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”, 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 two-to-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” 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-to-maturity, 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 quarter. (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 T-note 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.” 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.
The two charts, “Yields and rates” for eurodollar futures on March 17 and April 25 show the differences created by an increase in U.S. Treasury yields during that period. On March 17, the rate and yield curves begin at 2.58% then diverge as the quarterly rates first go below their corresponding yields and then climb smoothly higher through the 40th quarter. From the 8th quarter through the 10th year maturity, the yield curve computed from the eurodollar quarterly rates remains approximately parallel to the Treasury yield curve represented by dots at two, five and 10 years.
By April 25, increases in U.S. Treasury yields caused the rate and yield curves to start at a higher point, at 2.86%. For the eurodollar rates to perform their function in making the eurodollar yield curve parallel to Treasury yields, the rate curve had to flex, changing its shape so that it was no longer under the yield curve at any point. The rate curve again increased along a smooth upward track to the 40th quarter. All of the rate and yield curves shown on these charts appear to be artificially smoothed, but this is not the case. The charts present data drawn from the original listing by CME Group (eurodollar futures) and Bloomberg.com (Treasury yields).
The importance of the flexing action of the eurodollar rate curve on the spread profit/loss results is shown on “Rates to yields.” This chart follows the ratios of rates-to-yields on the previous rate and yield graphs for March 17 and April 25. After starting lower, the ratios on March 17 increase until at quarter 20 (corresponding to maturity of 5 years) the ratio equals 1.463.
On April 25 the rates-to-yields ratios were lower after quarter 8 and followed a relatively flat course over the last 30 quarterly contracts. The ratio of rate-to-yield at quarter 20 is 1.223. The 24 basis point difference between the two ratios benefited the spread in which eurodollar futures were held long against short interest rate swaps, causing long eurodollar futures to have a price advantage whether yields were increasing or decreasing.
DRAWING CONCLUSIONS
One idea that may be taken from this analysis is that in spreads between interest rate swaps and eurodollar futures, the flexing of the eurodollar rate curve is likely to represent a large portion of the overall price action. The differential benefits on “Rates to yields” occurred while U.S. Treasury yields were increasing. The opposite effect will occur when Treasury yields fall as the 20th quarter eurodollar rate-to-yield ratio increases due to the reverse flexing of the eurodollar rate curve.
U.S. Treasury yields for two, five and 10-year maturities increased from March 17 through April 25, 2008. Their increases were 104, 97, and 56 basis points, respectively. As the underlying cause of the eurodollar rate curve flexing movement from March 17 to April 25, the two-year and five-year Treasury yields are of specific interest. Future shifts in the eurodollar rate curve will require similar changes in Treasury yields, either by increases or decreases from current levels.
During the latter part of April and for most of May, Treasury yields have remained almost motionless with the five-year maturity at slightly more than 3%. “Five-year rates” and “Cumulative spread gain” reflect this pattern, with both relatively steady after April 25. On the latter two charts, it can be seen that over short periods between April 25 and May 23, decreases or increases in the five-year yields resulted in corresponding decreases or increases in the cumulative spread gain. These price changes reflect the expected price movements due to the flexing action of the eurodollar rate curve with particular emphasis at the five-year, 20th quarter for interest rate swaps and eurodollar futures.
The swaps-eurodollar spread results were also affected by a variable difference between the yields on the 20th quarter eurodollar futures contract and five-year interest rate swap. On “Yield differences,” there is normally a positive spread with the eurodollar yield above the swap yield; however, this varies within a range of approximately six basis points. As an effect on the swaps-eurodollar spread, the difference of eurodollar yield less the swap yield generally increased from mid-February until mid-March and began to decline after March 18. The eurodollar five-year yield was 5.3 basis points above the swap yield on March 18, and had fallen to 0.7 of one basis point by May 2. The decrease in the difference benefited the long eurodollar-short swap spread.
It would be hard to overestimate the influence of movements in U.S. Treasury yields in the markets for nominal T-note futures, interest rate swap futures and eurodollar futures. Essentially, minute-to-minute pricing and rate-setting for all three futures are determined by current levels or changes in Treasury yields. Because these derivative contracts are valued according to the present instead of the future, the knowledge of pricing relationships such as the continuous flexing of the eurodollar rate curve becomes an important aspect in trading interest-rate futures.
As always, the powerful computer programs and pricing systems that connect all of the components of the interest-rate futures markets never fail to awe. Nevertheless, shown by these charts, there are still variations from the expected norm that can be
exploited. The smooth mathematical base of futures valuation in the areas of interest rates and yields should be to a trader’s advantage when the expected relationships emerge.
Paul Cretien, CFA, is an investment analyst and financial case writer. He may be e-mailed at PaulDCretien@aol.com.