TM Interest Rate Swap

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TREASURY MANAGEMENT
Chapter 14 Interest Rate Swap

Swaps
Two parties exchange recurring payments (most
commonly)

the feature of recurring payments distinguishes a swap from a forward contract but, some swaps involve only a single exchange
(Thus, in practice it’s a swap if it is written up on swap documentation. That is, it’s a swap if it’s called a swap.)

Similar to series of forward contracts Common types:
interest rate, currency, equity, commodity

This class introduces interest rate swaps

Cash flow diagram of interest rate swap
Floating Rate (LIBOR) X Notional Principal Fixed-Rate Payer Fixed Rate of 7.00% X Notional Principal Note: LIBOR is London Interbank Offered Rate Fixed-Rate Receiver

1

Basic facts
Payments based on indices:
interest rates (most common) currency prices (actually an exchange of currencies) commodity prices equity prices or returns

Traded in “over-the-counter” markets large dealers include:
large U.S. commercial banks large U.S. investment banks some European banks (e.g. Swiss banks, Deutsche Bank) virtually all major banks do at least some swaps business

Interest rates used as indices
3-month and 6-month LIBOR most common But also:
3-month U.S. Treasury bill yield CMT (constant maturity Treasury) yields commercial paper rates almost any rate is possible

And of course, there are interest rate swaps in other currencies

Relevant parts of a swap confirmation
Contracting Parties: Little End-User (LEU) and Big Swap Dealer (BSD), with a guarantee to be provided by Big Swap Dealer Parent Corp. See Schedule A January 18, 1989 January 20, 1989 January 15, 1992

Notional Amount: Trade Date: Effective Date: Termination Date: Fixed Amounts: Fixed Rate Payor: Fixed Rate Payor Paryment Dates:

LEU

Each January 15, April 15, July 15 and October 15 starting with April 15, 1989; subject to adjustment in accordance with the Following Day Banking Convention.

Fixed Rate and Fixed Rate Day Count Fraction:

10.05%, 30/360

(First page would be a cover letter; in addition, a swap with any but the simplest features might include a few pages of definitions of the terms which appear in the confirmation.)

2

Parts of a swap confirmation
Floating Amou nts: Floating Rate Payor: Floating Rate Payor Payment D ates: BSD

Each January 15, April 15, July 15 and October 15 starting with April 15, 1989; subject to adjustment in accordance with the Follow ing Banking D ay Convention.*

Floating Rate for Initial Calculation Period: Floating Rate Option: Designated Maturity: Adjustment to Floating Rate Option:

9.742% LIBO R 3 month

3-month LIBOR will be divided by .97 each calculation period

Floating Rate Day Count Fraction: Reset Dates:

Actual/360 Two Days Prior to Each Floating Rate Payment Date

*While this swap uses the Following Banking Day Convention, the use of the Modified Following Banking Day Convention is more common. With payment dates in the middle of the month, the difference between these two conventions is not relevant.

Parts of a swap confirmation
Schedule A

Date 1-20-89 - 1-15-90 1-16-90 - 1-15-91 1-16-91 - 1-15-92

Notional Amount $75,000,000 70,000,000 60,000,000

Features of the confirmation:*
Contracting parties:
LEU is a telecommunications company BSD is the derivatives subsidiary of an investment bank

Fixed rate payer/floating rate payer:
fixed rate payer LUE pays fixed, receives floating floating rate payer BSD pays floating, receives fixed

Payment dates, floating rate option, designated maturity:
payments based on 3-month LIBOR are exchanged every 3 months in US, also common to have payments based on 6month LIBOR exchanged every 6 months possible for fixed leg to have a different payment frequency than floating leg

Notional amount (or principal):
is not exchanged, but simply determines size of payments
*Not in the order in which items appear.

3

Features of the confirmation: Dates
Trade date:
date the parties agree, exchange confirmations

Effective date:
date begin accruing interest; analogous to settlement date

termination date = date of last payment

Payment dates:
dates when payments are exchanged*

Reset dates:
dates when LIBOR quotes are observed note that LIBOR is observed at the beginning of the period due to this, the floating rate for the initial calculation period is known on the trade date, and included in the confirmation

•“Following Banking Day Convention” means that if the specified payment date is a weekend or a holiday, payment is made on the next business day.

Aside on interbank settlement convention
In the interbank deposit market, the settlement convention is 2 business days (in most currencies, including USD)
For example, if on 13 January I agree to borrow (accept a deposit of) $10 million at LIBOR, the actual deposit/loan period is from 15 January to 15 April That is, the rate quoted on 13 January applies to a loan/deposit beginning 2 days later Also (obviously), the rate is known at the beginning of the period

Floating leg of swap inherits these conventions

Relevant dates
Trade date Reset date for second payment Effective (value) date First payment date Reset date for third payment Second payment date Reset date for final payment Eleventh payment date Termination and final payment date

1/18/89

1/20/89

4/13/89

4/17/89

7/13/89

7/17/89



10/11/91

10/15/91

1/15/92

Remarks: 4/15/89 is a Saturday, so the payment is made on Monday 4/17/89 7/15/89 is a Saturday, so the payment is made on Monday 7/17/89 10/13/91 is a Sunday, so the reset date is Friday 10/11/91

Second payment is based on LIBOR quoted 3 months and 2 (business) days earlier “Floating Rate for Initial calculation Period” is known on the trade date, and thus included in the confirmation

4

Discussion of the confirmation: Day-count fractions
Floating rate day-count fraction:
USD money market convention: Actual/360 floating leg generally follows money market convention in that currency (Act/360 or Act/365)

Fixed rate day count fraction:
U.S. bond market convention: 30/360 convention for fixed leg generally follows bond convention in that currency/region

Aside about day counts
What is the role of day counts? If you borrow/deposit $10 million for one year in the interbank market when 1-year LIBOR is 5%:
you do not pay/receive $10(1.05) million at yearend instead, you pay/receive (days / 360)0.05) $10(1 + million, where days is the actual number of days in the period this is actual/360; actual/365 should be clear

In 30/360, when counting days you pretend that each month has 30 days

Payment conventions
What if the payment date specified in the contract is a weekend or holiday? Need to consider two issues:
When is the payment date? If the payment date is adjusted, do we also adjust the amount of interest paid?

5

Payment Date: Following and Modified Following Business Day Convention
The following business (banking) day convention states that the payment date is the first following day that is a business day. The modified following business (banking) day convention states that the payment date is the first following day that is a business day, unless that day falls in the next calendar month. In this case only, the maturity date will be the first preceeding business day. Most common market practice is to use the Modified Following Business Day Convention, but the Following Business Day Convention is sometimes used (for example, in the confirmation above)

Adjusted versus unadjusted
Example from the fixed leg of a swap:
Fixed rate 6%, 30/360, Modified Following, scheduled payment date is 15 April, But, 15 April is Saturday Modified Following ⇒ payment is made/received on Monday, 17 April

Question: How large is the interest payment?
Is it (180/360)×0.06×N? (N = notional amount of swap) Or do we add 2 days to the payment period, i.e. is the payment (182/360)×0.06×N? (If we add 2 days to this payment period, we would also then subtract 2 days from the next payment period)

Adjusted versus unadjusted
Unadjusted: shift payment date, but do not change the amount of the payment
payment = (180/360)×0.06×N Interest payments on bonds are generally unadjusted, i.e. if the payment date gets shifted due to a weekend or holiday, the payment amount is not changed

Adjusted: shift payment date and change the interest accrual (that is, change the amount of the payment)
payment = (182/360)×0.06×N Most commonly, but not always, swap payments are adjusted. Swap payments might be unadjusted if the swap is intended to exactly hedge an underlying bond on which payments are unadjusted.

6

Discussion of the confirmation: Adjustment to floating rate option
Adjustment to floating rate option:
if there is an adjustment to the floating rate it usually comes in the form of adding or subtracting an amount, e.g. LIBOR + 40 basis points in fact, the most common “adjustment” is no adjustment, i.e. LIBOR + 0 basis points or “LIBOR flat” In this deal, I have no idea why the adjustment comes in the form of dividing by 0.97

Confirmation: Notional amount
Schedule A

Notional amount (or principal):
Most commonly the notional amount is just a number, e.g. $100 million In this swap the notional amount varies over time because the swap was being used to hedge a loan with a principal amount that changed over time as principal payments were made

Date 1-20-89 - 1-15-90 1-16-90 - 1-15-91 1-16-91 - 1-15-92

Notional Amount $75,000,000 70,000,000 60,000,000

Changes in notional amount reflect fact that: (a) LEU borrowed $75 million (b) repaid $5 million on 15 Jan 1990 (c) Repaid $10 million on 15 Jan 1991 (d) Repaid the remaining $60 million on 15 Jan 1992

Cash flows (from perspective of LEU)
Trade Date 1/18/1989 1/20/1989 Payment Reset Date Date 4/17/1989 7/17/1989 4/13/1989 10/16/1989 7/13/1989 1/15/1990 10/12/1989 4/16/1990 1/11/1990 7/16/1990 4/12/1990 10/15/1990 7/12/1990 1/15/1991 10/11/1990 4/15/1991 1/11/1991 7/15/1991 4/11/1991 10/15/1991 7/11/1991 1/15/1992 10/11/1991 Days for Fraction Notional LIBOR on Floating Floating Amount reset date Payment Payment $75,000,000 9.7420% 87 0.2417 $75,000,000 10.1875% 91 0.2528 $75,000,000 8.8125% 91 0.2528 $75,000,000 8.7500% 91 0.2528 $70,000,000 8.1875% 91 0.2528 $70,000,000 8.4375% 91 0.2528 $70,000,000 8.3125% 91 0.2528 $70,000,000 8.2500% 92 0.2556 $60,000,000 7.3125% 90 0.2500 $60,000,000 6.1250% 91 0.2528 $60,000,000 5.9375% 92 0.2556 $60,000,000 5.3750% 92 0.2556 Cash Flow Due to Floating Payment $1,820,348 $1,991,114 $1,722,374 $1,710,159 $1,493,539 $1,539,143 $1,516,341 $1,521,478 $1,130,799 $957,689 $938,574 $849,656 Days for Fraction Fixed Fixed Fixed Rate Payment Payment 10.05% 87 0.24167 10.05% 90 0.25000 10.05% 89 0.24722 10.05% 89 0.24722 10.05% 91 0.25278 10.05% 90 0.25000 10.05% 89 0.24722 10.05% 90 0.25000 10.05% 90 0.25000 10.05% 90 0.25000 10.05% 90 0.25000 10.05% 90 0.25000 Cash Flow Due to Fixed Payment -$1,821,563 -$1,884,375 -$1,863,438 -$1,863,438 -$1,778,292 -$1,758,750 -$1,739,208 -$1,758,750 -$1,507,500 -$1,507,500 -$1,507,500 -$1,507,500 Net Cash Flow -$1,215 $106,739 -$141,063 -$153,279 -$284,753 -$219,607 -$222,867 -$237,272 -$376,701 -$549,811 -$568,926 -$657,844

It is crucial to understand that the cash flow on say 7/17/89 is based on LIBOR observed on 4/13/89, …., cash flow on 1/15/92 is based on LIBOR observed on 10/11/91.
Note that this column reflects the “adjustment To floating rate option,” that is the floating Rate is divided by 0.97

7

Why did LEU do the deal?
LEU was a relatively new telecom. company Borrowed $75 million from a bank on a 3-year note
floating rate loan interest payments every 3 months based on 3-month LIBOR partial principal payments discussed above

Condition of loan was that LEU swap from floating to fixed
LEU receives floating, pays fixed on swap Pays floating on bank loan

Net effect is that LEU has a synthetic fixed-rate loan

How does the dealer profit?
For this swap, dealer
receives 10.05% Pays 3-month LIBOR

In an ideal world, dealer would do another swap (of same size) in which it:
Pays 9.95% Receives 3-month LIBOR

Dealer gross profit is 0.10% or 10 basis points Exactly offsetting swaps only rarely (if ever) occur

Steps in Dealing
Negotiate terms by telephone
convention is LIBOR flat as a result, dealer quotes the fixed rate fixed rate is chosen so that the swap has value 0 on the trade date

Fax confirmation (this is what you have) Exchange signed ISDA Master Agreement
ISDA master defines terms, contains detailed provisions

8

Swap quotes
Hypothetical Indicative U.S. Dollar Interest Rate Swap Quotes Maturity /tenor 2Y 3Y 4Y 5Y 7Y 10Y Spread over Treasury yield if dealer pays fixed 25 basis points 28 basis points 30 basis points 30 basis points 33 basis points 37 basis points Spread over Treasury yield if dealer receives fixed 27 basis points 30 basis points 34 basis points 35 basis points 38 basis points 42 basis points

For each maturity/tenor, the spread would be added to the yield on the “current” Treasury note of the same maturity. For example, if the dealer pays fixed on a 5 year swap, the fixed rate of the swap would be equal to the yield on the 5 year note plus 30 basis. If the dealer pays floating and receives fixed, the fixed rate of the swap would be equal to the yield on the 5 year note plus 35 basis points.

Swap Quotes from GovPX

(4.420+4.416)/2 + 0.51 = 4.928

Using a swap: A stylized example
Company issued a $200 million floating rate note with interest payments based on 3-mo. LIBOR
assume quarterly payments

Interest payment: LIBOR × 0.25 × $200 Million LIBOR currently is 7% Company exposed to risk of increases in LIBOR

9

Cash flow at each int. payment date
(<0 because int. exp. is an outflow)
6

4 Cash flow at int. pymnt. date ($ millions)

2

0 0% -2 5% 10% 15%

-4 7%, -$3.5 million -6

-8 3-mo. LIBOR

Interest expense at each interest payment date
6

Int. exp. at int. pymnt. date ($ millions)

4

7%, -$3.5 million

2

0 0% 5% 3-mo. LIBOR 10% 15%

Risk Management Tool: Interest Rate Swap
Company with Exposure
Receive Floating Rate (LIBOR) × 0.25 × Notional Amount

Bank or Other Intermediary

Fixed-Rate Payer
Pay 7.00% Fixed Rate × 0.25 × Notional Principal

Fixed-Rate Receiver

10

Risk management tool: interest rate swap
Pay fixed, receive floating swap with fixed rate of 7%, notional prin. = $200m (quarterly payments)
pay LIBOR = 7% , rec. f ixed rate of 7%

6

Int. exp. at int. pymnt. date ($ millions)

4

2

0 0% 5% 10% 15%

-2

-4 3-mo. LIBOR

Net cash flow at each interest payment date
4 Net cash flow at int. pymnt. date ($ millions)

2

0 0% 5% 10% 15%

-2

-4

Cash f low = -$3.5 million

-6 3-mo. LIBOR

Swap cash flows
A tabular representation is also useful:
Time Swap Cash Flows 0 0 0.25 0.25[r0(0, 0.25) − 0.07] 0.5 0.25[r0.25(0.25, 0.5) − 0.07] ... ... T 0.25[rT-0.25(T−0.25, T) − 0.07]

Here:
cash flows are from perspective of counterparty who is receiving floating, paying fixed rt(t, t+0.25) is a floating interest rate observed at time t, for a deposit/loan from time t to time t + 0.25 7% is the fixed rate we ignore notional principal (notional = $1) and the details of day-counts

11

Transaction Cash Flows
Here is a tabular summary of the transaction:
Time Cash flows of original position Swap Cash Flows (pay fixed, receive floating) Net Cash Flows (orig. position + swap = synthetic fixed rate note) 0 1 0 0.25 −0.25r0(0, 0.25) 0.25[r0(0, 0.25) − 0.07] 0.5 −0.25r0.25(0.25, 0.5) 0.25[r0.25(0.25, 0.5) − 0.07] ... ... ... T −[1 + 0.25rT-0.25(T−0.25, T)] 0.25[rT-0.25(T−0.25, T) − 0.07]

1

−0.25( 0.07)

−0.25( 0.07)

...

−[1 + 0.25(0.07)]

Here the end-user has hedged cash flows (interest expense) by swapping from floating to fixed

Swapping from fixed to floating
This table shows swapping from fixed to floating:
Time Cash flows of original position Swap Cash Flows (pay floating, rec. fixed) Net Cash Flows (orig. position + swap = synthetic floating rate note) 0 1 0.25 −0.25( 0.07) 0.5 −0.25( 0.07) ... ... T −[1 + 0.25(0.07)]

0

0.25[0.07−r0(0, 0.25)]

0.25[0.07−r0.25(0.25, 0.5)]

...

0.25[0.07−rT-0.25(T−0.25, T)]

1

−0.25r0(0, 0.25)

−0.25r0.25(0.25, 0.5)

...

−[1 + 0.25rT-0.25(T−0.25, T)]

The net position is a synthetic floating rate bond

Which is hedging?
Swapping from floating to fixed creates a synthetic fixed-rate bond Swapping from fixed to floating creates a synthetic floating-rate bond Which is less risky:
a fixed rate bond?; or a floating rate bond?

Which is “hedging,” swapping from floating to fixed? Or fixed to floating?

12

Which is hedging?
Swapping from floating to fixed:
reduces the variability of interest expense increases the variability of the value of the (synthetic) bond

Swapping from fixed to floating:
increases the variability of interest expense reduces the variability of the value of the (synthetic) bond

Which of these is “hedging”? What is the definition of “hedging,” anyway?

Uses of Interest Rate Swaps
Hedging
We have already seen this (LEU was hedging)

Speculation on interest rates - obvious
If you think rates will decrease, enter into a swap to receive fixed and pay floating If you think rates will increase, enter into a swap to pay fixed and receive floating

Managing accounting income and/or cash flows
The next few slides present an example of this

Using swaps to manage cash flows and/or accounting incomes: An example
Gibson Greeting Cards
was one of the companies involved in the wave of derivatives “disasters” of 1994. During 1991-1993 it engaged in a series of interest rate swap transactions with Bankers Trust In retrospect, some of these transactions seem nutty We look at the first transaction, which consisted of 2 different swaps transacted at the same time This first transaction was not nutty, but is a nice example illustrating how to use swaps to move income from the future into the current period

13

The first Gibson/BT transaction
On 21 Nov. 1991 Gibson and BT entered into the following two interest rate swap transactions:
A 5-year swap based on 6-month LIBOR:
Gibson pays (BT receives) floating BT pays (Gibson receives) 7.12% fixed

A 2-year swap based on 6-month LIBOR:
BT pays (Gibson receives) floating Gibson pays (BT receives) 5.91% fixed

Both swaps had a notional amount of $30 million

2-year swap
$1,500,000

$1,000,000

Hypothetical floating payments
Swap payments $500,000

$0 0 1 2 3 4 5

Fixed payments
-$500,000

-$1,000,000 Time (years)

5-year swap
$1,500,000

Fixed payments

$1,000,000

$500,000 Swap payments

$0 0 -$500,000 1 2 3 4 5

-$1,000,000

Hypothetical floating payments
-$1,500,000 Time (years)

14

Net cash flows
$1,500,000

$1,000,000

Fixed payments
$500,000 Swap payments

$0 0 -$500,000 1 2 3 4 5

-$1,000,000

-$1,500,000 Time (years)

Hypothetical floating payments

Net cash flows
$1,500,000

Net payment in years 3-5 must have negative present value

$1,000,000

Fixed payments

$500,000 Swap payments

$0 0 -$500,000 1 2 3 4 5

-$1,000,000

-$1,500,000 Time (years)

Hypothetical floating payments

The first Gibson/BT transaction
Cash flows from perspective of Gibson (per $1 of notional principal; to get actual cash flows, multiply by $30
million):
Time in years (Nov. 1991 = time 0) 5-year swap (receive 7.12%, pay floating) 2-year swap (pay 5.91%, rec. floating) Net Cash Flows 0 0.5 ... 2.0 ... 2.5 ...

0

0.5[0.0712−r0(0, 0.5)]

...

0.5[0.0712−r1.5(1.5, 2.0)]

...

0.5[0.0712−r2(2, 2.5)]

...

0

0.5[r0(0, 0.5) −0.0591]

...

0.5[r1.5(1.5, 2.0)−0.0591]

0

0.5[0.0712−0.0591]

...

0.5[0.0712−0.0591]

...

0.5[0.0712−r2(2, 2.5)]

...

Cash flows with negative present value Positive cash flows

15

The first Gibson/BT transaction
What is going on in this transaction?
Each swap has value = 0 on the trade date (that is, the present value of the cash flows over the life of swap = 0) Thus, PV of the net cash flows of the 2 swaps together = 0 But, cash flows over first 2 years (times 0.5, 1, 1.5, 2) > 0 Thus, the present value of the cash flows during the next three years (times 2.5, …, 5) must be < 0

Gibson has shifted income from years 3 through 5 into years 1 and 2.

Remarks re the Gibson/BT transaction
This transaction “worked” to shift income because the 5year swap rate (7.12%) exceeded the 2-year swap rate (5.91%) If the 2-year rate was greater than the 5-year rate, then the opposite positions in the swaps would achieve the same effect Gibson could shift as much income as it wanted by increasing the notional principal of the swaps Why might such a transaction be appealing to Gibson? The transaction will not shift income if the swaps are accounted for on a fair value or “mark-to-market” basis (but it will still shift cash flows, that is it will still be equivalent to borrowing)

Other swaps
Ordinary (“plain-vanilla”) swap: swap fixed for floating Basis swap: swap one floating rate for another Currency swaps: the two legs are denominated in different currencies
Both, either, or neither legs may be fixed In a currency swap, principals typically are exchanged

16

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