Data for: 3673362

Excel Workbook Implementation Targeted Stress: In practice, risk measurement of the majority of enterprise-level portfolios, and even many investment portfolios, requires stressing the correlation matrix directly, rather than (solely) stressing its underlying variables, due to 1. data paucity or incomplete time series, 2. matrices where at least some of the values are based on subject-matter expertise, and/or 3. the need to specify and test the effects of correlation values nowhere close to those reflected in historical data (i.e. the majority of extreme scenarios used in forward-looking stress testing). Surprisingly few papers in the literature address this common, real-world situation, and their approaches arguably are either ad-hoc, lack solid statistical underpinnings, do not allow for direct, probability-based stressing, and/or remain non-robust as they fail under empirically challenging conditions (e.g. near-zero eigenvalues resulting from the need to first enforce positive definiteness of the matrix). We borrow from recent advances in the literature for generating random correlation matrices (based on the identity matrix) to design a method that both mitigates and eliminates these drawbacks when directly stressing real-world correlation matrices (other than the identity matrix). Our approach can be used for both generalized and targeted stressing. The former perturbs the entire correlation matrix, which can be used to account for difficult-to-model or difficult-to-anticipate second and third order effects of extreme scenarios, as well as providing much needed percentiles of the distribution of the entire matrix. Targeted stressing, on the other hand, allows for particular correlation values to be changed by specified amounts based directly on the probability of observing such changes due to the event/scenario. And both generalized and targeted stressing can be performed concurrently, based on the same proposed approach, which provides full probabilistic control while automatically enforcing positive definiteness. We demonstrate the method on realistic, reasonably large matrices (100x100) that have had positive definiteness enforced via Higham (2002), reflecting a common occurrence for most enterprise-level portfolios and even many investment portfolios. Although it requires numeric integration for all but very small matrices, our approach’s runtimes are comparable to those of competing methods. Implementation is straightforward, and results robustly outperform existing methods in the literature, especially when matrices are empirically challenging (e.g. near-zero eigenvalues).