清华大学：《期权、期货衍生产品》（英文版） Chapter4 HedgingUsingFutures

4. Hedging Using Futures Summary Why hedge How to hedge What is the optimal hedge Charles cao

1 Charles Cao 4. Hedging Using Futures ◼ Summary ◼ Why Hedge ◼ How to Hedge ◼ What is the Optimal Hedge

Why hedge? Objective: Neutralize the risk a An example A firm is due to sell an asset at a particular time in the future. The firm can hedge by shorting a futures contract Charles cao 2

2 Charles Cao Why Hedge? ◼ Objective: Neutralize the risk ◼ An example: ◼ A firm is due to sell an asset at a particular time in the future. The firm can hedge by shorting a futures contract

Why hedge? If the price of the asset goes down the firm will lose money when it sells the asset, but gain on the short futures position If the price of the asset goes up, the firm will gain from the sale of the asset, but will take a loss on the futures position Charles cao 3

3 Charles Cao Why Hedge? ◼ If the price of the asset goes down, the firm will lose money when it sells the asset, but gain on the short futures position ◼ If the price of the asset goes up, the firm will gain from the sale of the asset, but will take a loss on the futures position

Short Hedges a Involves a short position in the futures contract It is appropriate when the hedger owns the asset and expects to sell it in the future It is also appropriate when the hedger does not own the asset now but will own it in the future Charles cao

4 Charles Cao Short Hedges ◼ Involves a short position in the futures contract ◼ It is appropriate when the hedger owns the asset and expects to sell it in the future ◼ It is also appropriate when the hedger does not own the asset now, but will own it in the future

Short Hedges: Example Today, May 15 Exxon signed a contract to sell 1 million barrels of oil. The selling price is the spot price on august 15 Spot Price: $19/barrel August oil futures price: $18.75/barrel Charles cao

5 Charles Cao Short Hedges: Example ◼ Today, May 15 ◼ Exxon signed a contract to sell 1 million barrels of oil. The selling price is the spot price on August 15 ◼ Spot Price: $19/barrel ◼ August oil futures price: $18.75/barrel

Short Hedges: Example a Hedging May 15: short 1000 August oil futures (each contract is written on 1000 barrels) August 15: close out the position Outcome Exxon effectively locks in a selling price of $1875/bae Charles cao

6 Charles Cao Short Hedges: Example ◼ Hedging: ◼ May 15: short 1000 August oil futures (each contract is written on 1000 barrels) ◼ August 15: close out the position ◼ Outcome: ◼ Exxon effectively locks in a selling price of $18.75/barrel

Short Hedges: Example If the oil price proves to be $17.50 on August 15 (spot price) ExXon receives $17. 50 under the sale contract ExXon receives $1.25 from the futures contract If the oil price proves to be $19.50 on August 15 (spot price) ExXon receives $19.50 under the sale contract Exxon loses $o.75 (19. 50-18.75) from the futures contract Charles cao

7 Charles Cao Short Hedges: Example ◼ If the oil price proves to be $17.50 on August 15 (spot price) ◼ Exxon receives $17.50 under the sale contract ◼ Exxon receives $1.25 from the futures contract ◼ If the oil price proves to be $19.50 on August 15 (spot price) ◼ Exxon receives $19.50 under the sale contract ◼ Exxon loses $0.75 (19.50-18.75) from the futures contract

Long hedges Involves a long position in the futures contract It is appropriate when the hedger has to purchase assets in the future and wants to lock in a price now Charles cao

8 Charles Cao Long Hedges ◼ Involves a long position in the futures contract ◼ It is appropriate when the hedger has to purchase assets in the future and wants to lock in a price now

Hedging using futures contracts It is not perfect There may be a difference between the hedged asset and the asset underlying the futures contracts You do not know the date when the asset will be purchased or sold Mismatch between the expiration date and the date when the asset will be bought or sold Charles cao

9 Charles Cao Hedging Using Futures Contracts ◼ It is not perfect: ◼ There may be a difference between the hedged asset and the asset underlying the futures contracts ◼ You do not know the date when the asset will be purchased or sold ◼ Mismatch between the expiration date and the date when the asset will be bought or sold

Hedging Using Futures Contracts all these issues relate to the basis risk Basis risk spot price of asset to be hedged- futures price of contract used If the hedged asset is the same as the asset underlying the futures contract, the basis risk is 0 on the expiration day Before the expiration day the basis risk could be positive or negative (see the picture) Charles cao

10 Charles Cao Hedging Using Futures Contracts ◼ All these issues relate to the basis risk ◼ Basis risk = spot price of asset to be hedged - futures price of contract used ◼ If the hedged asset is the same as the asset underlying the futures contract, the basis risk is 0 on the expiration day ◼ Before the expiration day, the basis risk could be positive or negative (see the picture)