Asset pricing with observable stochastic discount factors

The stochastic discount factor model provides a general framework for pricing assets. By specifying the discount factor suitably it encompasses most of the theories currently in use, including CAPM and consumption CAPM. The SDF model has been based on the use of single and multiple factors, and on latent and observed factors. In most situations, and especially for the term structure, single factor models are inappropriate, whilst latent variables require the somewhat arbitrary specification of generating processes and are difficult to interpret. In this paper we survey the principal different implementations of the SDF model for bonds, equity and FOREX and propose a new approach. This is based on the use of multiple factors that are observable and modelling the joint distribution of excess returns and the factors using a multi–variate GARCH–in–mean process. We argue that in general single equation and VAR models, although widely used in empirical finance, are inappropriate as they do not satisfy the no–arbitrage condition. Since risk premia arise from conditional covariation between the returns and the factors, both a multi–variate context and having conditional covariances in the conditional mean process, is essential. We explain how apparent exceptions, such as the CIR and Vasicek models, in fact meet this requirement — but at a price. We explain our new approach, discuss how it might be implemented and present some empirical evidence, mainly from our own researches. Partly, to enable comparisons to be made, the survey also includes evidence from recent empirical work using more traditional approaches.