Yields on Eurodollar futures are continuously adjusted to form curves that are approximately parallel to the U.S. Treasury yield curve. The space between the two curves is attributed to a credit spread dictated by the higher risk perceived by the market for private bank deposits vs. the relative safety of securities issued by the U.S. government. There’s also a spread that makes up for the lack of convexity on the part of Eurodollar futures contracts.
By taking a closer look at this relationship, particularly in light of current monetary policy, we can uncover market tendencies that can be used to predict Eurodollar futures rates and prices.
For more than a year, starting in the fall of 2005 and extending into the first months of 2007, Federal Reserve monetary policy has maintained interest rates for the shortest maturities at a higher level than long-term yields. The resulting Treasury yield curve is inverted — sloping down through the first eight to 10 quarters and then becoming almost flat through the tenth year of maturity. For example, at midday on Jan. 18, 2007, U.S. Treasury yields listed by Bloomberg.com for two-, three-, five- and 10-year maturities were 4.90%, 4.82%, 4.77%, and 4.77%, respectively.
SEEING THE LINK
The Chicago Mercantile Exchange (CME) lists a Eurodollar price for each quarterly contract. The rate of interest associated with each quarter is equal to 100 minus the price of the futures. This is a rate that applies only to one specific quarter, described by the delivery date of the futures.
The yield-to-maturity for any future quarter may be found by computing the geometric mean of successive quarterly rates. Eurodollar yields calculated in this manner are comparable with U.S. Treasury yields for the same maturity, given the credit and convexity spreads differences mentioned earlier.
It must be understood that the rates on Eurodollar futures are the end of a process beginning with the yields on U.S. Treasury notes and bonds, and then, with the corrections for the credit and convexity spreads, progressing to Eurodollar yields, and finally, through the reversal of geometric mean calculations, to rates on Eurodollar futures contracts.
In the current interest rate environment, to create a Eurodollar yield curve that is roughly parallel to the Treasury yield curve, and offset by the necessary spreads, the Eurodollar rates must first curve down lower than the Treasury yields and also below the Eurodollar yield curve. As shown in “Yields and rates,” (below) the rates on Eurodollar futures then rise along a sloped line, ultimately increasing above Eurodollar yields.
The difference between Eurodollar rates and Eurodollar yields is also shown by an example on “Bookend calculations” (below). For the June 2012 contract, the rate for that quarter is 5.255%: subtracting the price listed by the CME, 94.745, from 100.
While the rate applies to only one quarter in the future, the corresponding yield (5.1379%) is the yield-to-maturity for the same period, approximately five-and-a-half years from January 2007. Both rates and yields on Eurodollar futures are nominal figures because futures do not pay interest or principal.
BUILDING THE BOOKENDS
By using the quarterly Eurodollar futures prices, starting with the December 2009 contract and ending with December 2016, the process of constructing a forecast using bookend data can be described in five steps.
Step one: Find the current yield on U.S. Treasury notes listed at Bloomberg.com or other sources for the three-year and 10-year maturities. To these yields add estimated credit and convexity spreads. The example on “Bookend calculations” uses an 18-basis-point spread for the three-year maturity and 57 basis points for the 10-year yield. The sum of the current market yield and estimated spread equals the Eurodollar futures yield at each end of the 29-quarter series of futures contracts.
Step two: By dividing the difference between the two estimated Eurodollar yields by 29 and adding the resulting amount to each quarter’s yield starting December 2009, estimate the predicted yields for each quarterly contract plus an additional estimated yield one quarter previous to the December 2009 yield. The predicted yields, like the rates and prices computed in the bookend process, are points on a straight line between the two end-points.
Step three: Begin with the last quarterly yield at the 40th quarter and by reversing the geometric mean calculations, moving backward though the succession of estimated yields, compute the predicted rates on the series of Eurodollar futures for quarters 12 through 40 (see “Getting to know TED,” August 2005).
The bookend process assumes that the Eurodollar futures yields and corresponding quarterly rates will increase from the December 2009 contract to December 2016 along a straight line. To the extent that the actual rates and yields follow a curved line or deviate from a straight-line slope in other ways, the predicted rates will not accurately reflect actual rates.
The curved rates and prices caused by the Eurodollar price wave for short-term maturities are the reason for starting the bookend predictions at the 12th quarter futures contract (“Riding the Eurodollar price wave,” April 2006).
Step four: Adjust the two spreads after the actual futures prices are entered for quarters 12 through 40 until the average absolute difference between predicted and actual rates is minimized. The average difference is generally less than one basis point (1/100th of 1%). The spreads at each end of the straight-line slope are the only variables entered, given the current market yields on Treasury securities. All other calculations depend on these two numbers, and minimizing the total difference between predicted and actual market rates is accomplished by trial and error with the two spreads (see “Rates and prices,” below).
Step five: The remaining small variations from predicted rates for each quarterly contract are associated with seasonal differences between quarters.
On “Seasonal variations” (below) differences between predicted and actual rates for each quarter are charted.
Each four-quarter set of rates has a separate seasonal pattern, reflecting the succession of quarter-to-quarter variations described in “Trading interest rate inefficiencies” January 2006. Correcting the bookend predicted rates and prices for seasonal variations can result in a further reduction in the average difference between predicted and actual Eurodollar rates and prices.
The bookend example shows the dependence of Eurodollar prices on the U.S. Treasury yield curve. Predictions along the yield curve may be made minute-to-minute during the trading day. The computations of rates and prices between two Treasury maturities separated by seven years help to explain the basis of Eurodollar prices and may help Eurodollar traders refine hedging and speculative trading.
Paul D. Cretien is a retired professor of finance at Baylor University and a chartered financial analyst. He is the author of the book The Basics of Bank Investments (Graduate School of Banking at LSU, 2004).
