1. Options and Speculative Markets 2003-2004 Hedging with Futures Professor André Farber Solvay Business School Université Libre de Bruxelles

2. OMS 03 Hedging with Futures |2 2.Hedging with futures Objectives for this session: –1. –2. –3.

3. OMS 03 Hedging with Futures |3 Identifying the exposure Exposure: position to be hedged Cash flow(s) –Future incomeEx: oil/gold producer –Future expenseEx: user of commodity Value –AssetEx: asset manager –LiabilityEx: financial intermediary General formulation: Exposure = M  S with: M = quantity, size (M > 0 asset, income M < 0 liability, expense) S = market price

4. OMS 03 Hedging with Futures |4 Setting up the hedge Futures position: Number of contracts n (n>0 long hedge – n<0 short hedge)  Size of one contract N  Futures price F Hedge = n  N  F Perfect hedge: choose n so that value of hedged position does not change if S changes

5. OMS 03 Hedging with Futures |5 Hedge ratio To achieve ∆V = 0 Hedge ratio: To achieve ∆V = 0 If M >0 : n <0 short hedge If M 0 long hedge

6. OMS 03 Hedging with Futures |6 Perfect hedge Assume F and S are perfectly correlated: then: h = - β and

7. OMS 03 Hedging with Futures |7 Example: Stock index futures

8. OMS 03 Hedging with Futures |8 Minimum variance hedge Real life more complex: –1. asset to be hedged might differ from underlying the futures contract –2. basis (S –F) might vary randomly More general specification: Choose n to minimize the variance of ∆V

9. OMS 03 Hedging with Futures |9 Some math Take derivative and set it equal to 0: Solve for n: