relative changes in long-term and short-term interest rates

The expectations theory does help to explain an interesting phenomenon in the financial markets. Long-term interest rates tend to change slowly over time, while short-term interest rates are highly volatile and often move over wide ranges. The expectations hypothesis argues that the long-term interest rate is the geometric average of a series of rates on short-term loans whose combined maturities equal that of the long-term loan. The rate of interest on a 20-years bond, for example, is equivalent to the geometric average of the rates on a current 1-year loan plus the rates attached to series of 19 future (forward) 1-year loans, adding to 20 years. Experience teaches us that average changes much more slowly than the individual components making up an average. If the long-term interest rate is a geometric average of current and future short-term rates, it is not at all surprising that long-term rates tend to lag behind short-term rates and are less volatile.