SWAP(mod).ppt

Swaps

Swaps

Swaps

Swaps

Chapter 7

International investment and capital Prof. Kang

082SIS68 Choi Eunyoung

Swap

Swap

s

s

Swap

Swap

s

Contents

Plain vanilla interest swap

1

1

Currency

Currency

swap

swap

Interest swap

Interest swap

2

2

Nature of Swaps

A swap

A swap

is

an agreement

to exchange

cash flows at specified future times

according to certain specified rules



the date when the cash flows are paid

the date when the cash flows are paid



the way in which they are calculated

the way in which they are calculated

“Plain Vanilla” Interest Rate Swap

The most common type of IRS

Paying cash flows equal to interest

at a predetermined fixed rate on a NP

NP: Notional Principal

(not exchanged in IRS)

(not exchanged in IRS)

Receiving interest at a floating rate on NP

“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 on March 5, 2007

Intel

Intel

Microsoft

Microsoft

Floating-rate payer

Fixed-rate payer

5.0% 5.0%

Cash Flows to Microsoft

---Millions of

Dollars---LIBOR FLOATING FIXED Net Date Rate Cash Flow Cash Flow Cash Flow Mar.5, 2007 4.2%

Sept. 5, 2007 4.8% +2.10 –2.50 –0.40 Mar.5, 2008 5.3% +2.40 –2.50 –0.10 Sept. 5, 2008 5.5% +2.65 –2.50 +0.15 Mar.5, 2009 5.6% +2.75 –2.50 +0.25 Sept. 5, 2009 5.9% +2.80 –2.50 +0.30 Mar.5, 2010 6.4% +2.95 –2.50 +0.45

Intel

Intel

Microsoft

Microsoft

Floating-rate payer Fixed-rate payer

5.0%:$2.5m

5.0%:$2.5m

LIBOR:2.1

LIBOR:2.1

6m

Semi annual com

Plain Vanilla Swap

Intel

Intel

Microsoft

Microsoft

Floating-rate payer Fixed-rate payer

5.0% 5.0%

LIBOR

Long a fixed rate bond

Long a fixed rate bond

Short a floating rate bond

Long a floating rate bond

Long a floating rate bond

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

Intel

Intel

Microsoft

Microsoft

Intel and Microsoft (MS) Transform a Liability

(Figure 7.2, page 150)

LIBOR 5%

LIBOR+0.1% 5.2%

-(LIBOR+0.1%) +LIBOR-5%

=-5.1

Intel and Microsoft (MS) Transform an Asset

(Figure 7.3, page 151)

4.7-5+LIBOR = LIBOR -0.3

LIBOR-0.2-LIBOR+5 = 4.8

Intel

Intel

Microsoft

Microsoft

LIBOR 5%

Financial Institution is Involved

5.1

LIBOR+0.2%

Intel

Intel

Microsoft

Microsoft

LIBOR 5% 5.2% LIBOR+0.1% 5.115% LIBOR+0.215%

Intel

Intel

MS

MS

Financial Institution is Involved

LIBOR-0.3

4.8%

Intel

Intel

Microsoft

Microsoft

LIBOR 5% LIBOR-0.2% 4.7% 4.7% 4.785%

Intel

Intel

MS

MS

Role of Financial Institution

 Two nonfinancial companies don’t get in touch directly to arrange a swap

 If one of the companies defaults, FI honors its agreement with the other company

 The spread earned is to partly compensate it for the risk of the default on the swap

Market maker

• Bonds

• Forward rate agreements

• Interest rate futures

A

A

B

B

C

C

Market

Market

Maker

Maker

bid

bid

Quotes By a Swap Market Maker

Maturity

Maturity Bid (%)Bid (%) Offer (%)Offer (%) Swap Rate (%)Swap Rate (%) 2 years

2 years 6.03 6.06 6.045

3 years

3 years 6.21 6.24 6.225

4 years

4 years 6.35 6.39 6.370

5 years

5 years 6.47 6.51 6.490

7 years

7 years 6.65 6.68 6.665

10 years

10 years 6.83 6.87 6.850

The Comparative Advantage Argument

(Table 7.4, page 155)

 AAACorp wants to borrow floating

 _{BBBCorp wants to borrow fixed}

Fixed Floating

AAACorp 4.0% 6-month LIBOR − 0.10%

BBBCorp 5.2% 6-month LIBOR + 0.6%

$10 million

The Swap

Fixed Floating

AAACorp 4.0% 6-month LIBOR − 0.10%

BBBCorp 5.2% 6-month LIBOR + 0.6%

1.2%

-

=

AAA Corp

AAA Corp

BBB Corp

BBB Corp

LIBOR 4.35%

LIBOR-0.35% _4.95%

LIBOR+0.6% 4.0%

The Swap when a Financial Institution is Involved

(Figure 7.7, page 156)

AAA Corp

AAA Corp

BBB Corp

BBB Corp

LIBOR 4.35% LIBOR-0.35% 4.95% LIBOR+0.6% LIBOR-0.33%

AAA

AAA

BBB

BBB

Criticism of the Comparative Advantage Argument



Why spread differential appear?

 The nature of the contracts in fixed and floating

Fixed

Fixed Floating 6-m LIBORFloating 6-m LIBOR

the firm issue 5 yr fixed rate bond

Opportunity to review floating rate every 6 Creditworthiness

(By lender) LIBOR + spread

Creditworthiness

No option to change

The Nature of Swap Rates

 _{Six-month LIBOR is a short-term AA}

borrowing rate

 _{Not risk free lending rates but close to risk}

free by entering into a swap to exchange the LBIOR income for the 5 year swap rate.

6m LIBOR Interest rate

5yrSwap rate 6m LIBOR

Interest rate

5 year swap rates < AA borrowing rates

LIBOR

reciever

Using Swap Rates to Bootstrap

the LIBOR/Swap Zero Curve

 Consider a new swap where the fixed rate is the

swap rate

 When principals are added to both sides on the

final payment date the swap is the exchange of a fixed rate bond for a floating rate bond

 The floating-rate rate bond is worth par. The

swap is worth zero. The fixed-rate bond must therefore also be worth par

 This shows that swap rates define par yield

Valuation of an Interest Rate Swaps

 _{Interest rate swaps can be valued as the}

difference between the value of a fixed-rate bond and the value of a floating-fixed-rate bond

 _{Alternatively, they can be valued as a}

Cash Flows to Microsoft

---Millions of Dollars---LIBOR FLOATING FIXED Net Date Rate Cash Flow Cash Flow Cash Flow Mar.5, 2007 4.2%

Valuation in Terms of Bonds

short position in a floating rate bond

V

=

B

- B

Long position in a floating rate bond

short position in a fixed rate bond

V

=

B

- B

Floating rate payer

Floating rate payer

Fixed rate payer

Fixed rate payer

Valuation in Terms of Bonds

 Value of the fixed rate bond

 R_m = m(eRc/m – 1)

 Rc: a rate of interest with continuous compounding R_m: a rate with compounding m times per annum m: the compounding frequency

Note : the floating rate bond is worth the notional principal immediately after an interest payment L: notional principal

t*: the next exchange of payment is at time t*

k*: _{the floating payment that will be made at t}*

r*: the LIBOR/swap zero rate for a maturity of t*

right after the payment B_fl=L right before the payment B_fl=L + k*:

Example

 Pay six-month LIBOR, receive 8% (s.a.

compounding) on a principal of $100 million

 Remaining life 1.25 years

 LIBOR rates for 3-months, 9-months and 15-months are 10%, 10.5%, and 11% (cont comp)

 6-month LIBOR on last payment date was 10.2% (s.a. compounding)

Valuation Using Bonds

Time Bfix cash flow

B_fl cash flow

Disc factor

PV B_fix

PV B_fl

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



Calculation for valuing the swap in terms of bonds

e

e

e

t*=0.25(90/360) L + k*=105.1 million

Valuation in Terms of FRAs

Each exchange of payments in an interest rate swap

is an FRA(Forward Rate Agreement)

 A certain interest rate will apply to either borrowing or

lending a certain principal during a specified future period of time.

 The swap was nothing more than a portfolio of forward rate agreements, so that the swap can be valued

• Use the LIBOR/swap zero curve to calculate forward rates for each of the LIBOR rates

• Calculate swap cash flows

Cash Flows to Microsoft

---Millions of Dollars---LIBOR FLOATING FIXED Net Date Rate Cash Flow Cash Flow Cash Flow Mar.5, 2007 4.2%

Sept. 5, 2007 4.8% +2.10 –2.50 –0.40 Mar.5, 2008 5.3% +2.40 –2.50 –0.10 Sept. 5, 2008 5.5% +2.65 –2.50 +0.15 Mar.5, 2009 5.6% +2.75 –2.50 +0.25 Sept. 5, 2009 5.9% +2.80 –2.50 +0.30 Mar.5, 2010 6.4% +2.95 –2.50 +0.45

Intel

Intel

Microsoft

Microsoft

Floating-rate payer Fixed-rate payer

5.0%

5.0%

Example

 Pay six-month LIBOR, receive 8% (s.a.

compounding) on a principal of $100 million

 Remaining life 1.25 years

 LIBOR rates for 3-months, 9-months and 15-months are 10%, 10.5%, and 11% (cont comp)

 6-month LIBOR on last payment date was 10.2% (s.a. compounding)

Valuation of Example Using FRAs

Total -4.267 Fixed :4.0=100x0.08(8%)x0.5 Floating: 5.1=100x0.102(10.2%)x0.5 Fixed :4.0=100x0.08(8%)x0.5 Floating: 5.1=100x0.102(10.2%)x0.5 0.5 0.105x0.75-0.10x0.25

T₂

-

R_1,R₂ is the zero rate to maturities T₁ T₂

=> 0.1075 =

 R_m = m(eRc/m– 1) = 2(e0.1075/2 -1) = 11.044%

Definition of a Currency Swap

An arrangement in which two parties

exchange specific amounts of different

currencies initially, and a series of

interest payments on the initial cash

flows are exchanged

Example of Currency Swap

IBM

IBM British

Petroleum

$ 6%

£ 5%

An agreement to pay 5% on a sterling

principal of £10,000,000 & receive 6% on a US$ principal of $18,000,000 every year for 5 years

$1.08 million

£0.50 million

$18million x 0.06 = 1.08 $10million x 0.05 = 0.50

Principal £ 10 million

Exchange of Principal



In an interest rate swap the principal is

not exchanged



In a currency swap the principal is

Typical Uses of a Currency Swap



Conversion from a liability in one

currency to a liability in another

currency

The Cash Flows

Year ---millions---$

2004 –18.00 +10.00 2005 +1.08 –0.50 2006 +1.08 –0.50 2007 +1.08 –0.50 2008 +1.08 –0.50 2009 +19.08 −10.50

£

IBM

IBM British

Petroleum

$ 6%

£ 5%

$1.08 million

Comparative Advantage Arguments for

Currency Swaps



General Electric wants to borrow

AUD

Qantas wants to borrow USD

USD AUD

General Electric 5.0% 7.6% Qantas 7.0% 8.0%

2.0%

-

=

1.6

Quantas Airways General

Electric

$6.2%

A$ 6/8%

$5.0% A$ 8.0%

Comparative Advantage Arguments for

Currency Swaps



Currency swap with FI

Financial institution

Quantas Airways General

Electric

$5.0% $6.3%

A$8.0% A$6.9%

$5.0%

A$8.0%

USD AUD

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

 V _swap=B_d-S_oB_f / V_swap= S_oB_f-B_d

 _{So : spot exchange rate(number of dollars per unit}

of foreign currency)

 _{Bf:the value of the bond defined by foreign cash}

flows on the swap

 _{Bd: the value of the bond defined by domestic}

Example

All Japanese LIBOR/swap rates are 4%

_{All USD LIBOR/swap rates are 9%}

_{5% is received in yen; 8% is paid in dollars.}

Payments are made annually

Principals are $10 million and 1,200 million yen

_{Swap will last for 3 more years}

Valuation in Terms of Bonds

(Table 7.9, page 167)

Time Cash Flows ($) PV ($) Cash flows (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 1,064.30 Total 9.6439 1,230.55

Valuation in Terms of Forwards

(Table 7.10, page 168)

Time $ cash flow Yen cash flow Forward Exch rate Yen cash flow in $

Net Cash Flow

Present value

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 -10.0 1200 0.010562 12.6746 +2.674

6

2.0417

Total 1.5430

 F_o=S_oe(r-rf)T

 rf: the value of the foreign risk free interest rate when invested for time T

Swaps & Forwards

_{A swap can be regarded as a convenient}

way of packaging forward contracts

_{Although the swap contract is usually}

Credit Risk

 Chance that one party defaults while FI

honors the contract with the other party

 If one party defaults, to induce 3rd party &

the similar amount

 The company has credit risk exposure only

when its value is positive

 Some swaps are more likely to lead to credit

risk exposure than others (CRS>IRS)

Other Types of Swaps

 Floating-for-floating interest rate swaps, amortizing swaps, step up swaps, forward swaps, constant maturity swaps,

compounding swaps, LIBOR-in-arrears swaps, accrual swaps, diff swaps, cross

currency interest rate swaps, equity swaps, extendable swaps, puttable swaps,