Part 4.1 Applications of Financial Futures And Forwards

1. Part 4.1Applications of Financial Futures And Forwards Derivative Instruments Introduction To Mechanisms, Applications and Valuation 1

2. Spot Rates and Forward Rates Forward Rate Agreements Euro-Bund-Futures SWAPS How to Set Up A Hedge Using Swaps Topics Covered

3. Long & Short Hedges A long futures hedge is appropriate when you know you will purchase an asset in the future and want to lock in the price A short futures hedge is appropriate when you know you will sell an asset in the future and want to lock in the price 3

4. Arguments in Favor of Hedging Companies should focus on the main business they are in and take steps to minimize risks arising from interest rates, exchange rates, and other market variables 4

5. Arguments against Hedging Shareholders are usually well diversified and can make their own hedging decisions It may increase risk to hedge when competitors do not Explaining a situation where there is a loss on the hedge and a gain on the underlying can be difficult 5

6. Convergence of Futures to Spot(Hedge initiated at time t1 and closed out at time t2) Futures Price Spot Price Time t1 t2 6

7. Basis Risk Basis is the difference between the spot and futures price Basis risk arises because of the uncertainty about the basis when the hedge is closed out 7

8. Long Hedge We define F1: Initial Futures Price F2: Final Futures Price S2: Final Asset Price If you hedge the future purchase of an asset by entering into a long futures contract then Cost of Asset=S2– (F2– F1)= F1+ Basis 8

9. Short Hedge Again we define F1: Initial Futures Price F2: Final Futures Price S2: Final Asset Price If you hedge the future sale of an asset by entering into a short futures contract then Price Realized=S2+(F1 – F2)= F1+Basis 9

10. Choice of Contract Choose a delivery month that is as close as possible to, but later than, the end of the life of the hedge When there is no futures contract on the asset being hedged, choose the contract whose futures price is most highly correlated with the asset price. This is known as cross hedging. 10

11. Optimal Hedge Ratio (page 55) Proportion of the exposure that should optimally be hedged is where sS is the standard deviation of DS, the change in the spot price during the hedging period, sF is the standard deviation of DF, the change in the futures price during the hedging period r is the coefficient of correlation between DS and DF. 11

12. Tailing the Hedge Two way of determining the number of contracts to use for hedging are Compare the exposure to be hedged with the value of the assets underlying one futures contract Compare the exposure to be hedged with the value of one futures contract (=futures price time size of futures contract The second approach incorporates an adjustment for the daily settlement of futures 12

13. Hedging Using Index Futures To hedge the risk in a portfolio the number of contracts that should be shorted is where P is the value of the portfolio, b is its beta, and F is the value of one futures contract 13

14. Example S&P 500 futures price is 1,000 Value of Portfolio is $5 million Beta of portfolio is 1.5 What position in futures contracts on the S&P 500 is necessary to hedge the portfolio? 14

15. Changing Beta What position is necessary to reduce the beta of the portfolio to 0.75? What position is necessary to increase the beta of the portfolio to 2.0? 15

16. Hedging Price of an Individual Stock Similar to hedging a portfolio Does not work as well because only the systematic risk is hedged The unsystematic risk that is unique to the stock is not hedged 16

17. Why Hedge Equity Returns May want to be out of the market for a while. Hedging avoids the costs of selling and repurchasing the portfolio Suppose stocks in your portfolio have an average beta of 1.0, but you feel they have been chosen well and will outperform the market in both good and bad times. Hedging ensures that the return you earn is the risk-free return plus the excess return of your portfolio over the market. 17

18. Rolling The Hedge Forward (page 64-65) We can use a series of futures contracts to increase the life of a hedge Each time we switch from one futures contract to another we incur a type of basis risk 18

19. Term – Structure of Interest Rates and related Spot Rates (Calculation) Example:

20. Spot Rates and related Forward Rates (Calculation Scheme)

21. Homemade Forward Rate Contracts Forwards simply consist of borrowing and lending at different maturities. Referring to our time struc-ture, the cash flow of a forward contract that starts in one year for one year can be duplicated as follows:

22. Fixed Rate: 3,30% Example: F.R.A. 12x24 12 months 12 months Maturity of F.R.A. Time to Market Forward Rates (F.R.A. - Application) To contract a Forward-Rate means to lock in an interest rate concerning a future period. Your corporation might use an F.R.A. (= Forward Rate Agreement) to make sure, that her future costs of financing a 1-year 10 Mio € loan will not exceed 3,30 %.

23. Profit Long F.R.A. Locked-in Rate: 3,3% Loss Forward Rates (F.R.A. - Application) Scenario 1:Short rate in t1 is at 5%. Financing costs will be 500 T€. Compensations on F.R.A. will be (5%-3,3%)x10 Mio = +170 T€. Total costs: (500-170)=330 T€ (= 3,3%) Scenario 2:Short rate in t1 is at 2%. Financing costs will be 200 T€. Payments on F.R.A. will be (2%-3,3%)x10 Mio = -130 T€. Total costs: (200 +130)=330 T€ (= 3,3%)

24. Euro-Bund-Future: Characteristics Contract Size: 100.000 € Settlement: 6% German Federal Bonds with 8,5 to 10,5 years remaining term upon delivery Delivery day: 10th of March, June, September, December Quotation: percentage at a minimum price movement of 0,01% (10 €). Buyer (long) has to bedelivered Seller (short) mustdeliver Clearing Eurex

25. Euro-Bund-Futures Delivery Day/Months Purchaseat 10th March Delivery latestat 10th Dec. 10. March 10. June 10. Sept. 10. Dec. Time to maturity max. 9 month

26. The market yield of 10y governmental german bonds is at 6% and does not change to the maturity of the future:The seller must deliver 100.000 € nominal at futures maturity. This will cost 100.000 €. 1 The market yield drops from 6% to 5%, i.e. the bond‘s price will rise to 107,72:The seller must deliver 100.000 € nominal, which now equals 107.720 Euro.  At the settlement date, the buyer receives a payment of 7.720 €. 2 The market yield rises to 10%, i.e. the price then will drop to 75,42.Now the seller has to pay 75.420 € to deliver 100.000 € nominal. At settlement the seller gets a payment of 24.580 € per contract. 3 Euro-Bund-Future: Mechanisms

27. Euro-Bund-Futures: Pricing Pricing Euro - Bund Future at 18th June 2002: 106,41 (Term-structure as of 17th June)

28. Short-Future-Position and Margin - Account 5 Days to Settlement Futures -1 -1 -1 -1 0 Interest Rate 8,00% 8,50% 7,50% 7,00% 7,00% Future 86,58% 83,60% 89,70% 92,98% 92,98% Change 0,00% -2,98% 6,10% 3,28% 0,00% Value 0,00 2.980,00 -6.100,00 -3.280,00 0,00 Margin 2.500,00 2.500,00 5.480,00 2.500,00 2.500,00 Credits/Debits 2.980,00 -6.100,00 -3.280,00 -6.400,00 Current Balance 2.500,00 5.480,00 -620,00 -780,00 0,00 Maintenance 0,00 0,00 3.120,00 3.280,00 Taking a short position would only make sense, if the future interest rate is expected to rise (see the profit of 2,980 due to a rise of 50 BP). Only in that case the Future, contracted at 86,58% could be „delivered“ at lower prices. As this is not the case, 4 days the game ends with a total loss of 6,400 Euro.

29. How to Hedge a Bond – Portfolio UsingBund Futures Assume a small bond – portfolio, that contains following positions. Current prices are calculated at an 8% flat rate: Now you expect the term – structure to rise to 10% flat. Due to the rising rates your devaluation risk is as follows:

30. How to Hedge a Bond – Portfolio UsingBund Futures Due to the expected future interest rate scenario, you are exposed to the risk of devaluation. According to Internationalo Financial Reporting Standards you will have to depreciate your bond – portfolio. The depreciation of 2,215 mio € is going to worsen your profit and loss account. To compensate for this risk, you decide to hedge using an instrument, that will profit from rising rates. A short position in Bund Futures, where the seller has to deliver 100.000 € nominal per contract, will gain from rising rates. A declining Bund Future price allows for a „cheap“ delivery.

31. How to Hedge a Bond – Portfolio UsingBund Futures Profits + 7,900 Rising interest rates cause declining Future Prices Future Price 78,66 86,56 Today (flat rate at 8%) you may take a short Bund-Future position at a Future-price of 86.56. If the interest rates rise to a level of 10%, the Bund – Future will be quoted at 78.66. The short position will gain 7.900 € (86,560 – 78,660) per contract, thus you need to short 280 contracts ( 2,215 mio€ / 7,900 T€), to hedge the risk of a portfolio devaluation at 2,215 mio €. (In this Ex. 156 K to hedge A and 124 K to hedge B.)

32. How to Hedge a Bond – Portfolio UsingBund Futures After the interest rate has risen to 10%, the total account of your bond – and your hedge (Bund-Future) – portfolio looks as follows: The total loss in your bond – portfolio (- 2,215 Mio €) is compensated by profits from your hedge – portfolio (+2,212 Mio €).