Transcript Introduction to Bond Markets, Analysis, and Strategies

Interest Rate Swaps and
Agreements
Chapter 28
Swaps
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CBs and IBs are major participants
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dealers
traders
users
regulatory concerns regarding credit risk exposure
five generic types of swaps
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interest rate swaps
currency swaps
credit swaps
commodity swaps
equity swaps
Interest Rate Swaps
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OTC instruments
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investors can go through securities firm or commercial
bank
firms can act as brokers or dealers for investor
counterparty risk can be significant
Swap can be viewed as
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package of forward/future contracts
package from CFs from buying and selling cash market
instruments
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fixed rate payer has position similar to long position in floating
rate bond and short in fixed rate (borrowing by issuing fixed
rate bond)
floating payer has position like purchasing fixed rate bond and
financing purchase at floating rate
Interest Rate Swaps
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counterparties agree to exchange periodic
interest payments with dollar amount based
on notional principal
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plain vanilla – fixed-rate payer and floating-rate
payer
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reset frequency
reference rates
Plain Vanilla Interest Rate Swap Example
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Consider money center bank that has raised
$100 million by issuing 4-year notes with 10%
fixed coupons. On asset side: C&I loans linked
to LIBOR. Duration gap is negative.
DA - kDL < 0
Second party is savings bank with $100 million
in fixed-rate mortgages of long duration funded
with CDs having duration of 1 year.
DA - kDL > 0
Interest Rate Swaps
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We depict this fixed-floating rate swap
transaction in the following
Interest Rate Swaps
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The expected net financing costs for the FIs are
shown below
Interest Rate Swaps
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Assume that the realized path of LIBOR over the 4
year life of the contract would be as follows 9%, 9%,
7%, and 6% at the end of each of the 4 years. The
money center bank’s variable payments to the thrift
are indexed to these rates by the formula:
(LIBOR + 2%) * $100m
The annual payments made by the thrift were the
same each year
10% * $100m.
Interest Rate Swaps
End of year One-Year
LIBOR
1
9%
2
9%
3
7%
4
6%
LIBOR +
2%
11%
11%
9%
8%
TOTAL
Pmt by
MCB
$11
$11
$9
$8
$39
Pmt by thrift Net Pmt by
MCB
$10
+$1
$10
+$1
$10
-$1
$10
-$2
$40
-$1
Interest Rate Swaps
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example
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notional of $50m where X is fixed rate payer and
Y is floating rate payer – X pays 10% per year and
Y pays the 6-month LIBOR – payments every 6
months for next 5 years
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what will payments be if 6-month LIBOR is 7%
Swaps
Swaps
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trade date
effective date
maturity date
dates can differ for counterparties in same swap
terminology to describe position
Swaps
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fixed rate payer is short the bond market –
explain
fixed rate payer – position that is exposed to
the price sensitivities of a longer-term liability
and a floating-rate bond
floating rate payer – position that is exposed
to the price sensitivities of a fixed-rate bond
and a floating-rate liability
Swaps
• dealer quotes fixed payer to pay 8.85% and receive LIBOR “flat” – bid price
dealer quotes floating payer is to pay LIBOR flat and receive 8.75% - spread is
10bp
• fixed rate is spread above Treasury yield curve – say 10 year Treasury yield is
8.35% - offer price dealer quoted is 10 year Treasury plus 50bp vs. receiving
LIBOR flat
• bid price dealer quoted for floating payer is LIBOR flat vs. 10 year Treasury
plus 40bp
• dealer quotes swap as 40-50 – dealer willing to enter into swap to receive
LIBOR and pay fixed rate equal to 10-yr Treas. plus 40bp – willing to enter into
swap to pay LIBOR and receive fixed rate equal to 10-yr. Treas. plus 50bp
Swap Rate
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to determine rate, remember that no upfront CFs are
made, so PV of payments must be equal
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swap rate for floating payer must be rate that makes PV of
payments on fixed-rate side equal to payments on floating
rate side
what rate do we use to discount CFs to find PV?
example
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swap settlement date is January 1 at year 1
floating-rate payments made quarterly based on actual/360
reference rate is 3-month LIBOR
notional amount is $100m
term of swap is 3 years
Swap Example
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today 3-month LIBOR is 4.05%
floating payment is
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fixed rate payer receives payment on March 31 of
next payment from April 1 to June 30 – 91 days
3 month Eurodollar CD futures contract for
settlement on June 30 of year 1 is 95.85 so
Eurodollar futures rate is 4.15%
Swap Example
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for the fixed-rate payment
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suppose swap rate is 4.98% and quarter has
90 days
Swap Rate
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key principle in finding swap rate is no
arbitrage opportunity – PV of payments
received must equal PV of payments made
rate used for discounting?
forward discount factor is PV of $1 received
at period t
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find forward discount factor for period using forward
rates – but adjust rates for number of days in quarter
Forward Discount Factors
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for period 1
for period 2
for period 3
Swap Rate
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no arbitrage – PV of fixed = PV of floating
fixed rate pmt for period t
PV of fixed rate payment for period t is
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PV of fixed rate payments
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no arbitrage so
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Valuing a Swap
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one year later, rates change so payments by
floating rate side change – how does this
affect value?
Asset/Liability Management
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bank has portfolio of $50m of 5-year loans
with fixed rate of 10% - loans are interest only
with semiannual pmts and principal due at
end of 5 yrs – CF is $2.5m every 6 months
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to fund, bank will issue 6 month CDs on which it
pays 6-month LIBOR plus 40bp
at what LIBOR rate is bank in trouble?
bank wants to lock in spread over cost of funds
Asset/Liability Management
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life insurance firm pays 9% over next 5 years
on GIC – amount is $50m
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firm can invest $50m in 5 year floating rate
security on which rate is 6-month LIBOR plus
160bp with coupon reset every 6 months
risk for insurance firm?
Asset/Liability Management
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swap available in market has terms:
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every 6 months bank pays 8.45% (annual rate)
every 6 months bank receives LIBOR
every 6 months insurance firm pays LIBOR
every 6 months insurance firm receives 8.40%
what does swap do for each party?
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bank locks in spread of 155bp
insurance firm locks in spread of 100bp
For the bank
For the insurance firm
Asset/Liability Management
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bank – alters CF of assets from fixed to
floating
life insurance firm – alters CF of assets from
floating to fixed
asset swap – in above example
liability swap