Stress testing correlation matrices for risk management

Evaluating portfolio risk typically requires that correlation estimates of security returns be made. Historical financial events have shown that correlations can rise quickly, causing a huge increase in portfolio risk. Therefore, in stress testing portfolios, it is important to consider the influence of a sudden surge in selected correlations. Standard correlation stress testing mechanisms require us to change the selected correlations to designated values. However, the correlation matrix may become non-positive definite after some of its entries are altered. This paper proposes a blocking method by which an existing correlation matrix can be converted to incorporate change while keeping the matrix positive definite. In comparison with existing methods that usually only achieve semi-positive definiteness, the proposed method outperforms in the revised elements, while the approximation error of the non-revised elements is maintained within acceptable levels. Simulations show that our method is efficient and performs well for dimensions of 100, 500 and 1000. Our method is also shown to be more reliable in stress testing higher dimension correlation matrices. Information on the performance of the blocking method using a high-dimensional real data is also provided.