Risk factor aggregation and stress testing

Abstract

Stress testing refers to the application of adverse financial or macroeconomic scenarios to a portfolio. For this purpose, financial or macroeconomic risk factors are linked with asset returns, typically via a factor model. We expand the range of risk factors by adapting dimension-reduction techniques from unsupervised learning, namely PCA and autoencoders. This results in aggregated risk factors, encompassing a global factor, factors representing broad geographical regions, and factors specific to cyclical and defensive industries. As the adapted PCA and autoencoders provide an interpretation of the latent factors, this methodology is also valuable in other areas where dimension-reduction and explainability are critical.

Keywords:

• Factor model
• Principal component analysis
• Autoencoder
• (Explainable) machine learning
• Financial stress testing

JEL Classifications:

• C53
• C63
• G17

Acknowledgments

I would like to thank two anonymous referees for suggestions that have helped improve the paper. I would also like to thank student assistants Marie Bernière and Lukas Schimpf.

Data availability statement

The data used is provided through Refinitiv Eikon and cannot be made available by the author. Readers interested in the Mathematica code should contact the author by email.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Regulators require financial institutions to conduct stress tests, see e.g. the European Capital Requirements Regulation (CRR), Article 290: ‘[The stress testing programme for CCR (credit counterparty risk)] shall provide for at least monthly exposure stress testing of principal market risk factors such as interest rates, FX, equities, credit spreads, and commodity prices for all counterparties of the institution, in order to identify, and enable the institution when necessary to reduce outsized concentrations in specific directional risks.’ and ‘It shall apply at least quarterly multifactor stress testing scenarios and assess material non-directional risks including yield curve exposure and basis risks. Multiple-factor stress tests shall, at a minimum, address the following scenarios in which the following occurs: (a) severe economic or market events have occurred; …’. See https://www.eba.europa.eu/regulation-and-policy/single-rulebook/interactive-single-rulebook/12240. See also EBA (2021a) for details on regulatory requirements of stress testing.

2 Some strands of the literature (e.g. Kent et al. 1979) call the correlations between data and scores loadings, while other authors (e.g. James et al. 2013) call ${\varphi }_{\mathrm{ji}}$, $i=1,\dots ,d$, $j=1,\dots ,d$, loadings. We stick with the latter.

3 In order to use longer time series and include young firms, one could attempt to replace the missing data with synthetic data, which is a popular technique in machine learning, when the training data set is too small (see e.g. Ni et al. 2021, Dogariu et al. 2022, Freeborough and van Zyl 2022, Park et al. 2022).

Additional information

Funding

This research was supported by IFAF Berlin (Institut für angewandte Forschung Berlin e.V.) under the IFAF Explorativ scheme.