**Unformatted text preview: **INTEREST RATE SWAPS AND FRN’S REFERENCES Hogan, W. et ai ., 2004. Management of Financial Institutions, Brisbane
Wiley, Chapter 15. Lange, H. et al., 2007. Financial Institutions Management. Sydney:
McGraw Hill, Chapter 20. Marshall, HF. and Kapner. KR. 1993. Understanding Swaps, New York:
Wiley, Chapter 7. 1.0 Overview - This topic is primarily concerned with interest rate
swaps. These involve the exchange of a sequence of
ﬁxed—rate payments that resemble the coupon
payments from a bond for a sequence of ﬂoating rate
payments that resemble the interest payments from a
ﬂoating rate note. 0 The features of bonds have been covered extensively
in previous topics. The features of ﬂoating rate
instruments however, will be discussed brieﬂy. ° Interest rate swaps are used by banks to hedge
exposures to interest rate changes. This may be
achieved on a micro level by hedging their exposure
to a particular liability, or on a macro level by
hedging their total interest rate exposure. - Major international banks may also perform the role
of swap dealer by running a “swap book’ by offering
both sides of a swap to counterparties. 2.0 Floating Rate Instruments
- Floating Rate Bonds and Loans Deﬁned as coupon bonds or loans with payment tied
to a market rate of interest such as T»bill rate, LIBOR or bank bill rate (BBR). 0 Characteristics of Floaters (1) Price Stability
Consider'a 15% coupon rate bond with 5 years to
maturiw fand face (value of $1000 and interest paid anm‘i‘ally. ISOL ‘ 150L 11 150jL 1150i
1 2 3 4 5 If the discount rate is 15% then the price of the
bond equals $1000. If the discount rate changes to 10% and the bond
is a fixed rate then the price of the bond equals approximately $1 189. If the discount rate changes to 10%, and the bond
is a variable rate then the price of the bond equals approximately $1000. The price of a ﬂoating rate instrument returns to
exactly the par value at the interest rate reset date.
The price is therefore equal to the par value
discounted at the current market interest rate over the period to the next reset. (2) Duration
After reset, the floater's duration will equal the remaining time to reset. Examine two strategies rolling over of T- bills and
the alternative of purchasing a ﬂoater " Strategy 1: Rolling over T- Bills every 90 days or
0.25 year ._ . $1000 1000(l+r0) 1000(1—11-1) l U. ii 0.25 0.50 Strategy 2: Purchase of a ﬂoater L3:1000 1000 (r0)i 1000 (r1:l
0.25 0.50 Since the net cash ﬂows are identical then
duration at the beginning of each roll over is 0.25 year. 3.0 Interest Rate Swaps - Features of interest rate swap:
- Both parties exchange periodic cashﬂows based on
— notional principal amount
- market interest rates
- “Plain vanilla’ swap trades a ﬁxed interest rate
for a ﬂoating interest rate
- In practice only net cashﬂows are paid ° It is useful to review an example of a swap
arrangement that was presented in BUSZ44 Treasury Management. 3.1 Example of InterestRate Swap * Suppose two parties, Bill and Ben need to borrow
$2 million for four years. Bill is of higher credit
standing and borrows at: ﬁxed rate with semi-annual
interest payments to exploit his comparative
advantage. Ben however uses short—term money
market instruments that can be rolled over on a sixw
monthly basis. Relative to the form of their
incomes, both however have an interest rate exposure as indicated below: F Income Liability
Bill Libor + 2% pa. 9.5% p.a. ﬁxed
Ben 11.5% p.a. ﬁxed Libor + 0.5% p.a. Weed bank has the following indicative pricing
schedule for plain-vanilla interest rate swaps: Maturity Mid-rate
2 years 9. 00%
3 years 9.20%
4 years 9.35%
5 years 9.45% For dealer pays ﬁxedwrate, subtract 10 basis points
and for dealer receives ﬁxed, add 10 basis points.
Quotes are against 6-month AUD Liborﬂat. The, following swap arrangement removes the
interest rate risk for both Bill and Ben, allowing Bill
to earn 1.75% pa. and Ben to earn 1.55% p.21.
irrespective of interest rates. Weed Bank would
earri.‘0.2% p.a. A This followed because: Bill effectively borrows at:
9.5 ~ 9.25 + libor = libor+~0.25% p.a. Ben effectively borrows at:
1ibor+0.5 + 9.45 — libor = 9.95% pa. - The following example from Hogan (p473) explains
the concept of “comparative advantage, and why
Bill and Ben may have borrowed at fixed and ﬂoating rate respectively in spite .of having income
that was respectively ﬂoating and fixed rate. Borrowing opportunities, Aqua Ltd and Brown Ltd BBSW
BBSW + 50 bps Aqua Ltd
Brown Ltd
Aqua Ltd advantage over Brown Ltd : 3—year’l‘reasury L ii: W; 3‘YeaFT1'easu1—y .15 : rate plus 48 bps rate plus 53 bps
I Barrows ({3} £313st
plus 50 pbs
‘ Sorrows (ti) 6'35‘36: Gains to Swaps
'I'Aqua has exploited its comparative advantage in the capital market of SObp
o? Split: 23bp to Aqua
22bp to Brown, and
pr to the swap dealer
eioBrown has taken on the risk that the spread paid
over BB SW may change over the 3 years 4.0 Micro Hedging ' North Bank 1n the previous lecture had made loans of
$10 million at 10% p. a., payable semi- annually, that
mature in 10 years. Suppose that 6- month CDs were
used to ﬁnance these loans and that they would be
rolled over on maturity. Currently, the CD rate is 8% p a., but may increase by 0.5% p. a. over the
following 3 months (as before). Assuming there is no other interest rate change over
the life of the loans, the present value of North
Bank’s interest margin would decrease by: l x 1.0425
+ (0.015 x 0.5 x $10 Willi0n)A19,4.25%] — (0.02 x 0.5 >< $10 million)A20=4_00%
: $1,021,058 — $1,359,033
m ~£337,975 x [0.02 x 0.5 x $10 million Note that this is similar to the decrease in the value of
the $10 million loan arising from the 0.5% p.a.
increase in interest rates that was hedged against
using futures (the difference is because the loan was
discounted at the lending rate). - By entering an interest rate swap to receive 6— month
libor and pay fixed rate semiaannually, North Bank
would avoid the decrease in net interest margin
(aside from differences in changes to 6-month libor
compared to changes to 6-month CD rates) and thus a
decrease in the value of its equity. Further, the swap
hedge has the advantage over the futures hedges-in the
previous lecture in that it does not have to be‘v‘Frolled
over prior to expiry of the futures contract (every 3
months) with the associated basis risk. " '520 Hedging the Duration Gap ' * Bank’s can use swaps to hedge against changes to
interest rates adversely affecting the value of the
bank’s equity. Rather than by micro-«hedging each
asset and liability mismatch on the balance sheet, it
can apply a macrowhedge to the duration gap. - The key to hedging using swaps is to note that a
fixed-rate payer is effectively short in a fixed—rate
bond, and long in a floating-rate note. Both will
change in value as interest rates change, but as the
duration of a floatingwrate note is short, being equal
to the time until repricing, the change in the value of the swap is approximately equal to the change in the
value of the bond. That is: AS W AB ° For a bond: AR 1+ R
Where DB is the duration of the ﬁxed rate bond. ABz—DBX XB ° For value of a bank’s equity: L AR
.. AE:W(DA —ZDL)~X 1+R XAV ' Hence the: value of a bank’s—"i'equity can be hedged by
setting AB S AE . I AR L AR
xB=—D —~—D ><
1+R (A A L) 1+R L
DB.B : (DA ”EDL).A XA will provide a hedge for the bank’s equity, Where B is
the notional value of the swap, and DB is determined
as the duration of the bond representing the ﬁxed-rate leg of the swap. If the duration gap is positive, a short position in a
bond would be required as a hedge, and therefore the
bank would enter the swap as the ﬁxed-rate payer. ~ Consider East Bank in the previous lecture (pl 1):
A = $100 million DA = 6.5 years
L = $90 million
D1, = 2.0 years int = 10% pa. (all maturities) Suppose that a four-year swap in which the ﬁxed—rate
payer pays 10% pa. semiwannually against 6—month
libor was available.- The duration of the swap would
be approximated as 3.39 years. ‘ L
13,13 2(1),, ~2DL).A L29", 3.39X B 2 (6.5 #2,,ng 20)){100 100
B: 470
3.39 B = $138.64 million Thus East Bank would enter a 4-year plain-vanilla
interest rate swap with a notional $138.64 million principal, as ﬁxed-rate payer. ° It was calculated in the previous lecture (pl 1) that a
l% increase in interest rates would result in a
decrease in the value of East Bank’s equity by $4,272,727. 10 The present value of the payment obligation on the
ﬁxed-rate leg would decrease from $138,640,000
million to $134,248,900. That is a decrease of
$4,391,100. Hence, the decrease in the value of the bank’s equity
is approximately offset by the decrease in the value
of the bank’s payment obligations under the swap. 0 Note however, that this is an approximation since the
change in the value of a swap following an interest
rate change should properly take into account the
change in the value of the ﬂoating rate payments as
well. It should also be noted that in this example, the
yield curve was assumed to be ﬂat, With a parallel
.. shift. This will not normally be the case. ' 6.0 Swap Pricing - ‘Pricing’ a swap refers to the process of determining
the interest rate that should be paid on the ﬁxed rate
(as a mid—rate) against a ﬂoating—rate. For an ‘on—
market’ ‘plain vanilla’ conﬁguration swap, the
floating rate is set to an indicator rate such as libor or
BBSW. The ‘indicative pricing schedule’ in the
example in section 1.1 results from swaps with
different maturities being priced. ll - Swap dealers must correctly price a swap in order to
successfully make both sides (i.e. the ‘dealer pays
ﬁxed’ side and the ‘dealer receives fixed” side) of the
swap attractive to the counterﬂparties. Note that it is
not necessary to have equal but opposite counter-
parties on each swap (as illustrated in the section 1.1
example), but rather, the dealer will offer several
swaps on each side (i.e. running a hook) with the aim
of them balancing in aggregate. ' The ‘price’ of a swap should not be confused with its
‘value’. At origination, the value of a swap is zero.
As interest rates change over time, the value of the
swap will take on aiepositive value to one party, and a
corresponding negative value to the other. 6.1 Pricing From the Yield Curve °§°Method 1: k
«2°Set PV(floating—rate stream) = PV(fixed-rate stream) eieMethod 2:
¢i°Set PV(fixed-rate bond) : par value ' Swap Pricing Example e? Find the fixed rate for a 4~year swap given a zero~ coupon spot yield curve of:
Years 1 2 3 1;
Spat rate 0.85 0.055 {1% 9.065 ®§°Step 1 ._ Find the zero-«coupon yield curve (given
above) 12 a? Step 2 — Calculate implied forward rates
Forward rates 1% f1 f2 fa
{105 0.06 0.07 8.08
°§°Step 3 — Calculate PV(floating stream) °§° Step 4 - Solve for P which has same PV - Swap Value After the Start Date °§° If the yield curve moves, then the value of the swap
.Will charrge fieThe value is computed as
PV(fixed — floating) Lei» Based on the new yield curve for the floating leg
and for the discount rates ' 9%» Based on. the original interest rate for the fixed leg 6.23 Pricing from Bank Bill Futures Strip $011 3 August we arrange a $100 million notional
swap with a 1 year maturity eWe pay fixed and receive BBSW every 3 months el’recise timing of payments will depend on the
nearest bill futures contract with a shorter ’stub’
period from origination. to the first payment date .3 Trade. Reset Reset Reset . i . Expiration : date 333 date we date £9112 date 1013 date 319 Q
' and 2nd and 311-} 3
pay date. 1333! date 13 etoAs indicated above, the first payment will be on 10
September, with 3 subsequent payments 3 months
apart Implied futures rates for discounting ﬁxed~rate leg of fixed-for—fleating swap 3 Aug. to 19 Sept.M
10 Sept. to 10 Dec. 10 Dec. to 10 March
10 March to 9 June
9 June to 8 Sept. 3 August
10 September
10 December 91
9?
9} September
Becember March 10 March
Eune 9 June * BBSW spot rate on 3 August (trade date).
** Stub period. - a Calcuiation of the value of a swap 3 August 0.994247 10 September 0.120548 0.994247 10 December 0.249315 0.987907 0.982223 1.224137 1.202376
10 March 0.249315 0.987129 ‘ 0.969581 1.303918 1.264254
9 June 0.249315 0.986861 0.956842 1.331342 1.273884
8 September 0.249315 0.986109 0.943551 1.413863 1.329114
SBM 5.069627 otoAt this point we need to solve for the fixed payment
P which gives a present value of 5.069627 P (0.98222 «+~ 0.96958 + 0.95684 + 0.94355) 2 5.069627
F .._., 1.3160 05A fixed payment of 1.3160 per quarter on a notional
principal of $100 implies an annual fixed interest rate
of: 14 13160 x 363 = 0.0528 100 91 6.3 Swap Credit Exposure °§°Swap participants are subject to counterparty risk as
there is no clearing house to guarantee performance #26 Generally, swap users maintain credit lines with
their banks to cover this risk °3°Credit exposure from swaps is included in riskwbased
capital computations 15 ...

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- Summer '19
- Interest Rates, Interest, Interest Rate, Interest rate swap