Risk, Return, and Equilibrium: A General Single Period Theory of Assest Selection and Capital Market Equilibrium

Uncertainty is a major concern in financial decision-making. Financial theory contains a number of conceptual frameworks that treat the effects of uncertainty; yet no one has attempted to put forth a general treatment of portfolio risk. This book fills the theoretical gap by developing a general measure of portfolio risk and formulating a general model of asset selection in the context of market equilibrium. The author seeks to define and elucidate theoretical issues through rigorous, quantitative arguments; and critical evaluation of the basic assumptions of the model.

Stone summarizes relevant aspects of the Markowitz theory of portfolio selection and presents a brief overview of the Sharpe, Lintner, and Mossin models in which asset selections are based on two parameters of choice—either mean return and variance, or mean return and standard deviation. He then generalizes these models to objective functions that are still functions of two parameters—expected return (or expected wealth), and a general measure of risk. Stone introduces a new global measure of risk, relating it to existing work in the theory of risk, and presents and compares two alternative risk-return representations of expected utility: the Generalized Markowitz Criterion (GMC) and the Two-Parameter Functional Representation (TPFR). The author provides a general analysis of asset selection and market equilibrium and examines the GMC and TPFR in greater detail. Finally, he investigates existing models of capital market equilibrium formulated by Sharpe, Lintner, and Mossin, and analyzes these models according to the previously developed general model.

Mathematical analysis and logical reasoning are the basic methodological tools used in this work. The author has, however, taken care to present proofs and derivations in sufficient detail to make them easy to follow at a graduate level. Students of economics and finance (particularly those in advanced courses dealing with risk, asset selection, or capital markets) and professionals in the field will find the book rich in constructive new theoretical material.