Portfolio optimization with CVXPY

Do a few classic portfolio optimizations using:

• CVXPY (paper), a modeling environment for convex optimization, supporting many back-end solvers.
• Data (mostly) from Prof. Aswath Damodaran and FRED

Online data

• Aswath Damodaran. See the FAQ tab in his XLS for details on individual asset returns.
• FRED
• Shiller data
• Ken French
• Macrotrends

Currently use Damodaran data for returns.

Steps

1. Load asset return data from Damodaran website using pd.read_excel.
2. Load GDP data from FRED using pandas_datareader module.
3. Compute covariance matrix, long-only efficient frontier, and transition map using historical data (see above). Also compute same outputs for 1972-present (post-gold standard) and 1983-present (post-inflation era).
4. Compute long-short efficient frontier and transition map, adding a random short asset with 5% annualized negative return and 90% correlation to S&P, and addig a 150% gross exposure constraint.
5. Compute some allocations using hierarchical risk parity model for comparison.
6. Compute an efficient frontier using a factor model, using a random set of returns for 1000 stocks and 10 random factor exposures and a random factor covariance matrix.

This mostly follows the cvxpy tutorial but uses real historical data, and visualizes the full efficient frontier and transition map.

Takeaways

• Gold adds some value for most portfolios, except in most disinflationary environment at higher risk tolerances.
• TIPS should be a more direct inflation hedge with a US government guaranteed real return but we don't have data back very far.
• If you can find good shorts and use leverage, you can supercharge returns.

Setup

1. git clone this repo, cd to repo directory

2. Install Anaconda

3. Create virtual environment

conda create -n portfolio_opt
conda activate portfolio_opt
pip install -r requirements.txt

or

conda env create -f environment.yaml
conda activate portfolio_opt

4. jupyter notebook

5. Run Portfolio optimization.ipynb

Further reading

• CVXPY tutorial
• Convex optimization short course

Asset allocation books:

• David Swensen - Pioneering Portfolio Management: An Unconventional Approach to Institutional Investment
• Bernstein - The Intelligent Asset Allocator: How to Build Your Portfolio to Maximize Returns and Minimize Risk
• Kinlaw et al - Asset Allocation: From Theory to Practice and Beyond (Wiley Finance) 1st Edition
• Fabozzi and Markowitz, ed. - The Theory and Practice of Investment Management: Asset Allocation, Valuation, Portfolio Construction, and Strategies
• Muralidhar - Innovations in Pension Fund Management 1st Edition
• Ferri - All About Asset Allocation Paperback
• Faber - Global Asset Allocation: A Survey of the World's Top Asset Allocation Strategies