Electronic, or automated, trading of interest rate swaps has created an easily accessible method for controlling interest rate risk as well as for hedging and speculating on interest rate movements. With increasing volume and improved trading platforms, this market is destined to become more popular for individual traders along with larger institutional users.
Over-the-counter (OTC) plain vanilla swaps allow two counterparties to exchange cash flows based on a nominal amount of principal, in which one of the parties wishes to swap fixed interest income for cash flows generated by floating rate. The fixed rate (the swap rate) is initially set to equalize the present values of fixed and floating cash flows. Depending on the movement of the floating rate, cash in each period may flow in either direction and by netting the fixed rate against the floating rate, only the net amount needs to be transferred.
The OTC interest rate swaps market is known for its large volume of trading and underlying principal value. According to the Chicago Board of Trade (CBOT) the notional amount of OTC U.S. dollar interest rate swaps equaled nearly $73 trillion in 2006. The CBOT instituted swap futures in 2001, starting with the 10-year maturity and following with five-year swap futures in 2002. In March 2007, the exchange added 30-year swap futures.
MARKET BENEFITS
Advantages of exchange-traded interest rate swap futures include standardization and elimination of most counterparty credit risk. CBOT swap futures have prices that are similar to Treasury note futures. Both the 10-year and five-year contracts are based on a notional $100,000 principal value with a 6% coupon rate. Interest is paid semi-annually.
Having the same price base as CBOT T-note futures permits the notional yield for interest rate swap futures to be calculated as the discount rate that makes the present value of semi-annual payments of $3,000 and $100,000 at maturity equal to the current price. Reversing this calculation allows a swap yield to be used in determining the price of a futures contract.
For example, a price for the five-year interest rate swap listed by the CBOT as 105-295 (105 points, each equal to $1,000, plus 29.5 32nds of a point, which in dollar terms is $105,922) has a related yield of 4.66%.
The yield computed for a five-year interest rate swap is likely to be close to the yield for Eurodollar futures at the same maturity of five years. The reason for this, as pointed out by Robert W. Kolb in “Futures, Options & Swaps” (Blackwell Publishers, 2000), is that a strip of Eurodollar contracts may be regarded as a substitute for an interest rate swap. Recall that the Eurodollar yield curve is composed of a series of geometric means, in which quarterly rates are successively multiplied and then the nth root of each product determines the yield to a specific future quarter.
The yields for five-year interest rate swaps over the August through October period in 2007 are compared with the Eurodollar yields each day on “Yield comparison” (below). The chart shows that the two yields are virtually the same at the end of each day. During the trading day, automated computer trading continuously adjusts the two yields to stay approximately equal.
A similar chart for 10-year swap yields vs. Eurodollar yields at the 40th quarter would show less equality between the yields. This difference is probably related to the shortage of trading volume at the longer maturity – for both the swap futures and the Eurodollar futures.
Although the yield on a five-year interest rate swap is essentially equal to the five-year yield for Eurodollar futures, the two yields are arrived at by different routes. As shown above, the swap yield is related to a 6% coupon note having semi-annual interest payments and a notional maturity value of $100,000. The Eurodollar yield at the five-year maturity is calculated as the last of 20 yields in a chain of yields based on the geometric mean through 20 quarterly rates. When all 40 Eurodollar future quarters are included, the entire Eurodollar yield curve is complete.
PARTS OF THE WHOLE
The structure of the Eurodollar yield at any maturity is composed of three segments: the U.S. Treasury yield at that maturity, a credit spread, and a correction to make up for the lack of convexity. Price changes for Eurodollar futures are always $25 per basis point regardless of movements in the U.S. Treasury yield. The yield structure of a five-year interest rate swap also has three parts, but it varies from the Eurodollar structure. The two are mutually dependent on the U.S. Treasury yield curve as the base yield. An interest rate swap also has a credit spread, which may be considered equal to the Eurodollar credit spread because they both are based on the London Interbank Offer Rate (LIBOR), which introduces a small amount of bank risk. The third element of the swap yield is convexity. Like T-note futures, interest rate swap futures have periodic notional coupon cash flows and principal value at maturity.
Price calculations for interest rate swaps are also different from prices of Eurodollar futures. As discussed, the price of a CBOT interest rate swap futures contract is the present value of a 6% coupon notional five-year or 10-year note. The Eurodollar price for the same maturity of five years is the quarterly rate for the 20th quarter subtracted from 100. In effect, there is no dollar price for the Eurodollar futures for a specific quarter; there is only an index equal to 100 minus the quarterly rate. However, the change in the index from one period to the next permits a price change to be calculated at $25 per basis point of change in the price index.
SPREAD DIFFERENCES
Because of the difference in pricing there are changes in the spread between the prices of interest rate swap futures and Eurodollar futures. The progression of spreads is shown on “Swap vs. Eurodollar price spreads” (below). The chart shows cumulative price changes for the five-year interest rate swap and the Eurodollar contract with five-year maturity.
It is expected that the average price change for an interest rate swap will exceed the average change in the corresponding Eurodollar futures. The proportional difference between the two changes may be estimated by comparing basis point values (BPV), and by computing the ratio between average absolute changes over an extended period.
Selling the swap vs. Eurodollar price spread implies that the trader believes interest rates will rise. The chart shows how the spread changes with no adjustment for the difference in comparative price movement. With this trade, Eurodollar futures are used to mitigate the negative effects of a price increase – with the swap futures rising at a faster rate than Eurodollar prices. The Eurodollar part of the spread also reduces profitability when interest rates increase.
While the Eurodollar yield curve is approximately parallel to U.S. Treasury yields, the quarterly rates that create the yield curve have a completely separate curve. The unusual shape is required for successive quarterly rates to result in the desired yield curve. This means that the swap vs. Eurodollar price spread is influenced by changes in Eurodollar quarterly rates (and corresponding price changes) that vary at some distance above the yield curve.
“Yield curves” (above) shows the Treasury yields at two-, three-, five- and 10-year maturities, the curves of Eurodollar quarterly rates and yields, and T-note futures yields at two-, five- and 10-year maturities on Nov. 2, 2007. A single dot on the Eurodollar yield curve shows the five-year swap yield.
The “Yield curves” chart indicates the problems that may be encountered in predicting price changes for the five-year interest rate swap and the swap vs. Eurodollar spread. As the Eurodollar quarterly rate curve bends to make the Eurodollar yield curve conform to the Treasury yield curve, resulting price changes may not follow usual interest rate/price patterns. As long as the swap yield follows changes in the Eurodollar yield curve, Eurodollar yields (and the underlying Eurodollar quarterly rates) are important price determinants of interest rate swaps. Over time, increased trading volume in all maturities of interest rate swap futures should result in improved hedging and trading possibilities. The relationships among swap futures, T-note futures, and Eurodollar futures should continue along the trends described here – with smoother curves and enhanced predictability as the exchange-traded market for interest rate swap futures progresses.
Paul Cretien, CFA, is an investment analyst and financial case writer. He may be e-mailed at PaulDCretien@aol.com.