Estimation and Stress-Testing via Time- and Market-Conditional Flexible Probabilities

12 Pages Posted: 19 Aug 2013 Last revised: 1 Jan 2014

See all articles by Attilio Meucci

Attilio Meucci

ARPM - Advanced Risk and Portfolio Management

Date Written: December 31, 2013

Abstract

In the Flexible Probabilities approach, given the historical distribution (histogram) of the returns of a portfolio, we can stress-test the portfolio under different time periods and market environments, by adjusting the relative weights (Flexible Probabilities) of the historical returns in the histogram.

This paper presents a detailed description of how to specify the Flexible Probabilities to perform the above stress-tests.

First, we discuss Time-Conditional Flexible Probabilities, which generalize the well-known GARCH-like exponential smoothing of the covariance matrix, and Market-Conditional Flexible Probabilities, which generalize the non-parametric technique known as kernel smoothing. Next, we discuss how to blend time conditioning and market conditioning via Entropy Pooling.

Finally, we show how to specify a whole set of Flexible Probabilities, each with a different weight. The ensuing ensemble of Flexible Probabilities allows us to perform distributional stress-testing of our portfolio.

Fully documented code is available for download.

Keywords: Effective number of scenarios, crisp conditioning, kernel conditioning, ensemble, historical scenarios, full-repricing, exponential smoothing, exponential kernel, Gaussian kernel, Bhattacharyya coefficient, Hellinger distance, UPGMA

JEL Classification: C1, G11

Suggested Citation

Meucci, Attilio, Estimation and Stress-Testing via Time- and Market-Conditional Flexible Probabilities (December 31, 2013). Available at SSRN: https://ssrn.com/abstract=2312126 or http://dx.doi.org/10.2139/ssrn.2312126

Attilio Meucci (Contact Author)

ARPM - Advanced Risk and Portfolio Management ( email )

HOME PAGE: http://www.arpm.co/

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