Title: Swaps
1Swaps
2Nature of Swaps
- A swap is an agreement to exchange cash flows at
specified future times according to certain
specified rules
3An Example of a Plain Vanilla Interest Rate Swap
- An agreement by Microsoft to receive 6-month
LIBOR pay a fixed rate of 5 per annum every 6
months for 3 years on a notional principal of
100 million - Next slide illustrates cash flows
4Cash Flows to Microsoft(See Table 6.1, page 127)
5Typical Uses of anInterest Rate Swap
- 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
6Intel and Microsoft (MS) Transform a
Liability(Figure 6.2, page 128)
5
5.2
Intel
MS
LIBOR0.1
LIBOR
7Financial Institution is Involved(Figure 6.4,
page 129)
4.985
5.015
5.2
F.I.
MS
Intel
LIBOR0.1
LIBOR
LIBOR
Dealer spread .03 evenly split
8Intel and Microsoft (MS) Transform an
Asset(Figure 6.3, page 128)
5
4.7
Intel
MS
LIBOR-0.25
LIBOR
9Financial Institution is Involved(See Figure
6.5, page 129)
5.015
4.985
4.7
F.I.
MS
Intel
LIBOR-0.25
LIBOR
LIBOR
Dealer spread .03
10The Comparative Advantage Argument (Table 6.4,
page 132)
- AAACorp wants to borrow floating
- BBBCorp wants to borrow fixed
11The Comparative Advantage Argument
- AAACorp has absolute advantage in both markets
- But a comparative advantage in fixed
- BBBCorp has comparative advantage in floating
- If AAA borrows fixed, the gain is 1.2
- If BBB borrows floating, the gain is reduced by
.7 - Therefore, we have a net gain of 1.2 - .7
.5 - If the gain is split evenly, we have a gain per
party of G (1.2 - .7)/2 .25
12Swap Design
- Design the swap so AAAs borrowing rate equals
the comparative disadvantage (CD) rate minus the
gain - LIBOR .3 - .25
- Do the same thing for BBB
- BBBs rate with swap
- 11.2 - .25
- Now, draw the diagram
13The Swap (Figure 6.6, page 132)
9.95
10
AAA
BBB
LIBOR1
LIBOR
The floating rate leg should be LIBOR
14Swap Design with FI
- Adjust swap gain for dealer spread
- Suppose dealer spread .04
- Then gain
- G (1.2 - .7 - .04)/2 .23
- AAAs rate with swap
- LIBOR .3 - .23 LIBOR .07
- BBBs rate with swap
- 11.2 - .23 10.97
- Draw swap diagram
15The Swap when a Financial Institution is Involved
(Figure 6.7, page 133)
9.93
9.97
10
AAA
F.I.
BBB
LIBOR1
LIBOR
LIBOR
Check that dealer spread .04
16Criticism of the Comparative Advantage Argument
- The 10.0 and 11.2 rates available to AAACorp
and BBBCorp in fixed rate markets are 5-year
rates - The LIBOR0.3 and LIBOR1 rates available in
the floating rate market are six-month rates - BBBCorps fixed rate depends on the spread above
LIBOR it borrows at in the future
17Valuation of an Interest Rate Swap
- Interest rate swaps can be valued as the
difference between the value of a fixed-rate bond
and the value of a floating-rate bond with the
same par value - Par values will cancel at maturity
18Swap Valuation
- Fixed Receive Vswap Vfixed Vfloating
- Fixed Pay Vswap Vfloating - Vfixed
- The fixed rate bond is valued using the term
structure of interest rates - The floating rate stream is valued by noting that
it is worth par immediately after the next
payment date
19Floating Rate Bond
- To create a floating rate bond, invest principal
value in 6-month LIBOR - At the end of 6-months, pay the interest and
reinvest the principal value at the new 6-month
LIBOR - At maturity pay last interest payment and
principal value - Therefore, the cost of a floating rate bond is
the principal value - It always sells for its par value immediately
after interest payment
20Swap Valuation
- The swap is structured such that initial value is
zero to either party - Set Vswap 0
- Vfixed Vfloating M
- Since the bond is selling at par, CR C/M y
- For the swap to have zero value the fixed rate
must equal the yield to maturity on a par bond - The swap rate is the coupon rate on a fixed rate
bond that causes it to be worth par
21Example
- Zero coupon LIBOR curve is 5, 6, and 7 for
one, two, and three years - What is the swap rate on a three year interest
rate swap? - Assume payments are annual and yields are
compounded annually - Solve for LIBOR par yield
- M CRxM(d1 d2 d3) Md3
22Example Continued
23Interest Rate Risk
- Receive Fixed Vswap Vfixed Vfloating
- Pay Fixed Vswap Vfloating Vfixed
24An Example of a Currency Swap
- An agreement to pay 11 on a sterling
principal of 10,000,000 receive 8 on a US
principal of 15,000,000 every year for 5 years
25Exchange of Principal
- In an interest rate swap the principal is not
exchanged - In a currency swap the principal is exchanged at
the beginning and the end of the swap
26Three Cash Flow Components
- t 0 exchange principal based upon
current exchange rates Pay
15 M
Rcv 10 M - t 1, 2, 3, 4, 5
Pay .11x10 1.1 M
Rcv
.08x15 1.2 M - t 5 Pay 10 M Rcv 15 M
27The Cash Flows (Table 6.6, page 140)
Dollars
Pounds
Years
------millions------
0
15.00
10.00
1.20
1
1.10
2
1.20
1.10
3
1.20
1.10
4
1.20
1.10
5
16.20
-11.10
28Typical Uses of a Currency Swap
- 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
29Comparative Advantage Arguments for Currency
Swaps (Table 6.7, page 141)
- General Motors wants to borrow AUD
- Qantas wants to borrow USD
30Comparative Advantage
- GM has absolute advantage in both markets
- But GM has comparative advantage in dollars
- Qantas has comparative advantage in Australian
dollars - So GM should borrow dollars and Qantas Australian
dollars - Then swap cash flows to earn gain from
comparative advantage
31Comparative Advantage
- Gain per party G (2 - .4)/2 .8
- GMs rate with swap 12. 6 - .8 AUD 11.8
- Qantas rate with swap 7 - .8 USD 6.2
32Qantas Assumes Exchange Rate Risk
USD 5
USD 5
AUD 13
GM
Qantas
AUD 11.8
33GM Assumes Exchange Rate Risk
USD 6.2
USD 5
AUD 13
GM
Qantas
AUD 13.0
34FI Assumes Exchange Rate Risk
- Adjust swap gain for dealer spread
- Suppose dealer spread .2
- Then gain
- Gain per party G (2 - .4 - .2)/2 .7
- GMs rate with swap 12. 6 - .7 AUD 11.9
- Qantas rate with swap 7 - .7 USD 6.3
35FI Assumes Exchange Rate Risk
USD 5
USD 6.3
USD 5
GM
F.I.
Q
AUD 13
AUD11.9
AUD 13
Check that dealer spread .2 Pay 13.0 11.9
AUD 1.1 Rcv 6.3 5.0 USD 1.3
36Valuation of Currency Swaps
- Like interest rate swaps, currency swaps can be
valued either as the difference between 2 bonds
or as a portfolio of forward contracts
37Swaps Forwards
- A swap can be regarded as a convenient way of
packaging forward contracts - The plain vanilla interest rate swap in our
example consisted of 6 Fraps - The fixed for fixed currency swap in our
example consisted of a cash transaction 5
forward contracts
38Swaps Forwards(continued)
- The value of the swap is the sum of the values of
the forward contracts underlying the swap - Swaps are normally at the money initially
- This means that it costs nothing to enter into a
swap - It does not mean that each forward contract
underlying a swap is at the money initially
39Credit Risk
- A swap is worth zero to a company initially
- At a future time its value is liable to be either
positive or negative - The company has credit risk exposure only when
its value is positive