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

In this article, we show how to analyse analytically the equilibrium policies and prices in an economy with a stochastic investment opportunity set and incomplete financial markets, when agents have power utility over both intermediate consumption and terminal wealth, and face portfolio constraints. The exact local comparative statistics and approximate but analytical expression for the portfolio policy and asset prices are obtained by developing a method based on perturbation analysis to expand around the solution for an investor with log utility. We then use this method to study a general equilibrium exchange economy with multiple agents who differ in their degree of risk aversion and face borrowing constraints. We characterize explicitly the consumption and portfolio policies and also the properties of asset returns. We find that the volatility of stock returns increases with the cross-sectional dispersion of risk aversion, with the cross-sectional dispersion in portfolio holdings, and with the relaxation of the constraint on borrowing. Moreover, tightening the borrowing constraint lowers the risk-free interest rate and raises the equity premium in equilibrium.