Abstract
This paper examines the behavior of the market equilibrium in an endowment economy in continuous time setting, in which a representative investor with exponential utility consumes the dividends generated by multiple risky assets. The dividends of the assets are assumed to be mutually independent and belong to a class of non-negative stochastic processes including square root processes and increasing Lévy processes. We then characterize expected returns and volatilities on the assets as well as interest rates which is defined by risk-free assets. Based on these quantities, we construct the capital asset pricing model in an infinitesimal time period and investigate the impacts of dividend fluctuations and the risk aversion of the investor to the market equilibrium. Numerical examples show 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 viewed as the small cap premium.
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