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) and refined by Vorobets (2021) with an introduction of Sequential Entropy Pooling (SeqEP).
For a detailed and pedagogical walkthrough of (almost) everything there is to know about Entropy Pooling, see the Portfolio Construction and Risk Management book.
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) model. 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 code, 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 here and the code for the second video here.
Entropy Pooling and CVaR optimization
Entropy Pooling integrates elegantly with CVaR optimization, 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 optimization.
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).
Everything you need to know about Entropy Pooling
Entropy Pooling can also be used for high-dimensional market simulation through the new Fully Flexible Resampling method. Details about this approach and much more can be found in the Portfolio Construction and Risk Management book as well as the Time- and State-Dependent Resampling article.
The Portfolio Construction and Risk Management book contains the most complete and cohesive presentation of Entropy Pooling and all its subtle nuances.