chuong3 swaps 2013 s

7/30/2019 Chuong3 Swaps 2013 S

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CHAPTER 3

SWAPS

(6 hours)


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Outline

I. Nature of swaps

II. Interest rate swaps1. Mechanics of interest rate swap

2. Typical uses of an interest rate swap

3. The comparative-advantage argument4. Valuation of interest rate swaps

III. Currency swaps

1. Mechanics of currency swaps2. Typical uses of a currency swap

3. The comparative-advantage argument

4. Valuation of currency swaps


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3

NATURE OF SWAPS

A swap is an agreement between two companies to

exchange cash flows in the future.

The agreement defines the dates when the cash flows

are to be paid and the way in which they are to be

calculated.

Usually the calculation of the cash flows involves the

future value of an interest rate, an exchange rate orother market variable.

Two popular swaps: plain vanilla interest rate swaps

and fixed-to-fixed currency swaps.


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4

Mechanics of interest rate swaps (a)

The most common type is a plain vanilla interest rate

swap.

A company agrees to pay cash flows equal to interest

at a predetermined fixed rate on a notional principal for

a number of years. In return, it receives interest at a

floating rate on the same notional principal for the same

period of time.

The floating rate in most interest rate swaps is the

London Interbank Offered Rate (LIBOR).


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Example

Consider a 3-year swap initiated on March 5, 2010,between Microsoft and Intel:

- Microsoft agrees to pay Intel an interest rate of 5% perannum on a principal of $100 million.

- Intel agrees to pay Microsoft the 6-month LIBOR rate

on the same principal.- The payments are to be exchanged every 6 months,

and 5% interest rate is quoted with semiannualcompounding.


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

LIBOR FLOATING FIXED Net

Date Rate Cash Flow Cash Flow Cash Flow

Mar.5, 2010 4.2%

Sept. 5, 2010 4.8% +2.10 2.50 0.40

Mar.5, 2011 5.3% +2.40 2.50 0.10

Sept. 5, 2011 5.5% +2.65 2.50 +0.15

Mar.5, 2012 5.6% +2.75 2.50 +0.25

Sept. 5, 2012 5.9% +2.80 2.50 +0.30

Mar.5, 2013 6.4% +2.95 2.50 +0.45

Cash Flows to Microsoft

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Mechanics of interest rate swaps (b)

The principal is used only for the calculation of

interest payments. The principal itself is notexchanged. The notional principal.

The floating rate is set 6 months before it is paid.The floating rate is the LIBOR rate prevailing 6months prior to the time when it is paid.

An interest rate swap is generally structured sothat one side remits the difference between the

two payments to the other side.


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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

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Transfo rm ing a liabi l i ty - Example (a)

Microsoft (MS) has arranged to borrow $100 million at

LIBOR plus 10 basis points. After entering into the

swap, MS has three sets of cash flows:

+ It pays LIBOR +0,1% per annum to its outside lenders+ It receives LIBOR under the terms of the swap.

+ It pays 5% under the terms of the swap.

For MS, the swap has the effect of transforming

borrowings at a floating rate of LIBOR +0.1% intoborrowings at a fixed rate of 5.1%.


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Transform ing a l iabi l i ty Example (b)

Intel has a 3-year $100 million outstanding on

which it pays 5.2%. After entering into the swap,Intel has three sets of cash flows:

+It pays 5,2% to its outside lenders.

+ It pays LIBOR under the terms of the swap+ It receives 5% under the terms of the swap.

For Intel, the swap has the effect of transforming

borrowings at a fixed rate of 5.2% into borrowingsat a floating rate of LIBOR plus 20 basis points.

.


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Options, Futures, and Other Derivatives,7th Ed, Ch 7, Copyright John C. Hull 2010

Intel and Microsoft (MS)

Transform a Liability

Intel MS

LIBOR

5%

LIBOR+0.1%

5.2%

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Transform ing an asset Examp le (a)

Microsoft (MS) owns $100 million in bonds that

will provide interest at 4.7% per annum over thenext 3 years. After entering into the swap, MShas three sets of cash flows:

+ It receives 4.7% on the bond

+ It receives LIBOR under the term of the swap.

+ It pays 5% under the term of the swap.

MS has transformed an asset earning 4.7% into

an asset earning LIBOR-0.3%.


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Transform ing an asset Example (b)

Intel has an investment of $100 million that

yields LIBOR minus 20 basis points. Afterentering into the swap, Intel has three sets ofcash flows:

+ It receives LIBOR-20 basis points on its

investment.+ It pays LIBOR under the term of the swap.

+ It receives 5% under the term of the swap.

Intel has transformed an asset earning LIBOR-0.2% into an asset earning 4.8%.


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Intel and Microsoft (MS)

Transform an Assets


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Role of Financial Intermediary

Usually MS and Intel each deal with a financial

intermediary such as a bank or other financialinstitution.

The financial institution earns about 3 or 4 basis

points (0.03% or 0.04%) on a pair of offsettingtransactions.


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Financial Institution is Involved

F.I.

LIBOR LIBOR

LIBOR+0.1%

4.985% 5.015%

5.2%

Intel MS

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Financial Institution is Involved

Intel F.I. MS

LIBOR LIBOR

4.7%

5.015%4.985%

LIBOR-0.2%

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Quotes By a Swap Market

Maker

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

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The comparat ive-advan tage argum ent (a)

Two companies AAA & BBB want to borrow $10 millionfor 5 years and have been offered the following rates.

Assume that AAA wants to borrow at a floating rate ofinterest. BBB wants to borrow at a fixed rate ofinterest.


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The comparat ive-advantage argument (b)

AAA borrows fixed rate funds at 4% per annum.BBB borrows floating-rate funds at LIBOR+0.6%

per annum.

Consider an interest rate swap: AAA agrees topay BBB interest at 6-month LIBOR on $10billion. In return, BBB agrees to pay AAA interestat a fixed rate of 4.35% per annum on $10

million.


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The comparat ive-advan tage argum ent (c)

AAA has three sets of cash flows:

- It pays 4.0% per annum to the bank

- It receives 4.35 % per annum from BBB

- It pays LIBOR to BBB.

Totally,AAA pays LIBOR-0.35%, 0.25% lowerthan the floating rate offered by the bank.


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The comparat ive-advan tage argum ent (d)

BBB has three sets of cash flows:

- It pays LIBOR +0.6% to the bank.

- It receives LIBOR from AAA

- It pays 4.35% to AAA

Totally, BBB pays 4.95% per annum, 0.25%lower than the fixed rate offered by the bank.


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The Swap

AAACorp BBBCorp

LIBOR

LIBOR+0.6%

4.35%

4%

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The Swap when a Financial

Institution is Involved

AAA F.I. BBB4%

LIBOR LIBOR

LIBOR+0.6%

4.33% 4.37%

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Problems1. Companies A and B have been offered the following

rates per annum on a $20 million 5-year loan:

Company A requires a floating-rate loan, company Brequires a fixed-rate loan. Design a swap that will neta bank, acting as intermediary, 0.1% per annum and

that will appear equally attractive to both companies.

Fixed rate Floating rate

Company A

Company B

5.0%

6.4%

LIBOR + 0.1%

LIBOR + 0.6%


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2. Companies X and Y have been offered the followingrates per annum on a $5 million 10-year investment

Company X requires a fixed-rate investment; companyY requires a floating-rate investment. Design a swapthat will net a bank, acting as intermediary, 0.2% per

annum and will appear equally attractive to X and Y.

Fixed rate Floating rate

Company X

Company Y

8%

8.8%

LIBOR

LIBOR


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Valuation of interest rate swaps

An interest rate swap is worth zero or close to

zero, when it is first initiated. After it has been inexistence, due to the variation of the marketrate, its value may become positive or negative.

Two ways to valuate an interest rate swap.

- Interest rate swaps can be valued as thedifference between the value of a fixed-ratebond and the value of a floating-rate bond.

- Alternatively, they can be valued as a portfolio offorward rate agreements (FRAs)


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The value of Intel (the floating-rate payer)

The value of Microsoft ( the fixed-rate payer)

Vswap =value of the swap

Bfix = value of the fixed-rate bond

Bfl = value of the floating-rate bond

flfixswap BBV

fixflswap BBV


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The value of the fixed-rate bond:

ti= the time at which interest payments are

exchanged.L= Notional principal

ri= LIBOR (discount rate) for a maturity ofti

k= the fixed interest payment

n

i

trtrfixnnii LekeB

1


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The value of the floating-rate bond

The bond is worth the notional principal

immediately after an interest payment, because:- Immediately after an interest payment, the floating-

rate bond is quite similar to a newly issuedfloating-rate bond.

- The value of a newly issued floating-rate bond thatpays 6-month LIBOR is always equal to itsprincipal value when the LIBOR curve is used fordiscounting.


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The next exchange of payment is at time t1. Thefloating payment that will be made at time t1 (whichwas determined at the last payment date) is k*. The

value of the floating-rate bond at time t1:

The current value of the floating-rate bond:

*kLBfl

11)( * trfl ekLB


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Example:

A financial institution has agreed to pay 6-

month LIBOR and receive 8% per annum (withsemiannual compounding) on a notionalprincipal of $100 million.

The swap has a remaining life of 1.25 years.

The LIBOR rates with continuous compoundingfor 3-month, 9-month and 15-month maturitiesare 10%, 10.5% and 11%, respectively. The 6-month LIBOR rate at the last payment date was

10.2% (with semiannual compounding).

Calculate the value of the swap from theposition of the institution.


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Valuation Using Bonds

Time Bf ix

CFs

Bf lCFs Disc

factor

PV Bf ix PVBf l

0.25 4.0 105.100 0.9753 3.901 102.505

0.75 4.0 0.9243 3.697

1.25 104.0 0.8715 90.640

Total 98.238 102.505


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Problems

3. A $100 million interest rate swap has a remaining lifeof 10 months. Under the term of the swap, 6-month

LIBOR is exchanged for 7% per annum (compoundedsemiannually). The average of the bid-offer rate beingexchanged for 6-month LIBOR in swaps of allmaturities is currently at 5% per annum with

continuous compounding. The 6-month LIBOR ratewas 4.6% per annum 2 months ago. What is thecurrent value of the swap to the party paying floating?What is its value to the party paying fixed?


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Currency swaps-mechanics

A currency swap involves exchanging principal

and interest payments in one currency forprincipal and interest payments in another. In acurrency swap the principal is usually exchangedat the beginning and the end of the swaps life.

Usually the principal amounts are chosen to beapproximately equivalent using the exchange rateat the swaps initiation. When they are exchanged

at the end of the life of the swap, their values maybe quite different.


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An Example of a Currency Swap

A5-year currency swap agreement

between IBM and BP was entered into onFeb 1,2007.

IBM agrees to pay 5% on a sterling

principal of 10,000,000 & receive 6% ona US$ principal of $18,000,000 every yearfor 5 years.


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An Example of a Currency Swap

IBM

BPUSD 6%

GBP 5%


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The Cash Flows to IBM in the currency

swap

Year

Dollars Pounds$

------millions------

2007 18.00 +10.00

2008 +1.08 0.50

2009 +1.08 0.50

2010 +1.08 0.50

2011+1.08 0.50

2012 +19.08 10.50


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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


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Example:

IBM can invest 10 million in the UK to

yield 5% per annum.

IBM feels that the USD will strengthenagainst sterling and prefer a USD-

denominated investment. The swap hasthe effect of transforming the UKinvestment into a $18 million investment in

the US yielding 6%.


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Comparative Advantage Arguments for Currency

Swaps

Example: The 5-year fixed-rate borrowingcosts to GE and Qantas Airways in USDand AUD:


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GE wants to borrow 20 million AUD andQantas Airways wants to borrow 15 million

USD. The current exchange rate:1 AUD=0.75 USD.

GE borrows USD, whereas Qantas

borrows AUD. Then, they use a currencyswap to transform GEs loan into an AUDloan andQantass loan into a USD loan.


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Comparative Advantage Arguments for Currency Swaps

An Example

GE F.I QANTASAUD

6.9%AUD

8%AUD

8%

USD

5%USD

6.3%USD5%

Problems


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ob e s

4. Company X wishes to borrow US dollars at a fixed rate ofinterest. Company Y wishes to borrow Japanese Yen at afixed rate of interest. The amounts required by the twocompanies are roughly the same at the current exchangerate. The companies are subject to the following interestrates:

Design a swap that will net a bank, acting as intermediary,50 basis points per annum. Make the swap equallyattractive to the two companies and ensure that all foreignexchange risk is assumed by the bank.

JPY USDCompany X

Company Y

5.0%

6.5%

9.6%

10.0%

5 C i A d B f th f ll i i t t t


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5. Companies A and B face the following interest rates:

Suppose company A wants to borrow USD at a

floating rate of interest and B wants to borrow CAD ata fixed rate of interest. A financial institution is planningto arrange a swap and requires a 50-basis-pointspread. If the swap is to appear equally attractive to Aand B, what rates of interest will A and B end uppaying?

Company A Company B

USD

CAD

LIBOR + 0.5%

5.0%

LIBOR + 1.0%

6.5%

V l ti f


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Valuation of currency swaps

The value of a swap in USD where

+ US dollars are received and a foreign currency is paid:

+ the foreign currency is received and dollars are paid:

BD =value of the bond measured in USD. BF =value of the bond measured in the foreign

currency.

S0 = the spot exchange rate

FDswap BSBV 0

DFswap BBSV 0


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Example:

A financial institution has entered into a currency

swap in which it receives 5% per annum in yenand pays 8% per annum in dollars once a year.The principals in the two currencies are $10million and 1,200 million yen. The swap will last

for another 3 years. The current exchange rateis 110 yen=$1.

Calculate the value of the swap to the institution.


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Valuation of the cu rrency swap

Time CFs

(USD)

PV(USD) CFs

(Yen)

PV(Yen)

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 1,063.30

Total 9.6439 1,230.55


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The value of the dollar bond is $9.6439million, the value of the yen bond is1,230.55

million yen. The value of the swap in dollars:

1,230.55/110 -9.6439 = 1.5430 million USD


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Problem

6. A currency swap has a remaining life of 15 months. It

involves exchanging interest at 10% on 20 million forinterest at 6% on $30 million once a year. The termstructure of interest rate in both the UK and the US iscurrently flat, and if the swap were negotiated todaythe interest rates exchanged would be 4% in dollarsand 7% in sterling. All interest rates are quoted withannual compounding. The current exchange rate(dollars per pound sterling) is 1.85000. What is thevalue of the swap to the party paying sterling? What is

the value of the swap to the party paying dollars?

chuong3 swaps 2013 s

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