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README.md

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

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