Portfolio Optimization

Portfolio Optimization: Quantitative Approaches

This project compares five portfolio optimization strategies on a diversified 16-asset portfolio spanning U.S. equities, international equities, real estate, commodities, and fixed income. Models were trained on 2014 to 2021 data and backtested on 2021 to 2024.

The Strategies

Mean-Variance Optimization (Efficient Frontier) minimizes portfolio volatility for a given target return:

\[\min_{\mathbf{w}} \left(\mathbf{w}^T \Sigma \mathbf{w}\right) \quad \text{s.t.} \quad \mathbf{w}^T \mu = \mu_p\]

Maximum Sharpe Ratio maximizes risk-adjusted return:

\[\max_{\mathbf{w}} \frac{\mathbf{w}^T \mu - R_f}{\sqrt{\mathbf{w}^T \Sigma \mathbf{w}}}\]

Global Minimum Variance minimizes total portfolio risk without requiring expected return estimates.

Risk Parity equalizes the risk contribution of each asset to the overall portfolio.

Equal Weights (Benchmark) assigns equal weight (1/N) to all assets.

Portfolio Assets

16 assets across 5 classes: U.S. Equities (SPY, AAPL, MSFT, JNJ, JPM, BA, NKE, AMZN), Non-U.S. Equities (IEMG, ILF, DB1.DE), Real Estate (IYR, REM), Commodities (GLD, CL=F), and Fixed Income (ISTB).

Interactive Demo

Key Findings

• EF_3 (aggressive) achieved 38.0% total return, beating SPY (32.9%)
• Max Sharpe and EF_2 performed comparably to SPY
• GMV underperformed at -1.1%, minimizing risk alone was insufficient
• Equal Weights outperformed most optimization strategies

Technology Stack

• Python 3.9+, SciPy (SQP optimization), pandas, NumPy, Plotly
• Data: Yahoo Finance (yfinance), U.S. Treasury rates (FRED)