Modeling Returns Generating Processes and Tests of the APT

Two approaches to the multi-factor modeling of security returns are evaluated. In the first, a variance/covariance matrix of security returns and macroeconomic factors is assembled and decomposed. Factors are generated through this algebraic decomposition and are thus unspecified. In the second, a macroeconomic variable model is proposed and a linear model estimating security returns as a function of innovations in the macroeconomic variables is developed. The factors are defined as the innovations in the macroeconomic variables. Tests of the Arbitrage Pricing Theory (APT) using the factor analytic and macroeconomic variable models are examined. An evaluation of the ability of the APT to model expected returns is conducted. Given certain disadvantages of the factor analytic approach and the intuitive appeal of the macroeconomic variable model, this second approach is favored.