Hedging Strategies Using Futures

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. ISSUES 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？

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

5. 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. 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. Long hedge can be used to manage an existing short position.

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

8. 3.2 Arguments For and Against Hedging • Hedging and Competitors If hedging is not the norm in a certain industry, it may not make sense for one particular company to choose to be different from all other.

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. 1 The hedger may be uncertain as to the exact when the asset will be bought or sold. 2 The hedge may require the futures contract to be closed out before its delivery month. 3 These problem gives rise to what is termedbasic risk.

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 = S – F An increase in the basis is referred to a . strengthening of the basis A decrease in the basis is referred to as a weakening of the basis

12. 3.3 Basis Risk Suppose that F1 : Initial Futures Price F2 : Final Futures Price S2 : Final Asset Price Spot price S1 b1 = S1 –F1 b2 =S2– F2 b1 F1 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 S2+ F1 – F2 = F1 + b2 S2 Futures price b2 F2 basis risk(基差風險) 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 S2+ F1 – F2 = F1 + b2 t1 t2 Figure 3.1 Variation of basic over time

13. 3.3 Basis Risk Choice of Contract • One key factor affecting basis risk is the choice of the futures contract to be used for hedging. This choice has two components: • The choice of the assets underlying the futures contracts • The choice of the delivery month A contract with a laterdelivery 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. σS : Standard deviation of ΔS σF : Standard deviation of ΔF

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

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 Example 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 One future contract is for delivery of $250 times the index Current value of one futures contract = 250*1000 = 250,000 Optimal number of futures contracts for hedging

18. 3.5 Stock Index Future Time to maturity The gain from the short futures position = 30* ( 1,010 – 902 ) *250 = $ 810,000 • 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 % • The risk-free interest rate = 1 % per 3 months • Expected return on portfolio • = 1 + 1.5*( – 9.75 – 1 ) = – 15.125 % = $ 5,000,000*(1 – 0.15125) = $4,243,750 =$ 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 TheHedge Forward • This involves entering into a sequence of futures • contracts to increase the life of a hedge • Rollover basis risk