1 . Bayesian Network Models of Portfolio Risk and Return

A Bayesian network is a tool for modeling large multivariate probability models and for making inferences from such models. A Bayesian network combines traditional quantitative analysis with expert judgement in an intuitive, graphical representation. In this paper, we show how to use Bayesian networks to model portfolio risk and return. Traditional financial models emphasize the historical relationship between portfolio return and market return. In practice, to forecast portfolio return, financial analysts include expert subjective judgement about other factors that may affect the portfolio. These judgmental factors include special knowledge about the stocks in the portfolio that is not captured in the historical quantitative analysis. We show how a Bayesian network can be used to represent a traditional financial model of portfolio return. Then we show how expert subjective judgement can be included in the Bayesian network model. The output of the model is the posterior marginal probability distribution of the portfolio return. This posterior return distribution can be used to obtain expected return, return variance, and value-at-risk.