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Quantitative Portfolio Optimization & Factor Analysis

Overview

This repository contains a comprehensive, end-to-end quantitative portfolio management project. It explores advanced asset allocation techniques, transitioning from traditional Modern Portfolio Theory (MPT) to factor-based risk analysis, Monte Carlo simulation boundaries, and finally, the implementation of the Black-Litterman model to incorporate subjective market views.

Project Architecture

The analysis is structured into four core phases, coded entirely in Python using Jupyter Notebooks:

1. Mean-Variance Optimization (MVO)

Calculates the optimal asset weights for a 10-stock universe (TSLA, WMT, BAC, GS, LLY, MRK, GOOG, META, AAPL, XOM) by maximizing the Sharpe ratio.

• Evaluates the mathematical impact of unconstrained vs. constrained (18% maximum weight) capital allocation.
• Visualizes the nested Efficient Frontiers.
• Conducts strict Out-of-Sample testing to demonstrate the dangers of overfitting and the real-world value of diversification constraints (evaluating Cumulative Returns, Sharpe Ratios, and Max Drawdown).

2. Fama-French 5-Factor Style Analysis

Deconstructs the constrained portfolio's historical returns to determine its underlying investment style.

• Extracts daily Fama-French data (Mkt-RF, SMB, HML, RMW, CMA) using pandas-datareader.
• Compares Ordinary Least Squares (OLS) with Huber's T Robust Linear Regression to account for fat-tailed market anomalies.
• Validates the regression model's predictive power on unseen Out-of-Sample data.

3. Hard Optimization vs. Monte Carlo Simulations

Investigates the computational efficiency and mathematical limitations of random simulation.

• Processes hundreds of thousands of simulated portfolios to map the feasible region of risk/return.
• Demonstrates the "Curse of Dimensionality" and high rejection rates when applying strict box constraints to random sampling compared to SLSQP algorithmic optimization.

4. The Black-Litterman Model

Resolves the estimation-error maximization problem inherent in traditional Markowitz optimization by blending market equilibrium with subjective manager views.

• Constructs a synthetic market composite using the S&P 500 (SPY).
• Translates absolute and relative market views into matrix algebra ($P$ and $Q$ matrices).
• Calculates posterior expected returns ($\mu_{BL}$) and covariance ($\Sigma_{BL}$) to output a balanced, intuitive asset allocation.

Technologies & Libraries

• Python 3.x
• yfinance (Data Acquisition)
• pandas, numpy (Data Wrangling & Matrix Algebra)
• scipy.optimize (SLSQP Optimization)
• statsmodels (OLS & Robust Factor Regressions)
• matplotlib (Data Visualization)

Repository Structure

• notebooks/ - Contains the primary Jupyter Notebooks with all execution code.
• TASKS.md - A detailed breakdown of the original project requirements and constraints.
• requirements.txt - Dependency list for environment replication.

Citation

If you use this project in academic research, publications, educational materials, or derivative works, please cite the project.

This repository includes a CITATION.cff file, so GitHub provides a "Cite this repository" button in the repository sidebar. You can use it to obtain citations in BibTeX, APA, and other supported formats.

Suggested citation:

Arain, S. U. R. (2026). quant-portfolio-optimization (Version 1.0) [Software]. https://github.com/sanaurrehmanarain/quant-portfolio-optimization

Author: Sana Ur Rehman Arain

Profession: Data Scientist

GitHub: https://github.com/sanaurrehmanarain

Contact: sana.arain.work@gmail.com

If you build upon this work, attribution is appreciated and helps others discover the original project.

Note: The MIT License requires that the original copyright notice be retained in copies of the Software.

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License

This project is licensed under the MIT License. See the LICENSE file for details.