The Magical Mystery Matrix

The Choleski factor matrix has been well known for many years; it is a triangular matrix that satisfies the condition that the factor matrix multiplied by its transpose is equal to a symmetric matrix. The concept has been used since the early 1980'g to generate asset returns with specified means and covariances. This paper develops some new uses of the factor matrix, including modeling serial correlation, adding asset classes with contingent returns, adjusting preliminary results to final targets and adjusting large, "unfactorable" matrices. Two appendices illustrate a numerical example and include listings of APL2/PC functions that implement the methodology.