An investigation of hypothetical variance-covariance matrix stress-testing

Attempting to put meaningful numbers to portfolio risks is challenging. Conventional risk measures are considered often not to fully capture all risks inherent in a portfolio, particularly under difficult market conditions. Under such conditions stress-testing against artificial scenarios may help identify and quantify risks within a portfolio. Stress-tests also help reassure a portfolio or risk manager as to how a portfolio might respond to specific concerns. This paper investigates an example of stress-testing a portfolio of conventional assets against market risks using artificial scenarios based around changes to the portfolio variance-covariance matrix. Hypothetical variance-covariance matrix stress-tests include making changes to correlations between assets to explore impacts on portfolio risks. Portfolio correlations, however, cannot be changed arbitrarily to reflect a risk manager’s concerns without running the risk of implausible stressed returns and variance-covariance matrices that are not positive semi-definite. Different methods have been proposed in the literature to overcome this. This paper applies two such methods to a portfolio of four assets with the aim of illustrating the processes involved as well as drawing out differences in the approaches, enabling a discussion of their strengths and weaknesses.