Expectations hypothesis

There are many arguments for the rational-expectations hypothesis. In the simple cobweb cycle, and even with adaptive expectations, we must assume that each agent believes himself to be the only one to adjust rationally to the circumstances and that others act in a more or less mechanical way But this is an irrational belief, which we should not impute to people without evidence. It is surely more plausible to assume that people believe others to be as rational as themselves. Also, in a rapidly changing world people would be silly to pay much attention to the past. When oil prices quadrupled in 1973, the prices of oil before 1973 lost all relevance as guides to future prices. And if ordinary people understood much less of the economy than economists do, we would expect the latter to make much more money than they in fact do. The reason economists don t make a killing by outguessing the market is that the market has access to whatever information they have and can use it just as efficiently. ... 

From Figure 7.3, we see fliat to price a very Iraig-dated bond off the yield of the 30-year government bond would lead to errors. The unbiased expectations hypothesis suggests that 100-year bond yields are essentially identical to 30-year yields however, this is in fact incorrect. The theoretical 100-year yield in fact will be approximately 20-25 basis points lower. This reflects the convexity bias in longer dated yields. In our illustration, we used a hypothetical scenario where only three possible interest-rate states were permitted. Dybvig and Marshall showed that in a more realistic environment, with forward rates calculated using a Monte Carlo simulation, similar observations would result. Therefore, the observations have a practical relevance. 

Dhillon, U., Lasser, D., 1998. Term premium estimates from zero-coupon bonds new evidence on the expectations hypothesis. J. Fixed Income 8, 52-58. 

There are four distinct and incompatible versions of the expectations hypothesis. The unbiased version states that current forward rates are unbiased predictors of future spot rates. Let ft T,T +1) be the forward rate at time t for the period from Tto T+ 1 and tt be the one-period spot rate at time T. The unbiased expectations hypothesis states that /Rt,t + i) is the expected value of rj. This relationship is expressed in (3.36). 

The retum-to-maturity expectations hypothesis states that the return generated by holding a bond for term tto Twill equal the expected return generated by continually rolling over a bond whose term is a period evenly divisible into T— t. This relationship is expressed formally in (3.37). 

From (3.36) and (3.37), it is clear that these two versions of the expectations hypothesis are incompatible unless no correlation exists between future interest rates. Ingersoll (1987) notes that although such an economic environment would be both possible and interesting to model, it is not related to reality, since interest rates are in fact highly correlated. Given a positive correlation between rates over a period of time, bonds with terms longer than two periods will have higher prices under the unbiased version than under the return-to-maturity version. Bonds with maturities of exactly two periods will have the same price under both versions. 

The yield-to-maturity expectations hypothesis is stated in terms of yields, as expressed in equation (3.38). 

The local expectations hypothesis states that all bonds will generate the same expected rate of return if held for a small term. It is expressed formally in (3.39). 

This version of the hypothesis is the only one that permits no arbitrage, because the expected rates of return on all bonds are equal to the risk-free interest rate. For this reason, the local expectations hypothesis is sometimes referred to as the risk-neutral expectations hypothesis. 

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