LIBOR Case

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Swaps

Chapter 7

Nature of Swaps

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

An Example of a “Plain Vanilla” Interest Rate Swap

An agreement by Apple 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 that could occur (Day count conventions are not considered)

---------Millions of Dollars---------

LIBOR

FLOATING

FIXED

Net

Date

Rate

Cash Flow

Mar. 8, 2016

4.2%

Sept. 8, 2016

4.8%

+2.10

–2.50

–0.40

Mar. 8, 2017

5.3%

+2.40

–2.50

–0.10

Sept. 8, 2017

5.5%

+2.65

–2.50

+0.15

Mar. 8, 2018

5.6%

+2.75

–2.50

+0.25

Sept. 8, 2018

5.9%

+2.80

–2.50

+0.30

Mar. 8, 2019

6.4%

+2.95

–2.50

+0.45

Cash Flows to Apple (See Table 7.1, page 163

Typical Uses of an Interest 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

Interest Rate Swap Between Apple and Citigroup (Figure 7.1, page 162)

Citi

Apple

3.0%

LIBOR

Apple Transforms a Liability from Floating to Fixed (Figure 7.2, page 164)

Citi

Apple

3.0%

LIBOR

LIBOR+0.1%

Interest Rate Swap Between Citigroup and Intel (Figure 7.3, page 165)

Citi

Intel

2.97%

LIBOR

Intel Transforms a Liability from Fixed to Floating (Figure 7.4, page 165)

Citi

Intel

2.97%

LIBOR

3.2%

Apple Transforms an Asset from Fixed to Floating (Figure 7.5, page 165)

Citi

Apple

3.0%

LIBOR

2.7%

Intel Transforms an Asset from Floating to Fixed (Figure 7.6, page 166)

Citi

Intel

2.97%

LIBOR

LIBOR−0.2%

Quotes By a Swap Market Maker (Table 7.3, page 167)

Maturity	Bid (%)	Offer (%)	Swap Rate (%)
2 years	2.55	2.58	2.565
3 years	2.97	3.00	2.985
4 years	3.15	3.19	3.170
5 years	3.26	3.30	3.280
7 years	3.40	3.44	3.420
10 years	3.48	3.52	3.500

Day Count

A day count convention is specified for fixed and floating payments

For example, LIBOR is likely to be actual/360 in the U.S. because LIBOR is a money market rate

Confirmations

Confirmations specify the terms of a transaction

The International Swaps and Derivatives has developed Master Agreements that can be used to cover all agreements between two counterparties

CCPs are used for most standard swaps

The Comparative Advantage Argument (Table 7.4, page 169)

AAACorp wants to borrow floating

BBBCorp wants to borrow fixed

Fixed

Floating

AAACorp

4.00%

6-month LIBOR − 0.1%

BBBCorp

5.20%

6-month LIBOR + 0.6%

A Swap where Companies Trade Directly with Each Other (Figure 7.7, page 170)

AAACorp

BBBCorp

4.35%

LIBOR

LIBOR+0.6%

The Swap when a Financial Institution (F.I.) is Involved (Figure 7.7, page 170)

AAACorp

BBBCorp

4.33%

LIBOR

LIBOR+0.6%

LIBOR

4.37%

F.I.

Criticism of the Comparative Advantage Argument

The 4.0% and 5.2% rates available to AAACorp and BBBCorp in fixed rate markets are 5-year rates

The LIBOR−0.1% and LIBOR+0.6% rates available in the floating rate market are six-month rates

BBBCorp’s fixed rate depends on the spread above LIBOR it borrows at in the future

Valuation of an Interest Rate Swap

Initially interest rate swaps are worth close to zero

At later times they can be valued as a portfolio of forward rate agreements (FRAs)

The procedure is to

Calculate LIBOR forward rates

Calculate the swap cash flows that will occur if LIBOR forward rates are realized

Discount these swap cash flows at OIS rates

Example 7.1 (page 172)

Swap involves paying 3% per annum and receiving LIBOR every six months on $100 million

Swap has 15 months remaining (exchanges in 3, 9, and 15 months)

LIBOR rate applicable to exchange in 3 months was determined 3 months ago and is 2.9%

Forward LIBOR rates for 3-9 month period and 9-15 month periods are 3.429% and 3.734%, respectively

OIS zero rates for maturities of 3, 9, and 15 months are 2.8%, 3.2%, and 3.4%, respectively

Calculations ($ million)

Time (yrs)	Fixed cash flow	Floating cash flow	Net cash flow	Discount factor	PV of net cash flow
0.25	−1.5000	+1.4500	−0.0500	0.9930	−0.0497
0.75	−1.5000	+1.7145	+0.2145	0.9763	+0.2094
1.25	−1.5000	+1.8672	+0.3672	0.9584	+0.3519
					+0.5117

Value of swap is $0.5117 million

Bootstrapping LIBOR forward rates: Example 7.2 (page 173)

6,12,18, and 24 month OIS rates are 3.8%, 4.3%, 4.6%, and 4.75% respectively with cont. comp.

6-month LIBOR rate is 4% (s.a. comp.)

Suppose forward LIBOR rates for 6-12 and 12-18 months have already been calculated as 5% and 5.5%, respectively (s.a comp)

The two year swap rate is 5%

The next step is to calculate the LIBOR forward rate, F, for the18-24 month period.

Bootstrapping LIBOR forward rates: Calculations

A 2-year swap where 5% is paid and LIBOR is received on $100 is worth zero.

Value of first three exchanges are

0.5×(0.04− 0.05)×100×e−0.038×0.5 = −0.4906

0.5×(0.05 − 0.05)×100×e−0.043×1.0 = 0

0.5×(0.055 − 0.05)×100×e−0.046×1.5 = +0.2333

The value of the fourth payment must be +0.2573 so that the total value is zero

0.5×(F−0.05)×100×e−0.0475×2.0 = 0.2573

F = 0.05566 or 5.566% per annum

An Example of a Fixed-for-Fixed Currency Swap (Figure 7.10, page 175)

Five year agreement by BP to

Pay 3% on a US dollar principal of $15,000,000

Receive 4% on a sterling principal of £10,000,000

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

The Cash Flows (Table 7.5, page 176)

Date	Dollar Cash Flows (millions)	Sterling cash flow (millions)
Feb 1, 2016	+15.00	−10.00
Feb 1, 2017	−0.45	+0.40
Feb 1, 2018	−0.45	+0.40
Feb 1, 2019	−0.45	+0.40
Feb 1, 2020	−0.45	+0.40
Feb 1, 2021	−15.45	+10.40

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

Comparative Advantage May Be Real Because of Taxes

General Electric wants to borrow AUD

Quantas wants to borrow USD

Borrowing costs after adjusting for the differential impact of taxes could be:

	USD	AUD
General Electric	5.0%	7.6%
Quantas	7.0%	8.0%

Valuation of Fixed-for-Fixed Currency Swaps

Fixed for fixed currency swaps can be valued either using forward rates or as the difference between 2 bonds

Examples 7.3 and 7.4 (pages 178-180)

All Japanese interest rates are 1.5% per annum (cont. comp.)

All USD interest rates are 2.5% per annum (cont. comp.)

3% is received in yen; 4% is paid in dollars. Payments are made annually

Principals are $10 million and 1,200 million yen

Swap will last for 3 more years

Current exchange rate is 110 yen per dollar

Valuation in Terms of Forward Rates (page 179)

Time	DollarCash Flow	Yen cash flow	Forward rate	Dollar value of yen cash flow	Net cash flow	Present value
1	−0.4	+36	0.009182	0.3306	−0.0694	−0.0677
2	−0.4	+36	0.009275	0.3339	−0.0661	−0.0629
3	−10.4	+1236	0.009368	11.5786	+1.1786	+1.0934
Total						+0.9629

Valuation in Terms of Bonds (page 180)

Time	Cash Flows ($ millions)	PV ($ millions)	Cash flows (millions of yen)	PV ( millions of yen)
1	0.4	0.3901	36	35.46
2	0.4	0.3805	36	34.94
3	10.4	9.6485	1,236	1,181.61
Total		10.4191		1,252.01

Value = 1,252.01/110−10.4191 = +0.9629 millions of dollars

Other Currency Swaps

Fixed-for-floating: equivalent to a fixed-for-fixed currency swap plus a fixed for floating interest rate swap

Floating-for-floating: equivalent to a fixed-for-fixed currency swap plus two floating interest rate swaps

Swaps & Forwards

A swap can be regarded as a convenient way of packaging forward contracts

When a swap is initiated the swap has zero value, but typically some forwards have a positive value and some have a negative value

Credit Risk

When derivatives transactions with a counterparty are cleared bilaterally, they are netted

There is exposure if the net value of outstanding transactions is greater than the collateral posted

Credit Default Swaps: A Quick First Look

Notional principal (e.g. $100 million) and maturity (e.g. 5 yrs) specified

Protection buyer pays a fixed rate (e.g. 150 bp) on the notional principal (the CDS spread)

If the reference entity (a country or company) defaults protection seller buys bonds issued by the reference entity for their face value and the spread payments stop. Total face value of bonds bought equals notional principal

Other Types of Swaps

Amortizing/ step up

Compounding swap

Constant maturity swap

LIBOR-in-arrears swap

Accrual swap

Equity swap

Other Types of Swaps continued

Cross currency interest rate swap

Floating-for-floating currency swap

Diff swap

Commodity swap

Variance swap