Entropy Pooling Collection
Entropy Pooling Collection
This article collects public resources related to the Entropy Pooling market views and stress-testing method.
Entropy Pooling (EP) is a very powerful method for implementing market views and stress-testing fully general return, price, and risk factors distributions. It was first introduced by Meucci (2008)1 and refined by Vorobets (2021)2 with an introduction of Sequential Entropy Pooling (SeqEP).
For a detailed and pedagogical walkthrough of (almost) everything there is to know about Entropy Pooling, you can get access to the Portfolio Construction and Risk Management book3.
Most people are still quite unfamiliar with Entropy Pooling, but it is being adopted at an accelerating rate among sophisticated institutional investors. You can loosely think about Entropy Pooling as a method that fixes the many deficiencies of the Black-Litterman (BL) model4. In reality, Entropy Pooling is much more than that, so the comparison with the BL model does not do it justice.
This article collects public references about the Entropy Pooling method, including scientific articles, videos, Python code5, and Substack posts.
Entropy Pooling Intuition
The video below gives you an explanation of the Entropy Pooling intuition.
Sequential Entropy Pooling refinement
While the original Entropy Pooling approach is powerful, certainly much more than the Black-Litterman model, it becomes significantly better and much more practically relevant if you use it in a clever sequential way. The sequential algorithms were introduced by Vorobets (2021) and usually give us much better results in addition to being capable of solving practically relevant problems that the original approach simply cannot.
The videos below give a walkthrough of the sequential algorithms’ theory and code. You can find the code for the first video here6 and the code for the second video here7.
Entropy Pooling and CVaR optimization
Entropy Pooling integrates elegantly with CVaR optimization8, because the two methods operate on the same market representation consisting of a Monte Carlo simulation R with associated joint scenario probability vector p.
The videos below show how you can use Entropy Pooling in combination with CVaR optimization of a derivatives portfolio as well as incorporate resampled parameter uncertainty into the portfolio optimization9.
An elegant feature of Entropy Pooling is that it implements views and stress-tests in a predictive way that introduces the least amount of spuriousness. Hence, we automatically get consistent derivatives P&L when we implement views and stress-tests for the underlying or other risk factors.
Causal and Predictive Framework
Entropy Pooling can be combined with a Bayesian network on top for causal and predictive analysis. The video below gives a presentation of this framework, which was introduced by Vorobets (2023)10.
Everything you need to know about Entropy Pooling
Entropy Pooling can also be used for market simulation through the new Fully Flexible Resampling approach. Details about this approach and much more can be found in the Portfolio Construction and Risk Management book, which generally gives a very pedagogical presentation of almost everything there is to know about Entropy Pooling, and how it integrates with various analysis and optimization methods. Watch the video below for information on how you get access to the book and accompanying Python code, what its current status is, and what you can expect in the future.
Meucci, Attilio, Fully Flexible Views: Theory and Practice, Risk, Vol. 21, №10, pp. 97–102, October 2008, Available at SSRN: https://ssrn.com/abstract=1213325
Vorobets, Anton, Sequential Entropy Pooling Heuristics (October 5, 2021). Available at SSRN: https://ssrn.com/abstract=3936392
Portfolio Construction and Risk Management book crowdfunding: https://igg.me/at/pcrm-book
Entropy Pooling vs Black-Litterman Substack post: https://antonvorobets.substack.com/p/entropy-pooling-vs-black-litterman-abb608b810cd
fortitudo.tech Python package: https://github.com/fortitudo-tech/fortitudo.tech
Sequential Entropy Pooling Python example: https://github.com/fortitudo-tech/fortitudo.tech/blob/main/examples/2_SequentialEntropyPooling.ipynb
Sequential Entropy Pooling Heuristics accompanying Python code: https://github.com/fortitudo-tech/fortitudo.tech/blob/main/examples/2_EntropyPooling.ipynb
Entropy Pooling and CVaR Portfolio Optimization in Python Substack post: https://antonvorobets.substack.com/p/entropy-pooling-and-cvar-portfolio-optimization-in-python-ffed736a8347
Portfolio Optimization and Parameter Uncertainty Substack post: https://antonvorobets.substack.com/p/portfolio-optimization-and-parameter
Vorobets, Anton, Causal and Predictive Market Views and Stress-Testing: https://ssrn.com/abstract=4444291