The following article is reprinted from the Quarter 1, 2004 issue of On the Edge,
the CMS BondEdge quarterly newsletter.

Back-to-Basics: Interest Rate Swaps

Teri Geske
Senior Vice President, Product Development

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For many investment professionals, derivatives represent one of the more challenging, even intimidating, areas of financial modeling and portfolio management. While there are many exotic types of derivatives whose price behavior and mathematical complexity is truly mind-boggling, the vast majority of over-the-counter derivatives contracts (in other words, excluding exchange-traded futures contracts) are fairly straightforward. In this Back-to-Basics article, we examine the most commonly used derivative, the Interest Rate Swap. We attempt to provide an intuition for understanding a swap’s risk characteristics and why they are so often used to hedge interest rate risk.

In its simplest form, an interest rates swap is an agreement between two parties to exchange a series of payments at a fixed rate for a series of payments tied to a floating rate index, on a periodic basis over some period of time. The payments are computed on the basis of a “notional” amount that itself is not exchanged. For example, a swaps contract might call for quarterly payments for five years, with the fixed rate equal to 3% and the floating rate equal to the prevailing 3-month LIBOR rate (observed at the beginning of each quarterly period), based on a $10 million notional amount. So, if LIBOR is equal to 1.5%, the floating-rate payer would owe [(0.015/4) x $10mm] = $37,500 to the fixed-rate payer for the quarter, while the fixed-rate payer would owe [(0.03/4) x $10mm] = $75,000 to the floating-rate payer (in practice, the net amount of these payments is exchanged). This “plain vanilla” structure can take on more complex forms (for example, the notional value can decline over time, called an amortizing swap, or the swap itself can be callable), but the basic concept still applies.

When the term structure of interest rates is upward-sloping (i.e., short-term rates are lower than intermediate and long-term rates), the fixed rate on a swap is higher than the initial value of the floating rate index and it may appear that the fixed rate payer is destined to lose money on the agreement. However, recall that an upward-sloping term structure reflects an implicit forecast that short-term interest rates will rise in the future. On the swap’s inception date, the fixed rate represents the swap market’s consensus view of the “fair” rate to pay, the rate that equates, on a present value basis, the series of fixed payments to the series of floating rate payments through the life of the contract. Thus, in a theoretical sense, on the day the swap is created the fixed-rate payer expects to pay, on a present value basis, the same amount he or she expects to receive from the floating rate payer over the life of the swap agreement, and the same is true for the floating-rate payer. So, the price of the swap when it is created is zero, because the present value of the future fixed rate and expected future floating rate payments cancel each other out.

The expected future path of the floating rate (which we’ll assume is LIBOR, as is most common in practice) can be derived from the swap market itself. Swaps dealers provide quotes on the fixed rate required for swaps of maturities ranging from 1-10 years or longer, and these rates (which typically vary by no more than 1 bp across dealers for most maturities) form the “swap yield curve”, or more simply, the “swap curve” just as the yield on Treasuries of varying maturities form the “Treasury yield curve”. The swap curve may be thought of as a “coupon curve”, or a “par curve” since a swap involves periodic interest payments (just like a bond – more about this similarity in a moment), and from this curve we can derive a spot curve, and from this spot curve we can derive a series of implied forward LIBOR rates . These rates are the market’s consensus estimate of the levels LIBOR is expected to obtain in the future. Alternatively, one can observe the prices on eurodollar futures contracts expiring on or near to the floating rate payment reset date over the life of the swap contract to see where the market believes LIBOR will be over the life of the swap. In practice, swap rates are closely related to the eurodollar futures market, as dealers use that market to hedge their swap positions.

For fixed income investors accustomed to thinking about bonds, it is convenient to think of interest rate swaps as combination of long and short positions in a fixed rate and a floating rate security. Using our example from above, paying the fixed rate of 3% while receiving 3-month LIBOR for five years is equivalent to shorting a five-year bond with a 3% coupon and purchasing a floating rate note that pays 3-month LIBOR. If you receive the fixed rate, it is the same as owning the 3% fixed rate bond and shorting the LIBOR floater. Since we said earlier that at the swap’s inception date its price is zero, and we can assume that the value of the floating rate note is always 100 (which implicitly assumes no default risk), we can see that the price of our hypothetical 3% bond must have been 100 at the time the swap was created (since owning a floater priced at 100 minus the short position in the fixed rate bond = zero, the fixed rate bond’s price must have been 100). Therefore, 3% must have been the fair market rate for a 5-year swap. Continuing with this line of thinking, we can estimate the interest rate sensitivity, or duration, of a swap by computing the difference between the duration of a fixed rate bond with a coupon and maturity equal to the fixed rate side of the swap, minus the duration of a floating rate note with the same maturity. Since the price of an uncapped floating rate note is not affected by changes in interest rates (its price is always 100), its duration is zero, so it does not affect the duration of the net short/long positions in our hypothetical fixed and floating rate securities. Thus, the duration of an interest rate swap is easily approximated as the duration of a fixed rate bond with a coupon rate, payment frequency and maturity date as set by the terms of the swap contract. Similarly, the convexity of a swap is similar to that of a bond with the same coupon rate and maturity date. Receiving the fixed rate in a swap increases a bond portfolio’s duration and improves convexity, while paying fixed will shorten a portfolio’s duration and decrease convexity.

In addition to offering duration and convexity characteristics that are essentially the same as owning (or shorting) a bond, the swap market is extremely liquid – with an estimated $95 trillion in notional amount outstanding as of June 2003, interest rate swaps are by far the largest single contract type in the OTC derivatives market (covering foreign exchange, equity-linked, interest rate related and commodity derivatives) . With these desirable characteristics, it is natural for fixed income market participants to use swaps as hedging instruments. When interest rates move, the value of the swap position will change – a decline in rates increases the value of receiving the fixed rate on a swap, for the same reason that falling rates cause bond prices to rise, and vice versa. A significant percentage of total activity in the swap market is attributable to mortgage-related hedging – as interest rates fall, the demand to receive the fixed rate in a swap increases from MBS investors who want to offset the contraction risk and negative convexity of holding MBS. Conversely, when rates rise, these same investors sell off their “receive fixed” swaps positions as the value of the swap declines. In a nutshell, the swap market is used just as one would use Treasuries and/or Treasury futures to hedge interest rate risk.

In summary, interest rate swaps are the most important OTC derivative contract in the world, with many applications for hedging and managing interest rate risk, and they are directly comparable to a combination of fixed and floating rate securities. We hope this article has been useful in understanding interest rate swaps and would appreciate your feedback or suggestions for future Back-to-Basics columns – please send your comments to teri.geske@be.ftid.com.