What is an interest rate swap?

**(i) ****An
interest rate swap is a contractual agreement entered into
between two counterparties under which each agrees to make
periodic payment to the other for an agreed period of time based
upon a notional amount of principal. The principal amount is
notional because there is no need to exchange actual amounts of
principal in a single currency transaction: there is no foreign
exchange component to be taken account of. Equally, however, a
notional amount of principal is required in order to compute the
actual cash amounts that will be periodically exchanged. **

**Under the commonest form of interest
rate swap, a series of payments calculated by applying a fixed
rate of interest to a notional principal amount is exchanged for
a stream of payments similarly calculated but using a floating
rate of interest. This is a fixed-for-floating interest rate
swap. Alternatively, both series of cashflows to be exchanged
could be calculated using floating rates of interest but floating
rates that are based upon different underlying indices. Examples
might be Libor and commercial paper or Treasury bills and Libor
and this form of interest rate swap is known as a basis or money
market swap. **

**(ii) Pricing Interest Rate Swaps **

**If we consider the generic
fixed-to-floating interest rate swap, the most obvious difficulty
to be overcome in pricing such a swap would seem to be the fact
that the future stream of floating rate payments to be made by
one counterparty is unknown at the time the swap is being priced.
This must be literally true: no one can know with absolute
certainty what the 6 month US dollar Libor rate will be in 12
months time or 18 months time. However, if the capital markets do
not possess an infallible crystal ball in which the precise trend
of future interest rates can be observed, the markets do possess
a considerable body of information about the relationship between
interest rates and future periods of time. **

**In many countries, for example, there
is a deep and liquid market in interest bearing securities issued
by the government. These securities pay interest on a periodic
basis, they are issued with a wide range of maturities, principal
is repaid only at maturity and at any given point in time the
market values these securities to yield whatever rate of interest
is necessary to make the securities trade at their par value. **

**It is possible, therefore, to plot a
graph of the yields of such securities having regard to their
varying maturities. This graph is known generally as a yield
curve -- i.e.: the relationship between future interest rates and
time -- and a graph showing the yield of securities displaying
the same characteristics as government securities is known as the
par coupon yield curve. The classic example of a par coupon yield
curve is the US Treasury yield curve. A different kind of
security to a government security or similar interest bearing
note is the zero-coupon bond. The zero-coupon bond does not pay
interest at periodic intervals. Instead it is issued at a
discount from its par or face value but is redeemed at par, the
accumulated discount which is then repaid representing compounded
or "rolled-up" interest. A graph of the internal rate
of return (IRR) of zero-coupon bonds over a range of maturities
is known as the zero-coupon yield curve. **

**Finally, at any time the market is
prepared to quote an investor forward interest rates. If, for
example, an investor wishes to place a sum of money on deposit
for six months and then reinvest that deposit once it has matured
for a further six months, then the market will quote today a rate
at which the investor can re-invest his deposit in six months
time. This is not an exercise in "crystal ball gazing"
by the market. On the contrary, the six month forward deposit
rate is a mathematically derived rate which reflects an arbitrage
relationship between current (or spot) interest rates and forward
interest rates. In other words, the six month forward interest
rate will always be the precise rate of interest which eliminates
any arbitrage profit. The forward interest rate will leave the
investor indifferent as to whether he invests for six months and
then re-invests for a further six months at the six month forward
interest rate or whether he invests for a twelve month period at
today's twelve month deposit rate.**

**The graphical relationship of forward
interest rates is known as the forward yield curve. One must
conclude, therefore, that even if -- literally -- future interest
rates cannot be known in advance, the market does possess a great
deal of information concerning the yield generated by existing
instruments over future periods of time and it does have the
ability to calculate forward interest rates which will always be
at such a level as to eliminate any arbitrage profit with spot
interest rates. Future floating rates of interest can be
calculated, therefore, using the forward yield curve but this in
itself is not sufficient to let us calculate the fixed rate
payments due under the swap. A further piece of the puzzle is
missing and this relates to the fact that the net present value
of the aggregate set of cashflows due under any swap is -- at
inception -- zero. The truth of this statement will become clear
if we reflect on the fact that the net present value of any fixed
rate or floating rate loan must be zero when that loan is
granted, provided, of course, that the loan has been priced
according to prevailing market terms. This must be true, since
otherwise it would be possible to make money simply by borrowing
money, a nonsensical result However, we have already seen that a
fixed to floating interest rate swap is no more than the
combination of a fixed rate loan and a floating rate loan without
the initial borrowing and subsequent repayment of a principal
amount. The net present value of both the fixed rate stream of
payments and the floating rate stream of payments in a fixed to
floating interest rate swap is zero, therefore, and the net
present value of the complete swap must be zero, since it
involves the exchange of one zero net present value stream of
payments for a second net present value stream of payments. **

**The pricing picture is now complete.
Since the floating rate payments due under the swap can be
calculated as explained above, the fixed rate payments will be of
such an amount that when they are deducted from the floating rate
payments and the net cash flow for each period is discounted at
the appropriate rate given by the zero coupon yield curve, the
net present value of the swap will be zero. It might also be
noted that the actual fixed rate produced by the above
calculation represents the par coupon rate payable for that
maturity if the stream of fixed rate payments due under the swap
are viewed as being a hypothetical fixed rate security. This
could be proved by using standard fixed rate bond valuation
techniques. **

**(iii) Financial Benefits Created By
Swap Transactions **

**Consider the following statements:**

**(a) A company with the highest credit
rating, AAA, will pay less to raise funds under identical terms
and conditions than a less creditworthy company with a lower
rating, say BBB. The incremental borrowing premium paid by a BBB
company, which it will be convenient to refer to as a
"credit quality spread", is greater in relation to
fixed interest rate borrowings than it is for floating rate
borrowings and this spread increases with maturity.**

**(b) The counterparty making fixed rate
payments in a swap is predominantly the less creditworthy
participant. **

**(c) Companies have been able to lower
their nominal funding costs by using swaps in conjunction with
credit quality spreads.**

**These statements are, I submit, fully
consistent with the objective data provided by swap transactions
and they help to explain the "too good to be true"
feeling that is sometimes expressed regarding swaps. Can it
really be true, outside of "Alice in Wonderland", that
everyone can be a winner and that no one is a loser? If so, why
does this happy state of affairs exist? **

**(a) The Theory of Comparative Advantage
**

**When we begin to seek an answer to the
questions raised above, the response we are most likely to meet
from both market participants and commentators alike is that each
of the counterparties in a swap has a "comparative
advantage" in a particular and different credit market and
that an advantage in one market is used to obtain an equivalent
advantage in a different market to which access was otherwise
denied. The AAA company therefore raises funds in the floating
rate market where it has an advantage, an advantage which is also
possessed by company BBB in the fixed rate market. **

**The mechanism of an interest rate swap
allows each company to exploit their privileged access to one
market in order to produce interest rate savings in a different
market. This argument is an attractive one because of its
relative simplicity and because it is fully consistent with data
provided by the swap market itself. However, as Clifford Smith,
Charles Smithson and Sykes Wilford point out in their book
MANAGING FINANCIAL RISK, it ignores the fact that the concept of
comparative advantage is used in international trade theory, the
discipline from which it is derived, to explain why a natural or
other immobile benefit is a stimulus to international trade
flows. As the authors point out: The United States has a
comparative advantage in wheat because the United States has
wheat producing acreage not available in Japan. If land could be
moved -- if land in Kansas could be relocated outside Tokyo --
the comparative advantage would disappear. The international
capital markets are, however, fully mobile. In the absence of
barriers to capital flows, arbitrage will eliminate any
comparative advantage that exists within such markets and this
rationale for the creation of the swap transactions would be
eliminated over time leading to the disappearance of the swap as
a financial instrument. This conclusion clearly conflicts with
the continued and expanding existence of the swap market. **

**It would seem, therefore, that even if
the theory of comparative advantage does retain some force -- not
withstanding the effect of arbitrage -- which it almost certainly
does, it cannot constitute the sole explanation for the value
created by swap transactions. The source of that value may lie in
part in at least two other areas. **

**(b) Information Asymmetries **

**The much- vaunted economic efficiency
of the capital markets may nevertheless co- exist with certain
information asymmetries. Four authors from a major US money
centre bank have argued that a company will -- and should --
choose to issue short term floating rate debt and swap this debt
into fixed rate funding as compared with its other financing
options if: **

**(1) It had information -- not available
to the market generally -- which would suggest that its own
credit quality spread (the difference, you will recall, between
the cost of fixed and floating rate debt) would be lower in the
future than the market expectation. **

**(2) It anticipates higher risk- free
interest rates in the future than does the market and is more
sensitive (i.e. averse) to such changes than the market
generally.**

**In this situation a company is able to
exploit its information asymmetry by issuing short term floating
rate debt and to protect itself against future interest rate risk
by swapping such floating rate debt into fixed rate debt. **

**(c) Fixed Rate Debt and Embedded
Options **

**Fixed rate debt typically includes
either a prepayment option or, in the case of publicly traded
debt, a call provision. In substance this right is no more and no
less than a put option on interest rates and a right which
becomes more valuable the further interest rates fall. By way of
contrast, swap agreements do not contain a prepayment option. The
early termination of a swap contract will involve the payment, in
some form or other, of the value of the remaining contract period
to maturity.**

**Returning, therefore, to our initial
question as to why an interest rate swap can produce apparent
financial benefits for both counterparties the true explanation
is, I would suggest, a more complicated one than can be provided
by the concept of comparative advantage alone. Information
asymmetries may well be a factor, together with the fact that the
fixed rate payer in an interest rate swap -- reflecting the fact
that he has no early termination right -- is not paying a premium
for the implicit interest rate option embedded within a fixed
rate loan that does contain a pre-payment rights. This saving is
divided between both counterparties to the swap. **

**(iv) Reversing or Terminating Interest
Rate Swaps **

**The point has been made above that at
inception the net present value of the aggregate cashflows that
comprise an interest rate swap will be zero. As time passes,
however, this will cease to be the case, the reason for this
being that the shape of the yield curves used to price the swap
initially will change over time. Assume, for example, that
shortly after an interest rate swap has been completed there is
an increase in forward interest rates: the forward yield curve
steepens. Since the fixed rate payments due under the swap are,
by definition, fixed, this change in the prevailing interest rate
environment will affect future floating rate payments only:
current market expectations are that the future floating rate
payments due under the swap will be higher than those originally
expected when the swap was priced. This benefit will accrue to
the fixed rate payer under the swap and will represent a cost to
the floating rate payer. If the new net cashflows due under the
swap are computed and if these are discounted at the appropriate
new zero coupon rate for each future period (i.e. reflecting the
current zero coupon yield curve and not the original zero coupon
yield curve), the positive net present value result reflects how
the value of the swap to the fixed rate payer has risen from zero
at inception. Correspondingly, it demonstrates how the value of
the swap to the floating rate payer has declined from zero to a
negative amount. **

**What we have done in the above example
is mark the interest rate swap to market. If, having done this,
the floating rate payer wishes to terminate the swap with the
fixed rate payer's agreement, then the positive net present value
figure we have calculated represents the termination payment that
will have to be paid to the fixed rate payer. Alternatively, if
the floating rate payer wishes to cancel the swap by entering
into a reverse swap with a new counterparty for the remaining
term of the original swap, the net present value figure
represents the payment that the floating rate payer will have to
make to the new counterparty in order for him to enter into a
swap which precisely mirrors the terms and conditions of the
original swap. **

**(v) Credit Risk Implicit in Interest
Rate Swaps **

**To the extent that any interest rate
swap involves mutual obligations to exchange cashflows, a degree
of credit risk must be implicit in the swap. Note however, that
because a swap is a notional principal contract, no credit risk
arises in respect of an amount of principal advanced by a lender
to a borrower which would be the case with a loan. Further,
because the cashflows to be exchanged under an interest rate swap
on each settlement date are typically "netted" (or
offset) what is paid or received represents simply the difference
between fixed and floating rates of interest. Contrast this again
with a loan where what is due is an absolute amount of interest
representing either a fixed or a floating rate of interest
applied to the outstanding principal balance. The periodic
cashflows under a swap will, by definition, be smaller therefore
than the periodic cashflows due under a comparable loan. **

**An interest rate swap is in essence a
series of forward contracts on interest rates.. In distinction to
a forward contract, the periodic exchange of payment flows
provided for under an interest rate swap does provide for a
partial periodic settlement of the contract but it is important
to appreciate that the net present value of the swap does not
reduce to zero once a periodic exchange has taken place. This
will not be the case because -- as discussed in the context of
reversing or terminating interest rate swaps -- the shape of the
yield curve used to price the swap initially will change over
time giving the swap a positive net present value for either the
fixed rate payer or the floating rate payer notwithstanding that
a periodic exchange of payments is being made. **

**(vi) Users and Uses of Interest Rate
Swaps **

**Interest rate swaps are used by a wide
range of commercial banks, investment banks, non-financial
operating companies, insurance companies, mortgage companies,
investment vehicles and trusts, government agencies and sovereign
states for one or more of the following reasons: **

**1. To obtain lower cost funding**

**2. To hedge interest rate exposure**

**3. To obtain higher yielding investment
assets**

**4. To create types of investment asset
not otherwise obtainable**

**5. To implement overall asset or
liability management strategies**

**6. To take speculative positions in
relation to future movements in interest rates.**

**The advantages of interest rate swaps
include the following:**

**1. A floating-to-fixed swap
increases the certainty of an issuer's future obligations. **

**2. Swapping from
fixed-to-floating rate may save the issuer money if interest
rates decline.**

**3. Swapping allows issuers
to revise their debt profile to take advantage of current or
expected future market conditions. **

**4. Interest rate swaps are a
financial tool that potentially can help issuers lower the amount
of debt service. **

**Typical transactions would certainly
include the following, although the range of possible
permutations is almost endless. **

**(a) Reduce Funding Costs. A US
industrial corporation with a single A credit rating wants to
raise US$100 million of seven year fixed rate debt that would be
callable at par after three years. In order to reduce its funding
cost it actually issues six month commercial paper and
simultaneously enters into a seven year, nonamortising swap under
which it receives a six month floating rate of interest (Libor
Flat) and pays a series of fixed semi- annual swap payments. The
cost saving is 110 basis points.**

**(b) Liability Management. A company
actually issues seven year fixed rate debt which is callable
after three years and which carries a coupon of 7%. It enters
into a fixed- to- floating interest rate swap for three years
only under the terms of which it pays a floating rate of Libor +
185 bps and receives a fixed rate of 7%. At the end of three
years the company has the flexibility of calling its fixed rate
loan -- in which case it will have actually borrowed on a
synthetic floating rate basis for three years -- or it can keep
its loan obligation outstanding and pay a 7% fixed rate for a
further four years. As a further variation, the company's fixed-
to- floating interest rate swap could be an "arrears reset
swap" in which -- unlike a conventional swap -- the swap
rate is set at the end and not at the beginning of each period.
This effectively extends the company's exposure to Libor by one
additional interest period which will improve the economics of
the transaction.**

**(c) Speculative Position. The same
company described in (b) above may be willing to take a position
on short term interest rates and lower its cost of borrowing even
further (provided that its judgment as to the level of future
interest rates is correct). The company enters into a three year
"yield curve arbitrage swap" in which the floating rate
payments it makes under the swap are calculated by reference to a
formula. For each basis point that Libor rises, the company's
floating rate swap payments rise by two basis points. The
company's spread over Libor, however, falls from 185 bps to 144
bps. In exchange, therefore, for significantly increasing its
exposure to short term rates, the company can generate powerful
savings.**

**(d) Hedging Interest Rate Exposure. A
financial institution providing fixed rate mortgages is exposed
in a period of falling interest rates if homeowners choose to
pre- pay their mortgages and re- finance at a lower rate. It
protects against this risk by entering into an
"index-amortising rate swap" with, for example, a US
regional bank. Under the terms of this swap the US regional bank
will receive fixed rate payments of 100 bps to as much as 150 bps
above the fixed rate payable under a straightforward interest
rate swap. In exchange, the bank accepts that the notional
principal amount of the swap will amortize as rates fall and that
the faster rates fall, the faster the notional principal will be
amortized.**

**A less aggressive version of the same
structure is the "indexed principal swap". Here the
notional principal amount continually amortizes in line with a
mortgage pre- payment index such as PSA but the amortization rate
increases when interest rates fall and the rate decreases when
interest rates rise.**

**(e) Creation of New Investment Assets.
A UK corporate treasurer whose company has substantial business
in Spain feels that the current short term yield curves for
sterling and the peseta which show absolute interest rates
converging in the two countries is exaggerated. Consequently he
takes cash currently invested in the short term sterling money
markets and invests this cash in a "differential swap".
A differential swap is a swap under which the UK company will pay
a floating rate of interest in sterling (6 mth. Libor) and
receive, also in sterling, a stream of floating rate payments
reflecting Spanish interest rates plus or minus a spread. The
flows might be: UK corporation pays six month sterling Libor flat
and receives six month Peseta Mibor less 210 bps paid in
sterling. Assuming a two year transaction and assuming sterling
interest rates remained at their initial level of 5.25%, peseta
Mibor would have to fall by 80 bps every six months in order for
the treasurer to earn a lower return on his investment than would
have been received from a conventional sterling money market
deposit. **

**(f) Asset Management. A German based
fund manager has a view that the sterling yield curve will
steepen (i.e. rates will increase) in the range two to five years
during the next three years he enters into a "yield curve
swap "with a German bank whereby the fund manager pays semi-
annual fixed rate payments in DM based on the two year sterling
swap rate plus 50 bps. Every six months the rate is re- set to
reflect the new two year sterling swap rate. He receives six
monthly fixed rate payments calculated by reference to the five
year sterling swap rate and re- priced every six months. The fund
manager will profit if the yield curve steepens more than 50 bps
between two and five years.**

**To repeat: the possibilities are almost
endless but the above examples do give some general indication of
how interest rate swaps can be and are being used. **

© Green Interest Rate Swap Management 2004