Equilibrium in Securities Markets with Heterogeneous Investors and Unspanned Income Risk

Abstract

In a finite time horizon, incomplete market, continuous-time setting with dividends and investor incomes governed by arithmetic Brownian motions, we derive closed-form solutions for the equilibrium risk-free rate and stock price for an economy with a finite set of heterogeneous CARA investors and unspanned income risk. In equilibrium, the Sharpe ratio is the same as in an otherwise identical complete market economy, whereas the risk-free rate is lower and, consequently, the stock price is higher. The reduction in the risk-free rate is highest when the more risk-averse investors face the largest unspanned income risk. In numerical examples with reasonable parameters, the risk-free rate is reduced by several percentage points.

Keywords: Unspanned income, heterogeneous preferences, continuous-time equilibrium, risk-free rate puzzle, equity premium, incomplete markets, Brownian motion

JEL Classification: G12, G11, D53