Manipulating Valid Correlation Matrices

Abstract

Correlations play an important role in the construction of investment portfolios. In this research note, we explain why the manipulation of a valid correlation matrix is challenging. We also propose three methods to perform the following tasks: 1) Increase all correlations such that they converge to one in the limit. This method can be used to model unexpected high correlation values (for example, in a system crisis as experienced just recently). 2) Decrease correlations such that they shrink to zero or a minimum correlation. This procedure is needed to analyze hedged portfolios or, more generally formulated, absolute return strategies. 3) Change individual correlation values. Many times, analysts have a need to change an individual correlation to a certain value or in a certain direction. As we will see, this method is also a starting point to generate random correlations.

Keywords: Portfolio, Diversification, Risk, Correlation, Stress Test, Scenario Analysis, Matrix