2. slide no.: 1 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Betriebswirtschaftliche Bewertungsmethoden TOPIC 2 Grundlagen der Konstruktion, Bewertung und des Einsatzes von Zinsfutures und Zinsswaps zur Steuerun von zins- bedingten Risiken Prof. Dr. Rainer Stachuletz Corporate Finance

3. slide no.: 2 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics EURO – BUND FUTURES

4. slide no.: 3 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Buyer (long) has to be delivered Seller (short) must deliver Clearing Eurex 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 €). Euro-Bund-Future: Characteristics

5. slide no.: 4 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics 10. March 10. June 10. Sept. 10. Dec. Purchase at 10th March Delivery latest at 10th Dec. Time to maturity max. 9 month Euro-Bund-Futures Delivery Day/Months

6. slide no.: 5 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics 1 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 €. 2 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 €. 3 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. Euro-Bund-Future: Mechanisms

7. slide no.: 6 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Euro-Bund-Futures: Pricing

8. slide no.: 7 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Short-Future-Position and Margin - Account 5 Days to Settlement Futures 0 Interest Rate8,00%8,50%7,50%7,00% Future86,58%83,60%89,70%92,98% Change0,00%-2,98%6,10%3,28%0,00% Value0,002.980,00-6.100,00-3.280,000,00 Margin2.500,00 5.480,002.500,00 Credits/Debits2.980,00-6.100,00-3.280,00-6.400,00 Current Balance2.500,005.480,00-620,00-780,00 0,00 Maintenance0,00 3.120,003.280,00 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, after 4 days the game ends with a total loss of 6,400 Euro.

9. slide no.: 8 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics How to Hedge a Bond – Portfolio Using Bund 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:

10. slide no.: 9 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics How to Hedge a Bond – Portfolio Using Bund 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.

11. slide no.: 10 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics How to Hedge a Bond – Portfolio Using Bund Futures 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.) Future Price 86,56 Profits 78,66 + 7,900 Rising interest rates cause declining Future Prices

12. slide no.: 11 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics How to Hedge a Bond – Portfolio Using Bund 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 €).

13. slide no.: 12 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Interest Rate Swaps

14. slide no.: 13 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Basic Concept Interest Rate Swap 1.A swap is an agreement between two parties to exchange interest payments within a defined period of time, calculated of an agreed contract – volume. Frequently swaps simply regulate to exchange floating rate payments against fixed rate payments et vice versa. 2.The contract volume will not be exchanged. Also interest payments will not be fully exchanged, but only the saldo. 3.Plain-Vanilla-Swaps are based upon David Ricardo‘s Theory of Trade.

15. slide no.: 14 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics A B Fixed Rate Floating Rate The party paying the fixed rate is called to be in a Payer- Swap-position, while the party receiving fixed rates takes the Receiver-Swap-position. When the contract is signed, the N.P.V. of both cash flows, the variable and the fixed equal zero. Basic Concept Interest Rate Swap

16. slide no.: 15 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Plain Vanilla Interest Rate Swap Pricing Banks publish their swap-conditions. Usually the fixed rates offered referring payer or receiver-swaps are determined by the current term structure of interest rates: WestLB Maturityreceivespays 1J2.894-2.844 2J3.054-3.004 3J3.139-3.089 4J3.182-3.132 5J3.236-3.186 6J3.286-3.236 7J3.337-3.287 8J3.387-3.337 9J3.437-3.387 10J3.483-3.433 15J3.671-3.621 WestLB (26th Dec. 2005) Maturity Average returns 1y2,65% 2y2,82% 3y2,92% 4y3,01% 5y3,09% 6y3,16% 7y3,23% 8y3,29% 9y3,35% 10y3,41% Term structure (26th Dec. 2005)

17. slide no.: 16 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Plain-Vanilla Interest Rate Swap Example: Two corporations, A (Rating AAA) and B (Rating A) are exposed to very different market conditions: floating rate fixed rate target AEuribor5.0 %floating BEuribor + 0.506.5 %fixed

18. slide no.: 17 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics 1. Step: A and B chose financing contracts at their relatively best positions, i.e. A choses a fixed rate while B enters a floating rate loan. Plain-Vanilla Interest Rate Swap Straight Bond A 5% fixe rate A issues a straight bond at 5%. Floating rate loan B EURIBOR + 0.50 % B issues a floating rate loan at EUR + 0.5%.

19. slide no.: 18 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics 2. Step: A and B sign a swap-arrangement, with A receiving a fixed rate of 5.5 % from B and paying Euribor to B. SWAP Euribor Fixe rate 5.5 % Plain-Vanilla Interest Rate Swap Straight Bond A 5% fixe rate A issues a straight bond at 5%. Floating rate loan B EURIBOR + 0.50 % B issues a floating rate loan at EUR + 0.5%.

20. slide no.: 19 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics BOND Floating Loan A B 5% Fixed Rate EURIBOR + 0.50 % SWAP Euribor Fixed rate 5.5 % Balance of Payment A: FIXEDFLOAT. Bond- 5% Swap+ 5.5 %- Euribor Total+ 0.5- Euribor FIXEDFloating LOAN- Eur + 0.5 Swap- 5.5 %+ Eur Total- 5.5 %- 0.5 Plain-Vanilla Interest Rate Swap Balance of Payment B:

21. slide no.: 20 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Bond Floating Rate Loan A B 5% fixed EUR + 0.50 % JPSwap 5.25 % fixed EUR EURIBOR 5.75 % fixed More realistic: A und B contract a Swap – agreement by a financial intermediator (JPSwap). Plain-Vanilla Interest Rate Swap

22. slide no.: 21 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Straight Bond Float. Rate Loan A B 5% FIXED EUR + 0.50 % JPSwap 5.25 % FIXED EUR EURIBOR 5.75 % Fest Balance A: Balance B: FIXEDFLOAT. Bond- 5 % Swap+ 5.25 %- Euribor Total+ 0.25 %- Euribor FIXEDFLOAT. LOAN- Eur + 0.5 Swap- 5.75 %+ Eur Total- 5.75 %- 0.5 % Balance JPSwap: FIXEDFLOAT. Payer- 5.25 %+Euribor Receiver+ 5.75 %- Euribor Total+ 0.5 Plain-Vanilla Interest Rate Swap

23. slide no.: 22 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Example: Risk Management with Asset Swaps Corporation A receives interest revenues generated by a 100 Mio. € bond investment (6y to maturity, 8% coupon). The bonds have been put on the assets side at their costs of purchase (100%). The financial management of A forcasts the interest rates to rise by 1% over the next year. years 123456 r current 3,0%4,0%5,0%6,0%7,0%8,0% r in1year 4,0%5,0%6,0%7,0%8,0%9,0% r spot,0 3,0%4,02%5,07%6,16%7,31%8,55% r spot,1 4,0%5,03%6,08%7,2%8,4%9,6% Rising rates will lead to declining prices (deprecia- tions). Secondly, in case of rising rates, A is not proper- ly invested which may affect her competetive position. Risk management may prevent from losses.

24. slide no.: 23 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Swapbank Euribor 8% fixed rate Corporation A Bond Debtor Example: Risk Management with Asset Swaps To manage the forecasted interest rate related risk, A enters a 6y Payer-Swap (paying a fixed rate of 8%, receiving a floating rate at 12-m-Euribor. The contract volume mirrors the nominal value of the risky asset (100 Mio €): Payer Swap

25. slide no.: 24 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Example: Risk Management with Asset Swaps – Close out If, one year later, the interest rates would have risen by linearly 1.5%, the future cash flows referring the 100 Mio € Swap (which now matures in 5y !) could be valued using the new spot rates: Value of the swap contract is at 2,038,655 Mio €. To close out, A will be paid the swap‘s present value.

26. slide no.: 25 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Example: Risk Management with Asset Swaps – 2nd Swap Swapbank 1 Euribor 8% fixed rate Corporation A Bond Debtor 1st. Payer Swap Swapbank 2 Euribor 8,5% fixed rate 2nd. Receiver Swap Theoretically, after one year A could enter a second swap, where she becomes a fixed rate receiver (5y at 8,5%) The advantage of 0.5% or 500 T€ over a period of 5 years has a present value of 2.038.655 €. A second swap could be reasonable to ensure the advantage and to protect from tax payments.

27. slide no.: 26 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Example: Risk Management with Asset Swaps – Efficiency If interest rates rise as forcasted, the value of the 100 Mio. bonds investment will decrease to 97,961 Mio €: A necessary depreciation will affect the profit and loss account by a loss of 2.038.655 € (100 Mio purchase price minus 97,961,345 € current market price). In our case, the swap – based risk management has shown a positive present value of 2,038,655 €. A close out and the close out payment at this amount would perfectly compensate the loss from the bond‘s investment.