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Regress under stress: A simple least-squares method for integrating economic scenarios with risk simulations


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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, and more generally the full conditional distribution of all the factors, and of the portfolio profit and loss (P&L), can be estimated directly from a pre-computed simulation using least squares regression. 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 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 co-dependence structures, autocorrelation, etc. LSST further produces explicit risk factor P&L contributions. We demonstrate the methodology in detail with the practical example of a multi-asset investment portfolio and economic scenarios from an industry report.
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Keywords: conditional simulation; linear regression; risk contributions; risk management; scenario generation; stress testing

Document Type: Research Article

Publication date: October 1, 2016

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  • Journal of Risk Management in Financial Institutions is the essential professional and research journal for all those involved in the management of risk at retail and investment banks, investment managers, broker-dealers, hedge funds, exchanges, central banks, financial regulators and depositories, as well as service providers, advisers, researchers and academics. Guided by expert Editors and an eminent Editorial Board, each quarterly 100-page issue does not publish advertising but rather in-depth articles, reviews and applied research by leading professionals and researchers in the field on six key inter-related areas: strategic and business risk, financial risk, including traditional/exotic credit, market and liquidity risks, operational risk, regulatory and legal risks, systemic risk, and sovereign risk.

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