Portfolio Analysis with Factors and Scenarios

Recently there has been a growing interest in the scenario model of covariance as an alternative to the one-factor or many-factor models. We show how the covariance matrix resulting from the scenario model can easily be made diagonal by adding new variables linearly related to the amounts invested; note the meanings of these new variables; note how portfolio variance divides itself into “within scenario” and “between scenario” variances; and extend the results to models in which scenarios and factors both appear where factor distributions and effects may or may not be scenario sensitive.