Expectations Theory of Interest Rates

Source: Encyclopedia of Banking & Finance (9h Edition) by Charles J Woelfel
(We recommend this as work of authority and you can order it here)                  

A theory that purports to explain the shape of the yield curve, or the term structure of interest rates.  The forces that determine the shape of the yield curve have been widely debated among academic economists for a number of years.  The American economist Irving Fisher advanced the expectations theory of interest rates to explain the shape of the curve.  According to this theory, longer-term rates are determined by investor expectations of future short-term rates.

In mathematical terms, the theory suggests that:

(1 + R₂)²  =  (1 + R₁) x (1 + E(R₁))

where

R₂        =            the rate on two-year securities,

R₁        =            the rate on one-year securities,

E(R₁)    =            the rate expected on one-year securities one year from now.

The left side of this equation is the amount per dollar invested that the investor would have after two years if he invested in two-year securities.  The right side shows the amount he can expect to have after two years if he invests in one-year obligations.  Competition is assumed to make the left side equal to the right side.

The theory is easily generalized to cover any number of maturity classes.  And however many maturity classes there may be, the theory always explains the existence of longer-term rates in terms of expected future shorter-term rates.

The expectations theory of interest rates provides the theoretical basis for the use of the yield curve as an analytical tool by economic and financial analysts.  For example, an upward-sloping yield curve is explained as an indication that the market expects rising short-term rates in the future.  Since rising rates normally occur during economic expansions, an upward-sloping yield curve is a sign that the market expects continued expansion in the level of economic activity.

Financial analysts sometimes use this equation to obtain a market-related forecast of future interest rates.  It can be rewritten as follows:

E(R₁)  =  [(1 + R₂)²  /  (1 + R₁)]  -  1

The equation suggests that the short-term rate expected by the market next period can be obtained from knowledge of rates today.

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