1. Hedging Strategies Using Futures
Chapter 3
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

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 Derivatives 6th Edition, Copyright © John C. Hull 2005

3. Example of short hedge
In May 15 an oil producer has negotiated a contract to sell 1 million barrels of crude oil. The price that will apply is the market price on August 15.
He will gain $ for each 1 cent increase in the price of oil over the 3 months
We will lose $ for each 1 cent decrease in the price of oil over the period
On May 15 the spot price is $19 per barrel.
The crude oil futures price for August delivery is $18.75
Each futures contract is for delivery of 1000 barrels
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005 18

4. Example of short hedge (continued)
The company hedge its exposure by shorting 1000 futures contracts
The effect of the strategy should be to lock in a price close to $18.75
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005 18

5. Example of short hedge (continued)
Suppose that the spot price on August 15 is $17.50 The company realizes $17.5 million for the oil under its sales contract. The gain from the futures contracts is $18.75-$17.50=$1.25 per barrel. Total amount is $17.5+$1.25=$18.75 million
Suppose that the spot price is $19.50 on August 15. The company realizes $19.50 million from the contract and loses $19.50-$18.75=$0.75 per barrel. Total amount is $19.5-$0.75=$18.75 million
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005 18

6. Example of long hedge
In January 15 a copper fabricator has negotiated a contract to buy pounds of copper on May 15.
On January 15 the spot price of copper is 140 cents per pound
The copper futures price for May delivery is 120 cents per pound
Each futures contract is for delivery of pounds of copper
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005 18

7. Example of long hedge (continued)
The company hedge its exposure by going long 4 futures contracts
The effect of the strategy should be to lock in a price close to 120 cents per pound
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005 18

8. Example of long hedge (continued)
Suppose that the spot price on May 15 is 125. The company pays *1.25= for the copper. The gain from the futures contracts is *( )= Total cost is =
Suppose that the spot price is 105 on August 15. The company pays *1.05= The losses from the futures contracts are *( )= Total cost is =
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005 18

9. 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 6th Edition, Copyright © John C. Hull 2005

10. 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 6th Edition, Copyright © John C. Hull 2005

11. Basis Risk In practice, hedging is often not quite as straightforward:
The asset whose price is to be hedged may not be exactly the same as the asset underlying the futures contract
The hedger may be uncertain as to the exact date when the asset will be bought or sold
The hedge may require the futures contract to be closed out before its delivery month
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

12. Basis Risk Basis is the difference between spot & futures
Basis =Spot price of asset to be hedged-
Futures price of contract used
Basis risk arises because of the uncertainty about the basis when the hedge is closed out
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

13. Variation of basis over time
Futures
Price
Spot
Price
Time t1 t2
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

14. The basis Suppose that F1 : Initial Futures Price at time t1
F2 : Final Futures Price at time t2
S1 : Spot Asset Price at time t1
S2 : Final Asset Price at time t2
b1 = S1 - F1
b2 = S2 – F2
The hedging risk is the uncertainty associated with b2 = basis risk
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

15. Example Suppose that F1 = $2.20 F2 = $1.90 S1 = $2.50 S2 = $2.00
b1 = S1 - F1 = 0.30
b2 = S2 – F2 = 0.10
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

16. Long Hedge
Suppose that a hedger knows that he will buy an asset at time t2.
He hedges the future purchase of the asset by entering into a long futures contract at time t1.
The price paid for the asset is S2 and the loss on the hedge is F1 – F2
Cost of Asset=S2 + F1– F2 = F1 + Basis = $2.30
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

17. Short Hedge
Suppose that a hedger knows that the asset will be sold at time t2.
He hedges the future sale of the asset by entering into a short futures contract at time t1.
The price realized for the asset is S2 and the profit on the hedge is F1 – F2
The price that is obtained is: S2 + F1 – F2 = F1 + Basis = $2.30
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

18. 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 6th Edition, Copyright © John C. Hull 2005

19. Example
In June 8 a company knows that will purchase barrels of crude oil in October or November.
It takes a long position in 20 December contracts
The futures price on June 8 is $18.00 per barrel.
The company purchases the crude oil on November 10, when the spot and futures prices are S2 = $20.00 and F2 = $19.10.
The gain on the futures contract is =1.10.
The basis is =0.90. The price paid is =18.90 =
The total price paid is 18.90*20.000=
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005 18

20. Cross Hedging
Cross Hedging occurs when the asset underlying the contract is different than the asset whose price is being hedged
Hedge Ratio is the ratio of the size of the position taken in futures contracts to the size of the exposure.
When the asset is the same, the hedge ratio is 1.
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

21. Optimal Hedge Ratio
Proportion of the exposure that should optimally be hedged is
where
DS is the change in spot price during the life of hedge
DF is the change in futures price during the life of hedge
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 6th Edition, Copyright © John C. Hull 2005

22. Optimal Number of Contracts
the optimal number of Futures contracts required for hedging is
where
ΝA is the size of position being hedged (units)
QF is the size of one futures contracts (units)
N is the optimal number of futures contracts for
hedging
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

23. Example
An airline expects to purchase 2 million gallons of jet fuel in 1 month and decides to use heating oil futures for hedging.
The variances of the spot and futures prices are calculated: sS = 0.026, sF = , and r =0.928.
Each heating oil contract is on gallons of oil.
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

24. Hedging Using Index Futures (Page 63)
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 A is the value of the assets underlying one futures contract
In general, h=b
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

25. Example Value of S&P 500 index is 1,000
Value of Portfolio is $5 million
Beta of portfolio is 1.5
Risk free interest rate is 4% per annum
Dividend Yield on index is 1% per annum
A 4 months futures contract is used to hedge the portfolio over the next 3 months
The current futures price of the contract is 1.010
One futures contract is for delivery of $250 times the index, so A=250*1.000=
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

26. Continued
The number of futures contracts that should be shorted to hedge the portfolio is
1.5*( / )=30
Suppose in 3 months Value of S&P 500 index is 900, and the futures price is 902
The gain from the short futures position is then 30*( )*250=
The loss on the index is 10%. When dividends are taken into account, an investor in the index earn –0.975% (dividends 0.25% / 3m)
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

27. Continued
The CAPM gives E(R )=Rf+β(RM - Rf) = [1.5*( )]=
The expected value of the portfolio at the end of the 3 months is therefore *( )=
It follows that the expected value of the hedger’s position, including the gain on the hedge is =
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

28. Value of index in 3 months Futures price of Index today
Performance of Stock Index Hedge
Value of index in 3 months
Futures price of Index today
Futures price of Index in 3 months
Gain on futures position
Return on Market
Expected return on portfolio
Expected portfolio value in 3 months
Total expected value in 3 months
-9.75% % % % %
% % % % %
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

29. 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.)
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005

30. 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 6th Edition, Copyright © John C. Hull 2005

31. Rolling The Hedge Forward (page 67-68)
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
Options, Futures, and Other Derivatives 6th Edition, Copyright © John C. Hull 2005