Portfolio Optimization & Risk Modeling (Python)

End-to-end MVO (Min-Var / Max-Sharpe), Efficient Frontier with Monte Carlo, Risk Parity, Black–Litterman, and optional regime-aware risk targeting. Runs on Yahoo Finance data.

Quick start

pip install -r requirements.txt
python portfoliooptplusregime.py --download --rf 0.045 --benchmark VTI   --marketequal --tau 0.2   --regime --regime-window 60 --regime-proxy VTI   --regime-low-pct 0.2 --regime-high-pct 0.8   --regime-low-scale 1.3 --regime-mid-scale 1.0 --regime-high-scale 0.7 --view "BTC-USD:+0.08@0.001,BIL:+0.02@0.001"
🧠 How It Works
Data ➜ Returns ➜ Optimization ➜ Risk Models ➜ Views ➜ Backtest
Data & Cleaning — Downloads Adjusted Close prices (Yahoo Finance), aligns to business days, forward-fills small gaps.
Returns — Computes log returns (daily or weekly).  
Optimization — Builds Mean–Variance portfolios under constraints (long-only, fully invested):  
   - Min-Variance (minimizes \( w^\top \Sigma w \))  
   - Max-Sharpe (maximizes \( \frac{w^\top \mu - r_f}{\sqrt{w^\top \Sigma w}} \))  
Efficient Frontier — Plots the long-only frontier; overlays Monte Carlo random portfolios for context.  
Risk Parity — Solves for equal risk contributions (each asset contributes equally to total variance).  
Black–Litterman — Blends equilibrium returns with investor views (e.g., "BTC-USD:+0.08@0.001,BIL:+0.02@0.001"), where @ is the view variance (smaller = higher confidence).  
Backtest — In-sample fixed-weight backtest vs a benchmark (e.g., VTI) + optional regime-aware scaling of risk based on a volatility proxy.

📐 Key Formulas
Portfolio Variance
$$ \sigma_p^2 = w^\top \Sigma w $$
Sharpe Ratio
$$ \text{Sharpe}(w) = \frac{w^\top \mu - r_f}{\sqrt{w^\top \Sigma w}} $$
Risk Contribution
$$ RCi = \frac{wi \cdot (\Sigma w)_i}{w^\top \Sigma w} $$
Reproduce the Figures

bash pip install -r requirements.txt python scripts/portfoliooptplus_regime.py --download --rf 0.045 --benchmark VTI \ --market_equal --tau 0.2 \ --regime --regime-window 60 --regime-proxy VTI \ --regime-low-pct 0.2 --regime-high-pct 0.8 \ --regime-low-scale 1.3 --regime-mid-scale 1.0 --regime-high-scale 0.7 \ --view "BTC-USD:+0.08@0.001,BIL:+0.02@0.001" ```

Example output