purpose of using futures contract for hedging The ultimate aim for futures market transactions, in this context, is to reduce risk. These risks stem from price fluctuations in stock market, commodity market, forex, interest rates. Perfect hedges are rare so we cannot eliminate risk but we can at least mitigate risk. Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 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 because you expect the price to rise A short futures hedge is appropriate when you know you will sell an asset in the future and want to lock in the price because you expect the price to fall Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 3 Long Hedge Now its January 15 A copper fabricator will require 100,000 pounds of copper on May 15 Spot price now is 340 cents per pound Future price for May delivery is 320 cents per pound The futures contracts are written over 25,000 pounds of copper Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 4 Long Hedge So, they need to go long on 4 future contracts to hedge their position This will lock in the price @320 cents per pound What are the possible outcomes in four months time i.e. on May 15 The spot price is 325 cents per pound 100,000($3.25-$3.20)=$5000 so they gain on the futures contract What they will do is that they will close the future position and take the $5000 while buying @spot i.e. 325 cents per pound. Why? Futures delivery is inconvenient and costly They will end up with an approximate cost of 325,0005000=$320,000 5 Long Hedge The spot price is 305 cents per pound 100,000($3.05-$3.20)=-$15000 so they lose on the futures contract what they will do is that they will close the future position and incur the $15000 while buying @spot i.e. 305 cents per pound. They will end up with an approximate cost of 305,000+15000=$320,000 it is a cost that the company incurred this is why we add it 6 Long Hedge Anyhow, hedging is better than buying on January 15 @ a spot price of 340 cents per pound but why? the purchasing cost is lower avoid the storage cost and the opportunity cost of not earning interest  This case is a perfect hedge 7 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, 9th Edition, Copyright © John C. Hull 2014 8 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 hedge. (in which situation?) 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, 9th Edition, Copyright © John C. Hull 2014 9 Basis Risk The examples that we discussed are theoretical in practice it is very hard to find a perfect hedge. Because of: There no future contract for the asset to be hedged. The hedger is uncertain as to the exact date on which the asset will be bought or sold. The hedger may require the future contract to be closed out before the delivery month. 10 Basis Risk (cont.) 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. Why is that? Next page  Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 11 Basis Risk The asset in the existing position is often not the same as that underlying the futures contract The hedging horizon may not perfectly match the maturity of the futures contract How to minimized basis risk? Select the futures contract on an asset that is most highly correlated with the spot position Select the futures contract with the closest maturity to the hedging horizon. Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 12 Long Hedge for Purchase of an Asset Define F1 : Futures price at time hedge is set up F2 : Futures price at time asset is purchased S2 : Asset price at time of purchase b2 : Basis at time of purchase Cost of asset S2 Gain on Futures F2 −F1 Net amount paid S2 − (F2 −F1) =F1 - b2 Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 13 Short Hedge for Sale of an Asset Define F1 : F2 : S2 : b2 : Futures price at time hedge is set up Futures price at time asset is sold Asset price at time of sale Basis at time of sale Price of asset S2 Gain on Futures F1 −F2 Net amount received S2 + (F1 −F2) =F1 +b2 Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 14 Example 3.1 On March 1, US company expects to receive ¥50 million at the end of July. Yen futures contracts have delivery months of March, June, September, and December. One contract is for the delivery of ¥12.5 million. What should the company do? Short hedge but how many contracts? 50/12.5=4 contacts. Which delivery month? September. Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 15 Example 3.1 futures price on March in cents per yen is 0.7800 Because the delivery date do not match accurately the delivery month of the future contact, the position is closed out at the end of July. The Spot and future price are, therefore, not the same.. The spot price is 0.72 the future price is 0.725 16 Example 3.1 Gain on Futures=F1 −F2 =(0.78 −0.725)=0.055 Net amount received=S2 + (F1 −F2) =F1 + b2 S2 + (F1 −F2)=0.72+0.055=0.775 Convert from cents to dollars 0.775/100=0.00775 0.00775*50,000,000=$387,500 Why he could not lock in the 0.78 exchange rate? Because b2≠0 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. This is known as cross hedging. Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 18 Cross hedging Cross hedging is needed when the underlying asset has not futures contract available. So we will use a futures contract that is highly correlated with the asset. So we should not except a perfect relation between the two Therefore we need to estimate the hedge ratio. Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 19 Optimal Hedge Ratio (page 59) Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 20 Example (Page 61) Airline will purchase 2 million gallons of jet fuel in one month and hedges using heating oil futures (cross hedge) From historical data sF =0.0313, sS =0.0263, and r= 0.928 Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 21 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 is which rounds to 37 Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 22 Alternative Definition of Optimal Hedge Ratio Optimal hedge ratio is where variables are defined as follows Correlation between percentage daily changes for spot and futures SD of percentage daily changes in spot SD of percentage daily changes in futures Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 23 Optimal Number of Contracts QA Size of position being hedged (units) QF Size of one futures contract (units) VA Value of position being hedged (=spot price time QA) VF Value of one futures contract (=futures price times QF) Optimal number of contracts if adjustment for daily settlement Optimal number of contracts after “tailing adjustment” to allow or daily settlement of futures Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 24 Hedging Using Index Futures (Page 64) To hedge the risk in a portfolio the number of contracts that should be shorted is where VA is the value of the portfolio, b is its beta, and VF is the value of one futures contract Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 25 Example S&P 500 futures price is 1,000 Value of Portfolio is $5 million Beta of portfolio is 1.5; The CME group has two futures contracts on the S&P 500 index the one considered in this example is the $250 times the index. Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 26 What position in futures contracts on the S&P 500 is necessary to hedge the portfolio? N= 1.5($5000000/$(250*1000))=30 contracts short position in 30 contracts Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 27 Changing Beta Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 28 Changing Beta Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 29 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 riskfree return plus the excess return of your portfolio over the market. Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 30 Stack and Roll (page 68-69) We can roll futures contracts forward to hedge future exposures Initially we enter into futures contracts to hedge exposures up to a time horizon Just before maturity we close them out an replace them with new contract reflect the new exposure etc 31 Liquidity Issues (See Business Snapshot 3.2) In any hedging situation there is a danger that losses will be realized on the hedge while the gains on the underlying exposure are unrealized This can create liquidity problems One example is Metallgesellschaft which sold long term fixed-price contracts on heating oil and gasoline and hedged using stack and roll The price of oil fell..... Options, Futures, and Other Derivatives, 9th Edition, Copyright © John C. Hull 2014 32