CVaR optimization benchmark problems

This repository contains Conditional Value-at-Risk (CVaR) portfolio optimization benchmark problems for fully general Monte Carlo distributions and derivatives portfolios.

The starting point is the Fully General Investment Framework (FGIF) market representation given by the matrix $R\in \mathbb{R}^{S\times I}$ and associated joint scenario probability vectors $p,q\in \mathbb{R}^{S}$.

The 1_CVaROptBenchmarks notebook illustrates how the benchmark problems can be solved using Fortitudo Technologies' Investment Analysis module.

The 2_OptimizationExample notebook shows how you can replicate the results using the fortitudo.tech open-source Python package for the efficient frontier optimizations of long-only cash portfolios, which are the easiest problems to solve.

Installation Instructions

It is recommended to install the code dependencies in a conda environment:

conda create -n cvar-optimization-benchmarks python=3.13 conda activate cvar-optimization-benchmarks pip install cvar-optimization-benchmarks

After this, you should be able to run the code in the 2_OptimizationExample notebook.

The code in 1_CVaROptBenchmarks notebook can only be run by people who subscribe to the Investment Analysis module.

Portfolio Construction and Risk Management book

You can read much more about the Fully General Investment Framework (FGIF) in the Portfolio Construction and Risk Management book, including a thorough description of CVaR optimization problems and Resampled Portfolio Stacking.