A Dynamic Equilibrium for the Ross Arbitrage Model.

The structure of security returns has been an object of constant attention in the financial economics literature. Several stochastic models for security returns have been proposed, and many of these subjected to strenuous empirical testing. Yet theory demands closure: security returns do not exist in isolation, but are intimately interconnected to all the other features of an economy in equilibrium. Of concern are the consistency of contemporaneous features, such as interest rates and prices, and importantly the dynamic characteristics, i.e., whether equilibrium is sustained over a multiperiod environment. In this paper, we develop a consistent, dynamic equilibrium for the Ross arbitrage model of capital asset pricing. Our objective is to develop a multi-period model which is consistent with the Ross K-factor linear return generating process and its associated single-period equilibrium. Section 2 of the paper gives the initial description of the Ross model. In section 3 we construct a dynamic equilibrium. The state space is given by current dividends and these in turn are mapped into current prices. Section 4 demonstrates that additional state variables of an "informational" nature can also be introduced without damaging the essential structure of equilibrium. Several of the points developed herein are also discussed in Garman and Ohlson where the focus centers on valuation in arbitrage-free markets generally; here we concentrate purely on the dynamic equilibrium nature of the Ross model in particular. [ABSTRACT FROM AUTHOR]