Content area
Abstract
To perform risk and portfolio management, the authors must represent the distribution of the risk factors that affect the market. The most flexible approach is in terms of scenarios and their probabilities, which includes historical scenarios, pure Monte Carlo and importance sampling. Here, they present a simple method to generate scenarios from elliptical distributions with given sample means and covariances. This is very important in applications such as mean-variance portfolio optimization, which are heavily affected by incorrect representations of the first two moments. Risk managers can now proceed to stress test the correlation C using the Cholesky decomposition of the new stress-test matrix and the J x 2I panel Y of uncorrelated standard normal simulations in the above process. Then they can analyze the impact of the stress test on a risk report, confident that the stress-test assumptions will be faithfully reflected in the simulations.