# 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 [next-generation investment framework's market representation](https://youtu.be/4ESigySdGf8?si=yWYuP9te1K1RBU7j&t=46)
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](https://github.com/fortitudo-tech/cvar-optimization-benchmarks/blob/main/1_CVaROptBenchmarks.ipynb)
illustrates how the benchmark problems can be solved using Fortitudo Technologies' Investment
Analysis module.
The [2_OptimizationExample notebook](https://github.com/fortitudo-tech/cvar-optimization-benchmarks/blob/main/2_OptimizationExample.ipynb)
shows how you can replicate the results using the [fortitudo.tech open-source Python package](https://github.com/fortitudo-tech/fortitudo.tech)
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](https://conda.io/projects/conda/en/latest/user-guide/concepts/environments.html):
conda create -n cvar-optimization-benchmarks python
pip install cvar-optimization-benchmarks
After this, you should be able to run the code in the [2_OptimizationExample notebook](https://github.com/fortitudo-tech/cvar-optimization-benchmarks/blob/main/2_OptimizationExample.ipynb).
## Portfolio Construction and Risk Management book
You can read much more about the [next-generation investment framework](https://antonvorobets.substack.com/p/anton-vorobets-next-generation-investment-framework)
in the [Portfolio Construction and Risk Management book](https://antonvorobets.substack.com/p/pcrm-book),
including a thorough description of CVaR optimization problems and
[Resampled Portfolio Stacking](https://antonvorobets.substack.com/p/resampled-portfolio-stacking).
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"description": "# CVaR optimization benchmark problems\nThis repository contains Conditional Value-at-Risk (CVaR) portfolio optimization benchmark\nproblems for fully general Monte Carlo distributions and derivatives portfolios.\n\nThe starting point is the [next-generation investment framework's market representation](https://youtu.be/4ESigySdGf8?si=yWYuP9te1K1RBU7j&t=46)\ngiven by the matrix $R\\in \\mathbb{R}^{S\\times I}$ and associated joint scenario probability\nvectors $p,q\\in \\mathbb{R}^{S}$.\n\nThe [1_CVaROptBenchmarks notebook](https://github.com/fortitudo-tech/cvar-optimization-benchmarks/blob/main/1_CVaROptBenchmarks.ipynb)\nillustrates how the benchmark problems can be solved using Fortitudo Technologies' Investment\nAnalysis module.\n\nThe [2_OptimizationExample notebook](https://github.com/fortitudo-tech/cvar-optimization-benchmarks/blob/main/2_OptimizationExample.ipynb)\nshows how you can replicate the results using the [fortitudo.tech open-source Python package](https://github.com/fortitudo-tech/fortitudo.tech)\nfor the efficient frontier optimizations of long-only cash portfolios, which are the easiest problems to solve.\n\n## Installation Instructions\nIt is recommended to install the code dependencies in a \n[conda environment](https://conda.io/projects/conda/en/latest/user-guide/concepts/environments.html):\n\n conda create -n cvar-optimization-benchmarks python\n pip install cvar-optimization-benchmarks\n\nAfter this, you should be able to run the code in the [2_OptimizationExample notebook](https://github.com/fortitudo-tech/cvar-optimization-benchmarks/blob/main/2_OptimizationExample.ipynb).\n\n## Portfolio Construction and Risk Management book\nYou can read much more about the [next-generation investment framework](https://antonvorobets.substack.com/p/anton-vorobets-next-generation-investment-framework)\nin the [Portfolio Construction and Risk Management book](https://antonvorobets.substack.com/p/pcrm-book),\nincluding a thorough description of CVaR optimization problems and\n[Resampled Portfolio Stacking](https://antonvorobets.substack.com/p/resampled-portfolio-stacking).\n",
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