When investors choose between a five and 10-year bond, they compare expected rates of return over the near future. Whether the five-year return on the 10-year bond is to equal the locked-in return on the five-year bond depends, however, on the yield on the 10-year bond at the end of five years. The initial yield on the 10-year bond may impound an expectation of a very different yield five years hence.

The yield on a long bond over the near future is the sum of its beginning yield to maturity and the annualized percentage price change resulting from the change in yield. The yield change that equates its total return with the locked-in return on an instrument maturing over that period the author terms the “breakeven yield change.”

Sir John Hicks termed the fraction of expected change in short-term rates that is reflected in the expected change in short-term rates one period hence the “coefficient of expectation.” The expected change in long interest rates will equal the average of expected changes in future short rates, calculated by applying the coefficient of expectation to the expected change in current short rates. The author calculates breakeven yield changes from observations of actual yield for various terms to maturity and then solves for the value of Hicks’ coefficient that gives the best fit to the calculated breakeven yield changes.

Actual data demonstrate that the pattern of breakeven yield changes is well behaved and smooth. On the other hand, when the best fitting patterns are translated back into the corresponding yield curves, they have the full variety of complex curvatures observed in reality.