Portfolio Optimization & Asset Allocation

This project focuses on portfolio construction and asset allocation using quantitative methods widely applied in finance.

The analysis is based on real market data and combines statistical estimation, optimization techniques, and equilibrium models.

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🔍 Objectives

• Estimate expected returns and covariance matrix for a set of equities
• Construct efficient portfolios under different assumptions
• Analyze the impact of constraints on portfolio allocation
• Evaluate market risk exposure using CAPM
• Implement the Black-Litterman framework to incorporate investor views

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📊 Data

• Daily returns and market capitalizations
• 6 US equities across different sectors
• S&P 500 index used as market benchmark
• Time period: 2003 – 2025

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⚙️ Methodology

Covariance Estimation

• Historical covariance matrix
• Shrinkage toward constant correlation (SCC) for improved robustness

Expected Returns

• Exponentially weighted average of returns
• Emphasis on recent data

Portfolio Optimization

• Mean-variance optimization (Markowitz framework)
• Efficient frontier with:
  • Risk-free asset
  • Additional constraints (equality & inequality)

CAPM Analysis

• OLS regression to estimate:
  • Beta (market exposure)
  • Alpha (excess return)
• Statistical significance analysis

Black-Litterman Model

• Implied equilibrium returns
• Integration of subjective views:
  • Absolute view
  • Relative view
• Analysis of impact on portfolio weights

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📊 Results

• Shrinkage improves stability of covariance estimation
• Unconstrained portfolios exhibit strong leverage and concentration
• Constraints reduce risk but lower expected returns
• CAPM results show:
  • Moderate market exposure (β < 1 for most assets)
  • Statistically significant alpha for selected stocks
• Black-Litterman:
  • Significantly shifts portfolio allocation
  • Highlights sensitivity to confidence levels in views

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Key Insights

• Portfolio optimization is highly sensitive to input estimation errors
• Shrinkage techniques are essential for robust allocation
• Constraints play a critical role in making portfolios realistic
• CAPM provides useful diagnostics but has limitations in practice
• Black-Litterman offers a flexible framework but requires careful calibration of views

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Technologies

• Python
• NumPy
• Pandas
• SciPy
• Matplotlib

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📁 Project Structure

• notebooks/ → data analysis and portfolio construction
• report/ → full project report

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Possible Extensions

• Use of alternative risk models (e.g. factor models)
• Out-of-sample backtesting
• Transaction cost modeling
• Robust optimization techniques

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Author

Elia Ceolini