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.

Market relationships

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.