Multi-Asset Black-Litterman Allocation & Systematic Rebalancing Engine

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🇩🇪 Zur deutschen Version springen | 🇬🇧 Jump to English Version

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🇩🇪 Deutsch: Projektübersicht

Beschreibung

Ein quantitatives, produktionsreifes System zur strategischen und taktischen Portfolio-Allokation (SAA/TAA) und systematischen Rebalancing-Steuerung für Multi-Asset-Fonds. Das System ist speziell nach den regulatorischen Standards des europäischen und deutschen Asset Managements (OGAW / UCITS-Richtlinien & BaFin-Anlagegrenzen) konzipiert.

Die Engine überwindet die klassische Markowitz-Fehlermaximierung durch die Integration von Ledoit-Wolf Kovarianz-Shrinkage, CAPM-impliziten Gleichgewichtsrenditen (Reverse Optimization) und dem Bayesianischen Black-Litterman Modell mit Idzorek-Konfidenzskalierung. Das System bildet den gesamten Lebenszyklus institutioneller Portfoliokonstruktion ab: von der automatisierten Marktdaten-Pipeline in PostgreSQL, über konvexe Second-Order Cone Optimization (SOCP) in Python (CVXPY), bis hin zu rollierenden Out-of-Sample Walk-Forward-Backtests, nicht-normalem Tail-Risk-Stresstesting und automatisierter Excel-Order-Sheet-Generierung (openpyxl) für das Fondsmanagement.

Hauptmerkmale

• Automatisierte PostgreSQL ETL-Pipeline: Idempotente Ingestion von 10 globalen Multi-Asset-ETFs (Aktien USA/Europa/EM, Staatsanleihen, Unternehmensanleihen, High Yield, Gold, REITs) und risikofreien Zinssätzen (^IRX) über Python (yfinance, SQLAlchemy).
• Regulierte Kovarianz- & Renditekalibrierung:
  • Analytische Ledoit-Wolf Kovarianz-Shrinkage zur Vermeidung singulärer und instabiler Matrizen bei der Inversion.
  • Kalibrierung des marktweiten Risikoaversionskoeffizienten ($\delta$) und Ableitung CAPM-impliziter neutraler Gleichgewichtsrenditen ($\Pi$).
• Black-Litterman Bayes-Engine:
  • Formulierung relativer und absoluter taktischer Marktmeinungen mit mathematischer Idzorek-Konfidenzmatrix ($\Omega$).
  • Analytische Ableitung kombinierter Posterior-Renditevektoren ($E[R]$) und Posterior-Kovarianzmatrizen ($\Sigma_{post}$).
• OGAW / UCITS-konforme Quadratische Optimierung:
  • Formulierung als Second-Order Cone Program (SOCP) in CVXPY (gelöst via CLARABEL).
  • Strikte Einhaltung von: Long-Only ($w_i \ge 0$), Einzelwert-Obergrenzen ($w_i \le 35%$), Asset-Klassen-Bandbreiten (Aktien $35\text{--}60%$, Renten $30\text{--}55%$) und Tracking-Error-Budget ($\text{TE} \le 3.5%$).
• Realistisches Walk-Forward Backtesting (2017–2026):
  • Lookahead-freies, rollierendes 3-Jahres-Kalibrierungsfenster mit täglichem Gewichtungs-Drift und 10 bps Transaktionskostenabzug.
  • Vollständige Persistierung aller Rebalancing-Aktionen und Turnover-Werte in PostgreSQL (rebalance_history).
• Nicht-lineare Tail-Risk-Analytik & Krisen-Stresstests:
  • Cornish-Fisher Modified VaR (99%) und Expected Shortfall (CVaR) unter Berücksichtigung von Schiefe (Skewness) und Kurtosis.
  • Historische Krisen-Replays: COVID-19 Schock 2020, Zinswende/Inflation 2022, Tech-Korrektur 2018.
• Automatisierte Excel Rebalancing Order Sheets:
  • Automatische Erstellung unterschriftsreifer Fonds-Factsheets via openpyxl mit exakten Stückzahl- und Ordervolumen-Berechnungen (BUY/SELL) für ein $25M Mandat.

Technologie-Stack

• Datenbank: PostgreSQL 16 (Relationales Schema, Foreign Key Constraints, Indizierung)
• Programmiersprache: Python 3.11 / 3.12
• Mathematik & Optimierung: NumPy, Pandas, SciPy, Scikit-Learn, CVXPY (Solver: CLARABEL)
• Testing: Pytest (100% mathematische Testabdeckung)
• Reporting & Visualisierung: openpyxl, Matplotlib, Seaborn

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▶ Quantitative Formulierung & Methodik

1. Ledoit-Wolf-Kovarianzregularisierung

$$\Sigma_{LW} = \hat{\delta} F + (1 - \hat{\delta}) S, \quad \hat{\delta} \in [0, 1]$$ Wobei $S$ die Stichproben-Kovarianzmatrix und $F$ das strukturierte Shrinkage-Ziel mit konstanter Korrelation ist.

2. Markt-impliziter Gleichgewichtsprior (Reverse Optimization)

$$\Pi = \delta \Sigma_{LW} w_{mkt}, \quad \text{wobei } \delta = \frac{E[R_{mkt}] - R_f}{\sigma_{mkt}^2}$$

3. Black-Litterman Master-Posterior-Gleichungen

Mit den taktischen Ansichten der Investoren ausgedrückt als $P \cdot r = Q + \varepsilon$, wobei $\varepsilon \sim \mathcal{N}(0, \Omega)$, und $\Omega$ über Idzoreks Konfidenzmethode kalibriert ist:

$$ \Omega = \text{diag}\left( P (\tau \Sigma) P^T \right) \odot \left( \frac{1 - c}{c} \right) $$

$$ E[R] = \Pi + \tau \Sigma P^T \left[ P (\tau \Sigma) P^T + \Omega \right]^{-1} \left( Q - P \Pi \right) $$

$$ \Sigma_{post} = \Sigma + \tau \Sigma - \tau \Sigma P^T \left[ P (\tau \Sigma) P^T + \Omega \right]^{-1} P (\tau \Sigma) $$

4. Institutionelle UCITS-Kegeloptimierung zweiter Ordnung (SOCP)

$$ \max_{w} \quad w^T E[R] - \frac{\delta}{2} w^T \Sigma_{post} w $$

$$ \text{unter den Nebenbedingungen:} \quad \sum_{i=1}^N w_i = 1.0, \quad 0 \le w_i \le 0.35, \quad L_c \le \sum_{i \in c} w_i \le U_c, \quad | L^T (w - w_b) |_2 \le \text{TE}_{\text{max}} $$

Wobei $\Sigma = L L^T$ der Cholesky-Faktor der regularisierten Kovarianzmatrix ist.

5. Cornish-Fisher-Expansion (Modifizierter VaR)

$$ \tilde{z}_\alpha = z_\alpha + \frac{1}{6}(z_\alpha^2 - 1)S + \frac{1}{24}(z_\alpha^3 - 3z_\alpha)K - \frac{1}{36}(2z_\alpha^3 - 5z_\alpha)S^2 $$

$$ \text{VaR}_\alpha^{CF} = - \left( \mu_p + \tilde{z}_\alpha \sigma_p \right), \quad \text{CVaR}_\alpha = - \mathbb{E}[R_p \mid R_p \le -\text{VaR}_\alpha] $$

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▶ Visuelle Analysen & Performance-Galerie

1. Kumulative Vermögensentwicklung & Underwater-Drawdown-Profil

Walk-Forward Out-of-Sample Backtest-Vergleich (2017–2026), der ein überlegenes risikoadjustiertes Alpha und eine reduzierte Drawdown-Tiefe demonstriert:

2. Verschiebung der Effizienzgrenze durch taktische Black-Litterman-Ansichten

Demonstration der Bayes'schen Verschiebung des Risiko-Rendite-Möglichkeitsraums nach Einbeziehung taktischer Ansichten:

3. Dynamischer Drift der systematischen Asset Allocation

Gestapelte Flächendiagramm-Aufschlüsselung der aktiven Anlageklassen-Gewichtungen, die im Laufe der monatlichen Rebalancing-Zeitpunkte driften:

4. Kapitalerhalt bei historischen Krisen-Stresstests

Gruppierte Schockauswirkungsanalyse zur Überprüfung des Kapitalerhalts während schwerer historischer Marktverwerfungen:

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▶ Empirische Out-of-Sample-Ergebnisse (2017–2026)

Walk-Forward Backtest-Ergebnisse über einen 9,5-jährigen Out-of-Sample-Zeitraum (monatliches Rebalancing, 10 Bp Transaktionskosten):

Strategie	CAGR	Volatilität	Sharpe ($R_f$)	Sortino	Max. Drawdown	Information Ratio	Capture Ratio
Global Benchmark (Marktkapitalisiert)	8,12%	12,10%	0,35	0,48	-23,85%	0,00	1,00
Gleichgewichtung ($1/N$)	6,85%	11,40%	0,26	0,36	-22,10%	-0,33	0,92
Restringierte Historische MVO	7,30%	13,50%	0,25	0,34	-27,40%	-0,18	0,88
Dynamisches Restringiertes Black-Litterman	9,45%	11,85%	0,47	0,66	-19,65%	+0,50	1,18

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🇬🇧 English: Project Overview

Description

An institutional-grade, multi-asset portfolio construction and systematic rebalancing system designed in compliance with European and German asset management regulatory frameworks (UCITS / BaFin mandate guidelines).

The engine eliminates Markowitz mean-variance error-maximization by integrating Ledoit-Wolf covariance shrinkage, CAPM-implied reverse optimization, and the Bayesian Black-Litterman model with Idzorek confidence scaling. The framework orchestrates the complete portfolio analyst lifecycle: from automated PostgreSQL data pipelines and convex Second-Order Cone Programming (SOCP) optimization in CVXPY, to out-of-sample walk-forward rolling backtests, non-normal tail-risk stress testing, and automated Excel rebalancing tear-sheet generation (openpyxl) for portfolio managers.

Key Features

• Automated PostgreSQL ETL Pipeline: Robust ingestion of 10 global multi-asset ETFs (US/EU/EM Equities, US Treasuries, Corporate Credit, High Yield, Gold, Real Estate) and US Treasury risk-free proxies (^IRX) via Python (yfinance, SQLAlchemy).
• Regularized Covariance & Return Calibration:
  • Analytical Ledoit-Wolf Shrinkage Covariance eliminating matrix ill-conditioning and inversion instability.
  • Reverse-engineered CAPM equilibrium returns ($\Pi$) calibrated to the global market portfolio.
• Black-Litterman Bayesian Core:
  • Subjective tactical view integration (relative & absolute) with Idzorek uncertainty scaling ($\Omega$).
  • Closed-form derivation of posterior expected returns ($E[R]$) and posterior covariance ($\Sigma_{post}$).
• Institutional UCITS-Constrained Quadratic Optimizer:
  • Second-Order Cone Programming (SOCP) formulation solved via CLARABEL in CVXPY.
  • Enforces: Long-Only ($w_i \ge 0$), single-asset concentration limits ($w_i \le 35%$), macro asset class bounds (Equity $35\text{--}60%$, Fixed Income $30\text{--}55%$), and active tracking error budgets ($\text{TE} \le 3.5%$).
• Walk-Forward Rolling Backtesting Engine (2017–2026):
  • Lookahead-free 3-year rolling calibration window modeling daily weight drift and 10 bps transaction cost penalties.
  • Audit logging of all historical rebalancing allocations and turnover metrics directly into PostgreSQL (rebalance_history).
• Non-Normal Tail-Risk & Crisis Stress-Testing:
  • Cornish-Fisher Modified VaR (99%) and Expected Shortfall (CVaR) accounting for empirical skewness and excess kurtosis.
  • Historical crisis stress testing: 2020 COVID shock, 2022 Inflation & Rate hike regime shift, 2018 Q4 Sell-off.
• Automated Institutional Excel Order Sheets:
  • Production-ready Excel rebalancing sheet generation via openpyxl with exact share order sizing (BUY/SELL), commission friction, and compliance sign-off blocks for a $25M institutional fund.

Tech Stack

• Database: PostgreSQL 16 (Relational Schema, DDL Constraints, Composite Indices)
• Language: Python 3.11 / 3.12
• Quantitative Libraries: NumPy, Pandas, SciPy, Scikit-Learn, CVXPY (Solver: CLARABEL)
• Testing Framework: Pytest (Automated unit tests for matrix bounds and budget constraints)
• Reporting & Visuals: openpyxl, Matplotlib, Seaborn

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▶ Quantitative Formulations & Methodology

1. Ledoit-Wolf Covariance Regularization

$$\Sigma_{LW} = \hat{\delta} F + (1 - \hat{\delta}) S, \quad \hat{\delta} \in [0, 1]$$ Where $S$ is the sample covariance matrix and $F$ is the structured constant-correlation shrinkage target.

2. Market Implied Equilibrium Prior (Reverse Optimization)

$$\Pi = \delta \Sigma_{LW} w_{mkt}, \quad \text{where } \delta = \frac{E[R_{mkt}] - R_f}{\sigma_{mkt}^2}$$

3. Black-Litterman Master Posterior Equations

With investor tactical views expressed as $P \cdot r = Q + \varepsilon$, where $\varepsilon \sim \mathcal{N}(0, \Omega)$, and $\Omega$ calibrated via Idzorek's confidence method:

$$ \Omega = \text{diag}\left( P (\tau \Sigma) P^T \right) \odot \left( \frac{1 - c}{c} \right) $$

$$ E[R] = \Pi + \tau \Sigma P^T \left[ P (\tau \Sigma) P^T + \Omega \right]^{-1} \left( Q - P \Pi \right) $$

$$ \Sigma_{post} = \Sigma + \tau \Sigma - \tau \Sigma P^T \left[ P (\tau \Sigma) P^T + \Omega \right]^{-1} P (\tau \Sigma) $$

4. Institutional UCITS Second-Order Cone Optimization (SOCP)

$$ \max_{w} \quad w^T E[R] - \frac{\delta}{2} w^T \Sigma_{post} w $$

$$ \text{subject to:} \quad \sum_{i=1}^N w_i = 1.0, \quad 0 \le w_i \le 0.35, \quad L_c \le \sum_{i \in c} w_i \le U_c, \quad | L^T (w - w_b) |_2 \le \text{TE}_{\text{max}} $$

Where $\Sigma = L L^T$ is the Cholesky factor of the regularized covariance matrix.

5. Cornish-Fisher Expansion (Modified VaR)

$$ \tilde{z}_\alpha = z_\alpha + \frac{1}{6}(z_\alpha^2 - 1)S + \frac{1}{24}(z_\alpha^3 - 3z_\alpha)K - \frac{1}{36}(2z_\alpha^3 - 5z_\alpha)S^2 $$

$$ \text{VaR}_\alpha^{CF} = - \left( \mu_p + \tilde{z}_\alpha \sigma_p \right), \quad \text{CVaR}_\alpha = - \mathbb{E}[R_p \mid R_p \le -\text{VaR}_\alpha] $$

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▶ Visual Analytics & Performance Gallery

1. Cumulative Wealth Evolution & Underwater Drawdown Profile

Walk-forward out-of-sample backtest comparison (2017–2026) showcasing superior risk-adjusted alpha and drawdown reduction:

2. Efficient Frontier Shift via Tactical Black-Litterman Views

Demonstrating the Bayesian shift in the risk-return opportunity set after incorporating tactical views:

3. Dynamic Systematic Asset Allocation Drift

Stacked area breakdown of active asset class weights drifting across monthly rebalancing checkpoints:

4. Historical Crisis Stress-Test Capital Preservation

Grouped shock impact analysis verifying capital preservation during severe historical market dislocations:

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▶ Out-of-Sample Empirical Results (2017–2026)

Walk-forward backtest results over a 9.5-year out-of-sample period (monthly rebalancing, 10 bps friction):

Strategy	CAGR	Volatility	Sharpe ($R_f$)	Sortino	Max Drawdown	Information Ratio	Capture Ratio
Global Benchmark (Cap-Weighted)	8.12%	12.10%	0.35	0.48	-23.85%	0.00	1.00
Equal Weight ($1/N$)	6.85%	11.40%	0.26	0.36	-22.10%	-0.33	0.92
Constrained Historical MVO	7.30%	13.50%	0.25	0.34	-27.40%	-0.18	0.88
Dynamic Constrained Black-Litterman	9.45%	11.85%	0.47	0.66	-19.65%	+0.50	1.18

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📁 Repository Structure

multi-asset-bl-engine/
│
├── config/
│   └── config.yaml          <- Declarative YAML universe, views, and UCITS limits
├── sql/
│   ├── schema.sql           <- Relational DDL schema (PostgreSQL)
│   └── queries.sql          <- Validation and analytical return SQL queries
├── src/
│   ├── db/
│   │   ├── connection.py    <- SQLAlchemy PostgreSQL connection pool
│   │   └── ingest_prices.py <- Idempotent market data pipeline (yfinance)
│   ├── engine/
│   │   ├── data_loader.py   <- Matrix extraction & risk-free rate loaders
│   │   ├── covariance.py    <- Ledoit-Wolf shrinkage & condition diagnostics
│   │   ├── equilibrium.py   <- CAPM reverse optimization & risk aversion delta
│   │   ├── views.py         <- Tactical view manager & Idzorek uncertainty scaling
│   │   ├── black_litterman.py <- Bayesian posterior calculation engine
│   │   ├── constraints.py   <- UCITS / BaFin regulatory mandate models
│   │   ├── optimizer.py     <- CVXPY Second-Order Cone (SOCP) solver
│   │   ├── backtest.py      <- Walk-forward rolling backtest engine
│   │   ├── analytics.py     <- Sortino, Omega, Calmar & Capture ratio analytics
│   │   ├── stress_testing.py<- Cornish-Fisher VaR & Crisis Replay engine
│   │   └── pipeline.py      <- Master End-to-End Pipeline Orchestrator Class
│   └── analytics/
│       ├── rebalance_report.py <- Institutional Excel Order Sheet generator (openpyxl)
│       └── visualize.py     <- Publication-grade chart generation module
├── reports/                 <- Output directory for generated Excel Order Sheets
├── docs/
│   └── figures/             <- High-resolution (300 DPI) publication PNG charts
├── tests/
│   └── test_engine.py       <- Automated Pytest unit test suite
├── scripts/
│   ├── init_db.py           <- Database table seeder & metadata initializer
│   ├── run_ingest.py        <- Market data ingestion runner
│   ├── run_calibration.py   <- Covariance and equilibrium calibration runner
│   ├── run_black_litterman.py <- Black-Litterman posterior calculation runner
│   ├── run_optimizer.py     <- UCITS optimization comparative audit runner
│   ├── run_backtest.py      <- Rolling walk-forward backtest runner
│   ├── run_analytics.py     <- Performance tear-sheet runner
│   ├── run_stress_test.py   <- Tail-risk and crisis stress-test runner
│   ├── generate_excel_report.py <- Excel rebalance sheet exporter
│   └── generate_charts.py   <- High-resolution chart generator
├── main.py                  <- Master CLI execution entry point
├── requirements.txt
└── README.md