A GENERAL EQUILIBRIUM THEORY OF ASSET PRICES, WITH APPLICATIONS TO THE THEORY OF THE TERM STRUCTURE OF INTEREST RATES

Abstract

THE FIRST PART of this thesis presents a detailed general-equilibrium solution to the portfolio-allocation problem, based on Stone's synthesis of the portfolio models of Tobin, Sharpe, Lintner, and Mossin. The thesis shows that Stone's contribution revolves around introducing utility functions of the Lancaster type, i.e., utility functions whose arguments are a set of characteristics derived from the set of goods demanded by the consumer. Stone applies this approach to portfolio allocation by an investor limiting the characteristics to risk and return in his two-parameter functional representation or TPFR. It has been argued that the consumer and investor have different types of utility functions, the former's having quantities of consumption goods as its arguments and the latter's depending on parameters such as risk and return derived from the portfolio held. By formally establishing the correspondence between Stone's work and Lancaster's we show that the investor's demand for securities and the consumer's demand for consumption goods both result from maximizing utility as a function of characteristics and have the same mathematical structure. Placing Stone's synthesis of portfolio models in the Lancaster framework suggests interesting extensions of the TPFR. Our approach to these extensions draws on a contribution by Bierwag and Grove who argued that as long as portfolios are limited to financial assets, for every asset there must be an offsetting liability in the portfolio of another individual, so that the total amount of each asset outstanding sums to zero. This approach, as opposed to that of Tobin, Sharpe, Lintner, Mossin, and Stone, produces several interesting results. The extended TPFR is solved for explicit equations of security demand bringing the model a step closer to a form suitable for empirical applications. Demand for a security depends on the investor's marginal rate of substitution of risk for return and on two parameters of his subjective probability distribution on future security prices: the mean (expected future price) and some measure of dispersion of possible outcomes (confidence in expectations), not necessarily variance. We go on to investigate the implications of assuming that all investors hold identical subjective probability distributions on future prices (homogeneous expectations or perfect agreement) and show that it leads to zero demand for all risky assets in this type of model, as Bierwag and Grove were the first to demonstrate. The model reproduces their result in a more general context; we do not assume any specific utility function. We conclude that if homogeneous expectations prevail, there must be some real assets in the model, i.e., assets which are not offset by liabilities, if anyone is to hold risky assets in equilibrium. The second part of the thesis develops the extended TPFR into a model explaining the term structure of interest rates, recasting the list of variables from one-period securities into multi-period bonds and introducing real assets (consumer durables) into the investor's portfolio. We use this model to study the micro-economic basis