Swap Markets
What is a swap agreement/contract;
An Interest Rate Swap
•
An agreement between two organizations (e.g. a bank and a client) to exchange cash
flows in the future according to a pre-specified plan
•
For example, Company B agrees to pay to Company A a fixed interest rate once a
year on a nominal principal for a specified period (e.g. 1 to 15 years)
•
At the same time A agrees to pay to B a floating interest rate on the same principal
and for the same duration
What is a swap agreement/contract;
A Currency Swap
•
An agreement between two organizations (e.g. a bank and a client) to exchange
principal and cash flows in the future according to a pre-specified plan
•
For example, Company B agrees to pay to Company A a fixed interest rate on the
British Pound once a year on a principal for a specified period (e.g. 1 to 15 years)
•
At the same time A agrees to pay to B a floating interest rate on the US$ for the same
principal and for the same duration
Swap markets
•
The first swap was organized in 1981 between IBM and the World Bank; the global
swap market expanded rapidly due to technological innovations, capital market
liberalization and financial engineering innovations
•
Most swaps are traded over-the-counter (OTC), "tailor-made" for the counterparties.
•
Some types of swaps are also exchanged on futures markets such as the Chicago
Mercantile Exchange Holdings Inc., the largest U.S. futures market, the Chicago Board
Options Exchange, IntercontinentalExchange and Frankfurt-based Eurex AG.
•
The Bank for International Settlements (BIS) publishes statistics on the notional
amounts outstanding in the OTC derivatives market. At the end of 2006, this was USD
415.2 trillion, more than 8.5 times the 2006 gross world product.
•
Note that in 1985 ISDA (International Swaps and Derivatives Association) estimated the
notional size of the market to approximately $ 865.6 billion
•
In 2004 ISDA (International Swaps and Derivatives Association) estimated the notional
size of the market to approximately $ 127 trillion
•
In 2004 ISDA estimated the average daily trading volume to $ 600 billion
Swap markets
Swap markets
• Swaps are nowadays standardized financial instrument to a high
degree and have a large number of underlying assets; they are
traded in many platforms electronically.
• Short-term swaps (up to 2 years) are usually interbank instruments
while long-term swaps are often attractive to businesses and other
organizations
• A usual distinction is between simple swaps («vanilla swaps») and
more complex deals («exotic swaps»).
• Vanilla swaps (the most common) are usually agreements to swap
fixed with floating interest rate on the same currency
• Exotic swaps are less standardized and more “tailor made”
Swap markets
•
Another type of swap is the «asset swap», where an investor buys an asset (e.g. a
fixed rate bond) and at the same time agrees an interest rate swap (fixed for floating)
with the same duration of the bond.
•
The investor uses the coupon of the bond to pay the fixed payments and receives the
floating payments. In this case we usually say that the fixed rate return has been
transformed to a “synthetic” floating rate product; if the bond rate is higher than the
fixed swap rate the investor could benefit
•
Equity swap, example: I agree with bank X to receive the returns of S&P500 for five
years in monthly installments and pay the bank an interbank yield
Swap markets
• Swap buyer: the party that has agreed to pay the Fixed rate
• Swap seller: the party that has agreed to pay the Floating rate
Interest rate arbitrage
•
Co A wants to borrow for 10 years at a floating rate
•
Co Β wants to borrow for 10 years at a fixed rate
•
Assume they want to borrow the same amount
Fixed
Floating
Co A
(ΑΑΑ)
9.5%
LIBOR + 0.25%
Co Β
(ΒΒΒ)
11%
LIBOR + 0.75%
Comparative advantage
• Difference between fixed ΑΑΑ and ΒΒΒ: 1.5%
• Difference between floating ΑΑΑ and ΒΒΒ: 0.5%
• Co A has a comparative advantage for fixed rate loans
• Co B has a comparative advantage for floating rate loans
• BUT
• Co A wants to borrow for 10 years at a floating rate
• Co Β wants to borrow for 10 years at a fixed rate
Motive for swap – Profit
• If:
α = difference between fixed rates (1.5%)
β = difference between floating rates (0.5%)
• The profit from a swap is:
| α-β | =| 1.5 – 0.5 | = 1%
The swap
Result for Co A
(wants floating; would pay LIBOR + 0,25%)
• Pays Fixed
9.5%
(Loan)
• Pays Floating
Libor
(swap)
• Receives Fixed
9.75%
(swap)
-----------------------------------------------------------• Pays floating
Libor – 0.25%
• Improved by 0.5%
Result for Co B
(wants fixed; would pay 11%)
• Pays Floating
Libor+0.75% (Loan)
• Pays Fixed
9.75%
(swap)
• Receives Floating
Libor
(swap)
-----------------------------------------------------------• Pays fixed
105%%
• Improved by 0.5%
Another example
•
Co A wants to borrow for 10 years at a floating rate
•
Co Β wants to borrow for 10 years at a fixed rate
•
Assume they want to borrow the same amount
Fixed
Floating
Co A
(ΑΑΑ)
10%
LIBOR + 0.3%
Co Β
(ΒΒΒ)
11.2%
LIBOR + 1%
Comparative advantage
• Difference between fixed ΑΑΑ and ΒΒΒ: 1.2%
• Difference between floating ΑΑΑ and ΒΒΒ: 0.7%
• Co A has a comparative advantage for fixed rate loans
• Co B has a comparative advantage for floating rate loans
• BUT
• Co A wants to borrow for 10 years at a floating rate
• Co Β wants to borrow for 10 years at a fixed rate
Comparative advantage
• Profit:
| α-β | =| 1.2 – 0.7 | = 0.5%
Result for Co A
(wants floating; would pay LIBOR + 0.30%)
• Pays Fixed
10%
(Loan)
• Pays Floating
Libor
(swap)
• Receives Fixed
9.95%
(swap)
-----------------------------------------------------------• Pays floating
Libor + 0.05%
• Improved by 0.25%
Result for Β
(wants fixed; would pay 11.2%)
• Pays Floating
Libor+1%
(Loan)
• Pays Fixed
9.95%
(swap)
• Receives floating
Libor
(swap)
-----------------------------------------------------------• Pays Fixed
10.95%
• Improved by 0.25%
Cash Flows: Example; Co B
Use of interest rate swap
(i) Transform the nature of a liability
• Assume that Co A has issued a Loan (or bond) of $100
million at a floating rate of Libor+0.8%.
• Co A is afraid that interest rates will increase in the future
and would prefer fixed installments
• One solution would be to retire the loan (if possible) and
issue a new one (expensive solution)
• A cheaper solution would be to find a Co B that has the
opposite expectations and swap cash flows
• E.g. Co A pays fixed 5% and receives Libor
• What is the result?
Result
• Pays
Libor + 0.8% (Loan)
• Receives
Libor
(swap)
• Pays
5%
(swap)
-------------------------------------------------------• Pays
5.8%
(Fixed)
• Transformed a floating rate liability to a fixed rate liability
Use of interest rate swap
(i) Transform the nature of an asset
• Assume that Co A has invested in a fixed rate
bond $100 million at a rate of 4.7%
• Co A is afraid that interest rates will increase in
the future and would prefer floating cash flows
• One solution would be to sell the fixed rate bond
(if possible) and buy a new one with a floating
rate (expensive solution)
• A cheaper solution would be to find a Co B that
has the opposite expectations and swap cash
flows
• E.g. Co A pays fixed 5% and receives Libor
• What is the result?
Αποτέλεσμα
• Receives
4.7%
(Investment)
• Receives
Libor
(swap)
• Pays
5%
(swap)
-------------------------------------------------------• Receives
Libor - 0.3%
(Floating)
• Transformed a fixed rate investment to a floating
rate investment
The role of banks
• In practice it is difficult for two companies
to meet
• They will use a bank which will do two
transactions, one with each company
The role of banks
• Investment banks that are active in this market will
prepare quotation tables with indicative prices at which
they are willing to buy/sell swaps
• Traders will use these tables for pricing
• Tables will change constantly in order to incorporate
changing market conditions
• Prices are expressed in the form of interest rates in basis
points (1 bp = 0.1%)
The role of banks
• Example: the next Table presents the prices in spreads
over the US Treasury Note (TN) rates
• This is common for interest rate swaps on the US $.
• Assume that the current 2-year ΤΝ is 8.55%; then the
hypothetical bank is willing to pay for 2 year swap a fixed
rate of 8.75% (8.55% + 20 bps) and receive a floating
rate (e.g. LIBOR).
The role of banks
Structured Bonds
•
Another example (2007, Hellenic Republic):
Decision 2/8449/0023Α/6 Feb 2007 (Ministry of Finance and Defense)
Issue price:
100%
Maturity:
12 years (Issue date: Feb 2007)
Coupon rate: For the first two years 6,25%
For the remaining ten years
→
if the difference between the 10-year interbank
Euroswap rate and the 2-year interbank Euroswap
rate is below 1% it will pay the product of this
difference times five
→
If the difference between the 10-year interbank
Euroswap rate and the 2-year interbank Euroswap
rate is above 1% it will pay the 3-month
Euribor+1.5%
Structured Bonds
• Assume that
10-year interbank Euroswap rate = 3%
2-year interbank Euroswap rate = 2.5%
Difference: 0.5%
Coupon = 0.5% times 5 = 2.5%
• Assume that
10-year interbank Euroswap rate = 3%
2-year interbank Euroswap rate = 1.5%
Difference: 1.5%
Coupon = 3-month Euribor + 1.50 %
Structured Bonds, Pension Funds, Swaps
• With the same decision the Hellenic Republic decided an
interest rate swap with JΡ Μorgan:
a) JΡ Μorgan pays the interest of the bond that the
issuer has to pay to investors (i.e. the Pension
Funds) for 12 years
b) The issuer pays to JP Μorgan the annual
Εuribor-0.16%, for 12 years
The swap
A Currency Swap
•
An agreement between two organizations (e.g. a bank and a client) to exchange
principal and cash flows in the future according to a pre-specified plan
•
For example, Company B agrees to pay to Company A a fixed interest rate on the
British Pound once a year on a principal for a specified period (e.g. 1 to 15 years)
•
At the same time A agrees to pay to B a floating interest rate on the US$ for the same
principal and for the same duration
Example
• 5-year swap between A and B agreed on February 1999.
A pays fixed 11% on British Pounds (BP) and B pays
fixed 8% on US $.
• Payments take place on an annual basis an dteh par
values are 15 million $ and 10 million BP
Cash flows for A
Date
$ (million)
£(million)
Feb 1999
-15
+10
Feb 2000
+1.2
-1.1
Feb 2001
+1.2
-1.1
Feb 2002
+1.2
-1.1
Feb 2003
+1.2
-1.1
Feb 2004
+16.2
-11.1
Motive for a currency swap
• Α wants 4-year $ Australia
• B wants 4-year $ USA
$
Α$
Co A
(ΑΑΑ)
4%
11.6%
Co Β
(ΒΒΒ)
6%
12%
Comparative advantage
• Difference $ ΑΑΑ and $ ΒΒΒ: 2%
• Difference Α$ ΑΑΑ and Α$ ΒΒΒ: 0.4%
• Β has a Comparative advantage on Α$
• Α has Comparative advantage on US$
• Α wants Α$
• Β wants US$
• Profit:
| α-β | =| 2 – 0.4 | = 1,6%
• Assume bank organizes and keeps 0.2%
• Profit: 1.6 – 0.2 = 1.4% (from 0.7% each)
The Swap
Result for Α
(wantsΑ$, would pay 11.6%)
• Pays
$
4%
(Loan)
• Pays
Α$ 10.9%
(swap)
• Receives
$
4%
(swap)
----------------------------------------------------------• Pays
Α$ 10.9%
• Improved by 0.7%
Result for Β
(wants US$, would pay 6%)
• Pays
Α$ 12%
(Δάνειο)
• Pays
$
5.3%
(swap)
• Receives
Α$ 12%
(swap)
----------------------------------------------------------• Pays $
5.3%
• Improved by 0.7%
Result for Bank
• Receives
Α$ 10.9%
(swap)
• Pays
Α$ 12%
(swap)
• Pays
$
5.3%
(swap)
• Receives
$
4%
(swap)
----------------------------------------------------------• Receives
0.2%
• Currency risk to be hedged
Uses of currency swaps
(a)
Transform liabilities
• 7 years ago Co A issued 10-year bond with a Par
of $30 million and coupon rate = 7%
• Today Co Α believes that a bond in British
Pounds would be more preferable
• What can A do?
• Retire the $ bond and issue a new one (expensive
solution)
• Alternatively, Co A could find another Co B and
exchange cash flows
• Assume a Par of $30 million and BP15 million
Result for Co A
•
•
•
•
•
Pays
$2.1 million annually on Bond
Receives
$2.1 million annually on swap
Pays
ΒΡ1.5 million annually on swap
-------------------------------------------------------Pays
ΒΡ1.5 million annually to Co B
• Transformed a $ liability (bond) to a BP liability without
the cost of restructuring the portfolio
Uses of currency swaps
(a) Transform assets
•
Assume Co A has a 3-year investment worth of
BP15 million with a rate of return of 10%
•
Today Co Α believes that an investment in US $
would be more preferable
•
What can A do?
• Sell the BP investment and buy a new one in US
$ (expensive solution)
• Alternatively, Co A could find another Co B and
exchange cash flows
• Assume a Par of $30 million and BP15 million
Result for Co A
•
•
•
•
•
Receives
ΒΡ1.5 mil annually from investment
Receives
$2.1 million annually on swap
Pays
ΒΡ1.5 million annually on swap
-------------------------------------------------------Receives
$2.1 million annually from Co B
• Transformed a BP asset to a $ asset without the cost of
restructuring the portfolio
Valuation of Swaps
• The value of the swap will change on a daily basis for
both parties
• Present value of future cash flows (with continuous
compounding)
• E.g. an interest rate or a currency swap is may be
viewed as:
• Two positions (long/short) on two different bonds
• A position in a series of forward contracts
Interest rate swaps
• VSwap
=
Present Value of the swap
• ΒFix
=
Present value of the fixed rate
bond
• ΒFloat
=
Present value of the floating rate
bond
Interest rate swaps
• When we receive fixed and pay floating :
• VSwap = BFix – BFloat
• When we receive floating and pay fixed:
• VSwap = BFloat – BFix
Continuous compounding
• Present Value (once a year):
PV = FV / (1+r)n
• Present Value (m times a year):
PV = FV / (1+r/m)nm
• Present Value (continuous):
PV = FV / e r n = FV e –r n
• e= 2,71828 (constant)
For a series of cash flows
• Present Value (once a year):
PV =
[C1 / (1+r)] + …………
+
[Cn / (1+r)n] + [P / (1+r)n]
• Present Value (continuous):
PV =
C1 e-rt +.....+ Cn e-rt + P e-rt
For a series of cash flows
• For a fixed rate bond
• BFix = C1 e-rt +....+ Cn e-rt + P e-rt
• For a floating rate bond discount the only known cash
flows:
• BFloat = (P + c1) e-r1t1
• C1 = the next cash flow
Example interest rate swap
• Consider a bank that has a swap where the bank pays
Libor and receives 8% on a principal of $100 million,
twice a year
• There are 1.25 years left to maturity and the 3-month, 9month, 15-month discount rates are 10%, 10.5%, 11%,
respectively
• During the last payment the Libor was 10.2%
• What is the value of the swap for the bank?
The value of the swap
• The bank receives fixed and pays floating, thus:
VSwap = BFix – BFloat
• BFix = C1 e-rt +....+ Cn e-rt + P e-rt
• BFloat = (P + c1) e-r1t1
Let’s find BFix
•
•
•
•
•
The fixed is 8% on $100m, i.e. $4m semi-annually
C1 = C2 = C3 = $4 million
P = $100 million
r1 = 0.10
r2 = 0.105
r3 = 0.11
t1 = (3/12)
t2 = (9/12)
t3 = (15/12)
• BFix =
=
4 e-0.10(3/12) + 4 e-0.105(9/12)
$98.2 million
+ (104) e-0.11(15/12)
Let’s find BFloat
• BFloat = (P + c1) e-r1t1
• To find the floating payment look at the Libor oat the last
exchange (10.2%), i.e. 5.1% on $100 million, $5.1 million
• P = $100 million
• r1 = 0,10
• t1 = (3/12)
• BFloat = (100 + 5.1) e-0.10(3/12)= $102.51 million
The Value of the Swap today
• VSwap = BFix – BFloat
• BFix
• BFloat
=
=
$98.2 million
$102.51 million
• VSwap = $98.2 – $102.5 = -$4.27 million
Valuation of a Currency Swap
• VSwap
=
The Present Value of the swap in
domestic currency
• ΒD
=
• ΒF
=
The Present Value of the swap in
foreign currency
• S0
=
The Present Value of the bond in
domestic currency
The current exchange rate
Valuation of a Currency Swap
• When we receive domestic currency and pay foreign
currency:
• VSwap = BD – S0BF
• When we receive foreign currency and pay domestic
currency:
• VSwap =S0BF – BD
Example
• Consider a US Bank that has a 3-year swap from which
the bank receives 4% in ¥ and pays 7% in $, annually
• The principal is $20 million and και 2,400 million ¥
• The current exchange rate is ¥115=$1 (S0 = 1/115)
• The discount rates are: 3.5%, 4%, 4.5% in Japan and
9%, 9.5%, 10% in the US
• What is the current value of the swap for the bank?
Let’s find BD
•
•
•
•
•
Payment 7% on $20 million, thus $1.4 million
C1 = C2 = C3 = $1.4 million
P = $20 million.
r1 = 0.09
r2 = 0.095
r3 = 0.10
t1 = 1
t2 = 2
t3 = 3
• BD =
=
1,4 e-0.09(1) + 1,4 e-0.095(2) + (21,4) e-0.10(3)
$18.3 εκ
Let’s find BF
•
•
•
•
•
Payment 4% on ¥2,400 million, thus ¥96 million
C1 = C2 = C3 = ¥96 million
P = ¥2.400 million.
r1 = 0,035
r2 = 0,04
r3 = 0,045
t1 = 1
t2 = 2
t3 = 3
• BF =
=
96 e-0.035(1) + 96 e-0.04(2) + (2.496) e-0.045(3)
2.362,5 εκ
Swap Value
• Bank receives foreign currency and pays domestic
• VSwap =S0BF – BD
• BF =
• BD =
• S0 =
¥ 2,362.5 million
$18.3 million
(1/115)
VSwap =(1/115) (2,362.5) – (18.3) = $2.25 million