Research

You can find links to our publicly available research articles below. The accompanied code is usually given by examples that use our open-source software. Please visit our open-source site for more information about how to install our open-source Python package and documentation of its functionality.

Variance for Intuition, CVaR for Optimization

Abstract: This article presents some of the pros and cons of variance and CVaR as portfolio risk measures in mean-risk optimization. While variance is the original risk measure, thoroughly studied for the past 70 years, this article argues that there are practically no reasons for continuing to use variance instead of CVaR in mean-risk optimization. However, there are several reasons for using CVaR instead of variance. Nonetheless, mean-variance can be a useful tool for illustrating fundamental investment concepts and principles. The case study illustrates that mean-variance and mean-CVaR optimization converge to the same results when demeaned Gaussian P&L is used in CVaR optimization. Hence, contrary to what seems to be the current industry standard, it is recommended to use demeaned P&L for CVaR optimization.

Keywords: Portfolio optimization, mean-variance, mean-CVaR, Monte Carlo simulation, synthetic market data generator, tail risks, convex optimization, Python Programming Language.

Link: https://ssrn.com/abstract=4034316

Sequential Entropy Pooling Heuristics

Abstract: This article introduces two sequential heuristics that are designed to overcome some of the practical limitations of the Entropy Pooling (EP) method. Both of these heuristics repeatedly apply the original EP method to sequentially arrive at the posterior probability and usually lead to significantly better solutions than a simple application of the original approach. In some cases, the sequential heuristics coincide with the original approach, while they help to automatically ensure logical consistency in others. Given the benefits of the sequential heuristics, this article argues that they should become the standard for future EP applications.

Keywords: Entropy Pooling, relative entropy, Kullback-Leibler divergence, change of measure, market views, stress-tests, Monte Carlo simulation, nonlinear convex optimization, heuristic algorithms, Python Programming Language.

Link: https://ssrn.com/abstract=3936392