# Examples

Jupyter Notebook examples are available in the fortitudo.tech GitHub repository. The repository contains the following examples:

How to combine CVaR optimization with Entropy Pooling views / stress-tests

A replication of the results from Vorobets [2021] for the original Entropy Pooling heuristic and a separate bonus sequential Entropy Pooling example using the H1 heuristic to implement views on S&P 500 and STOXX 50 mean and volatility

The accompanied code for Vorobets [2022] with a comparison of mean-CVaR and mean-variance optimization explaining why we use demeaned CVaR as default (it’s not recommended to run this example with 1,000,000 scenarios on Binder, see the comments below)

An illustration of how to work with the time series simulation that follows with this package

The accompanied code for Vorobets [2022] with an example of how to use the relative market values \(v\) parameter for portfolio optimization

How to use the exponential decay simulation / P&L modeling functionality with historical time series for FAANG stocks

How to use the time series simulation for risk factor and P&L simulation and combine this with Entropy Pooling views on risk factors

The accompanied code for Vorobets [2023] illustrating how Bayesian networks can be used in combination with Entropy Pooling for causal and predictive market views and stress-testing

The accompanied code for Kristensen and Vorobets [2024], illustrating the effect of parameter uncertainty and introducing Exposure Stacking.

The accompanied code for Vorobets [2024], illustrating how to optimize derivative portfolios using Entropy Pooling and Expsoure Stacking.

See this YouTube playlist for a walkthrough of the package’s functionality and examples. The examples are good places to start exploring the functionality of this package. We have very limited resources for support in relation to these, but please let us know if you have suggestions for how we can improve them and make them easier to understand.

For a high-level introduction to the investment framework, see this YouTube video and Medium article. For an in-depth mathematical introduction to the investment framework, see these SSRN articles.

For a careful and pedagogical presentation of the investment framework, see the Portfolio Construction and Risk Management Book crowdfunding campaign.

You can explore the examples in the cloud without any local installations using Binder. However, note that Binder servers have very limited resources and might not support some of the optimized routines this package uses. If you want access to a stable and optimized environment with persistent storage, please subscribe to our Data Science Server.