Swaps vs. eurodollar spreads

Futures, Aug 2008 by Cretien, Paul D

An increase in U.S. Treasury yields can cause the eurodollar rate curve to flex. This movement is predictable and should be reversed if Treasury yields start to fall from their current levels. Here's how to read the data.

The close connection between the yields of five-year interest rate swaps and eurodollar futures for delivery at the 20th quarter makes this pair an interesting spread candidate. Not only does its analysis tell us a bit about the dynamics of the eurodollar market, but we can use it to predict changes in rates.

On "Five-year yields" (right), the yields for the two contracts are shown over the period of Feb. 19 through May 23, 2008. The chart makes clear the high degree of correlation, and at the same time it shows the small differences that support trading spreads between futures on interest rate swaps and the corresponding quarterly eurodollar futures.

However, before we can match the two contracts, we must make some accommodations for relative sizes. The interest rate swap vs. eurodollar futures spread requires using approximately twice the number of long or short eurodollar futures contracts for each $100,000 swap futures sold short or bought long, respectively. For example, on May 22, 2008, the five-year swap closing price was 108-220, or a decimalized price of $108,687.50 (108% of par plus 22/32 of 1%). The price difference computed by adding and subtracting half a basis point from the yield of 4.0625% is $47.11. Because each basis point increase or decrease in a eurodollar futures rate results in a $25 price change - and because during this time period a basis point change between $47 and $49 was typical for the five-year swap futures - the twoto-one ratio of eurodollar futures to interest rate swap futures makes sense for our purposes.

CHANGES IN SPREADS

Beginning on Feb. 19 and extending through May 23, 2008, "Cumulative spread gain" (right) shows the profit potential from spreading two long eurodollar 20th quarter futures against a short sale of one five-year swap futures. As the chart shows, the available profit came fast and furious. The cause of this increase will imply conclusions that should help in trading similar spreads as rates and yields vary in the future.

The spread between interest rate swap futures and eurodollar futures in the present analysis uses a yield-tomaturity, for example the five-year maturity for the swap, against a quarterly rate - the interest rate applicable to a specific quarter, in this case the 20th quaner. (The possibility of using multiple quarters of eurodollar futures instead of the single 20th quarter is not considered here.)

Keep in mind that neither interest rate swap futures nor eurodollar futures provide real interest income or principal to the trader. Like nominal T-note futures, they are contracts that are bought and sold with the intent of hedging or speculating on price changes. For eurodollar futures, the price of a quarterly contract is equal to the interest rate applied to that particular quarter subtracted from 100. Interest rate swaps are priced by discounting $100,000 principal plus 6% semiannual interest back to present value at the current market yield. Thus, given the listed price of the five-year swap, the yield is found by trial and error as the discount rate that results in matching the present value of nominal interest and principal cash flows with the price.

The three yields , eurodollar, interest rate swaps and nominal T-note futures, are all approximately parallel to the U.S. Treasury yield curve. Nominal Tnote futures have the lowest yield of the three, separated from Treasury yields by a convexity differential that shifts as yields change. Swap yields are higher than nominal T-note yields due to added risk, and eurodollar yields must account for risk equal to the risk associated with interest rate swaps as well as a correction for lack of convexity.

Spreads between interest rate swaps and eurodollar futures add another complexity since the eurodollar rate curve is not parallel to the eurodollar yield curve. That is, the use of spreads between these contracts requires knowledge about the possible bending or flexing of the eurodollar rate curve.

The impact of eurodollar quarterly rates on spread results is shown graphically on "Rate less yield" (below). At the beginning of the period, Feb. 19 to May 23, the rate for the 20th quarter is 1.49% above the yield for that quarter. From March 17 through April 25 the difference falls by 55 basis points.

With eurodollar and swap yields relatively stable, the decline in the relative size of rates gave a price advantage to eurodollar futures and helped create the cumulative profit from the long eurodollar, short swap spread. The charts for eurodollar rate less yield and cumulative spread gain are almost mirror images. As the 20th quarter eurodollar rate declined from March 17 to April 25, the cumulative spread gain increased by approximately $2,400.

FLEX BEHIND THE PROFIT

The reason why the 20th quarter (corresponding in maturity to the five-year interest rate swap) difference between rate and yield decreased over the period analyzed can be found in the flexing of the eurodollar futures 40-quarter rate curve.