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

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