Asset Pricing with Non-Geometric Type of Dividends

Abstract

This paper examines the behavior of the market equilibrium in an endowment economy in continuous time, in which a representative investor with exponential utility consumes the dividends generated by multiple risky assets. The dividends are assumed to be mutually independent and belong to a class of non-negative stochastic processes including square root processes, increasing Levy processes, and non-Gaussian OU processes. We then characterize expected returns and volatilities on the assets as well as interest rates. Based on these quantities, we construct the CAPM in an infinitesimal time period and investigate the impacts of dividend fluctuations and the risk aversion of the investor to the market equilibrium. It is shown that even if the dividends are independent, the asset returns may have strong positive correlations. Moreover, heterogeneous dividend processes generate Jensen's alpha that can be interpreted as the small cap premium.

Keywords: Lucas model, exponential utility, asset pricing, interest rate, Sharpe ratio, return correlation, Jensen's alpha, small cap premium

JEL Classification: G12, E43, D51