Rational Expectations and Bond Pricing: Modelling the Term Structure With and Without Certainty Equivalence

Abstract

When I shall call the 'fundamental theorem' of bond pricing asserts that the redemption yield on an N-period bond is an average of the expected future spot one-period interest rates over the remaining life of the bond. The theorem assumes certainty-equivalent behaviour for which risk-neutrality is necessary, but sufficient only if the underlying structure is also linear. The fundamental theorem has formed the basis of analysis of the term structure of interest rates since Keynes (1936) and Hicks (1939), though it has sometimes been recognised that risk aversion might lead to a systematic discrepancy or liquidity premium between the N-period redemption yield and the average of expected future spot rates over the same period. Even where the problem of risk has been addressed, usually in an ad hoc manner, the comparison of N-period yields on competing assets has usually remained the condition by which asset market equilibrium is characterised. Intertemporal models require an assumption about expectations formation. In this paper I consider the implication of rational expectations for models of the term structure. When behaviour is certainty-equivalent Mishkin (1978; 1980) has shown that the fundamental theorem has a striking implication: the N-period yield should follow a random walk. In Section I I argue that Mishkin's result is irrelevant since the fundamental theorem is the wrong characterisation of asset market equilibrium under certainty-equivalence. I propose an alternative characterisation of asset market equilibrium and derive the behaviour of bond yields and prices under certainty equivalence and rational expectations. The random walk property does not generally result. Within this framework it is also straightforward to analyse the effect on bond prices of variations in bond coupons and the relative tax rate on income and capital gains. Elsewhere (Begg, 1982) I have argued that the analysis of certainty