Term Structure Based Capital Asset Pricing in a General Multi-Agent Dynamically Incomplete Setting with Intertemporally Dependent Preferences.

Rallis, N (1999) Term Structure Based Capital Asset Pricing in a General Multi-Agent Dynamically Incomplete Setting with Intertemporally Dependent Preferences. Working Paper. London Business School IFA Working Paper.

Abstract

This paper derives a twofactor asset pricing model based on the term structure and aggregate consumption in a general, multiagent, Continuous time setting where an individual's utility function is a concave function of current consumption and the historical consumption path. Markets are generally assumed to be dynamically incomplete and no assumption is made about the existence of a representative agent. In addition there are no assumptions regarding the dynamics of either the asset prices of the riskfree rate, both of which are endogenously determined at equilibrium. It is shown that an asset's risk premium is determined by its instantaneous covariances with changes in (a) aggregate consumption and (b) the price of a "pivotal" bond which pays a continuous coupon that is a simple exponential function of time. Essentially, the model utilises the observability of the stochastically changing term structure to capture the impact on instantaneous risk premia of term (as distinct form instantaneous) uncertainty in the aggregate consumption process. This impact is due to the intertemporal dependence, the term structure related component of the risk premium is shown to dominate the consumption driven term. This bond driven term is expressed independently of the utility functions of individuals. In the special case where aggregate consumption is assumed to be locally deterministic, yet discretely stochastic, which is broadly consistent with empirical evidence, the general result simplifies to a simple singlebeta form, with risk premia on all assets being proportional to their betas with the pivotal bond. This may provide a resolution of the "equity premium puzzle", as substantial risk premia can arise even in the absence of instantaneous uncertainty in aggregate consumption, as long as term uncertainty exists. In addition, a generalised "dividend discount" model for asset prices and an equilibrium evaluation of the riskfree rate are obtained.