1. Hedging Strategies Using Futures

2. ISSUES ASSUME 3.1 Basic Principle 3.2 Arguments For and Against Hedging 3.3 Basis Risk 3.4 Cross Hedging 3.5 Stock Index Futures 3.6 Rolling the Hedging Forward

3. 1. When is a short futures position appropriates ？ 2. When is a long futures position appropriate ？ 3. Which futures contract should be used ？ 4. What is the optimal size of the futures position for reducing risk ？ ISSUES

4. ASSUME Hedge-and forget Futures contracts as forward contracts 1 2

5. A hedge involves a short position in futures. A short hedge is appropriate when the hedger already owns an assets and expects to sell it at some time in the future. A short hedge can also be used when an assets is not owned right but will be owned at some time in the future. 3.1 Basic Principles-Short Hedge ( 空頭避險 )

6. 3.1 Basic Principles-Long Hedge ( 多頭避險 ) Hedges that involve taking a long position in a futures contract are known as long hedges. Long hedge can be used to manage an existing short position. A long hedge is appropriate when a company knows it will have to purchase a certain assets in the future and wants to lock a price now.

7. 3.2 Arguments For and Against Hedging Hedging and Shareholders Shareholders can do the hedging themselves. It assumes that shareholders have as much information about the risks faced by a company as does the company’s management. Shareholders can do far more easily than a corporation is diversify risk. 1 2 3

8. 3.2 Arguments For and Against Hedging Hedging and Competitors

9. 3.2 Arguments For and Against Hedging All implications of price changes on a company’s profitability should be taken into account in the design of a hedging strategy to protect against the price changes.

10. 3.3 Basis Risk 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 when the asset will be bought or sold. The hedge may require the futures contract to be closed out before its delivery month. These problem gives rise to what is termed basic risk. 1 2 3

11. 3.3 Basis Risk The basis in a hedging situation is as follows: Basis = Spot price of asset to be hedged – Futures price of contract used An increase in the basis is referred to a. A decrease in the basis is referred to as a = S – F strengthening of the basis weakening of the basis

12. 3.3 Basis Risk Spot price Futures price t1t1 t2t2 Figure 3.1 Variation of basic over time S1S1 F1F1 F2F2 S2S2 b2b2 b1b1 b 1 = S 1 –F 1 b 2 =S 2 – F 2 Suppose that F 1 : Initial Futures Price F 2 : Final Futures Price S 2 : Final Asset Price Long Hedge : You hedge the future purchase of an asset by entering into a long futures contract The effective price( 有效支付價格 ) that is paid with hedge is S 2 + F 1 – F 2 = F 1 + b 2 Short Hedge : You hedge the future sold of an asset by entering into a short futures contract The effective price( 有效價格 ) that is obtained for the asset with hedge is S 2 + F 1 – F 2 = F 1 + b 2 basis risk( 基差風險 )

13. One key factor affecting basis risk is the choice of the futures contract to be used for hedging. This choice has two components: 1.The choice of the assets underlying the futures contracts 2.The choice of the delivery month 3.3 Basis Risk Choice of Contract A contract with a later delivery month is usually chosen in these circumstances.

14. 3.4 Cross Hedging Calculating the Minimum Variance Hedge Ratio ( 最小變異的避險比率 ) h* : Hedge ratio that minimizes the variance of the hedger’s position.  : Coefficient of correlation between ΔS and ΔF ΔS : Change in spot price, S, during a period of time equal to the life of the hedge. ΔF : Change in future price, F, during a period of time equal to the life of the hedge. σ S : Standard deviation of ΔS σ F : Standard deviation of ΔF

15. 3.4 Cross Hedging Optimal Number of Contracts ( 最適契約數量 ) N A : Size of position being hedged (unit) Q F : Size of one futures contract (unit) N* : Optimal number of futures contracts for hedging The futures contracts used should have a face value of h* N A

16. 3.5 Stock Index Future Hedging Using Stock Index Futures N*: Optimal number of futures contracts for hedging P : Current value of the portfolio A : Current value of one futures contract β : From the capital asset pricing model to determined the appropriate hedge ratio

17. 3.5 Stock Index Future Value of S&P 500 index =1000 S&P 500 futures price =1010 Value of portfolio = $5,000,000 Risk-free interest rate = 4% per annum Dividend yield on index = 1% per annum Beta of portfolio = 1.5 Example Current value of one futures contract = 250*1000 = 250,000 One future contract is for delivery of $250 times the index Optimal number of futures contracts for hedging

18. Value of index in three months ： 9009501,0001,0501,100 Futures price of index today ： 1,010 Futures price of index in three months ： 9029521,0031,0531,103 Gain on futures position ： 810,000435,00052,500 – 322,500 – 697,500 Return on market ： – 9.750%– 4.750%0.250%5.250%10.250% Expected return on portfolio ： – 15.125% – 7.625%– 0.125%7.375%14.875% Expected portfolio value in three months (including dividends) ： 4,243,7504,618,7504,993,750 5,368,75 0 5,743,750 Total expected value of position in three months ： 5,053,750 5,046,250 3.5 Stock Index Future The gain from the short futures position = 30* ( 1,010 – 902 ) *250 = $ 810,000 Time to maturity = $ 5,000,000*(1 – 0.15125) = $4,243,750 The risk-free interest rate = 1 % per 3 months Expected return on portfolio = 1 + 1.5*( – 9.75 – 1 ) = – 15.125 % The loss on the index = 10 % The index pays a dividend of 0.25%per 3 months An investor in the index would earn = – 9.75 % =$ 4,243,750 + $810,000

19. 3.5 Stock Index Future Reasons for Hedging an Equity Portfolio A hedge using index futures removes the risk arising from market and leaves the hedger exposed only to the performance of the portfolio relative to the market. The hedger is planning to hold a portfolio for a long period of time and requires short-term protection.

20. 3.5 Stock Index Future Changing the Beta of a Portfolio  To reduce the beta of the portfolio to 0.75  To increase the beta of the portfolio to 2.0

21. 3.5 Stock Index Future Exposure to the Price of an Individual Stock  Similar to hedging a well-diversified stock portfolio  The performance of the hedge is considerably worse, only against the risk arising from market movements

22. 3.6 Rolling The Hedge Forward  This involves entering into a sequence of futures contracts to increase the life of a hedge  Rollover basis risk