Stress testing correlation matrix: a maximum empirical likelihood approach

ABSTRACT

Stress testing correlation matrix is a challenging exercise for portfolio risk management. Most existing methods directly modify the estimated correlation matrix to satisfy stress conditions while maintaining positive semidefiniteness. The focus lies on technical optimization issues but the resultant stressed correlation matrices usually lack statistical interpretations. In this article, we suggest a novel approach using Empirical Likelihood method to modify the probability weights of sample observations to construct a stressed correlation matrix. The resultant correlations correspond to a stress scenario that is nearest to the observed scenario in a Kullback–Leibler divergence sense. Besides providing a clearer statistical interpretation, the proposed method is non-parametric in distribution, simple in computation and free from subjective tunings. We illustrate the method through an application to a portfolio of international assets.