Risk Aversion and Optimal Portfolio Policies in Partial and General Equilibrium Economies

Abstract

In this article, we examine analytically the optimal consumption and portfolio policies in an economy with incomplete financial markets where agents have power utility over intermediate consumption and bequest, and face portfolio constraints and a stochastic investment opportunity set. The source of changes in the investment opportunity set could be a stochastic instantaneous interest rate, stochastic volatility, and/or a stochastic risk premium. We find analytically the conditions under which investment in the risky asset can increase with risk aversion. We then nest this portfolio problem in a general equilibrium setting (for a production economy and also for an exchange economy) with multiple agents who differ in their degree of risk aversion. We derive the optimal portfolio policies when the evolution of the investment opportunity set is determined endogenously and also characterize explicitly the interest rate, stock price and risk premium in general equilibrium. The exact local comparative statics and approximate but analytical expressions for the optimal policies are obtained by developing a method based on perturbation analysis to expand around the solution for an investor with log utility.

Keywords: Asset allocation, stochastic investment opportunities, incomplete markets, borrowing constraints, asymptotic analysis

JEL Classification: G12, G11, D52, C63