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

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

3. 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.

4. 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 ( ) =$5,000
Suppose spot price is 305 cents per pound.
Loss= 100,000 x ( ) = $15,000

5. 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.

6. 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.

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

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

9. Convergence of Futures to Spot (Hedge initiated at time t1 and closed out at time t2)
Price
Spot
Price
Time t1 t2
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

10. 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, 7th International Edition, Copyright © John C. Hull 2008

11. Short Hedge Again we define F1 : Initial Futures Price
F2 : Final Futures Price
S2 : Final Asset Price
If you hedge the future sale of an asset by entering into a short futures contract then
Price Realized=S2+ (F1 – F2) = F1 + Basis
F1– F2 : Profit on futures position
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

12. Long Hedge We define F1 : Initial Futures Price
F2 : Final Futures Price
S2 : Final Asset Price
If you hedge the future purchase of an asset by entering into a long futures contract then
Cost of Asset=S2 + (F1– F2) = F1 + Basis
F1– F2: Loss on futures position
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

13. 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.

14. 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, 7th International Edition, Copyright © John C. Hull 2008

15. 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.

16. 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 cents.
1. Short four Sep futures contracts on March 1 at a futures price of
2. Close out the position when the yen arrive at the end of July.

17. Spot price at the end of July is 0.7200.
Sep futures price at the end of July is
Basis at the end of July =
Net exchange rate after hedging:
Spot price on July + Gain on futures = ( )= 0.775
Futures price in March +Basis in July = 0.78 – =0.775

18. 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

19. 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

20. Optimal Hedge Ratio (page 55)
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.
Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

21. 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, 7th International Edition, Copyright © John C. Hull 2008

22. 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, 7th International Edition, Copyright © John C. Hull 2008

23. 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, 7th International Edition, Copyright © John C. Hull 2008

24. 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?

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

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

27. 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, 7th International Edition, Copyright © John C. Hull 2008