Regress Under Stress: A Simple Least-Squares Method for Integrating Economic Scenarios with Risk Simulations

Abstract

Scenarios are the language of Risk. While scenario analysis and stress testing have been an explicit part of risk management methodologies and systems for over two decades, the typical scenario and stress testing tools haven’t evolved much and are still generally quite static and largely subjective. In this paper, we present a simple and powerful approach to create meaningful stress scenarios for risk management and investment analysis of multi-asset portfolios, which effectively combines economic forecasts and “expert” views with portfolio simulation methods.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 factors that affect the portfolio. We need to understand how these market risk factors behave, conditional on the outcome of the economic factors. The key insight to our approach is that the conditional expectation, or 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 Regressions (LSR). All the conditional scenario analytics can be derived from the regression results. We refer to this approach as Least Squares Stress Testing (LSST). 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 a large number of risk factors, which can follow completely general joint stochastic processes, with fat-tails, non-parametric and general codependence structures, autocorrelation, etc. LSST further produces explicit risk factor P&L contributions.We illustrate the application of the methodology through the analysis of the performance of a real-life portfolio under recent economic research reports.