From the July 01, 2011 issue of Futures Magazine • Subscribe!

Government bond yields and forward rates

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:

  1. that the yield curves on government securities are the prime determinants of interest rates in every market;
  2. 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
  3. 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.


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