Market Expectations Hypothesis
The mathematical representation of market expectations hypothesis explaining the yield curve is given by the following formula:
(1 + ilt)n = (1 + iyear1 st ) (1 + iyear2 st) (1 + iyear3 st) (1 + iyearn st)
According to the market expectations hypothesis, the various maturities are supposed to be the perfect substitutes. The hypothesis also suggests that the shape of the yield curve is dependent on the expectations of the market participants on the future interest rates. The assumptions of the arbitrage opportunities being minimal, the expected rates offer enough information in order to construct a yield curve in a complete manner.
An example on this hypothesis will make it easy to understand. For example, when the investors have an assumption of what the 1-year interest rate will be in the next year, the 2-year interest rate can be determined as compounding the interest rate of the present year by the interest rate of the next year.
Here, it can also be said that the long-term instrument rates are equal to the geometric mean of the series of short-term instrument yields.By following the market expectations hypothesis theory, the stylized movement of yield curve can be explained. But the hypothesis is unable to explain the shape of the yield curve being persistent.