Swaps

7.1

Swaps

Chapter 7

7.2

Nature of Swaps

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

7.3

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

Uncertainty about LIBOR receipt at end of reset period (6 months) is resolved at start of the reset period: the start of the 6-month period is the reset date

7.4

---------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

Cash Flows to Microsoft

7.5

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

7.6

Intel and Microsoft (MS) Transform a Liability

Intel MS

LIBOR

5%

LIBOR+0.1%

5.2%

Result: MS pays fixed 5.1%; Intel pays float. L+0.2%

7.7

Financial Institution is Involved

F.I.

LIBOR LIBORLIBOR+0.1%

4.985% 5.015%

5.2%Intel MS

F.I. earns 3 basis points, i.e. 0.03%

7.8

Intel and Microsoft (MS) Transform an Asset

Intel MS

LIBOR

5%

LIBOR-0.2%

4.7%

Result: MS earns float. L-0.3%; Intel earns fixed 4. 8%

7.9

Financial Institution is Involved

Intel F.I. MS

LIBOR LIBOR

4.7%

5.015%4.985%

LIBOR-0.2%

7.10

Quotes of a Swap Market Maker F.I.

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

F.I. pays Bid to receive LIBOR; F.I. requires Offer to pay LIBOR

7.11

The Comparative Advantage Argument: for both counterparties desired loan differs from that in which comparative advantage lies

AAACorp (less default risk) absolute advantage in both types AAACorp wants to borrow floating but comp. ad. in fixed BBBCorp wants to borrow fixed but comp. ad. in floating Comparative advantage: interest rate differences are different

Fixed 120 bps, Floating 70 bps Total gain = difference of differences = 50 bps

Fixed Floating

AAACorp 4.00% 6-month LIBOR + 0.30%

BBBCorp 5.20% 6-month LIBOR + 1.00%

7.12

The Swap

AAA BBB

LIBOR

LIBOR+1%

3.95%

4%

Each counterparty initially issues debt in which comp. advantage lies then enters into swap to obtain desired debt financing

Total Gain (50 bps) partitioned

Gain = interest rate paid in absence of swap – interest rate paid via swap

AAA gain: (L +.3%) – (L +.05%) = 25 bps BBB gain: 5.2% - 4.95 % = 25 bps

7.14

The Swap when a Financial Institution (earns 4 bps) is Involved

AAA F.I. BBB4%

LIBOR LIBOR

LIBOR+1%

3.93% 3.97%

Total Gain (50 bps) partitioned

AAA gain: (L+.3%) – (L+.07%) = 23 bps BBB gain: 5.2% - 4.97% = 23 bps Bank gain: 3.97% - 3.93% = 4 bps

7.16

Criticism of the Comparative Advantage Argument

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

The LIBOR+0.3% and LIBOR+1% rates available to the same corps. are six-month rates

Floating rate loans have more scope for renegotiation than fixed rate loans

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

7.17

The Nature of Swap Rates

Six-month LIBOR is a short-term AA borrowing rate

The 5-year swap rate has a risk corresponding to the situation where 10 six-month loans are made to AA borrowers at LIBOR

This is because the lender can enter into a swap where income from the LIBOR loans is exchanged for the 5-year swap rate

Swap Rate = Par Yield (N-year)

Used in boot strapping procedure True if swap reset period is 6 months Otherwise, must calculate equivalent

interest rate with semiannual compound. For newly issued float rate Bfloat = 100 For newly issued swap Bfloat = Bfix; swap

rate is the coupon rate of fix rate bond Bfix = 100; thus swap rate = par yield

7.19

Valuation (post-inception) 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

Alternatively, they can be valued as a portfolio of forward rate agreements (FRAs)

7.20

Valuation in Terms of Bonds

The fixed rate bond is valued in the usual way

The floating rate bond is valued by noting that it is worth par immediately after the next payment date

Bfloat = PV ( next payment* + par value ) *next payment is know at start of the reset

period

7.21

Example

Receive 8% and pay floating LIBOR both semiannually on a principal of $100 million

1.25 years to go and next floating payment ($5.1 million) will occur 3 months from now

On last reset date (3 months ago) LIBOR = 10.2% 3-, 9-, 15- month zero rates are 10%, 10.5%, 11%

Swap value = 98.238 −102.505= − 4.267; Why negative?

Time Fixed Floating Disc PV fixed PV floatingBond Bond Factor Bond Bond

0.25 4 105.1 0.9753 3.901 102.50450.75 4 0.9243 3.6971.25 104 0.8715 90.64

98.238 102.505

7.22

Valuation (post-inception) in Terms of portfolio of staggered FRAs

Each exchange of payments in an interest rate swap is an FRA

The FRAs can be valued on the assumption that today’s forward rates are realized

7.23

Example ($ amounts in M)

Time Fixed Floating Net Disc PV of NetCash Flow Cash Flow Cash Flow Factor Cash Flow

0.25 4 -5.100 -1.100 0.9753 -1.0730.75 4 -5.522 -1.522 0.9243 -1.4071.25 4 -6.051 -2.051 0.8715 -1.787

-4.267

Float. CF for T=.75 is -5.522

Infer F pertaining to T=.25 to T=.75 F = (10.5%(.75)+10%(.25)) / .5 = 10.75% Convert from cc to semiannual compound. F2 = 11.044% T=.75: CF = -100Mx11.044%x.5 = -.522M

Float. CF for T=1.25 is -6.051

Infer F pertaining to T=.75 to T=1.25 F = (11%(1.25)+10.5%(.75)) / .5 = 11.75% Convert from cc to semiannual compound. F2 = 12.1% T=1.25: CF = - 100Mx12.1%x.5 = -6.051M

7.26

An Example of a Currency Swap

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

7.27

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

Difference shows up in swap valuation approach via portfolio of staggered forwards

7.28

The Cash Flows

Year

Dollars Pounds$

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

2007 –18.00 +10.002008 +1.08 –0.5

2009 +1.08 –0.5 2010 +1.08 –0.5

2011 +1.08 –0.5 2012 +19.08 –10.5

£

7.29

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

7.30

Comparative Advantage Argument for Currency Swaps

General Electric wants to borrow AUD but comp. ad. in USD

Qantas wants to borrow USD but comp. ad. in AUD.

Precondition for viable swap satisfied!

Comparative advantage: interest rate differences are different

USD: 200 bps; AUD: 40 bps; Total Swap Gain = 160 bps.

USD AUD

General Electric 5.0% 7.6%

Qantas 7.0% 8.0%

7.31

Valuation (post-inception) 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

Currency Swap Valuation: difference between 2 bonds approach

Test Bank 7.5

Currency Swap Valuation: portfolios of forwards approach Bank previously entered into a swap: receives

5% in JPY, pays 8% in USD Zero curves are flat: JPY 4%, USD 9% Principals: USD10M, JPY1,200M Current spot = JPY110/USD Swap has 3 years remaining CF exchange occurs annually; a CF exchange

has recently occurred Intuition: Vswap > 0 since JPY R has dropped,

USD R has risen. Also, JPY has appreciated; USD has depreciated since contract signed.

Swap Value = USD 1.543M = PV of last column entries

Time USD CF JPY CF Forward Rates

NCF in USD

1 -.8 60 104.64 -.2266

2 -.8 60 99.53 -.1647

3 -10.8 1,260 94.68 1.9148

7.35

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

7.36

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

Credit Risk Exposure of Entity

Vswap to entity

Credit risk exposure only if Vswap > 0