tm interest rate swap
TRANSCRIPT
8/6/2019 TM Interest Rate Swap
http://slidepdf.com/reader/full/tm-interest-rate-swap 1/16
1
TREASURY MANAGEMENT
Chapter 14
Interest Rate Swap
Swaps
Two parties exchange recurring payments (most
commonly)
the feature of recurring payments distinguishes aswap 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 swapdocumentation. 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
Note: LIBOR is London Interbank Offered Rate
Fixed-Rate
Payer
Fixed-Rate
Receiver
Floating Rate
(LIBOR)
X Notional Principal
Fixed Rate
of 7.00%
X Notional
Principal
Cash flow diagram of interest rate swap
8/6/2019 TM Interest Rate Swap
http://slidepdf.com/reader/full/tm-interest-rate-swap 2/16
2
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, DeutscheBank)
virtually all major banks do at least some swapsbusiness
Interest rates used as indices
3-month and 6-month LIBOR mostcommon
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 rateswaps 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 BigSwap Dealer Parent Corp.
Notional Amount: See Schedule A
Trade Date: January 18, 1989
Effective Date: January 20, 1989
Termination Date: January 15, 1992
Fixed Amounts:
Fixed Rate Payor: LEU
Fixed Rate PayorParyment Dates: Each January 15, April 15, July 15 and October
15 starting with April 15, 1989; subject toadjustment in accordance with the FollowingDay Banking Convention.
Fixed Rate and FixedRate 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.)
8/6/2019 TM Interest Rate Swap
http://slidepdf.com/reader/full/tm-interest-rate-swap 3/16
3
Parts of a swap confirmation
Floating Amounts:
Floating Rate Payor: BSD
Floating Rate PayorPayment Dates: Each January 15, April 15, July 15 and October
15 starting with April 15, 1989; subject toadjustment in accordance with the FollowingBanking Day Convention.
Floating Rate for InitialCalculation Period: 9.742%
Floating Rate Option: LIBOR
Designated Maturity: 3 month
Adjustment to FloatingRate Option: 3-month LIBOR will be divided by .97 each
calculation period
Floating Rate Day CountFraction: Actual/360
Reset Dates: Two Days Prior to Each Floating Rate PaymentDate
*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 Notional Amount
1-20-89 - 1-15-90 $75,000,0001-16-90 - 1-15-91 70,000,0001-16-91 - 1-15-92 60,000,000
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, designatedmaturity:
payments based on 3-month LIBOR are exchangedevery 3 months
in US, also common to have payments based on 6-month LIBOR exchanged every 6 months
possible for fixed leg to have a different paymentfrequency than floating leg
Notional amount (or principal):
is not exchanged, but simply determines size of payments
*Not in the order in which items appear.
Features of the confirmation:*
8/6/2019 TM Interest Rate Swap
http://slidepdf.com/reader/full/tm-interest-rate-swap 4/16
8/6/2019 TM Interest Rate Swap
http://slidepdf.com/reader/full/tm-interest-rate-swap 5/16
5
Discussion of the confirmation:Day-count fractions
Floating rate day-count fraction:
USD money market convention: Actual/360
floating leg generally follows money marketconvention in that currency (Act/360 orAct/365)
Fixed rate day count fraction:
U.S. bond market convention: 30/360
convention for fixed leg generally followsbond 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 inthe interbank market when 1-year LIBOR is 5%:
you do not pay/receive $10(1.05) million at year-end
instead, you pay/receivemillion, where days is the actual number of days in
the period this is actual/360; actual/365 should be clear
In 30/360, when counting days you pretend thateach month has 30 days
)05.0)360 / (days1(10$ +
Payment conventions
What if the payment date specifiedin the contract is a weekend orholiday?
Need to consider two issues:
When is the payment date?
If the payment date is adjusted, do wealso adjust the amount of interestpaid?
8/6/2019 TM Interest Rate Swap
http://slidepdf.com/reader/full/tm-interest-rate-swap 6/16
6
Payment Date: Following and ModifiedFollowing Business Day Convention
The following business (banking) day conventionstates that the payment date is the first followingday that is a business day.
The modified following business (banking) dayconvention states that the payment date is thefirst following day that is a business day, unlessthat day falls in the next calendar month. In thiscase only, the maturity date will be the firstpreceeding business day.
Most common market practice is to use theModified Following Business Day Convention, butthe Following Business Day Convention issometimes used (for example, in the confirmationabove)
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 onMonday, 17 April
Question: How large is the interest payment?
Is it (180/360)×0.06×N ? (N = notionalamount of swap)
Or do we add 2 days to the payment period, i.e. isthe payment (182/360)×0.06×N ?
(If we add 2 days to this payment period, we wouldalso then subtract 2 days from the next paymentperiod)
Adjusted versus unadjusted
Unadjusted: shift payment date, but do not change theamount of the payment
payment = (180/360)×0.06×N
Interest payments on bonds are generally unadjusted, i.e. if thepayment date gets shifted due to a weekend or holiday, thepayment amount is not changed
Adjusted: shift payment date and change the interestaccrual (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 toexactly hedge an underlying bond on which payments areunadjusted.
8/6/2019 TM Interest Rate Swap
http://slidepdf.com/reader/full/tm-interest-rate-swap 7/16
7
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 basispoints or “LIBOR flat”
In this deal, I have no idea why theadjustment comes in the form of dividing by 0.97
Confirmation: Notional amount
Notional amount (orprincipal):
Most commonly thenotional amount is justa number, e.g. $100million
In this swap thenotional amount variesover time because theswap was being usedto hedge a loan with aprincipal amount thatchanged over time asprincipal paymentswere made
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
ScheduleA
Date Notional Amount
1-20-89- 1-15-90 $75,000,0001-16-90- 1-15-91 70,000,0001-16-91- 1-15-92 60,000,000
Cash flows (from perspective of LEU)
It is crucial to understand that the cash flow on say 7/17/89 is based on LIBOR observedon 4/13/89, …., cash flow on 1/15/92 is based on LIBOR observed on 10/11/91.
Days for Fraction Cash Flow Days for Fraction Cash Flow
Trade P ayment Reset Not ional LIBOR on Floating Float ing Due t o Floati ng Fi xed Fixed F ixed Due t o Fi xed Net C ashDate Date Date Amount reset date Payment Payment Payment Rate Payment Payment Payment Flow
1/18/1989 4/17/1989 $75,000,000 9.7420% 87 0.2417 $1,820,348 10.05% 87 0.24167 -$1,821,563 -$1,2151 /2 0/ 198 9 7/ 17 /1 989 4/ 13 /1 98 9 $7 5, 00 0, 00 0 1 0 .1 875% 9 1 0. 252 8 $1 ,99 1, 11 4 1 0. 05 % 90 0 .2 500 0 - $1 ,8 84 ,37 5 $ 106 ,7 39
1 0/ 16 /1 989 7/ 13 /1 98 9 $ 75 ,00 0, 00 0 8 .8 125% 9 1 0. 252 8 $1 ,72 2, 37 4 1 0. 05 % 89 0 .2 472 2 - $1 ,8 63 ,43 8 - $141 ,0 631/ 15 /1 990 1 0/ 12 /1 98 9 $ 75 ,00 0, 00 0 8 .7 500% 9 1 0. 252 8 $1 ,71 0, 15 9 1 0. 05 % 89 0 .2 472 2 - $1 ,8 63 ,43 8 - $153 ,2 79
4/16/1990 1/ 11/1990 $70,000, 000 8.1875% 91 0. 2528 $1, 493,539 10. 05% 91 0.25278 -$1,778,292 -$284,753
7/16/1990 4/ 12/1990 $70,000, 000 8.4375% 91 0. 2528 $1, 539,143 10. 05% 90 0.25000 -$1,758,750 -$219,6071 0/ 15 /1 990 7/ 12 /1 99 0 $ 70 ,00 0, 00 0 8 .3 125% 9 1 0. 252 8 $1 ,51 6, 34 1 1 0. 05 % 89 0 .2 472 2 - $1 ,7 39 ,20 8 - $222 ,8 67
1/ 15 /1 991 1 0/ 11 /1 99 0 $ 70 ,00 0, 00 0 8 .2 500% 9 2 0. 255 6 $1 ,52 1, 47 8 1 0. 05 % 90 0 .2 500 0 - $1 ,7 58 ,75 0 - $237 ,2 724/15/1991 1/ 11/1991 $60,000, 000 7.3125% 90 0. 2500 $1, 130,799 10. 05% 90 0.25000 -$1,507,500 -$376,701
7/15/1991 4/ 11/1991 $60,000, 000 6.1250% 91 0. 2528 $957,689 10. 05% 90 0.25000 -$1,507,500 -$549,81110/15/1991 7/ 11/1991 $60,000, 000 5.9375% 92 0. 2556 $938,574 10. 05% 90 0.25000 -$1,507,500 -$568,926
1/15/1992 10/ 11/1991 $60,000, 000 5.3750% 92 0. 2556 $849,656 10. 05% 90 0.25000 -$1,507,500 -$657,844
Note that this column reflects the “adjustmentTo floating rate option,” that is the floating
Rate is divided by 0.97
8/6/2019 TM Interest Rate Swap
http://slidepdf.com/reader/full/tm-interest-rate-swap 8/16
8
Why did LEU do the deal?
LEU was a relatively new telecom. company
Borrowed $75 million from a bank on a 3-yearnote
floating rate loan
interest payments every 3 months based on 3-monthLIBOR
partial principal payments discussed above
Condition of loan was that LEU swap from floatingto 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 doanother 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 value0 on the trade date
Fax confirmation (this is what you have)
Exchange signed ISDA Master Agreement
ISDA master defines terms, contains detailedprovisions
8/6/2019 TM Interest Rate Swap
http://slidepdf.com/reader/full/tm-interest-rate-swap 9/16
9
Swap quotes
Hypothetical Indicative U.S. Dollar Interest Rate Swap Quotes
Maturity /tenor
Spread over Treasuryyield if dealer pays fixed
Spread over Treasury yieldif dealer receives fixed
2Y 25 basis points 27 basis points3Y 28 basis points 30 basis points4Y 30 basis points 34 basis points5Y 30 basis points 35 basis points7Y 33 basis points 38 basis points10Y 37 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 theswap would be equal to the yield on the 5 year note plus 30 basis. If the dealer pays floating andreceives fixed, the fixed rate of the swap would be equal to the yield on the 5 year note plus 35basis points.
Swap Quotes from GovPX
(4.420+4.416)/2 + 0.51 = 4.928
Using a swap: A stylized example
Company issued a $200 millionfloating rate note with interestpayments 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
8/6/2019 TM Interest Rate Swap
http://slidepdf.com/reader/full/tm-interest-rate-swap 10/16
10
as ow a eac n . paymendate(<0 because int. exp. is an outflow)
3-mo. LIBOR
C a s h f l o w
a t i n t . p y m n t . d a t e ( $ m i l l i o n s )
-8
-6
-4
-2
0
2
4
6
0% 5% 10% 15%
7%, -$3.5 million
Interest expense at each interestpayment date
3-mo. LIBOR
I n t . e x p . a t i n t . p y m n t . d a t e ( $ m i l l i o n s )
0
2
4
6
0% 5% 10% 15%
7%, -$3.5 million
Fixed-Rate
Payer
Company with
Exposure
Bank or Other
IntermediaryReceive Floating Rate
(LIBOR) × 0.25 ×
Notional Amount
Pay 7.00%
Fixed Rate × 0.25 ×
Notional Principal
Risk Management Tool:
Interest Rate Swap
Fixed-Rate
Receiver
8/6/2019 TM Interest Rate Swap
http://slidepdf.com/reader/full/tm-interest-rate-swap 11/16
11
Risk management tool: interestrate swap
Pay fixed, receive floating swap withfixed rate of 7%, notional prin. =$200m (quarterly payments)
3-mo. LIBOR
I n t . e x p . a t i n t . p y m n t . d a t e ( $ m i l l i o n s )
-4
-2
0
2
4
6
0% 5% 10% 15%
pay LIBOR= 7%,rec. fixed rate of 7%
Net cash flow at each interestpayment date
3-mo. LIBOR
N e t c a s h f l o w
a t i n t . p y m n t . d a t e ( $ m i l l i o n s )
-6
-4
-2
0
2
4
0% 5% 10% 15%
Cash flow = -$3.5 million
Swap cash flows
A tabular representation is also useful:
Here:
cash flows are from perspective of counterparty whois receiving floating, paying fixed
r t (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 thedetails of day-counts
Time 0 0.25 0.5 ... T
Swap CashFlows
0 0.25[r 0(0, 0.25) − 0.07] 0.25[r 0.25(0.25, 0.5) − 0.07] ... 0.25[r T -0.25(T −0.25, T ) − 0.07]
8/6/2019 TM Interest Rate Swap
http://slidepdf.com/reader/full/tm-interest-rate-swap 12/16
12
Transaction Cash Flows
Here is a tabular summary of the transaction:
Here the end-user has hedged cash flows(interest expense) by swapping from floatingto fixed
Time 0 0.25 0.5 ... T
Cash flows of original position
1 −0.25r 0(0, 0.25) −0.25r 0.25(0.25, 0.5) ... −[1 + 0.25r T -0.25(T −0.25, T )]
Swap CashFlows (pay fixed,receive floating)
0 0.25[r 0(0, 0.25) − 0.07] 0.25[r 0.25(0.25, 0.5) − 0.07] ... 0.25[r T -0.25(T −0.25, T ) − 0.07]
Net Cash Flows(orig. position +swap = syntheticfixed rate note)
1 −0.25( 0.07) −0.25( 0.07) ... −[1 + 0.25(0.07)]
Swapping from fixed to floating
This table shows swapping from fixed tofloating:
The net position is a synthetic floating ratebond
Time 0 0.25 0.5 ... T
Cash flows of original position
1 −0.25( 0.07) −0.25( 0.07) ... −[1 + 0.25(0.07)]
Swap CashFlows (payfloating, rec.fixed)
0 0.25[0.07−r 0(0, 0.25)] 0.25[0.07−r 0.25(0.25, 0.5)] ... 0.25[0.07−r T -0.25(T −0.25, T )]
Net Cash Flows(orig. position +swap = syntheticfloating ratenote)
1 −0.25r 0(0, 0.25) −0.25r 0.25(0.25, 0.5) ... −[1 + 0.25r T -0.25(T −0.25, T )]
Which is hedging?
Swapping from floating to fixed creates asynthetic fixed-rate bond
Swapping from fixed to floating creates asynthetic floating-rate bond
Which is less risky:
a fixed rate bond?; or
a floating rate bond?
Which is “hedging,” swapping fromfloating to fixed? Or fixed to floating?
8/6/2019 TM Interest Rate Swap
http://slidepdf.com/reader/full/tm-interest-rate-swap 13/16
8/6/2019 TM Interest Rate Swap
http://slidepdf.com/reader/full/tm-interest-rate-swap 14/16
14
The first Gibson/BT transaction
On 21 Nov. 1991 Gibson and BT enteredinto the following two interest rate swaptransactions:
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 $30million
2-year swap
-$1,000,000
-$500,000
$0
$500,000
$1,000,000
$1,500,000
0 1 2 3 4 5
Time (years)
S w
a p p a y m e n t s
Fixed payments
Hypothetical floating payments
5-year swap
-$1,500,000
-$1,000,000
-$500,000
$0
$500,000
$1,000,000
$1,500,000
0 1 2 3 4 5
Time (years)
S w a p p a y m e n t s
Hypothetical floating payments
Fixed payments
8/6/2019 TM Interest Rate Swap
http://slidepdf.com/reader/full/tm-interest-rate-swap 15/16
15
Net cash flows
-$1,500,000
-$1,000,000
-$500,000
$0
$500,000
$1,000,000
$1,500,000
0 1 2 3 4 5
Time (years)
S w a p p a y m e n t s
Fixed payments
Hypothetical floating payments
Net cash flows
-$1,500,000
-$1,000,000
-$500,000
$0
$500,000
$1,000,000
$1,500,000
0 1 2 3 4 5
Time (years)
S w a
p p a y m e n t s
Fixed payments
Hypothetical floating payments
Net payment in years
3-5 must have negative
present value
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)
0 0.5 ... 2.0 ... 2.5 ...
5-year swap
(receive7.12%, payfloating)
0 0.5[0.0712−r 0(0, 0.5)] ... 0.5[0.0712−r 1.5(1.5, 2.0)] ... 0.5[0.0712−r 2(2, 2.5)] ...
2-year swap
(pay 5.91%,rec. floating)
0 0.5[r 0(0, 0.5) −0.0591] ... 0.5[r 1.5(1.5, 2.0)−0.0591]
Net CashFlows
0 0.5[0.0712−0.0591] ... 0.5[0.0712−0.0591] ... 0.5[0.0712−r 2(2, 2.5)] ...
Positive cash flows
Cash flows with negative present value
8/6/2019 TM Interest Rate Swap
http://slidepdf.com/reader/full/tm-interest-rate-swap 16/16
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 nextthree years (times 2.5, …, 5) must be < 0
Gibson has shifted income from years 3through 5 into years 1 and 2.
Remarks re the Gibson/BTtransaction
This transaction “worked” to shift income because the 5-year swap rate (7.12%) exceeded the 2-year swap rate(5.91%)
If the 2-year rate was greater than the 5-year rate, thenthe opposite positions in the swaps would achieve thesame effect
Gibson could shift as much income as it wanted byincreasing the notional principal of the swaps
Why might such a transaction be appealing to Gibson?
The transaction will not shift income if the swaps areaccounted for on a fair value or “mark-to-market” basis(but it will still shift cash flows, that is it will still beequivalent to borrowing)
Other swaps
Ordinary (“plain-vanilla”) swap: swapfixed for floating
Basis swap: swap one floating rate foranother
Currency swaps: the two legs aredenominated in different currencies
Both, either, or neither legs may be fixed
In a currency swap, principals typically areexchanged