Computing equilibrium prices for a capital asset pricing model with heterogeneous beliefs and margin-requirement constraints

Abstract

The mean-variance capital asset pricing model (CAPM) is a useful mathematical tool for studying a variety of financial problems. In contrast to existing work in the literature, which has primarily focused on deriving analytical solutions under restrictive assumptions, we propose a numerical algorithm for efficiently computing the set of equilibrium prices of a CAPM model with heterogeneous investors and arbitrary margin requirements. We present the mathematical formulation of the CAPM model, derive structural properties of the portfolio selection and excess demand functions, and establish the asymptotic convergence of the proposed algorithm under mild conditions. To illustrate the utility of the algorithm, we perform sensitivity analysis on a simple example to study the impact of marginal requirements and interest rates on the resulting equilibrium prices. Numerical studies are also carried out to compare the performance of the algorithm with that of two other popular methods, namely, the fixed point method and the brand-and-bound algorithm.