A series of flat U.S. Treasury yield curves during 2006 has permitted an especially clear view of the structure of Eurodollar futures market rates and yields. As shown on “Rates and yields”, Eurodollar futures’ quarterly market rates may be converted into Eurodollar yields by computing the geometric means of successive strips of Eurodollar futures contracts. The resulting Eurodollar futures yield curve is approximately parallel to the Treasury yield curve, with two important exceptions.
The first exception to the parallel relationship is the rate and price wave occurring at the far left of the chart. Described in “Riding the Eurodollar price wave,” April 2006, the current shape of the Treasury yield curve forces Eurodollar rates into a wave pattern that is not parallel to Treasury yields. The price wave on Aug. 8, 2006, is shown in “Eurodollar price wave” (below). The wave occurs in the first 10 quarterly Eurodollar futures contracts.
The second exception that causes the Eurodollar yield curve to veer away from a parallel relationship with Treasury yields is illustrated on “Yield differences” (above). This chart shows that on Aug. 8, 2006, there was a roughly linear increase in the TED spread, rising from 20 basis points at the end of the fifth quarter to sixty basis points at the farthest Eurodollar futures maturity, 40 quarters. Thus, about one basis point per quarter was added to the yield curve that otherwise would have been parallel to the Treasury yield curve. This correction in Eurodollar yields was stable throughout 2006, with the average addition to the yield each quarter varying around one basis point.
swap hedges
The TED spread is usually defined as the credit difference between private bank deposits of Eurodollars and U.S. Treasury securities. As market confidence increases or declines, the TED spread should grow smaller or larger, respectively. Another factor determining the difference between Eurodollar and Treasury yields is the need to correct Eurodollar rates and yields for “convexity bias.”
Short positions in Eurodollar futures are used to hedge receive-fixed, pay-floating interest rate swaps. Because the receive-fixed swap declines in value when the floating rate increases (generally Libor, the same quarterly rate basis of Eurodollar futures), selling short a strip of Eurodollar futures that matches the timing of the swap’s floating rates will hedge the swap’s interest rate risk.
The problem is that the market values of interest rate swaps lie along a curve that is convex with changing market yields, as opposed to Eurodollar futures prices that do not exhibit convexity. Each basis point of yield change in a forward quarter results in a $25 increase or decrease in the price of a Eurodollar futures contract.
The convex curve of interest rate swap prices means that if market yields rise, swap values decline, but at a slower than straight-line rate. Convexity also means that when interest rates fall, swap values rise at a faster than straight-line rate. Either direction of changing market yields would give an advantage to a short hedge with Eurodollar futures.
Correcting for CONVEXITY
Convex bond price curves are illustrated in “Convexity of bonds” (below). The chart shows prices of two 5% coupon bonds as market yields change from 2% to 9%. Both bonds are priced at face value of $1 million at the yield of 5%, but the 10-year bond has more curvature or convexity with changing market yields.
If the convexity correction indicated on “Yield differences” is assumed to be approximately one basis point per quarter, the yield spread attributed to credit risk appears to be 20 to 25 basis points. While the TED spread at the five-year maturity has remained relatively constant at around 40 basis points, the first 20 quarters have varied — being level when near-term Eurodollar rates were equal to Eurodollar yields in January 2005 and declining to the five-year midpoint when short-term rates were significantly higher than yields in January 1995. The current curve of yield differences appears to be lower than normal for the first 20 quarters because short-term Eurodollar rates are lower than the corresponding yields.
Traders and hedgers using Eurodollar futures may take advantage of the finely tuned structure of rates and yields that compose this market. Yields on U.S. Treasury securities provide the basic foundation, with Eurodollar yields following the addition of a convexity correction to the Treasury yield curve.
The resulting Eurodollar yields are converted to Eurodollar rates by reversing the calculation of geometric mean yields of successive strips of Eurodollar futures contracts (see “Trading interest rate inefficiencies,” January 2006).
Two additional structures are added to Eurodollar futures rates and yields. The first one is temporary and depends on the shape of the Treasury yield curve being relatively flat. This is the Eurodollar price wave that has been present during 2006 but will disappear when the Treasury yield curve returns to a more normal up-sloping shape.
The second and more subtle addition to Eurodollar yield components is the seasonal structure of calendar spreads (“Getting to know TED,” August 2005). It is the stability and/or predictability of this and other components that make trading Eurodollar futures interesting and different from other markets.
Throughout each trading day, market rates covering 40 quarters of Eurodollar futures contracts may be viewed as the top layer of the structural components described in this article. The full range of Eurodollar futures rates can be simulated by adding credit spreads and convexity corrections to Treasury yields to produce Eurodollar yields, and then reversing the geometric mean calculation to generate Eurodollar futures market rates. In actual market pricing, small adjustments are made for seasonal differences in calendar spreads and to smooth the progression of rates from one quarter to the next.
The final market rates are arrived at through massive computerized trading systems in a remarkable continuous balancing act. Simulated rates are compared with market rates in “Eurodollar rate simulation” (above).
Information on relationships between Eurodollar futures, interest-rate swaps and Treasury yields assists hedging and trading in this highly structured market. It is possible to simulate Eurodollar yields based on their predictable association with U. S. Treasury yields. At the same time, it is necessary to watch the Treasury market, Federal Reserve Board actions and other indicators of interest rate and yield changes.
Paul D. Cretien is a retired professor of finance at Baylor University and a chartered financial analyst. He is the author of The Basics of Bank Investments (Graduate School of Banking at LSU, 2004). E-mail him at paulcretien@aol.com.
