Transcript Swaps - AWARDSPACE.COM

Swaps
Finance (Derivative Securities) 312
Tuesday, 5 September 2006
Readings: Chapter 7
Nature of Swaps
Agreement to exchange cash flows at
specified future times according to certain
rules
Example of a plain vanilla swap
• agreement by Microsoft to receive 6-month
LIBOR & pay a fixed rate of 5% per annum
every six months for three years on a notional
principal of $100 million
Cash Flows
---------Millions of Dollars--------LIBOR FLOATING
FIXED
Net
Date
Rate
Cash Flow Cash Flow Cash Flow
Mar.5, 2001
4.2%
Sept. 5, 2001
4.8%
+2.10
–2.50
–0.40
Mar.5, 2002
5.3%
+2.40
–2.50
–0.10
Sept. 5, 2002
5.5%
+2.65
–2.50
+0.15
Mar.5, 2003
5.6%
+2.75
–2.50
+0.25
Sept. 5, 2003
5.9%
+2.80
–2.50
+0.30
Mar.5, 2004
6.4%
+2.95
–2.50
+0.45
Use of Swaps
Converting a liability from
• fixed rate to floating rate
• floating rate to fixed rate
Converting an investment from
• fixed rate to floating rate
• floating rate to fixed rate
Transforming a Liability
5%
5.2%
Intel
MS
LIBOR+0.1%
LIBOR
Involving a Financial Institution
4.985%
5.015%
5.2%
Intel
F.I.
MS
LIBOR+0.1%
LIBOR
LIBOR
Transforming an Asset
5%
4.7%
Intel
MS
LIBOR–0.2%
LIBOR
Involving a Financial Institution
4.985%
5.015%
4.7%
F.I.
Intel
MS
LIBOR–0.2%
LIBOR
LIBOR
Market Maker Quotes
Maturity
Bid (%)
Offer (%)
Swap Rate (%)
2 years
6.03
6.06
6.045
3 years
6.21
6.24
6.225
4 years
6.35
6.39
6.370
5 years
6.47
6.51
6.490
7 years
6.65
6.68
6.665
10 years
6.83
6.87
6.850
Comparative Advantage
AAACorp wants to borrow floating
BBBCorp wants to borrow fixed
Fixed
Floating
AAACorp
10.00%
6-month LIBOR + 0.30%
BBBCorp
11.20%
6-month LIBOR + 1.00%
The Swap
9.95%
10%
AAA
BBB
LIBOR+1%
LIBOR

P
A
Involving a Financial Institution
9.93%
9.97%
10%
AAA
F.I.
BBB
LIBOR+1%
LIBOR
LIBOR
Critique
10.0% and 11.2% rates available to
AAACorp and BBBCorp in fixed rate
markets are 5-year rates
LIBOR+0.3% and LIBOR+1% rates
available in the floating rate market are 6month rates
BBBCorp’s fixed rate depends on the
spread above LIBOR it borrows at in the
future
Swap Rates
6-month LIBOR is a short-term AA
borrowing rate
5-year swap rate has a risk corresponding
to the situation where ten 6-month loans
are made to AA borrowers at LIBOR
• Lender can enter into a swap where income
from the LIBOR loans is exchanged for the 5year swap rate
Valuation of Swaps
Valued as the difference between the
value of a fixed-rate bond and the value of
a floating-rate bond
• Fixed rate bond is valued in the usual way
• Floating rate bond is valued by noting that it is
worth par immediately after the next payment
date
Valuation of Swaps
Suppose that:
• A bank agrees to pay 6-month LIBOR and
receive 8% p.a. with semiannual
compounding on notional principal of $100m
• Remaining life of 1.25 years
• 3-month rate 10%, 6-month rate 10.2%,
9-month rate 10.5%, 15-month rate 11%
What is the value of this swap?
Valuation of Swaps
Time Bfix CF Bfl CF Discount PV Bfix CF PV Bfl CF
factor
0.25
4.0 105.1# 0.9753*
3.901
0.75
4.0
0.9243
3.697
1.25
104.0
0.8715
90.640
Total
* e-0.1(0.25)
98.238
#
102.505
102.505
0.5 x 0.102 x 100 = 5.1
Value of swap: 98.238 – 102.505 = –4.267m
Valuation of Swaps
Alternatively, can be valued as a portfolio
of forward rate agreements (FRAs)
• Each exchange of payments in an interest
rate swap is an FRA
• FRAs can be valued on the assumption that
today’s forward rates will be realised
Valuation of Swaps
Time
Fixed Floating Net CF
CF
CF
Discount PV Net CF
Factor
0.25
4.0 -5.100#
-1.100
0.9753*
-1.073
0.75
4.0 -5.522†
-1.522
0.9243
-1.407
1.25
4.0 -6.051
-2.051
0.8715
-1.787
Total
-4.267
# 0.5 x 0.102 x 100 = 5.1
* e-0.1(0.25)
† using rate [0.105(0.75) – 0.10(0.25)/0.5] = 0.1075
convert to semiannual compounding: 0.1044
Currency Swaps
Agreement to pay 11% on a sterling
principal of £10,000,000 & receive 8% on
a US dollar principal of $15,000,000 every
year for five years
• Principal is exchanged at the beginning and
the end of the swap, unlike in an interest rate
swap
Currency Swaps
Year
2001
2002
2003
2004
2005
2006
Dollars Pounds
$
£
------millions-----–15.00 +10.00
+1.20 –1.10
+1.20 –1.10
+1.20 –1.10
+1.20 –1.10
+16.20 -11.10
Use of Currency Swaps
Conversion from a liability in one currency
to a liability in another currency
Conversion from an investment in one
currency to an investment in another
currency
Comparative Advantage
 General Motors wants to borrow AUD
 Qantas wants to borrow USD
USD
AUD
General Motors
5.0%
12.6%
Qantas
7.0%
13.0%
 Can be valued either as the difference between
two bonds or as a portfolio of forward contracts
The Swap
USD 5.0%
USD 6.3%
USD 5.0%
GM
F.I.
QAN
AUD 13.0%
AUD 11.9%
AUD 13.0%
Alternative Swap
USD 5.0%
USD 5.2%
USD 5.0%
GM
F.I.
QAN
AUD 13.0%
AUD 11.9%
AUD 11.9%
Swaps v Forwards
Swaps can be regarded as a convenient
way of packaging forward contracts
“Plain vanilla” interest rate swap in earlier
example consisted of six FRAs
“Fixed for fixed” currency swap in other
example consisted of a cash transaction &
five forward contracts
Valuing Currency Swaps
Suppose that:
• Term structure of LIBOR/swap rates is flat in
Japan and the US
• Japan rate is 4%, US rate is 9% p.a.
(continuous compounding)
• A bank enters a swap paying 8% and
receiving 5% p.a., USD10m against JPY1.2bn
• 3-year swap, current rate USD1 = JPY110
What is the value of the swap?
Valuation as Bonds
Time
USD
CF
PV ($)
JPY
CF
PV (¥)
1
0.8 0.7311
60
57.65
2
0.8 0.6682
60
55.39
3
0.8 0.6107
60
53.22
3
10.0 7.6338
1,200 1,064.30
9.6439
1,230.55
Total
Value of swap: 1,230.55/110 – 9.6439 = USD1.5430m
Swaps v Forwards
 Value of a swap is the sum of the values of the
forward contracts underlying the swap
 Swaps are normally “at the money” initially
• It costs nothing to enter into a swap
• It does not mean that each forward contract
underlying a swap is “at the money” initially
Valuation as FRAs
Time
USD
CF
JPY
CF
Forward
Rate
JPY CF
in USD
Net CF
in USD
PV
1
-0.8
60 0.009557
0.5734 -0.2266 -0.2071
2
-0.8
60 0.010047
0.6028 -0.1972 -0.1647
3
-0.8
60 0.010562
0.6337 -0.1663 -0.1269
3
Total
-10.0
1,200 0.010562
12.6746
2.6746 2.0417
1.5430
Credit Risk
 A swap is worth zero to a company initially
 At a future time its value is liable to be either
positive or negative
 Firm has credit risk exposure only when swap
value is positive
Exposure
Swap Value