Computer programs enabling analysts to calculate minor changes between interest rates and yields throughout the fixed income world create exploitable opportunities for the bond trader. Here, we will review the efficient relationships between various rates and yields to arrive at several conclusions:
- that the yield curves on government securities are the prime determinants of interest rates in every market;
- that forward rates are not predictors of future interest rates, but are determined by the need to conform to the current government bond yield curve, and
- that the terms "forward" and "futures" are misleading if Eurodollar rates and forward rates are tied continuously and directly to government securities yields-to-maturity.
Yields at specific maturities for bonds and interest rate futures represent one side of the rate-yield coin. For any maturity, the yield is the end product of a sequence of shorter-term rates that progress in terms of geometric mean rates to the listed yield for a bond or interest rate futures contract. Knowing the yield at a given maturity and the immediately preceding yield permits calculation of the rate of interest (the forward rate) for the corresponding short-term period. Interest rates that cover a single short-term period are forward rates, while yields are the result of linked forward rate sequences.
Because of the relatively large number of short-term rates for eurodollar futures — 40 quarterly rates leading to yields-to-maturity up to 10 years — these contracts are ideal for analyzing long- and short-term interest rate markets. Trading through each day shows continuous pricing patterns for the 40 quarterly Eurodollar futures rates. Eurodollar yields are not listed, and must be calculated from the chain of geometric means computed from short-term quarterly Eurodollar futures rates, beginning with the London Interbank Offered Rate (Libor).
Conversely, the yields on U.S. Treasury notes and bonds at different maturities are known, while the implied 90-day forward rates leading to yields at specific maturities are not listed and must be calculated by reversing the sequence of geometric means from the longest-term yield back down the yield curve. When both sets of calculations are complete, as shown on "Eurodollar and Treasury forward rates" (below), we can see that the computed Eurodollar yields are intrinsically tied to the U.S. Treasury yield curve, and that the computed Treasury forward rates are aligned closely with Eurodollar quarterly rates.
Comparing yields
The Eurodollar yield curve is higher than the U.S. Treasury yield curve because of the risk differential between risk-free government securities and 90-day dollar deposits, and the need for Eurodollar futures to offset their lack of convexity — a straight-line price change at $25 per basis point compared to the convex bond price curve. On "Two yield curves" (below) the risk/convexity spread of Eurodollar yields over Treasury yields is approximately 50 basis points on April 19, 2011.
"Two yield curves" shows how closely correlated the Eurodollar yield curve is with the U.S. Treasury yield curve. Each Eurodollar quarterly rate must be in its proper place for the two curves to fit together, and a shift in Treasury yields must be reflected in Eurodollar rate and yield changes. At the same time, the Treasury yield curve immediately determines, through arbitrage, the yields and prices of other interest rate futures, including two-, five- and 10-year T-note futures and futures contacts on interest rate swaps.
Just as the Eurodollar yield curve can be used to describe the shape and individual quarterly yields along the U.S. Treasury yield curve, the 90-day interest rate futures of non-U.S. markets should respond to their individual government security yield curves. For example, "Short sterling rates and yields" (below) shows 90-day short sterling futures rates and the yield curve that is created from quarterly sterling rates. The risk-convexity spread between the yield curves is 50 basis points for most of 16 quarters of futures delivery dates.
Similar to the implied forward rates computed from the U.S. Treasury yield curve, forward rates for the United Kingdom can be found by reversing back down the government yield curve. The implied forward rates approximately are parallel to — and slightly lower than — the short sterling rates. The government yield curve in each country or market is the determinant of short-term interest rate futures as well as the forward rates on government interest-bearing securities.
Four currently-traded interest rate futures contracts are shown on "90-day interest rate futures" (below). In addition to Eurodollar rates listed by CME Group, these include euribor, NYSE Liffe Eurodollar and short-sterling futures. Although they start at different rates, the four contracts converge at approximately 4% after 16 quarters on April 14, 2011. With the Federal Reserve holding U.S. rates for one-quarter delivery dates at extremely low levels, the 1.50% euribor rate (for 90-day euro-related rates) looks surprisingly high in comparison. The shortest-term rate on 90-day sterling futures is in the middle at 1.00%.
The curves of 90-day rate-to-yield ratios also vary between interest-rate futures markets. These are the "flex" curves described in "Eurodollar futures: Rate, yield and price structures" (May 2010). When interest rates are at a low level, as they currently are in the United States, the ratio of rates-to-yields will increase. As shown on "Ratios of rates to yields" (below), on April 19, 2011 Eurodollar futures rates topped a two-to-one ratio over yields at approximately the two-year, or eight-quarter, mark in number of quarters to maturity. At the same time, the ratios for the European Central Bank (ECB) on average increased from 1.0 to 1.4.
Tracing ratios
The ratio of rates-to-yields is not a predictor of rate changes, but can be an important factor when rates change. As interest rates rise in the United States — which they invariably will do at some point — the ratio will fall, rewarding long positions in Eurodollar futures over a range of expiration dates compared to the more stable yields on T-note and interest rate swaps futures at the same maturities.
On April 22, 2011 the price of a five-year T-note futures contract was 116-07, or $116,227, with a yield of 2.525%. An immediate increase of 100 basis points in yield would result in a new price of $111,255 — down $4,972 due to the increase in yield. A spread trade using a two-to-one ratio of March 2016 Eurodollar futures against the five-year T-note produces a slight loss, with the long-side Eurodollar futures down 2 x $2,500. However, "Ratios of rates-to-yields" shows that the increase in yield should be accompanied by a decrease in the rate-to-yield ratio from 1.80 to 1.40 or lower. This should give an edge in trade results to the long Eurodollar futures as they lose less than the short T-note futures.
At any time, the structure of Eurodollar yields at different maturities is determined by the sequence of short-term (quarterly) rates, with the underlying objective of matching the U.S. Treasury yield curve. The same process is at work in different interest-rate markets, although the levels of rates, yields and ratios of rates-to-yields vary.
Whether or not a trader believes that interest rates can be predicted by looking at forward rates or the yield curve — or whether changes in government bond yields precede or follow shifts in forward rates — it still is worthwhile to observe the relationships between quarterly rates and yields at various maturities. Changes in the curves of quarterly rates, forward rates or longer-term yields provide the speculative profits and losses as well as the benefits of hedging that are the underlying reasons for the existence of the market for interest-rate futures and options.
Paul Cretien is an investment analyst and financial case writer. His e-mail is PaulDCretien@aol.com.
