# Hedging Strategies Using Futures Chapter 3 Options Futures

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Hedging Strategies Using Futures Chapter 3 Options, Futures, and Other Derivatives, 7 th International Edition, Copyright © John C. Hull 2008 1

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 and want to lock in the price Options, Futures, and Other Derivatives, 7 th International Edition, Copyright © John C. Hull 2008 2

Example 3. 1: Long Hedges It is Jan 15. A copper fabricator knows it will require 100, 000 pounds of copper on May 15 to meet a certain contract. The spot price of copper is 340 cents per pound. May futures price is 320 cents per pound. Jan 15: Take a long position in four May futures contracts on copper (each contract is for the delivery of 25, 000 pounds). May 15: Close out the position.

After gains and looses on the futures are taken into account, the price paid by the company is close to 320 cents per pound. Suppose spot price on May 15 is 325 cents per pound. Gain= 100, 000 x (3. 25 -3. 20) =$5, 000 Suppose spot price is 305 cents per pound. Loss= 100, 000 x (3. 20 -3. 05) = $15, 000

Example 3. 2: Short Hedges It s May 15. An oil producer has negotiated a contract to sell 1 million barrels of crude oil. The price in the sales contract is the spot price on Aug. 15. Spot price on May 15: $60 per barrel. Aug. Oil futures: $59 per barrel. May 15: Short 1000 Aug. Futures contract (each futures contract is for the delivery of 1000 barrels) Aug 15: Close out futures position.

After gains and looses on the futures are taken into account, the price received by the company is close to $59 per barrel. Suppose spot price on Aug. 15 is $55 per barrel. Gain: $59 -$55 = $4 per barrel ($4 million in total) Suppose the price of oil on Aug 15 is $65 per barrel. Loss: $65 -$59 = $6 per barrel. In all cases, the company ends up with app. $59 million.

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, 7 th International Edition, Copyright © John C. Hull 2008 7

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, 7 th International Edition, Copyright © John C. Hull 2008 8

Convergence of Futures to Spot (Hedge initiated at time t 1 and closed out at time t 2) Futures Price Spot Price Time t 1 t 2 Options, Futures, and Other Derivatives, 7 th International Edition, Copyright © John C. Hull 2008 9

Basis Risk Basis is the difference between the spot and futures price As time passes, the spot and futures price do not change by the same amount, as a result basis changes. Basis risk arises because of the uncertainty about the basis when the hedge is closed out Options, Futures, and Other Derivatives, 7 th International Edition, Copyright © John C. Hull 2008 10

Short Hedge Again we define F 1 : Initial Futures Price F 2 : Final Futures Price S 2 : Final Asset Price If you hedge the future sale of an asset by entering into a short futures contract then Price Realized=S 2+ (F 1 – F 2) = F 1 + Basis F 1– F 2 : Profit on futures position Options, Futures, and Other Derivatives, 7 th International Edition, Copyright © John C. Hull 2008 11

Long Hedge We define F 1 : Initial Futures Price F 2 : Final Futures Price S 2 : Final Asset Price If you hedge the future purchase of an asset by entering into a long futures contract then Cost of Asset=S 2 + (F 1– F 2) = F 1 + Basis F 1– F 2: Loss on futures position Options, Futures, and Other Derivatives, 7 th International Edition, Copyright © John C. Hull 2008 12

Short Hedge: If the basis strengthens, the hedger’s postion improves. If the basis weakens, the hedger’s position worsens. Long Hedge. If the basis strengthens, the hedger’s position worsens. If the basis weakens, the hedger’s position improves.

Choice of Contract One key factor affecting basis risk is the choice of futures contract. This choice has two components: The choice of the asset underlying the futures contract The choice of the delivery month. Options, Futures, and Other Derivatives, 7 th International Edition, Copyright © John C. Hull 2008 14

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.

Example 3. 3 It is March 1. A U. S company expects to receive 50 million yen at the end of July. Yen futures contracts on CME have delivery months of March, June, Sep and Dec. One contract is for the delivery of 12. 5 million. Sep contract is chosen for hedging purposes. The Sep Futures price for yen is 0. 7800 cents. 1. Short four Sep futures contracts on March 1 at a futures price of 0. 7800. 2. Close out the position when the yen arrive at the end of July.

Spot price at the end of July is 0. 7200. Sep futures price at the end of July is 0. 7250 Basis at the end of July = -0. 0050 Net exchange rate after hedging: Spot price on July + Gain on futures = 0. 72+ (0. 78 - 0. 725)= 0. 775 Futures price in March +Basis in July = 0. 78 – 0. 0050 =0. 775

Example 3. 4 It is June 8. A company knows that it will need to purchase 20, 000 barrels of crude oil some time in Oct or Nov. The current Dec oil futures price is $68 per barrel. Hedging strategy: 1. Take a long position in 20 Dec oil futures contracts on June 8 at a futures price of $68 2. Close out the contract when ready to purchase the oil

Company is ready to purchase oil on Nov 10 Spot price on Nov 10 is $75 Dec futures price on Nov 10 is $72. Basis on Nov 10 is $3 Net cost: Spot price on Nov 10 + Gain on Futures = $75 – ($68 -$72) = $71 Futures price on June 8 + Basis on Nov 10 = $68 +$3 = $71

Optimal Hedge Ratio (page 55) Proportion of the exposure that should optimally be hedged is where s. S is the standard deviation of DS, the change in the spot price during the hedging period, s. F 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, 7 th International Edition, Copyright © John C. Hull 2008 20

Tailing the Hedge Two way of determining the number of contracts to use for hedging are Compare the exposure to be hedged with the value of the assets underlying one futures contract Compare the exposure to be hedged with the value of one futures contract (=futures price times size of futures contract The second approach incorporates an adjustment for the daily settlement of futures Options, Futures, and Other Derivatives, 7 th International Edition, Copyright © John C. Hull 2008 21

Hedging Using Index Futures (Page 61) To hedge the risk in a portfolio the number of contracts that should be shorted is where P is the value of the portfolio, b is its beta, and F is the value of one futures contract Options, Futures, and Other Derivatives, 7 th International Edition, Copyright © John C. Hull 2008 22

Example 3. 5 Portfolio worth $5. 05 million mirrors the S&P 500. The index futures price is 1, 010 and each futures is on $250 x the index. Value of the portfolio (P) = 5, 050, 000 Value of one futures contract (F) = 250 x 1, 010 = 252, 500 Optimal number of contract (N) =5, 050, 000/252, 500 = 20 contracts Options, Futures, and Other Derivatives, 7 th International Edition, Copyright © John C. Hull 2008 23

If the portfolio does not exactly mirror the index, we use beta. Suppose that a futures contract with 4 months to maturity is used to hedge the value of a portfolio over the next 3 months. S&P 500 index is 1, 000 S&P 500 futures price is 1, 010 Value of Portfolio is $5, 050, 000 Beta of portfolio is 1. 5 Risk-free rate is 4% per annum Div yield on index is 1% per annum What position in futures contracts on the S&P 500 is necessary to hedge the portfolio?

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, 7 th International Edition, Copyright © John C. Hull 2008 25

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, 7 th International Edition, Copyright © John C. Hull 2008 26

Rolling The Hedge Forward (page 64 -65) We can use a series of futures contracts to increase the life of a hedge Each time we switch from one futures contract to another we incur a type of basis risk Options, Futures, and Other Derivatives, 7 th International Edition, Copyright © John C. Hull 2008 27