Betriebswirtschaftliche
Bewertungsmethoden
TOPIC 2
Grundlagen der Konstruktion,
Bewertung und des Einsatzes von
Zinsfutures und Zinsswaps
zur Steuerun von zinsbedingten Risiken
Prof. Dr. Rainer Stachuletz
Corporate Finance
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
slide no.: 1
EURO – BUND
FUTURES
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
slide no.: 2
Euro-Bund-Future: Characteristics
Contract Size: 100.000 €
Buyer (long)
has to be
delivered
Settlement: 6% German
Federal Bonds with 8,5 to
10,5 years remaining term
upon delivery
Delivery day: 10th of March,
June, September, December
Seller (short)
must
deliver
Quotation: percentage at a
minimum price movement of
0,01% (10 €).
Clearing
Eurex
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
slide no.: 3
Euro-Bund-Futures
Delivery Day/Months
Purchase
at 10th March
10.
March
Delivery latest
at 10th Dec.
10.
June
10.
Sept.
10.
Dec.
Time to maturity max. 9 month
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
slide no.: 4
Euro-Bund-Future: Mechanisms
1
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
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.
slide no.: 5
Euro-Bund-Futures: Pricing
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
slide no.: 6
Short-Future-Position and Margin - Account
5 Days to Settlement
Futures
Interest Rate
Future
Change
Value
-1
-1
-1
-1
0
8,00%
86,58%
0,00%
0,00
8,50%
83,60%
-2,98%
2.980,00
7,50%
89,70%
6,10%
-6.100,00
7,00%
92,98%
3,28%
-3.280,00
7,00%
92,98%
0,00%
0,00
Margin
2.500,00
Credits/Debits
Current Balance 2.500,00
Maintenance
0,00
2.500,00
2.980,00
5.480,00
0,00
5.480,00
-6.100,00
-620,00
3.120,00
2.500,00
-3.280,00
-780,00
3.280,00
2.500,00
-6.400,00
0,00
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.
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
slide no.: 7
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:
Bonds
Nominal Value
(Purchase Price)
Coupon
Time to
Maturity
Current
Price
A
B
10.000.000,00
10.000.000,00
8%
6%
10y
8y
10.000.000,00
8.851.000,00
Total
20.000.000,00
18.851.000,00
Now you expect the term – structure to rise to 10% flat. Due to
the rising rates your devaluation risk is as follows:
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
Bonds
Nominal Value
(Purchase Price)
Coupon
Time to
Maturity
Current
Price
A
B
10.000.000,00
10.000.000,00
8%
6%
10y
8y
8.770.000,00
7.866.000,00
Total
20.000.000,00
16.636.000,00
slide no.: 8
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.
Bonds
Nominal Value
(Purchase Price)
Current
Price at 8%
Current
Price at 10%
Profit
Loss
A
B
10.000.000,00
10.000.000,00
10.000.000,00
8.851.000,00
8.770.000,00
7.866.000,00
1.230.000,00
985.000,00
Total
20.000.000,00
18.851.000,00
16.636.000,00
2.215.000,00
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.
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
slide no.: 9
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
Profits
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 €.
+ 7,900
(In this Ex. 156 K to hedge A
and 124 K to hedge B.)
78,66
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
86,56
Future
Price
Rising interest rates
cause declining
Future Prices
slide no.: 10
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:
Bonds
Nominal Value
(Purchase Price)
A
B
10.000.000,00
10.000.000,00
Total
20.000.000,00
Profit/Loss
Bonds
Profit / Loss
Bund Future
Profit / Loss
Total
-1.230.000,00
-985.000,00
1.232.400,00
979.600,00
2.400,00
-5.400,00
2.212.000,00
-3.000,00
-2.215.000,00
The total loss in your bond – portfolio (- 2,215 Mio €) is
compensated by profits from your hedge – portfolio (+
2,212 Mio €).
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
slide no.: 11
Interest Rate
Swaps
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
slide no.: 12
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.
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
slide no.: 13
Basic Concept Interest Rate Swap
Fixed Rate
B
A
Floating Rate
The party paying the fixed rate is called to be in a PayerSwap-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.
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
slide no.: 14
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:
Term structure (26th Dec. 2005)
WestLB (26th Dec. 2005)
Maturity
1J
2J
3J
4J
5J
6J
7J
8J
9J
10J
15J
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
WestLB
receives
2.894
3.054
3.139
3.182
3.236
3.286
3.337
3.387
3.437
3.483
3.671
-
WestLB
pays
2.844
3.004
3.089
3.132
3.186
3.236
3.287
3.337
3.387
3.433
3.621
1y
2y
3y
4y
5y
6y
7y
8y
9y
Average
returns
2,65%
2,82%
2,92%
3,01%
3,09%
3,16%
3,23%
3,29%
3,35%
10y
3,41%
Maturity
slide no.: 15
Plain-Vanilla Interest Rate Swap
Example:
Two corporations, A (Rating AAA) and B (Rating A) are
exposed to very different market conditions:
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
floating
rate
fixed
rate
target
A
Euribor
5.0 %
floating
B
Euribor + 0.50
6.5 %
fixed
slide no.: 16
Plain-Vanilla Interest Rate Swap
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 issues a
straight
bond at 5%.
A
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
5% fixe rate
Floating rate loan
B issues a
floating rate
loan at EUR
+ 0.5%.
EURIBOR
+ 0.50 %
B
slide no.: 17
Plain-Vanilla Interest Rate Swap
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.
Straight Bond
A issues a
straight
bond at
5%.
Floating rate loan
B issues a
floating rate
loan at EUR
+ 0.5%.
5% fixe rate
EURIBOR
+ 0.50 %
B
A
Euribor
SWAP
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
Fixe rate 5.5 %
SWAP
slide no.: 18
Plain-Vanilla Interest Rate Swap
Balance of Payment A:
FIXED
Balance of Payment B:
FLOAT.
FIXED
Floating
Bond
- 5%
Swap
+ 5.5 %
- Euribor
Swap
- 5.5 %
+ Eur
Total
+ 0.5
- Euribor
Total
- 5.5 %
- 0.5
LOAN
BOND
- Eur + 0.5
Floating Loan
EURIBOR
+ 0.50 %
5%
Fixed Rate
A
SWAP
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
Euribor
Fixed rate 5.5 %
B
SWAP
slide no.: 19
Plain-Vanilla Interest Rate Swap
More realistic: A und B contract a Swap – agreement by a
financial intermediator (JPSwap).
Floating Rate Loan
Bond
EUR
+ 0.50 %
5% fixed
EUR
A
5.75 %
fixed
5.25 %
fixed
B
EURIBOR
JPSwap
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
slide no.: 20
Plain-Vanilla Interest Rate Swap
Balance A:
FIXED
Balance JPSwap:
Balance B:
FIXED
FLOAT.
FIXED
Payer
- 5.25 %
+Euribor
LOAN
- Euribor
Swap
- 5.75 %
+ Eur
Total
- 5.75 %
- 0.5 %
FLOAT.
Bond
-5%
Swap
+ 5.25 %
- Euribor
Receiver
+ 5.75 %
Total
+ 0.25 %
- Euribor
Total
+ 0.5
Straight Bond
- Eur + 0.5
Float. Rate Loan
EUR
+ 0.50 %
5% FIXED
EUR
A
FLOAT.
5.75 %
Fest
5.25 %
FIXED
B
EURIBOR
JPSwap
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
slide no.: 21
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
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%
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
2
3
4
7,2%
5
8,4%
6
9,6%
Rising rates will lead to
declining prices (depreciations). Secondly, in case of
rising rates, A is not properly invested which may affect
her competetive position.
Risk management may
prevent from losses.
slide no.: 22
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 €):
Bond Debtor
Payer Swap
8%
fixed rate
8% fixed rate
Corporation A
Swapbank
Euribor
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
slide no.: 23
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%
5,50%
6,50%
7,50%
8,50%
9,50%
4,50000%
5,52777%
6,58990%
7,70163%
8,88307%
10,16229%
0
1
2
Cash Flow
100.000.000 -8.000.000 -8.000.000
Spot rates
4,50%
5,53%
Present values 100.000.000 -7.655.502 -7.183.836
3
-8.000.000
6,59%
-6.606.050
4
5
NPV
-8.000.000 -108.000.000
7,70%
8,88%
-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.
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
slide no.: 24
Example: Risk Management with Asset
Swaps – 2nd Swap
Bond Debtor
1st. Payer Swap
8%
fixed rate
Theoretically, after one
year A could enter a
second swap, where she
becomes a fixed rate
receiver (5y at 8,5%)
8% fixed rate
Corporation A
Swapbank 1
Euribor
8,5%
fixed
rate
Euribor
Swapbank 2
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
2nd.
Receiver
Swap
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.
slide no.: 25
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
Cash Flow
8.000.000 8.000.000
Spot rates
4,50%
5,53%
PV
97.961.345 7.655.502 7.183.836
3
8.000.000
6,59%
6.606.050
4
8.000.000
7,70%
5.945.671
5
108.000.000
8,88%
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.
Prof. Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics
slide no.: 26