What a citation supports
Sources are attached to the question or convention they inform. The bundled numbers are our own synthetic examples, not historical data extracted from the cited documents. A link to a source does not mean that its author reviewed or endorsed this publication.
Access and redistribution
Publicly readable documentation is not automatically licensed for bulk republication. This site links to third-party research and standards without redistributing their full text or market data. Original example code and inputs carry MIT terms; the statistical dependency and icons retain their separate licences. Source availability was checked for this edition; later access may change.
- Dirk Tasche: Capital Allocation to Business Units and Sub-Portfolios, the Euler Principle, section 3.1
- Creative Commons: Attribution 4.0 International legal code
- MOSEK Portfolio Optimization Cookbook: Dealing with estimation error, covariance shrinkage
- MOSEK: portfolio variance and allocation constraints
- MOSEK: risk budgeting and contributions
- SciPy: least-squares regression
- Federal Reserve Bank of St. Louis: FRED legal notices and data restrictions
- Pro Git: lightweight and annotated tags
- JSON Schema: object properties, required fields and additional properties
- Kenneth R. French: Description of Fama/French Factors
- Decimal.js: arbitrary-precision arithmetic and conversion
- NumPy: numpy.cov, covariance definition, normalization and observation orientation
- NumPy: random stream compatibility policy
- Open Source Initiative: MIT licence text
- pandas: pairwise covariance and positive-semidefinite limitations
- pandas: DataFrame.ewm, adjusted and recursive weighting and missing-value semantics
- pandas: fractional change and explicit missing-value treatment
- pandas: merge_asof direction, tolerance and sorting requirements
- Aswath Damodaran: Estimating Risk Parameters
- pip: secure installs and dependency hash checking
- Daniel P. Palomar: Portfolio Optimization, section 11.3, Risk Contributions
- Reproducible Builds: definitions and artifact comparison
- Gabriel Hawawini: Why Beta Shifts as the Return Interval Changes, public abstract
- scikit-learn: preprocessing and data leakage
- scikit-learn: covariance estimation and shrinkage
- scikit-learn: cross-validation and time-series evaluation
- scikit-learn: LedoitWolf covariance estimator, target formula and centering contract
- Scikit-learn documentation: TimeSeriesSplit
- PerformanceAnalytics: cumulative return
- PerformanceAnalytics documentation: Drawdowns and findDrawdowns
- PerformanceAnalytics: maximum drawdown
- Semantic Versioning 2.0.0: public interface and compatibility rules
- Simple Statistics: reference implementation and API
- William F. Sharpe: differential-return ratios and time aggregation
- CFA Institute: Analysis of Active Portfolio Management, public summary
- CFA Institute: Using Multifactor Models, active risk and information ratio definitions
- CVX Group: Portfolio optimization, constraints and leverage limits
- Cvxportfolio: turnover constraints and cash conventions
- Cvxportfolio: proportional transaction costs
- Bailey, Borwein, Lopez de Prado and Zhu: The Probability of Backtest Overfitting, author-hosted February 2015 manuscript
- GIPS Standards Handbook for Firms: Input data and calculation methodology
- NIST e-Handbook: Measures of Scale
- NIST e-Handbook: Least Squares
- NIST e-Handbook: Predicting a single response and its uncertainty
- NIST e-Handbook: Bonferroni's method
- RiskMetrics technical document, fourth edition
- NASA Systems Engineering Handbook: Product Realization, verification and validation
- NIST Statistical Reference Datasets: Linear Regression background and limitations
- RFC 8259: JSON numbers and interoperability limits
- S&P Dow Jones Indices: S&P Risk Control 2.0 Indices Methodology, construction and rebalance lags
- S&P Dow Jones Indices: S&P U.S. Indices Methodology, equal-weight construction and maintenance
- S&P Dow Jones Indices: FAQ, S&P 500 Equal Weight Index