Around and Around: The Expectations Hypothesis

Authors

  • Mark Fisher,

    1. Board of Governors of the Federal Reserve System
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  • Christian Gilles

    1. Bear, Stearns & Co.
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    • Fisher is with the Board of Governors of the Federal Reserve System and Gilles is with Bear, Stearns & Co. The views expressed herein are the authors' and do not necessarily reflect those of the Board of Governors or the Federal Reserve System. We thank Greg Duffee and Huston McCulloch for extensive comments, and an anonymous referee for suggesting improvements in the exposition.

Abstract

We show how to construct models of the term structure of interest rates in which the expectations hypothesis holds. McCulloch (1993) presents such a model, thereby contradicting an assertion by Cox, Ingersoll, and Ross (1981), but his example is Gaussian and falls outside the class of finite-dimensional Markovian models. We generalize McCulloch's model in three ways: (i) We provide an arbitrage-free characterization of the unbiased expectations hypothesis in terms of forward rates; (ii) we extend this characterization to a whole class of expectations hypotheses; and (iii) we show how to construct finite-dimensional Markovian and non-Gaussian examples.

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