Swaps

1
Swaps
2
Nature of Swaps

• A swap is an agreement to exchange cash flows at
  specified future times according to certain
  specified rules

3
An 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

4
Cash Flows to Microsoft(See Table 6.1, page 127)
5
Typical 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

6
Intel and Microsoft (MS) Transform a
Liability(Figure 6.2, page 128)
5
5.2
Intel
MS
LIBOR0.1
LIBOR
7
Financial 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
8
Intel and Microsoft (MS) Transform an
Asset(Figure 6.3, page 128)

5
4.7
Intel
MS
LIBOR-0.25
LIBOR
9
Financial 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
10
The Comparative Advantage Argument (Table 6.4,
page 132)

• AAACorp wants to borrow floating
• BBBCorp wants to borrow fixed

11
The 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

12
Swap 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

13
The Swap (Figure 6.6, page 132)

9.95
10
AAA
BBB
LIBOR1
LIBOR
The floating rate leg should be LIBOR

14
Swap 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

15
The 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
16
Criticism 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

17
Valuation 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

18
Swap Valuation

• Fixed Receive Vswap Vfixed Vfloating
• Fixed Pay Vswap Vfloating - Vfixed
• The fixed rate stream is valued as an annuity
• The floating rate stream is valued by noting that
  it is worth par immediately after the next
  payment date

19
Floating Rate Perpetuity

• To create a floating rate perpetuity, invest
  principal value in 6-month LIBOR
• At the end of 6-months, remove the interest and
  reinvest the principal value at the new 6-month
  LIBOR
• Therefore, the cost of a floating rate perpetuity
  is principal value
• It always sells for its par value immediately
  after interest payment

20
Floating Rate Instrument with Maturity T

• At the end of T years, floating rate perpetuity
  is worth the principal value M
• Therefore, the floating rate instrument is worth
  M MdT
• Or M - M/(1y/2)2T, where is the rate on a
  zero-coupon bond maturing in T years

21
Swap Valuation

• The floating rate instrument is worth
  Vfloating M M/(1y/2)2T
• The fixed rate stream is worth Vfixed
  (C/2)(Annuity Factor)
• So for Fixed Receive Swap
  Vswap
  (C/2)(Annuity Factor) - M M/(1y/2)2T

22
Swap Valuation

• The swap is structured such that initial value is
  zero to either party
• Set Vswap 0
• Rearrange terms M(C/2)(Annuity
  Factor) M/(1y/2)2T
• The left-hand side is the present value of a bond
  at y
• 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 LIBOR bond
  that causes it to be worth par

23
Example

• 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

24
Example Continued

• Solution

25
Interest Rate Risk

• Receive Fixed Vswap Vfixed Vfloating
• Pay Fixed Vswap Vfloating Vfixed

26
An 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

27
Exchange 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

28
Three 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

29
The 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
30
Typical 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

31
Comparative Advantage Arguments for Currency
Swaps (Table 6.7, page 141)

• General Motors wants to borrow AUD
• Qantas wants to borrow USD

32
Comparative 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

33
Comparative 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

34
Qantas Assumes Exchange Rate Risk
USD 5
USD 5
AUD 13
GM
Qantas
AUD 11.8
35
GM Assumes Exchange Rate Risk
USD 6.2
USD 5
AUD 13
GM
Qantas
AUD 13.0
36
FI 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

37
FI 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
38
Valuation 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

39
Swaps 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

40
Swaps 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

41
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
• The company has credit risk exposure only when
  its value is positive