Regulatory and expert scenarios are typically described in terms of a small number of key economic variables or factors. However, when applied to a portfolio, they are incomplete – they generally do not describe what occurs to all relevant market risk and credit risk factors that affect a portfolio. We need to understand how these risk factors behave, conditional on the outcome of the economic factors, and the map this to portfolio losses. We introduce a new approach called Least Squares Stress Testing (LSST). The key insight is that the conditional expectation, and more generally the full conditional distribution of all the factors, and of the portfolio P&L, can be estimated directly from a pre-computed simulation using Least Squares Regression. LSST is a simulation-based conditional scenario generation method that offers many advantages over more traditional analytical methods. Simulation techniques are simple, flexible, and provide very transparent results, which are auditable and easy to explain. LSST can be applied to both market and credit risk stress testing with a large number of risk factors, which can follow completely general stochastic processes, with fat-tails, non-parametric and general codependence structures, autocorrelation, etc. LSST further produces explicit risk factor P&L contributions. From a methodology perspective, we also discuss some of the assumptions the LSST approach, statistical tests to check when these assumptions fail, and remedies that can be applied.
Dan Rosen is currently a Visiting Researcher and the first Director of the Centre for Financial Industries at the Fields Institute for Research in Mathematical Sciences, as well as an Adjunct Professor of Mathematical Finance at the University of Toronto. Dr. Rosen was the co-founder and Chief Executive Officer of R2 Financial Technologies. A successful Risk and Portfolio Management Technology firm serving multi-asset hedge funds, asset managers, banks and regulators across the world, R2 was originally incubated at the Fields Institute, and then acquired by S&P Capital IQ in 2012, where Dr. Rosen served as the Managing Director for Risk and Analytics until 2015.
He holds an M.A.Sc. and PhD. in Chemical Engineering from the University of Toronto, and was a Post-Doctoral fellow and Research Associate at the Centre for Management of Technology and Entrepreneurship (CMTE). His B.A.Sc. is in Chemical Engineering from the Universidad Autonoma Metropolitana in Mexico City, where he was also later awarded in 2015 the recognition of Distinguished Alumni.