1. Hedging Strategies Using Derivatives

2. 1. Basic Principles Goal: to neutralize the risk as far as possible. I. Derivatives A. Option: contract that gives its holder the right to buy (or sell) an asset at a predetermined price within a specified period of time.

3. A-1) Call option: option to buy an underlying asset at a certain price within a specific period A-2) Put option: option to sell an underlying asset at a certain price within a specific period

4. call put Underlying asset + - Exercise price - + Time to expiration + + Risk free rate + - Variance of return + +

5. B. Forward Contracts: - agreements where one party agree to buy a commodity at a specific price on a specific future date and other party agrees to sell. - Physical delivery occurs

6. C. Future contracts: - similar to forward contracts - marked to market on a daily basis (margin account with minimum requirement, reducing default risk) - settled with cash - standardized

7. Ex) marking to market Setting up a margin account for futures contract with initial margin – e.g)$4000 Rebalanced daily to reflect investors’ gains or losses, using daily futures prices. If the balance below maintenance margin, there will be a margin call. The investor is entitled to withdraw any balance in the margin account in excess of the initial margin.

8. D. Swap: two parties agree to exchange obligations to make specified payment streams. Ex) Floating rate bond & Fixed rate bond E. Structured notes: a debt obligation derived from another debt obligation Ex) Stripping long term debts (30 years) to create a series of zero coupon bonds Ex) CMO with mortgages loans

9. F. Inverse Floaters A note in which the interest paid moves counter to market rates Ex) note at prime plus 1% II. Hedging with futures Short hedge: a hedge that involves a short position in futures contract. Here the hedger owns an asset and expects to sell it in the future.

10. Ex-1) suppose that an oil producer sell a August 15 futures contract at $18.75 per barrel. Now it is April. Suppose that the spot price on August 15 prove to be $17.50. And August 15 futures price will be close to $17.50. gain = Sales of oil + difference of futures price = 17.50+(18.75-17.50) = 18.75 If the spot price goes up to $19, gain = 19+ (18.75 -19) =18.75

11. Long hedges: hedges taking a long position in a futures contract. Here hedgers want to purchase a certain assets Ex) A copper fabricator buys a May futures contract at 120 cents per pound. He or she needs 10,000 pound in May. Now, It is January. If spot price goes up to 125 cents, costs = 10000*1.25- (1.25-1.20)*10000=120000 If spot price goes down to 105 cents, costs = 10000*1.05+(1.20-1.05)*10000=120000

12. 1)Basis Risk As shown in the previous examples, to achieve hedging, spot price and future contract prices should converge around the expiration date. If not,…… Basis = spot price of asset to be hedged – futures price of contract used. Reasons of basis: - the asset for hedging is not the same as the asset underlying the futures contract

13. - uncertain date when the asset will be bought or sold - closed out before its expiration date Strengthening of the basis: increasing basis Weakening of the basis: decreasing basis

14. 2) Minimum variance hedge ratio Ratio that minimize the variance of the hedger’s position

15. 3) Optimal Number of Contracts N: optimal number of contracts N A : Size of position hedged Q F : Size of one contract