Eurodollar futures contracts are priced as 100 minus the 90-day interest rate on dollar-denominated deposits in non-U.S. banks. Because of their ease of trading, liquidity and usefulness in hedging interest rate movements, eurodollar futures — with contracts priced over a 10-year span for 40 future quarters — exhibit their highest trading volume over the first 20 quarters or five-year maturities. Regardless of the diminished volume of trading on the remaining 20 quarters, the entire set of 40 quarterly contracts is continuously synchronized with corresponding quarterly U.S. Treasury yields.
“Eurodollar futures yields” shows the curve of quarterly interest rates calculated as 100 minus the price for each of 40 quarterly futures on Jan. 25, 2010. The quarterly rates are used to create a chain of quarterly yields in which each quarter’s yield is the geometric mean of rates to that point. The close relationship between eurodollar quarterly yields and U.S. Treasury yields at the same maturities is shown by comparison with eight Treasury yields extending from three-month to 10-year maturity. Interest rate arbitrage binds eurodollar futures, T-note futures and U.S. Treasury in common price and yield relationships. Four of these relationships, or structures, warrant a deeper look.
Structure #1 is the eurodollar yield curve in correspondence with the U.S. Treasury yield curve. The structure is useful primarily in spread trades between eurodollar futures at the 20-quarter maturity and five-year T-note futures contracts. The structure is hidden because it must be calculated from listed eurodollar prices and quarterly rates, but once exposed, it is a dependable aide in trading eurodollar/T-note futures price and rate spreads. Eurodollar yields that are more that five basis points more than, or less than, the yield on five-year T-note futures indicate the possibility of a spread trade. Eurodollar quarterly rates must adjust the eurodollar/T-note spread, causing the eurodollar prices to move in the opposite direction.
It may be noted that U.S. Treasury yields also have a hidden structure — the quarterly rates that the market implicitly uses to derive the listed yields to maturity. Considering that the yields to maturity for each Treasury security effectively result from the geometric means of invisible quarterly rates, the eurodollar quarterly rates show the underlying structure of U.S. Treasury yields — with a parallel adjustment for the additional risk and lack of convexity of eurodollar futures.
Structure #2 is the curve of ratios between eurodollar quarterly rates and yields. As shown in “Ratios of eurodollar rates-to-yields,” (right), Structure #2 on Jan. 25, 2010, peaked at approximately eight quarters with a ratio of 1.90. Structure #2 is intrinsically tied to Structure #1 because eurodollar quarterly rates are forced to rise quickly, so that the resulting geometric mean yields that average the chain of preceding yields may remain parallel and in close proximity to the corresponding U.S. Treasury yields.
The second structure of eurodollar futures is subject to Federal Reserve policy. While the Fed works to stabilize the U.S. economy, rates and yields on eurodollar futures and Treasury securities currently start near zero for the shortest maturities. Structure #2 reflects that, relative to its beginning at or near a zero yield, the Treasury yield curve has a significant upslope over the 10-year maturity, although U.S. interest rates seem historically low at the present time. Future changes in the shape of Structure #2 will depend on how quickly short-term Treasury yields rise in response to increases in long-term yields.
Structure #3 is the interplay between December eurodollar futures and the following March futures from the 12th quarter through 40th quarter maturity. “Eurodollar futures seasonality” shows that the ratio of change in rates between quarters has December high and March low in a pattern that holds over time. Although the underlying concepts are fundamentally different, it is tempting to compare the seasonal variations of eurodollar futures with a “standing wave” in physics or harmonics in music — wave patterns that are predictable and continuous as long as the underlying conditions persist.
Because the December-to-March waves occur primarily in the maturities that have relatively low trading volume, the chart pattern may be the result of assumptions built into computer pricing and trading systems. The curve of eurodollar rates that appears smooth on “Eurodollar futures yields” disguises hidden Structure #3 with its quarterly waves.
Structure #4 is the curve of eurodollar quarterly price changes for the 40 eurodollar futures quarterly contracts between two dates. As the foundation for the price change structure, “Rates-to-yields” (page 44) shows the curve of eurodollar quarterly rates-to-yield ratios on three days: Jan. 7, 13 and 19, 2010. Because of the relatively short time span, the curves are closely related, adding height as the ratios increased during this period.
If the yield curve and rate/price curve are stable, “Rates-to-yields” implies that, over time, eurodollar contracts on the left side of the rate/yield peak should have rates that fall, while rates on the right side should rise toward the peak at the eighth quarter.
Depending on the relative stability of the rate/yield curve and the underlying eurodollar /yield curve, contracts on the right side should gradually reach the peak and start down the left side toward a ratio of 1.0 near the delivery date.
When other factors remain constant, contracts on the left side should continuously gain value compared to contracts on the right side. The problem is that other factors do not remain constant. As market rates change, the curve of eurodollar rates-to-yields shifts in response, causing flexing movements that affect the results of potential calendar spreads.
Structure #4 is shown on “Price changes, falling rates”. Prices are increasing for all 40 eurodollar futures contracts as market interest rates fall – first from Jan. 7 to Jan. 19, 2010, and then from Jan. 13 to Jan. 19. Beyond the five-year maturity, price changes appear to become less organized; however, it is normal for price changes in the final five years of eurodollar futures to appear as a tail being wagged by the first 20 quarters.
“Price changes, rising rates” illustrates the impact of increasing interest rates over several days. As quarterly rates increase, the chart of price changes from June 6 to June 17, 2008, shows the largest price decline for contracts with maturities at approximately four quarters.
The price change charts confirm that market-driven eurodollar rates and prices occur within the first 20 quarters, with the following five years of quarterly rates and prices being produced by computer models that result in eurodollar yields that parallel the U.S. Treasury yield curve, while maintaining the seasonal pattern of rates shown in Structure #3.
Structure #4 suggests that speculative eurodollar trades should concentrate on maturities around eight quarters because these tend to have the greatest range of plus and minus price changes. “Price changes, falling rates” illustrates the progression in price change for the eighth quarter from 23 to 35 basis points over the additional six days from Jan. 7 to Jan. 13, 2010. With the shape of price change curves remaining relatively constant over a period of several days, trades that depend on differing volatilities between specific maturities may be planned and executed.
Because of the rate-setting and pricing connections to the U.S. Treasury yield curve as shown by eurodollar futures rate and price Structures #1, #2, and #3, the price changes of Structure #4 are part of a system that is coordinated with Treasury yields.
The progression of influence from Treasury securities to eurodollar futures is the following: 1) the market establishes yields on U.S. Treasury bonds and notes; 2) T-note futures are priced to yield slightly above Treasury yields at several maturities including five-years; 3) eurodollar futures at the 20-quarter maturity are priced to yield slightly above five-year T-note futures with variations generally within zero to five basis points above the T-note yield and 4) eurodollar quarterly futures contracts are traded primarily over the first 20 quarters, with the highest rate and price volatility occurring near the halfway point between the shortest maturities whose rates are set according to variations in London Interbank Offered Rate and a point (near the 20-quarter maturity) at which market pricing fades out and more automatic programmed pricing begins.
The four eurodollar rate, yield and price structures describe predictable and measurable connections for different aspects in this popular futures market.
Knowledge of the hidden rate, yield and price structures of eurodollar futures should assist in determining when calendar spreads are available, which maturities are most favorable for speculation, and what price changes may be caused by rising and falling market rates of interest as well as movements in U.S.
Paul Cretien is an investment analyst and financial case writer. His e-mail is PaulDCretien@aol.com.