Blog Posts — February 7, 2022

Reverse stress testing: How to do it using only historical simulation data

Any risk manager knows that portfolio reverse stress testing can be a very powerful tool in a scenario analysis toolkit. And providing the answers to the following questions is the main function of a reverse stress test:

  • How badly could a portfolio get hurt?
  • What scenario would be responsible for such a loss?
  • What are the main risk drivers in this scenario?
  • How plausible would such a scenario be?

However, the biggest question that needs to be answered is: “How do you go about designing an efficient reverse stress test?” 

In our latest whitepaper, ‘Hands-on reverse stress testing’, we provide a practical guide to do just this by leveraging our enterprise management platform Axioma RiskTM, used to extract portfolio historical simulation data and factor returns.

Generally speaking, the workflow can be broken down into the following steps:  

  1. Extract the simulated returns and the factor returns of a portfolio.
  2. Selecting the most important factors by fitting a linear or convex model using Lasso regression techniques.
  3. Fit a Gaussian mixture to the factor returns selected.
  4. Search for the worst-case scenario given a plausibility level defined by the Mahalanobis distance. This distance is estimated with either one of the covariance matrices provided by the Gaussian mixture reflecting normal and stressed market conditions respectively.

In ‘Hands-on reverse stress testing,’ we begin by presenting seven different use cases across equities, rates, credit, commodity and FX strategies spanning both linear and convex portfolios. Next, we review the methods used to find optimal scenarios for both linear and nonlinear portfolios, followed by how to fit a Gaussian mixture to a set of factor returns. We cover in detail different types of Lasso-based regressions techniques used to provide a parsimonious factor representation of the portfolio. Finally, we run the reverse stress tests on the original set of use cases.

Using this framework gives a risk manager unique insight to share with her portfolio manager. It helps him/her identify the key risk factors and contributions that could hurt a given portfolio under normal and stressed market conditions. Those same key factors can then be used in a more traditional correlated stress test to further analyze and confirm the results. Importantly, this approach can be applied to a granular risk resolution or by using factors that can demonstrate potential unintended systematic bets.

Download the whitepaper here.