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 portfolio_opt_plus_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:[email protected],BIL:[email protected]"
## 🧠 How It Works
**Data ➜ Returns ➜ Optimization ➜ Risk Models ➜ Views ➜ Backtest**
1. **Data & Cleaning** — Downloads Adjusted Close prices (Yahoo Finance), aligns to business days, forward-fills small gaps.
2. **Returns** — Computes log returns (daily or weekly).
3. **Optimization** — Builds **Mean–Variance** portfolios under constraints (long-only, fully invested):
- Min-Variance (minimizes \( w^\top \Sigma w \))
- Max-Sharpe (maximizes \( \frac{w^\top \mu - r_f}{\sqrt{w^\top \Sigma w}} \))
4. **Efficient Frontier** — Plots the long-only frontier; overlays **Monte Carlo** random portfolios for context.
5. **Risk Parity** — Solves for **equal risk contributions** (each asset contributes equally to total variance).
6. **Black–Litterman** — Blends equilibrium returns with **investor views** (e.g., `"BTC-USD:[email protected],BIL:[email protected]"`), where `@` is the view variance (smaller = higher confidence).
7. **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**
$$
RC_i = \frac{w_i \cdot (\Sigma w)_i}{w^\top \Sigma w}
$$
### Reproduce the Figures
```bash
pip install -r requirements.txt
python scripts/portfolio_opt_plus_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:[email protected],BIL:[email protected]"
Example output
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