Swap Agreements
I NTEREST R ATE S WAP A GREEMENTS
An interest rate swap is an agreement to exchange interest rate payments on a notional
p r i n c i p a l a m o u n t over a specific period of time. Generally a swap exchanges fixed rate
interest payments for floating rate payments.
L EXAMPLE:
The Bank of America is a large triple A rated commercial bank. Hypothetical
Resources is a triple B rated industrial corporation. Both firms require $100
million for 10 years.
The Bank of America could issue 10 year bonds at 10% or issue commercial
paper at T-Bill plus 30 basis points. It prefers to stay in the short end of the
market because its liabilities are short term.
Hypothetical Resources could issue 10 year bonds at 11.9% or issue
commercial paper at T-Bill plus 80 basis points. However, HR is engaged in
long term R&D and would prefer long term borrowing.
Rating
Bond Rate
Bank of America
AAA
10.00%
T-Bill + .30%
Hypothetical Resources
BBB
11.90%
T-Bill + .80%
Basis point difference
190
Commercial Paper
Rate
50
Note that the lower credit rating costs HR a full 190 basis points in
the bond market but only 50 basis points in the commercial paper
market.
The swap works like this.
The Bank of America issues 10 year bonds at 10% thus committing itself to
interest payments of $5 million every six months. Hypothetical Resources
issues commercial paper at T-Bill plus 80; the commercial paper is running on
a 182 day roll. Each corporation borrows in the market in which it
has a comparative advantage.
An intermediary (generally a commercial or investment bank) sets up a swap
arrangement on a notional principal amount of $100 million whereby
Hypothetical Resources pays the Bank of America 11% and the Bank of America
pays T-Bill plus 70 basis points. Of this 20 basis points goes to the
intermediary and T-Bill plus 50 goes to Hypothetical Resources. (We have set
up this swap so that the interest payments coincide,- payment every six
months,- but there is no reason why they must.)
[2]
Risk Management
As a result of the swap the Bank of America buys short term financing at the TBill rate less 30 basis points; 60 basis points less than it could do so in the
commercial paper market. Hypothetical Resources buys long term financing at
11.3%; 60 basis points less than it could do so in the bond market. This is a
Credit Arbitrage Swap.
Every six months we have the following cash flows:
Bank of America (sells the swap or is short a swap)
interest on bond issue
- 10.00%
interest received on swap
+ 11.00%
interest payment on swap
- (T-Bill + 0.70)%
TOTAL
- (T-Bill - 0.30)%
Hypothetical Resources (buys the swap or is long a swap)
interest on commercial paper
- (T-Bill + 0.80)%
interest received on swap
+ (T-Bill + 0.50)%
interest payment on swap
%y {
x
- 11.00%
TOTAL
- 11.30%
On the Bank of America we have:
- 10.00 + 11.00 - (T-Bill + 0.70)
= - 10.00 + 11.00 - T-Bill - 0.70
= 0.30 - T-Bill
= - (T-Bill - 0.30)
%y {
x
On Hypothetical resources we have:
- (T-Bill + 0.80) + (T-Bill + 0.50) - 11.00
= - T-Bill - 0.80% + T-Bill + 0.50 - 11.00
= - 11.30
A swap arrangement can be used to take advantage of differences in the credit spread in two
segments of the capital market (in the example this difference was between the long and the short
market) but there are swaps that arbitrage credit spreads in the US and Eurodollar market, etc.,
or to alter the cash flow characteristics of the firm's liabilities to better match its assets. There
are also Basis Rate Swaps in which both counter-parties pay floating rates.
III - Swaps
L EXAMPLE:
[3]
The Bank of America and the Bank of Montreal enter into a swap whereby the
Bank of Montreal pays Canadian T-Bill rate plus 30 basis points and receives US
T-Bill rate plus 30 basis points.
G Bullet Swap 6 In a bullet swap the notional principal amount is constant throughout the
term of the swap.
G Amortizing Swap 6 In an amortizing swap the notional principal decreases over the term of
the swap.
G Accreting Swap 6 In an accreting swap the notional principal increases over the term of the
swap.
G Roller Coaster Swap 6 In an roller coaster swap the notional principal amount increases
and decreases according to some predetermined formula.
T HE P RIMARY M ARKET
The primary market for swap agreements exists through intermediaries , generally large
commercial and investment banks, who sought out counter-parties and established the terms of
the swap agreement. As swaps became more common these intermediaries found themselves taking
on the other side of the swap and essentially making a market in swap agreements.
T HE S ECONDARY M ARKET
The secondary market for swaps is virtually non-existent. If the Bank of America wishes to close
out its position in the swap above, it has three alternatives:
G Swap reversal 6 The Bank of America would set up another swap with Fly-by-Night Industries
with exactly the opposite terms of its swap agreement with Hypothetical Resources. If all
goes well then the Bank of America acts as nothing more than a conduit for cash flows
between Hypothetical Resources and Fly-by-Night. However, if all does not go well with Flyby-Night then the Bank of America is still obliged to make payments on its swap
agreement with HR.
G Swap sale 6 The Bank of America sells its side of the swap agreement to Fly-by-Night
Industries. However, Hypothetical Resources might well refuse to authorize the sale since
the sale would increase the default risk increases.
G S w a p b u y - b a c k 6 The Bank of America sells its side of the swap agreement back to
Hypothetical Resources. Hypothetical Resources would require compensation to allow the
Bank out of the swap.
The lack of secondary market is primarily due to lack of standardization. However, some swap
[4]
Risk Management
markets are being superseded by other derivatives. For example, the Chicago Mercantile Exchange
bases its Weather Futures on an existing market in weather based OTC futures and swaps.
Things-To-Do: [ III - 1]
The Bank of Champaign buys a swap arrangement from The Bank of Urbana on a
notional principal of $100 million, with payments every six months for five years.
The buyer pays a fixed rate of 9.05% and receives the London InterBank Offered
Rate (LIBOR). The seller pays LIBOR and receives 9.0%.
!
A. On the first payment date LIBOR is 6.5%. What is each party's payment and
receipt on this date?
Things-To-Do: [ III - 2]
Busey Bank can borrow money in the ten year bond Market at 10% and in the six
month corporate note market at the T-Bill rate plus 0.40%. Technology Transfer
Inc can borrow in the ten year bond Market at 12% and in the six month corporate
note market at the T-Bill rate plus 1.0%.
!
A.
B.
Busey Bank has a advantage of how many points in each market?
In what market does Busey have a comparative advantage?
Set up a swap agreement such that Busey and Tech Transfer Inc. each borrow $1,000,000
in the market where they have the comparative advantage and then execute a swap
whereby Tech transfer pays 11.1% and Busey pays T-Bill plus 0.5. The Intermediary takes
.1% off the fixed payment (Tech transfer pays 11.1% and Busey Chase receives 11.0%).
payments are made every six months.
C.
How much of a basis point advantage does each party get from the swap?
D.
What is the notional principal amount?
At the end of six months the T-Bill rate is 9%.
E.
Calculate each party's payment and receipt (description, percentage, and amount)
on this date. (Don't forget to include payments on corporate debt issued and that
this is a semi-annual payment).
III - Swaps
[5]
Things-To-Do: [ III - 3]
The Chase Manhattan Bank can borrow money in the ten year bond market at 10%
and in the six month corporate note market at the T-Bill rate plus 1.0% Tardis
Intertemporal can borrow in the ten year bond market at 12% and in the six month
corporate note market at the T-Bill rate plus 1.8% Each corporation anticipates a
bond issue of $10 million.
!
A.
The Chase Manhattan has an advantage of how many basis points in each
market?
B.
In what market does the Chase Manhattan have the comparative advantage?
B.
Set up a swap agreement such that the gains from trade are the same for both
parties. Since you are setting up this swap as part of your graduation
requirements the intermediary gets nothing. (Start by having each corporation
borrow in the market where it has a competitive advantage and set the fixed
payment at 11.0%)
C.
At the end of six months the T-Bill rate is 7.0% What are the payments and
receipts for each party in the swap agreement.
S WAPTIONS
G Swaption 6 A swaption is an option on a swap agreement.
Call Swaption
If exercised
Buyer
buy a swap
pays a fixed rate an receives a floating rate
Writer
sell a swap
pays a floating rate and receives a fixed rate
Put Swaption
If exercised
Buyer
sell a swap
pays a floating rate and receives a fixed rate
Writer
buy a swap
pays a fixed rate and receives a floating rate
[6]
Risk Management
C URRENCY S WAP A GREEMENTS
A Currency swap is an agreement to exchange principal and interest over a specific period of time.
L EXAMPLE:
Boeing is a large triple A rated military and commercial industrial manufacturer.
Airlease is a triple B rated industrial leasing and service corporation. Both
corporations need $9 million over 10 years.
If Boeing issued 10 year bonds in the United States it would need to promise a
yield of 5%. The interest rates in Europe are higher and if it issued 10 year bonds
in Europe it would need to promise a yield of 12.60%. However inflation is higher
in Europe and real interest rates are comparable. Since the money is needed to
build facilities in Europe (to compete directly with Airbus) and most of the
revenue from its European division would be in Euros, Boeing would prefer to
borrow this money in Euros.
If Airlease issued 10 year bonds in the United States it would need to promise a
yield of 7%. If it issued 10 year bonds in Europe it would need to promise a yield
of 13.00%. Since most of its revenues are in dollars Airlease would prefer to
borrow in Euros.
Exchange Rate:
€1=$0.90
Rating
Rate in
Dollars
Rate in Euros
Boeing
AAA
5.00%
12.60%
Airlease
BBB
7.00%
13.00%
Basis point difference
200
40
Note that the lower credit rating costs Airlease a full 200 basis points
i n the US but only 40 basis points in Europe. This gives us a 160 basis
point driver.
The swap is engineered like this.
G
6 Each corporation borrows in the market in which it has a comparative advantage. Boeing
borrows $9 million and issues 10 year bonds at 5% in the US thus committing itself to
coupon payments of $225,000 every six months. Airlease borrows €10 million and issues
10 year bonds at 13.00% in Europe thus committing itself to coupon payments of
€650,000 every six months
III - Swaps
[7]
G 6 The principal is swapped. Boeing swaps the $9 million to Airlease and Airlease swaps €10
million to Boeing. Note that in a currency swap the principal amount (€10=$9) is
swapped.
G 6 Neutralize the currency risk. In this swap we will completely neutralize the currency risk to
which the counter-parties are exposed. Boeing must pay 5% on a $9 million bond issue so
Boeing receives a swap payment of 5% of $9 million. Airlease must pay 13.0% on a €10
million Eurobond issue so Airlease receives a swap payment of 13% of €10 million.
G 6 Distribute the advantage. We have a 160 basis point driver. We decide to give each counterparty 70 basis points and to keep 20 basis points for the intermediary.
If Boeing borrowed directly in the euro market then it would need to pay 12.60%. A 70
basis point advantage puts Boeing's payments at 11.90%. Since the first part of the swap
exactly neutralized Boeing's 5.00% dollar payments we set the Euro payments at 11.90%
of €10 million.
If Airlease borrowed directly in the dollar market then it would need to pay 7.00%. A 70
basis point advantage puts Airlease's payments at 6.30%. Since the first part of the swap
exactly neutralized Airlease's 13.00% euro payments we set the dollar payments at 6.30%
The differences between the payment amounts go to the intermediary. The dollar payment is paid
by Airlease. On a principal of $9 million Airlease must pay 6.3% and Boeing receives 5.0%. The
remaining 1.3% goes to the intermediary. The euro payment is paid by Boeing. On a principal of
€10 million Boeing must pay 11.90% and Airlease receives 13.00%. The 1.1% difference must be
made up by the intermediary.
Note that the swap does not eliminate currency risk; it reallocates currency risk to the
intermediary. Thus every six months the Intermediary receives a payment of $58,500 (1.3% of
$9m) and makes a payment of €55,000 (1.1% of € 10m). At an exchange rate of $0.90 this
translates into a net revenue of $9,000 (exactly 0.2% of $9m) but if the euro increases to $1.00
then the intermediary's net revenue falls to $3,500.
Every six months we have the following cash flows:
[8]
Risk Management
Boeing (borrows $9m and swaps it for €10m)
interest on $9 bond issue
- 5.00%
* $9m
-$225,000.
interest received on swap
0.05
* $9m
+$225,000.
- 11.90%
* €10m
- €595,000.
-11.90%
* €10m
- €595,000.
-13.00%
* €10m
- €650,000.
0.13
* €10m
+ €650,000.
- 6.30%
* $9m
- $283,500.
- 6.30%
* $9m
- $283,500.
interest received on swap
1.3%
* $9m
+ $58,500.
interest payment on swap
1.1%
* €10m
- €55,000.
interest payment on swap
TOTAL
Airlease (borrows €10m and swaps it for $9m)
interest on €10m bond issue
interest received on swap
interest payment on swap
TOTAL
Intermediary
Things-To-Do: [ III - 4]
Set up a currency swap between Boeing and Airlease such that Boeing gains a 90
point advantage but assumes all the foreign exchange risk in the swap.
!
III - Swaps
[9]
I NTEREST R ATE A GREEMENTS
An interest rate agreement is essentially interest rate insurance.
G Ceiling 6 In an interest rate cap or ceiling the buyer pays a premium and, in return, is
compensated by the seller if the interest rate rises above a specified strike rate.
G Floor 6 In an interest rate floor the buyer pays a premium and, in return, is compensated by
the seller if the interest rate falls below a specified strike rate.
G Strike Rate 6 the reference rate in an interest rate agreement.
G Notional Principal Amount 6 The dollar amount on which swap and interest rate
agreements are based.
L EXAMPLE:
January 1, 1999 Tardis Intertemporal buys an interest rate cap from the Illinois
Commercial Bank. The reference rate for the agreement is the 90-day T-Bill rate
and the cap is set at 4%. The agreement is for quarterly settlement for one year
and the notional principal amount is $1 million.
Date
T-Bill Rate
Payment
April 1, 1999
3.9%
$0
July 1, 1999
4.1%
$ 250 = [(0.1% * $1m)/4]
October 1, 1999
4.8%
$2,000 = [(0.8% * $1m)/4]
January 1, 2000
3.9%
$0
G Collar 6 Interest rate floors and ceilings can be combined to form a collar.
L EXAMPLE:
Hypothetical Resources finds itself in a position where, if the interest rate goes up
over 6% it is in deep financial trouble. However, if the interest rate goes down its
fixed income asset values increase substantially. HR can now set up a collar by
buying an interest rate cap at 6% and financing the cap by selling a floor at 4%.
If the interest rate goes up over 6% the cap pays off, mitigating the firm's
financial woes. If the interest rate goes down below 4% the increased value of the
firm's bond holdings can be used to make payments on the floor.
[ 10 ]
Risk Management
Things-To-Do: [ III - 5]
January 1, 1999 Hypothetical Resources buys an interest rate floor from the Illinois
Commercial Bank paying $1,000. The reference rate for the agreement is the 90day T-Bill rate and the floor is set at 4%. The agreement is for monthly settlement
for six months and the notional principal amount is $3 million.
!
The T-Bill rates are given by
the table to the right.
A.
B.
C.
Calculate the payment for
each month.
What is the net present value
of
this
interest
rate
agreement. Assume that the
rate on the first of the month
reflects the interest rate for
the previous month and
compound monthly.
Was
the
price
Tardis
Intertemporal paid for the
interest rate agreement a fair one?
Date
Rate
February 1
4.2%
March 1
4.0%
April 1
3.9%
May 1
3.8%
June 1
3.9%
July 1
4.1%
Payment