tests

A practitioner-grade implementation of the Black-Litterman model for European equity portfolio construction, applied to the SX5E top 15.

Black-Litterman starts from the market-cap–implied equilibrium return Π and tilts it only where you hold a view, sizing each tilt by your stated confidence (Idzorek). That fixes the central pathology of plain mean-variance — wild, corner-solution weights from tiny perturbations in the expected-return inputs. With no views the posterior reproduces the cap-weighted market exactly; with a 100%-confidence view the view is honoured exactly. The figure shows the efficient frontier on the EURO STOXX top 15 (left) and how a moderate view shifts the posterior expected returns away from the prior only on the names it touches (right).

Black-Litterman results — efficient frontier and prior-vs-posterior returns

Left: efficient frontier from the real covariance sweep, with the max-Sharpe point. Right: implied equilibrium Π vs the Black-Litterman posterior μ under one illustrative pair of views — the tilt is concentrated where the views apply. Regenerate with python make_figures.py.

• Combine market equilibrium (CAPM-implied returns) with investor views via Bayesian shrinkage to produce stable, intuitive portfolios.
• Build parallel Python and Excel implementations to demonstrate both quantitative depth and tooling fluency.
• Interactive Streamlit dashboard for live view-entry, sensitivity analysis, and efficient-frontier visualisation.

• Black, F. & Litterman, R. (1992). "Global Portfolio Optimization." Financial Analysts Journal.
• He, G. & Litterman, R. (1999). "The Intuition Behind Black-Litterman Model Portfolios." Goldman Sachs.
• Idzorek, T. M. (2005). "A Step-by-Step Guide to the Black-Litterman Model." Working paper.

bl-portfolio-optimiser/
├── market_data.py # Phase 1 — prices, returns, covariance, weights, rf
├── equilibrium.py # Phase 2 — reverse-optimisation → implied returns Π
├── views.py # Phase 3 — P, Q, Ω construction (Idzorek)
├── bl_model.py # Phase 4 — posterior μ and Σ computation
├── optimiser.py # Phase 5 — mean-variance, max Sharpe, efficient frontier
├── app.py # Phase 6 — Streamlit dashboard
├── sources.md # Data provenance
├── requirements.txt
└── README.md

pip install -r requirements.txt
python market_data.py # builds the data layer and exports CSVs
streamlit run app.py # interactive dashboard

• Phase 1 — Data layer
• Phase 2 — Equilibrium implied returns
• Phase 3 — Views (Idzorek confidence mapping)
• Phase 4 — BL posterior
• Phase 5 — Optimiser (with concentration caps)
• Phase 6 — Streamlit dashboard

Honest about what the model can and cannot do:

• Inputs drive everything. Π depends on the covariance estimate (Ledoit-Wolf shrinkage is used here) and on the risk-aversion coefficient λ (anchored to an assumed 5% ERP); the output is only as good as those.
• τ is set by convention, not estimated. The prior-scaling parameter (0.025) is a standard choice, and posterior weights are known to be sensitive to it — the dashboard's sensitivity view exists precisely because of this.
• View confidence is judgment, not data. The Idzorek mapping turns a stated confidence into Ω; it does not calibrate that confidence from any track record.
• Single-period and largely unconstrained. The objective is one-period mean-variance with a per-name cap; there are no transaction costs, turnover limits, or factor/sector constraints.
• Covariance is estimated on ~3y of daily history and assumed stationary — regime shifts and time-varying correlation are not modelled.

A pytest suite under tests/ covers the model's mathematical contracts — the properties a reviewer is most likely to probe in an interview — rather than just checking that functions run. All fixtures are synthetic, so the suite is offline and fast.

• No-views identity — with an empty view set the posterior mean collapses exactly onto the equilibrium prior Π.
• Confidence limits — as Idzorek confidence → 0 the view is ignored (posterior → prior); at 100% confidence it is enforced exactly (P · μ_BL = Q).
• Equilibrium round-trip — (1/λ) Σ−1 Π = w_mkt to machine precision.
• Two-form cross-check — the Theil and original Black-Litterman posteriors agree to ~1e-10.
• Risk decomposition — Euler risk contributions sum to portfolio volatility.
• Well-posedness — the posterior covariance stays symmetric and PSD; the optimisers respect the budget and per-name caps.

pip install -r requirements-dev.txt
pytest tests/ -q # 9 tests

Tests run automatically on every push via GitHub Actions (.github/workflows/tests.yml).