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📌 Portfolio Optimization Based on CAPM and Mean-Variance Optimization (MVO) Chinese

📖 1. Project Overview

This project applies the Capital Asset Pricing Model (CAPM) and Mean-Variance Optimization (MVO) to compute the optimal investment portfolio using Quadratic Programming (QP).

Project Goals:

  • Calculate CAPM parameters (β value, expected return, idiosyncratic risk)
  • Optimize portfolio weights to minimize risk
  • Plot the Efficient Frontier to analyze risk-return trade-offs

🏗 2. Project Structure

📂 FinancialMachineLearning
│── 📂 doc                     # Project Documentation
│   │── 📜 CF969.pdf           # Report Example
│   │── 📜 CF969 - SP ZU - Assignment.pdf # Assignment Requirements
│── 📂 report                  # Research Reports
│   │── 📜 report_cn.md        # Chinese Report
│   │── 📜 report_en.md        # English Report
│   │── 📜 capm_regression_*.png # CAPM Regression Analysis Charts
│   │── 📜 efficient_frontier.png # Efficient Frontier Chart
│   │── 📜 idiosyncratic_risk.png # Idiosyncratic Risk Bar Chart
│   │── 📜 optimal_portfolio_weights.png # Optimal Portfolio Weights Chart
│── 📂 result                  # Computation Results
│   │── 📜 adj_close_data.csv  # Adjusted Closing Price Data
│   │── 📜 capm_results.csv    # CAPM Calculation Results
│   │── 📜 efficient_frontier.png # Efficient Frontier Chart
│   │── 📜 optimal_portfolio_weights.csv # Optimal Portfolio Weights
│   │── 📜 returns_data.csv    # Daily Returns Data
│── 📜 .gitignore              # Git Ignore File
│── 📜 all_code.png            # Code Screenshot
│── 📜 financial.ipynb         # **Jupyter Notebook Containing All Code**
│── 📜 README.md               # README (English)
│── 📜 README_cn.md            # README (Chinese)

⚙️ 3. Environment Setup

🔹 3.1 Create Conda Virtual Environment

This project runs on Python 3.12.7, and it is recommended to use Conda for environment setup:

conda create -n financial python=3.12.7
conda activate financial

🔹 3.2 Install Dependencies

pip install -r requirements.txt

Or manually install:

pip install numpy pandas matplotlib statsmodels cvxopt yfinance

🚀 4. Running the Project

All code is stored in financial.ipynb, which includes data retrieval, CAPM calculation, portfolio optimization, and visualization. Follow the steps below to run the project:

🔹 4.1 Start Jupyter Notebook

jupyter lab

Or:

jupyter notebook

Then open financial.ipynb and execute the cells sequentially.

Code Execution Screenshot

all_code.png

🔹 4.2 Main Code Workflow

1️⃣ Data Retrieval

  • Fetch historical adjusted closing prices from Yahoo Finance
  • Compute daily returns
  • Save results to adj_close_data.csv and returns_data.csv

2️⃣ CAPM Computation

  • Compute β values (Beta), expected returns, and idiosyncratic risk
  • Store results in capm_results.csv

3️⃣ Optimal Portfolio Computation

  • Use Quadratic Programming (QP) to compute optimal weights
  • Target returns: 0.08, 0.12, 0.15
  • Save results in optimal_portfolio_weights.csv

4️⃣ Plot Efficient Frontier

  • Compute portfolio risk
  • Generate Efficient Frontier chart (efficient_frontier.png)

❗ 5. Issues and Solutions

During the computation process, several key issues were encountered. Below are their descriptions and solutions:

🔹 5.1 Singular KKT Matrix in cvxopt.solvers.qp()

(Complete issue description and solution remain unchanged)

🎯 6. Future Optimization Directions

✅ Expand asset classes (e.g., bonds, ETFs) for better portfolio optimization
✅ Incorporate market volatility modeling using GARCH or Fama-French factor models
✅ Optimize portfolio weights using dynamic asset allocation (DFA) strategies

📬 7. Contact & Contribution

🔹 Email: generalfly666@outlook.com
🔹 GitHub: GitHub Repository
🔹 Contribution: Fork this repository and submit a Pull Request.

🚀 This project optimizes CAPM calculations and portfolio optimization methods. Contributions and discussions are welcome! 😊