A Two State Capital Asset Pricing Model

A famous model in nancial theory is the Capital Asset Pricing Model (CAPM). In this paper we propose a two state CAPM in which we assume that excess returns for the market and for a particular security are bivariate normally distributed. The parameters of the distribution are determined by the state of an unobserved stationary Markov chain. Two states represent two business regimes that are characterized by low and high volatility. Maximum likelihood estimates for the parameters of the model are obtained via the Baum-Welch algorithm for local maximization of the likelihood function for Markov Regime Models (MRM), also known as Hidden Markov Models (HMM). We apply the model to monthly return data for three oil industry corporation securities. A comparison of the results with two simpler models, the independent switching regression model and the standard CAPM with one regime, shows a signi cant improvement in goodness of t obtained by the proposed two state MRM. Estimates of the periods of high volatility for each corporation depict a general e ect of the business cycles on all three processes combined with unique e ects steaming from corporation related events.