1. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 3.1 Hedging Strategies Using Futures Chapter 3

2. Margins in TURKDEX -FOREX Futures Size of the contract: $1000; 1000 Euro Maturities: February, April, June, August, October, December US Dollar:  Initial Margin: 180 TL/contract  Maintenance Margin: 135 TL/contract Euro:  Initial Margin: 240 TL/contract  Maintenance Margin: 180 TL/contract Long & short futures together: one initial margin is paid

3. Margins in TURKDEX -INDEX Futures Size of the contract: 100 shares/units ISE-30 & ISE-100:  Initial Margin: 500 TL/contract  Maintenance Margin: 375 TL/contract Long & short futures together: one initial margin is paid

4. Hedger Use futures markets to reduce a particular risk To make profit (not an objective) Perfect hedge: complete elimination of risk Hedge-and-forget strategies:  Hedge once  No change in position  Close out the position at the end of the life time of the hedge

5. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 3.5 Short Hedges Appropriate when the hedger already owns an asset, expects to sell it in the future & want to lock in the price Can be used when an asset is not owned right now but will be owned at some time in the future  Exporters  Farmers, producers

6. Long Hedges Appropriate when the hedger knows he will have to purchase an asset in the future and want to lock in the price now. Can be used to manage a short position No delivery (generally) High cost and inconvenience  Importers  Manufacturing companies

7. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 3.7 Arguments in Favor of Hedging Companies should: focus on the main business they are in take steps to minimize risks arising from interest rates, exchange rates, and other market variables

8. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 3.8 Arguments against Hedging Shareholders vs companies Competitors vs companies Problem: there is a loss on the hedge and a gain on the underlying asset

9. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 3.9 Convergence of Futures to Spot (Hedge initiated at time t 1 and closed out at time t 2 ) Time Spot Price Futures Price t1t1 t2t2

10. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 3.10 Basis Risk The asset whose price to be hedged ≠ the asset underlying the futures contract Basis: the difference between spot price of the asset to be hedged & futures price of the contract used (S - F) Strengthening of the basis: increase in spot price > increase in futures price Weakening of the basis: İncrease in futures price > increase in spot price

11. Basis risk: the uncertainty about the basis when the hedge is closed out Choice of the contract affects basis risk:  The choice of the asset underlying the futures contract  The choice of the delivery month Strategy: choose the contracts with futures prices highly correlated with the price of the asset being hedged

12. Time difference between the hedge expiration and delivery month: positively correlated with basis risk Strategy: choose a delivery month as close as to the delivery month

13. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 3.13 Short Hedge Suppose that F 1 : Initial Futures Price F 2 : Final Futures Price S 2 : Final Asset Price You hedge the future sale of an asset by entering into a short futures contract Price Realized= S 2 + ( F 1 – F 2 ) = F 1 + Basis

14. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 3.14 Long Hedge Suppose that F 1 : Initial Futures Price F 2 : Final Futures Price S 2 : Final Asset Price You hedge the future purchase of an asset by entering into a long futures contract Cost of Asset= S 2 + ( F 2 – F 1 ) = F 1 + Basis

15. Cross Hedging The asset whose price to be hedged ≠ the asset underlying the futures contract Using heating oil futures contracts to hedge jet fuel exposure

16. Hedge Ratio The ratio of the size of the position taken in futures contracts to the size of the exposure HR=1: if the asset underlying the futures contract is the same as the asset being hedged Not always optimal A value that minimizes the variance of the value of the hedged position: optimal hedge ratio

17. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 3.17 Optimal Hedge Ratio Proportion of the exposure that should optimally be hedged is where  S is the standard deviation of  S, the change in the spot price during the hedging period,  F is the standard deviation of  F, the change in the futures price during the hedging period  is the coefficient of correlation between  S and  F.

18. Hedge effectiveness (HE): the proportion of the variance that is eliminated by hedging HE: R 2 from the regression of  S against  F

19. Optimal Number of Contracts N* = ( h* N A )/Q F N A : Size of position being hedged (units) Q F : Size of one futures contract (units) N* : Optimal number of futures contracts for hedging

20. Stock Index Futures Stock index: tracks the changes in the value of a portfolio of stocks Omission of dividends Capital gain from investing in the portfolio Cash settlement for futures contracts on stock indices Marked to market of all contracts

21. Hedging Using Index Futures ( (if the portfolio exactly mirror the index Stock index futures can be used to hedge an equity portfolio If the portfolio mirrors the index, hedge ratio of 1 is appropriate. N* = P/A N* : number of contracts to be shorted P : current value of the portfolio A : current value of the stocks underlying one futures contract

22. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 3.22 Example Current value of S&P 500 is 1,000 Size of portfolio is $1 million One contract is on $250 times the index What position in futures contracts on the S&P 500 is necessary to hedge the portfolio?

23. P = 1,000,000 A = 250*1,000 N* = 1,000,000/250,000  N* =4

24. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 3.24 Hedging Using Index Futures (if the portfolio does not exactly mirror the index) To hedge the risk in a portfolio the number of contracts that should be shorted is where P is the value of the portfolio,  is its beta, and A is the value of the assets underlying one futures contract

25. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 3.25 Example Value of S&P 500 is 1,000 Size of portfolio is $5 million Beta of portfolio is 1.5 One contract is on $250 times the index Risk-free interest rate: 4 % per annum Dividend yield on index: 1 % per annum Current futures price: $ 1,010 Futures price (3 moths later): $ 902 What position in futures contracts on the S&P 500 is necessary to hedge the portfolio (short)?

26. Example (continued) We assume that a futures contract on the S&P 500 with four months to maturity is used to hedge the value of the portfolio over the next three months. One futures contract is for delivery of $250 times the index. (A = 250 x 1,000 = 250,000) Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 3.26

27. Example (continued) The number of futures contracts that should be shorted to hedge portfolio is Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 3.27

28. Example (continued) Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 3.28 Suppose the index turns out to be 900 in 3 months and futures price is 902. The gain from the short futures position is then 30 x (1010 – 902) x 250 = $810,000 The loss on the index is 10%. The index pays a dividend of 1% per annum, or 0.25% per 3 months. When dividends are taken into account, an investor in the index would therefore earn -9.75% in the 3- month period. The risk free interest rate is approximately 1% per 3 months. Because the portfolio has a β of 1.5, capital asset pricing model gives Expected return on portfolio: Risk free interest rate + 1.5 x (Return on index – Risk-free interest rate)

29. Example (continued) Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 3.29 It follows that the expected return (%) on the portfolio during the 3 months is 1.0+[1.5 x (-9.75-1.0)]=-15.125 The expected value of the portfolio (inclusive of dividends) at the end of the 3 month is therefore $5,000,000 x (1-0.15125) = $4,243,750 It follows that the expected value of the hedger’s position, including the gain on the hedge, is $4,243,750 + $810,000 = $5,053,750

30. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 3.30 Reasons for Hedging an Equity Portfolio Desire to be out of the market for a short period of time. (Hedging may be cheaper than selling the portfolio and buying it back.) Desire to hedge systematic risk (Appropriate when you feel that you have picked stocks that will outperform the market.)

31. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 3.31 Changing Beta Futures contracts can be used to change the beta of the portfolio. What position is necessary to reduce the beta of the portfolio from 1.5 to 0.75? What position is necessary to increase the beta of the portfolio from 1.5 to 2.0?

32. ↓ in beta, ↓ in number of contracts (short position) β > β* (short position)  (β – β*) (P/A)  (1.5-0.75) (5,000,000/250,000) = 15 β < β* (long position)  (β* – β) (P/A)  (2-1.5) (5,000,000/250,000) = 10

33. Exposure to the Price of an Individual Stock Trade of futures contracts on selected individual stocks If no, hedging of an individual stock by a stock index futures contract

34. Hedging provides protection only against the risk arising from market movements (small proportion of total risk) Appropriate when an investor feels that the stock outperform the market but not sure about the performance of the market Similarity with hedging a stock portfolio N* = β(P/A)  Β: beta of the stock  P: total value of the shares owned  A: current value of the stocks underlying one futures contact

35. Example Hoding 20,000 IBM shares in June, each worth $100 Expectation: volatility in the market & outperform of IBM Decision: use August futures contract on S&P 500 to hedge position Β of IBM: 1.1 Current level of S&P 500: 900 Current futures price for the August contract:908 Each contract: $250 times the index

36. P = 20,000 * 100 = 2,000,000 A = 900*250 = 225,000 N* = 1.1 (2,000,000/225,000) = 9,78 (10) If IBM rises to 125 and S&P 500 rises to 1080? Investor gains: 20,000 (125-100)=500,000 on IBM Investor loses: 10*250*(1080- 908)=430,000 on futures contacts

37. Fundamentals of Futures and Options Markets, 6 th Edition, Copyright © John C. Hull 2007 3.37 Rolling The Hedge Forward We can use a series of futures contracts to increase the life of a hedge Each time we switch from 1 futures contract to another we incur a type of basis risk

38. EXAMPLE Company realizes that it will have 100,000 barrels of oil to sell in June 2005. Decides to hedge its risk with hedge ratio of 1.0. Short futures 1,000 barrels/contract 100 contracts.

39. DateApr 2004Sept 2004Feb 2005June 2005 Oct 2004 Futures price 18.2017.40 Mar 2005 Futures price 17.0016.50 July 2005 Futures price 16.3015.90 Spot price 19.0016.00

40. Fundamentals of Futures and Options Markets, 5 th Edition, Copyright © John C. Hull 2004 3.40 The dollar gain per barrel of oil from short futures contracts is (18.20-17.40) + (17.00-16.50) + (16.30-15.90) = 1.70 The oil price declined from $19 to $16. Receiving only $1.70 per barrel compensation for a price decline of $3.00 may appear unsatisfactory. However, we cannot expect total compensation for a price decline when futures prices are below spot prices. The best we can hope for is to lock in the futures price that would apply to a June 2005 contract if it were actively traded.

41. TOTAL GAIN/LOSS (18.20-17.40) (17.00-16.50) (16.30-15.90) TOTAL GAIN = $ 1.70/barrel Lower than 19.00-16.00 = $ 3.00 (change in spot price)