slide no.: 1 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics...

slide no.: 1Prof. Dr. Rainer StachuletzCorporate FinanceBerlin 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 StachuletzCorporate Finance


EURO – BUND FUTURES


Buyer (long)

has to bedelivered

Seller (short)

mustdeliver

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


10. Marc

h

10. June

10. Sept

.

10. Dec

.

Purchaseat 10th March

Delivery latestat 10th Dec.

Time to maturity max. 9 month

Euro-Bund-Futures Delivery Day/Months


1The 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


Euro-Bund-Futures: Pricing


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 2.500,00Credits/Debits 2.980,00 -6.100,00 -3.280,00 -6.400,00Current Balance 2.500,00 5.480,00 -620,00 -780,00 0,00Maintenance 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, after 4 days the game ends with a total loss of 6,400 Euro.


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:

Bonds Nominal Value Coupon Time to Current(Purchase Price) Maturity Price

A 10.000.000,00 8% 10y 10.000.000,00B 10.000.000,00 6% 8y 8.851.000,00

Total 20.000.000,00 18.851.000,00

Bonds Nominal Value Coupon Time to Current(Purchase Price) Maturity Price

A 10.000.000,00 8% 10y 8.770.000,00B 10.000.000,00 6% 8y 7.866.000,00

Total 20.000.000,00 16.636.000,00



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.

Bonds Nominal Value Current Current Profit (Purchase Price) Price at 8% Price at 10% Loss

A 10.000.000,00 10.000.000,00 8.770.000,00 1.230.000,00B 10.000.000,00 8.851.000,00 7.866.000,00 985.000,00

Total 20.000.000,00 18.851.000,00 16.636.000,00 2.215.000,00



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



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 €).

Bonds Nominal Value Profit/Loss Profit / Loss Profit / Loss (Purchase Price) Bonds Bund Future Total

A 10.000.000,00 -1.230.000,00 1.232.400,00 2.400,00B 10.000.000,00 -985.000,00 979.600,00 -5.400,00

Total 20.000.000,00 -2.215.000,00 2.212.000,00 -3.000,00


Interest RateSwaps


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.


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


Plain Vanilla Interest Rate SwapPricing

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 WestLBMaturity receives pays1J 2.894 - 2.8442J 3.054 - 3.0043J 3.139 - 3.0894J 3.182 - 3.1325J 3.236 - 3.1866J 3.286 - 3.2367J 3.337 - 3.2878J 3.387 - 3.3379J 3.437 - 3.38710J 3.483 - 3.43315J 3.671 - 3.621

WestLB (26th Dec. 2005)

MaturityAveragereturns

1y 2,65%2y 2,82%3y 2,92%4y 3,01%5y 3,09%6y 3,16%7y 3,23%8y 3,29%9y 3,35%10y 3,41%

Term structure (26th Dec. 2005)


Plain-Vanilla Interest Rate Swap

Example:

Two corporations, A (Rating AAA) and B (Rating A) are exposed to very different market conditions:

floating rate

fixedrate

target

A Euribor 5.0 % floating

B Euribor + 0.50 6.5 % fixed


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.


Straight Bond

A

5% fixe rateA issues astraight bond at 5%.

Floating rate loan

B

EURIBOR+ 0.50 %

B issues afloating rate loan at EUR + 0.5%.


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 SWAPEuribor

Fixe rate 5.5 %


Straight Bond

A

5% fixe rateA issues astraight bond at 5%.

Floating rate loan

B

EURIBOR+ 0.50 %

B issues afloating rate loan at EUR + 0.5%.


BOND Floating Loan

A B

5% Fixed Rate

EURIBOR+ 0.50 %

SWAP SWAPEuribor

Fixed rate 5.5 %

Balance of Payment A:FIXED FLOAT.

Bond - 5%

Swap + 5.5 % - Euribor

Total + 0.5 - Euribor

FIXED Floating

LOAN - Eur + 0.5

Swap - 5.5 % + Eur

Total - 5.5 % - 0.5


Balance of Payment B:


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).



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:FIXED FLOAT.

Bond - 5 %

Swap + 5.25 % - Euribor

Total + 0.25 % - Euribor

FIXED FLOAT.

LOAN - Eur + 0.5

Swap - 5.75 % + Eur

Total - 5.75 % - 0.5 %

Balance JPSwap:FIXED FLOAT.

Payer - 5.25 % +Euribor

Receiver + 5.75 % - Euribor

Total + 0.5



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 1 2 3 4 5 6

rcurrent 3,0% 4,0% 5,0% 6,0% 7,0% 8,0%

rin1year 4,0% 5,0% 6,0% 7,0% 8,0% 9,0%

rspot,0 3,0% 4,02% 5,07% 6,16% 7,31% 8,55%

rspot,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.


Swapbank

Euribor

8% fixed rate

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


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:Average Returns Spot Rates

4,50% 4,50000%5,50% 5,52777%6,50% 6,58990%7,50% 7,70163%8,50% 8,88307%9,50% 10,16229%

0 1 2 3 4 5 NPVCash Flow 100.000.000 -8.000.000 -8.000.000 -8.000.000 -8.000.000 -108.000.000Spot rates 4,50% 5,53% 6,59% 7,70% 8,88%Present values 100.000.000 -7.655.502 -7.183.836 -6.606.050 -5.945.671 -70.570.285 2.038.655

Value of the swap contract is at 2,038,655 Mio €. To close out, A will be paid the swap‘s present value.


Example: Risk Management with Asset Swaps – 2nd Swap

Swapbank 1

Euribor

8% fixed rate

8 % fixed rate

Corporation A

Bond Debtor1st. Payer Swap

Swapbank 2

Euribor8,5%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.


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 €:

0 1 2 3 4 5Cash Flow 8.000.000 8.000.000 8.000.000 8.000.000 108.000.000Spot rates 4,50% 5,53% 6,59% 7,70% 8,88%

PV 97.961.345 7.655.502 7.183.836 6.606.050 5.945.671 70.570.285

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.

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slide no.: 1 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics...

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