Folio Lab/Documentation

References

Canonical bibliography for FolioLab. Every optimization method, performance metric, statistical inference procedure, and numerical technique that the platform actively uses is mapped to its primary academic source.

Table of Contents

  1. Foundations: Modern Portfolio Theory and the CAPM
  2. Optimization Methods
  3. Covariance and Mean Estimation
  4. Performance and Risk-Adjusted Metrics
  5. Risk and Drawdown Metrics
  6. Beta Variants
  7. Higher-Moment Cross Statistics
  8. Statistical Inference
  9. Diversification and Concentration
  10. Hierarchical Clustering and Distance Metrics
  11. Information Geometry and Bayesian View Construction
  12. Backtesting Methodology
  13. Solvers and Convex Optimization
  14. Data Processing and Numerical Conventions
  15. Foundational Textbooks
  16. Related Work (Cited but Not Actively Implemented)
  17. Software Libraries

1. Foundations: Modern Portfolio Theory and the CAPM

Mean-Variance Portfolio Theory

The foundational framework for trading off expected return against variance.

  • Markowitz, H. M. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77-91. https://doi.org/10.2307/2975974
  • Markowitz, H. M. (1959). Portfolio Selection: Efficient Diversification of Investments. John Wiley & Sons.

Capital Asset Pricing Model (CAPM)

Equilibrium pricing of risk; basis for beta, alpha, and excess-return regressions.

Efficient Frontier and Naive Diversification Benchmarks

  • DeMiguel, V., Garlappi, L., & Uppal, R. (2009). Optimal Versus Naive Diversification: How Inefficient Is the 1/N Portfolio Strategy? The Review of Financial Studies, 22(5), 1915-1953. https://doi.org/10.1093/rfs/hhm075
  • Michaud, R. O. (1989). The Markowitz Optimization Enigma: Is 'Optimized' Optimal? Financial Analysts Journal, 45(1), 31-42. https://doi.org/10.2469/faj.v45.n1.31

2. Optimization Methods

2.1 Mean-Variance family (Max Sharpe, Min Volatility, Max Quadratic Utility)

  • Markowitz, H. M. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77-91.
  • Sharpe, W. F. (1966). Mutual Fund Performance. The Journal of Business, 39(1), 119-138. https://doi.org/10.1086/294846
  • Pratt, J. W. (1964). Risk Aversion in the Small and in the Large. Econometrica, 32(1-2), 122-136. https://doi.org/10.2307/1913738
  • Arrow, K. J. (1971). Essays in the Theory of Risk-Bearing. Markham Publishing Company.
  • Clarke, R., de Silva, H., & Thorley, S. (2006). Minimum-Variance Portfolios in the U.S. Equity Market. The Journal of Portfolio Management, 33(1), 10-24. https://doi.org/10.3905/jpm.2006.661366
  • Haugen, R. A., & Baker, N. L. (1991). The Efficient Market Inefficiency of Capitalization-Weighted Stock Portfolios. The Journal of Portfolio Management, 17(3), 35-40. https://doi.org/10.3905/jpm.1991.409335
  • Jagannathan, R., & Ma, T. (2003). Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps. The Journal of Finance, 58(4), 1651-1683. https://doi.org/10.1111/1540-6261.00580

2.2 Critical Line Algorithm (CLA)

  • Markowitz, H. M. (1956). The Optimization of a Quadratic Function Subject to Linear Constraints. Naval Research Logistics Quarterly, 3(1-2), 111-133. https://doi.org/10.1002/nav.3800030110
  • Markowitz, H. M. (1987). Mean-Variance Analysis in Portfolio Choice and Capital Markets. Basil Blackwell.
  • Bailey, D. H., & Lopez de Prado, M. (2013). An Open-Source Implementation of the Critical-Line Algorithm for Portfolio Optimization. Algorithms, 6(1), 169-196. https://doi.org/10.3390/a6010169

2.3 Equal-Weighted Portfolio (1/N)

  • DeMiguel, V., Garlappi, L., & Uppal, R. (2009). Optimal Versus Naive Diversification. The Review of Financial Studies, 22(5), 1915-1953.
  • Benartzi, S., & Thaler, R. H. (2001). Naive Diversification Strategies in Defined Contribution Saving Plans. American Economic Review, 91(1), 79-98. https://doi.org/10.1257/aer.91.1.79
  • Windcliff, H., & Boyle, P. P. (2004). The 1/N Pension Investment Puzzle. North American Actuarial Journal, 8(3), 32-45. https://doi.org/10.1080/10920277.2004.10596151

2.4 Inverse Volatility

2.5 Maximum Diversification

2.6 CVaR Risk Budgeting (generalized risk contribution)

The active path uses CVaR as the risk measure, not variance. Each asset's tail-risk contribution is budgeted, so this generalizes classical Equal Risk Contribution. With equal budgets and CVaR replaced by variance, the method reduces to the Maillard-Roncalli-Teiletche ERC portfolio.

  • Roncalli, T. (2013). Introduction to Risk Parity and Budgeting. Chapman & Hall/CRC Financial Mathematics Series.
  • Bruder, B., & Roncalli, T. (2012). Managing Risk Exposures Using the Risk Budgeting Approach. SSRN Working Paper. https://doi.org/10.2139/ssrn.2009778
  • Cesarone, F., & Colucci, S. (2018). Minimum Risk versus Capital and Risk Diversification Strategies for Portfolio Construction. Journal of the Operational Research Society, 69(2), 183-200. https://doi.org/10.1057/s41274-017-0216-5
  • Rockafellar, R. T., & Uryasev, S. (2002). Conditional Value-at-Risk for General Loss Distributions. Journal of Banking & Finance, 26(7), 1443-1471. (Foundational CVaR formulation.)
  • Maillard, S., Roncalli, T., & Teiletche, J. (2010). The Properties of Equally Weighted Risk Contribution Portfolios. The Journal of Portfolio Management, 36(4), 60-70. (Special case: equal-budget, variance-based.)
  • Qian, E. (2005). Risk Parity Portfolios: Efficient Portfolios Through True Diversification. PanAgora Asset Management White Paper. (Foundational risk-parity intuition.)
  • Spinu, F. (2013). An Algorithm for Computing Risk Parity Weights. SSRN Working Paper. https://doi.org/10.2139/ssrn.2297383

2.7 Hierarchical Risk Parity (HRP)

  • Lopez de Prado, M. (2016). Building Diversified Portfolios that Outperform Out of Sample. The Journal of Portfolio Management, 42(4), 59-69. https://doi.org/10.3905/jpm.2016.42.4.059
  • Lopez de Prado, M. (2018). Advances in Financial Machine Learning. John Wiley & Sons.

2.8 Hierarchical Equal Risk Contribution (HERC and HERC2)

  • Raffinot, T. (2017). Hierarchical Clustering-Based Asset Allocation. The Journal of Portfolio Management, 44(2), 89-99. https://doi.org/10.3905/jpm.2018.44.2.089
  • Raffinot, T. (2018). The Hierarchical Equal Risk Contribution Portfolio. SSRN Working Paper. https://doi.org/10.2139/ssrn.3237540
  • Pfitzinger, J., & Katzke, N. (2019). A Constrained Hierarchical Risk Parity Algorithm with Cluster-Based Capital Allocation. Stellenbosch Economic Working Papers WP14/2019.

2.9 Nested Clustered Optimization (NCO)

2.10 Minimum CVaR (Conditional Value-at-Risk)

2.11 Minimum CDaR (Conditional Drawdown-at-Risk)

2.12 Distributionally Robust CVaR (Wasserstein DRO)

2.13 Sparse Markowitz with L1 Regularization

2.14 HMM Regime-Switching MVO

2.15 Black-Litterman with Measure-Tilted Views

2.16 Stacking Optimization (Ensemble Meta-Learner)

2.17 Benchmark Tracker (Tracking-Error Constrained)

2.18 Dividend Optimizer (Entropy-Tilted Dividend Yield)

  • Bera, A. K., & Park, S. Y. (2008). Optimal Portfolio Diversification Using the Maximum Entropy Principle. Econometric Reviews, 27(4-6), 484-512. https://doi.org/10.1080/07474930801960394
  • Philippatos, G. C., & Wilson, C. J. (1972). Entropy, Market Risk, and the Selection of Efficient Portfolios. Applied Economics, 4(3), 209-220. https://doi.org/10.1080/00036847200000017
  • Cover, T. M., & Thomas, J. A. (2006). Elements of Information Theory (2nd ed.). Wiley-Interscience.

3. Covariance and Mean Estimation

3.1 Ledoit-Wolf Linear Shrinkage

4. Performance and Risk-Adjusted Metrics

4.1 Sharpe Ratio

  • Sharpe, W. F. (1966). Mutual Fund Performance. The Journal of Business, 39(1), 119-138.
  • Sharpe, W. F. (1994). The Sharpe Ratio. The Journal of Portfolio Management, 21(1), 49-58. https://doi.org/10.3905/jpm.1994.409501

4.2 Sortino Ratio

  • Sortino, F. A., & van der Meer, R. (1991). Downside Risk. The Journal of Portfolio Management, 17(4), 27-31. https://doi.org/10.3905/jpm.1991.409343
  • Sortino, F. A., & Price, L. N. (1994). Performance Measurement in a Downside Risk Framework. Journal of Investing, 3(3), 59-64. https://doi.org/10.3905/joi.3.3.59
  • Kaplan, P. D., & Knowles, J. A. (2004). Kappa: A Generalized Downside Risk-Adjusted Performance Measure. Journal of Performance Measurement, 8(3), 42-54.

4.3 Treynor Ratio

  • Treynor, J. L. (1965). How to Rate Management of Investment Funds. Harvard Business Review, 43(1), 63-75.

4.4 Jensen's Alpha

4.5 Information Ratio

4.6 Tracking Error

  • Roll, R. (1992). A Mean/Variance Analysis of Tracking Error. The Journal of Portfolio Management, 18(4), 13-22.
  • Grinold, R. C., & Kahn, R. N. (2000). Active Portfolio Management (2nd ed.). McGraw-Hill.

4.7 Calmar Ratio

  • Young, T. W. (1991). Calmar Ratio: A Smoother Tool. Futures, 20(1), 40.
  • Bacon, C. R. (2013). Practical Risk-Adjusted Performance Measurement. John Wiley & Sons.

4.8 Sterling Ratio

The Sterling Ratio is widely attributed to Deane Sterling Jones & Co.; no peer-reviewed primary paper exists. Kestner (1996) and Bacon (2013) are the standard secondary sources.

  • Kestner, L. N. (1996). Getting a Handle on True Performance. Futures, 25(1), 44-46.
  • Bacon, C. R. (2013). Practical Risk-Adjusted Performance Measurement. John Wiley & Sons.
  • Lhabitant, F. S. (2004). Hedge Funds: Quantitative Insights. John Wiley & Sons.

4.9 V-squared (V2) Ratio

No peer-reviewed primary source introduces the V2 ratio in the form we compute. The references below are the most-cited comparative sources that include V2 in the family of drawdown-adjusted performance ratios.

  • Caporin, M., & Lisi, F. (2011). Comparing and Selecting Performance Measures Using Rank Correlations. Economics: The Open-Access E-Journal, 5, 1-34. (Comparative survey, not the introducing paper.) https://doi.org/10.5018/economics-ejournal.ja.2011-10
  • Eling, M., & Schuhmacher, F. (2007). Does the Choice of Performance Measure Influence the Evaluation of Hedge Funds? Journal of Banking & Finance, 31(9), 2632-2647. (Comparative survey, not the introducing paper.) https://doi.org/10.1016/j.jbankfin.2006.09.015
  • Bacon, C. R. (2008). Practical Portfolio Performance Measurement and Attribution (2nd ed.). Wiley. (Textbook treatment of drawdown-adjusted ratios.)

4.10 Modigliani Risk-Adjusted Performance (M2)

4.11 Omega Ratio

  • Keating, C., & Shadwick, W. F. (2002). A Universal Performance Measure. Journal of Performance Measurement, 6(3), 59-84.
  • Kazemi, H., Schneeweis, T., & Gupta, B. (2004). Omega as a Performance Measure. Journal of Performance Measurement, 8(3), 16-25.

4.12 Upside Potential Ratio

  • Sortino, F. A., van der Meer, R., & Plantinga, A. (1999). The Dutch Triangle. The Journal of Portfolio Management, 26(1), 50-58. https://doi.org/10.3905/jpm.1999.319775
  • Fishburn, P. C. (1977). Mean-Risk Analysis with Risk Associated with Below-Target Returns. American Economic Review, 67(2), 116-126.

4.13 Upside / Downside Capture Ratio

  • Bacon, C. R. (2008). Practical Portfolio Performance Measurement and Attribution (2nd ed.). John Wiley & Sons.
  • Morningstar (2016). Morningstar Methodology: Upside/Downside Capture Ratios. Morningstar Research.

4.14 Basic Return and Risk Statistics (CAGR, ROMAD, Expected Return, Volatility, VaR-90/CVaR-90, Beta significance)

The PortfolioPerformance schema also surfaces a number of standard descriptive and diagnostic quantities. These are textbook calculations rather than novel methods, but are listed here for completeness.

  • Expected Return and Volatility - sample annualized mean and standard deviation of portfolio returns. See Bodie, Z., Kane, A., & Marcus, A. J. (2014). Investments (10th ed.). McGraw-Hill, Ch. 5.
  • CAGR (Compound Annual Growth Rate) - geometric annualized growth rate (W_T / W_0)^(252/T) - 1. See Bacon, C. R. (2008). Practical Portfolio Performance Measurement and Attribution (2nd ed.). Wiley, Ch. 3.
  • ROMAD (Return Over Maximum Drawdown) - CAGR / |MDD|; algebraically identical to Calmar (4.7) and used widely in CTA reporting. Young, T. W. (1991). Calmar Ratio: A Smoother Tool. Futures, 20(1), 40.
  • VaR-90 and CVaR-90 - 10%-tail Value-at-Risk and Conditional Value-at-Risk. Same definition as 5.1 / 5.2 with confidence level 0.90.
  • Beta p-value and R-squared - reported alongside CAPM beta from the OLS market-model regression r_p = alpha + beta * r_m + e. Two-sided t-test on beta and the coefficient of determination of that regression. See Greene, W. H. (2018). Econometric Analysis (8th ed.). Pearson, Ch. 4-5.

5. Risk and Drawdown Metrics

5.1 Value-at-Risk (VaR)

  • Jorion, P. (2006). Value at Risk: The New Benchmark for Managing Financial Risk (3rd ed.). McGraw-Hill.
  • RiskMetrics Group (1996). RiskMetrics: Technical Document (4th ed.). J.P. Morgan/Reuters.
  • Basel Committee on Banking Supervision (1996). Amendment to the Capital Accord to Incorporate Market Risks. Bank for International Settlements.
  • Dowd, K. (2002). Measuring Market Risk. John Wiley & Sons.

5.2 Conditional Value-at-Risk (CVaR / Expected Shortfall)

  • Rockafellar, R. T., & Uryasev, S. (2000). Optimization of Conditional Value-at-Risk. Journal of Risk, 2(3), 21-42.
  • Rockafellar, R. T., & Uryasev, S. (2002). Conditional Value-at-Risk for General Loss Distributions. Journal of Banking & Finance, 26(7), 1443-1471.
  • Acerbi, C., & Tasche, D. (2002). On the Coherence of Expected Shortfall. Journal of Banking & Finance, 26(7), 1487-1503. https://doi.org/10.1016/S0378-4266(02)00283-2
  • Artzner, P., Delbaen, F., Eber, J.-M., & Heath, D. (1999). Coherent Measures of Risk. Mathematical Finance, 9(3), 203-228.
  • Basel Committee on Banking Supervision (2019). Minimum Capital Requirements for Market Risk. Bank for International Settlements.

5.3 Entropic Value-at-Risk (EVaR)

5.4 Maximum Drawdown

  • Magdon-Ismail, M., & Atiya, A. F. (2004). Maximum Drawdown. Risk, 17(10), 99-102.
  • Magdon-Ismail, M., Atiya, A. F., Pratap, A., & Abu-Mostafa, Y. S. (2004). On the Maximum Drawdown of a Brownian Motion. Journal of Applied Probability, 41(1), 147-161. https://doi.org/10.1239/jap/1077134674
  • Grossman, S. J., & Zhou, Z. (1993). Optimal Investment Strategies for Controlling Drawdowns. Mathematical Finance, 3(3), 241-276. https://doi.org/10.1111/j.1467-9965.1993.tb00044.x

5.5 Drawdown-at-Risk (DaR) and Conditional Drawdown-at-Risk (CDaR)

  • Chekhlov, A., Uryasev, S., & Zabarankin, M. (2005). Drawdown Measure in Portfolio Optimization. International Journal of Theoretical and Applied Finance, 8(1), 13-58.
  • Zabarankin, M., Pavlikov, K., & Uryasev, S. (2014). Capital Asset Pricing Model (CAPM) with Drawdown Measure. European Journal of Operational Research, 234(2), 508-517.
  • Alexander, G. J., & Baptista, A. M. (2006). Portfolio Selection with a Drawdown Constraint. Journal of Banking & Finance, 30(11), 3171-3189. https://doi.org/10.1016/j.jbankfin.2005.12.006

5.6 Ulcer Index

  • Martin, P. G., & McCann, B. B. (1989). The Investor's Guide to Fidelity Funds. John Wiley & Sons.

5.7 Gini Mean Difference

  • Yitzhaki, S. (2003). Gini's Mean Difference: A Superior Measure of Variability for Non-Normal Distributions. Metron, 61(2), 285-316.
  • Shalit, H., & Yitzhaki, S. (2005). The Mean-Gini Efficient Portfolio Frontier. The Journal of Financial Research, 28(1), 59-75. https://doi.org/10.1111/j.1475-6803.2005.00114.x
  • Yitzhaki, S. (1982). Stochastic Dominance, Mean Variance, and Gini's Mean Difference. American Economic Review, 72(1), 178-185.

6. Beta Variants

6.1 CAPM Beta

See Section 1 (CAPM) for primary citations.

6.2 Welch-Style Robust Beta

Implementation winsorizes the portfolio's excess return elementwise to [-2*|b|, 4*|b|] (where b is the contemporaneous benchmark excess return) and then applies plain cov/var. Welch (2022) uses the same -2/+4 slope-bounding logic but combined with age-decayed weighted least squares. We therefore label this a Welch-style robust beta rather than a literal reproduction.

6.3 Blume-Adjusted Beta

6.4 Vasicek Bayesian-Shrunk Beta

6.5 James-Stein Shrunk Beta

  • James, W., & Stein, C. (1961). Estimation with Quadratic Loss. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, 1, 361-379. University of California Press.
  • Efron, B., & Morris, C. (1973). Stein's Estimation Rule and Its Competitors: An Empirical Bayes Approach. Journal of the American Statistical Association, 68(341), 117-130. https://doi.org/10.1080/01621459.1973.10481350
  • Jorion, P. (1986). Bayes-Stein Estimation for Portfolio Analysis. Journal of Financial and Quantitative Analysis, 21(3), 279-292. https://doi.org/10.2307/2331042

6.6 Semi-Beta (Downside Beta)

6.7 Rolling (Time-Varying) Beta

7. Higher-Moment Cross Statistics

7.1 Skewness

7.2 Kurtosis

7.3 Coskewness

  • Kraus, A., & Litzenberger, R. H. (1976). Skewness Preference and the Valuation of Risk Assets. The Journal of Finance, 31(4), 1085-1100.
  • Harvey, C. R., & Siddique, A. (2000). Conditional Skewness in Asset Pricing Tests. The Journal of Finance, 55(3), 1263-1295.

7.4 Cokurtosis

8. Statistical Inference

8.1 Sharpe Ratio Standard Error and Confidence Interval

Variance correction with autocorrelation, skewness, and kurtosis.

8.2 Probabilistic Sharpe Ratio (PSR) and Minimum Track Record Length

8.3 Augmented Dickey-Fuller (ADF) Test for Stationarity

  • Dickey, D. A., & Fuller, W. A. (1979). Distribution of the Estimators for Autoregressive Time Series with a Unit Root. Journal of the American Statistical Association, 74(366a), 427-431. https://doi.org/10.1080/01621459.1979.10482531
  • Said, S. E., & Dickey, D. A. (1984). Testing for Unit Roots in Autoregressive-Moving Average Models of Unknown Order. Biometrika, 71(3), 599-607. https://doi.org/10.1093/biomet/71.3.599
  • MacKinnon, J. G. (1996). Numerical Distribution Functions for Unit Root and Cointegration Tests. Journal of Applied Econometrics, 11(6), 601-618.

8.4 Engle-Granger Cointegration Test

  • Engle, R. F., & Granger, C. W. J. (1987). Co-integration and Error Correction: Representation, Estimation, and Testing. Econometrica, 55(2), 251-276. https://doi.org/10.2307/1913236
  • Phillips, P. C. B., & Ouliaris, S. (1990). Asymptotic Properties of Residual Based Tests for Cointegration. Econometrica, 58(1), 165-193. https://doi.org/10.2307/2938339

8.5 Half-Life of Mean Reversion (Ornstein-Uhlenbeck / AR(1))

9. Diversification and Concentration

9.1 Effective Number of Constituents (inverse Herfindahl)

The function returns 1 / sum(w_i^2), which is the inverse Herfindahl-Hirschman concentration index on portfolio weights. It measures the effective number of holdings, treating assets as if uncorrelated. It is NOT Meucci's entropy-based Effective Number of Bets, which requires a PCA / torsion decomposition of the covariance matrix to count effective uncorrelated bets. We list this metric under the inverse-HHI lineage rather than Meucci ENB.

  • Herfindahl, O. C. (1950). Concentration in the U.S. Steel Industry. PhD dissertation, Columbia University.
  • Hirschman, A. O. (1964). The Paternity of an Index. American Economic Review, 54(5), 761-762.
  • Strongin, S., Petsch, M., & Sharenow, G. (2000). Beating Benchmarks. The Journal of Portfolio Management, 26(4), 11-27. (Inverse-HHI in portfolio diversification context.)
  • Related but not what we compute - Meucci, A. (2009). Managing Diversification. Risk, 22(5), 74-79. (Entropy-based ENB on uncorrelated bets - different formula.) https://doi.org/10.2139/ssrn.1358533

9.2 Portfolio Entropy (Shannon)

10. Hierarchical Clustering and Distance Metrics

10.1 Ward Linkage

10.2 Single, Complete, and Average Linkage

  • Sneath, P. H. A., & Sokal, R. R. (1973). Numerical Taxonomy. W.H. Freeman.
  • Murtagh, F., & Contreras, P. (2012). Algorithms for Hierarchical Clustering: An Overview. WIREs Data Mining and Knowledge Discovery, 2(1), 86-97. https://doi.org/10.1002/widm.53

10.3 Spearman Rank Correlation

  • Spearman, C. (1904). The Proof and Measurement of Association between Two Things. American Journal of Psychology, 15(1), 72-101. https://doi.org/10.2307/1412159

10.4 Silhouette Score for Cluster Validation

11. Information Geometry and Bayesian View Construction

11.1 Idzorek View-Confidence Method

  • Idzorek, T. (2005). A Step-by-Step Guide to the Black-Litterman Model. In Forecasting Expected Returns in the Financial Markets (pp. 17-38). Academic Press.

11.2 Exponential Tilting / KL-Targeted Measure Change

  • Csiszar, I. (1975). I-Divergence Geometry of Probability Distributions and Minimization Problems. The Annals of Probability, 3(1), 146-158.
  • Kitamura, Y., & Stutzer, M. (1997). An Information-Theoretic Alternative to Generalized Method of Moments Estimation. Econometrica, 65(4), 861-874. https://doi.org/10.2307/2171942
  • Meucci, A. (2008). Fully Flexible Views: Theory and Practice. Risk, 21(10), 97-102.

12. Backtesting Methodology

Walk-Forward / Rolling-Window / Expanding-Window Backtests

  • Bailey, D. H., Borwein, J. M., Lopez de Prado, M., & Zhu, Q. J. (2014). Pseudo-Mathematics and Financial Charlatanism. Notices of the AMS, 61(5), 458-471. https://doi.org/10.1090/noti1105
  • Harvey, C. R., & Liu, Y. (2015). Backtesting. The Journal of Portfolio Management, 42(1), 13-28. https://doi.org/10.3905/jpm.2015.42.1.013
  • Lopez de Prado, M. (2018). Advances in Financial Machine Learning, Chapters 11-12. John Wiley & Sons.

13. Solvers and Convex Optimization

13.1 Convex Optimization Theory

13.2 CVXPY (Problem Modeling)

  • Diamond, S., & Boyd, S. (2016). CVXPY: A Python-Embedded Modeling Language for Convex Optimization. Journal of Machine Learning Research, 17(83), 1-5.
  • Agrawal, A., Verschueren, R., Diamond, S., & Boyd, S. (2018). A Rewriting System for Convex Optimization Problems. Journal of Control and Decision, 5(1), 42-60. https://doi.org/10.1080/23307706.2017.1397554

13.3 MOSEK (Conic Interior-Point Solver)

13.4 CLARABEL (Interior-Point Conic)

  • Goulart, P. J., & Chen, Y. (2024). Clarabel: An Interior-Point Solver for Conic Programs with Quadratic Objectives. arXiv:2405.12762. https://arxiv.org/abs/2405.12762

13.5 SCS (Splitting Conic Solver)

  • O'Donoghue, B., Chu, E., Parikh, N., & Boyd, S. (2016). Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding. Journal of Optimization Theory and Applications, 169(3), 1042-1068. https://doi.org/10.1007/s10957-016-0892-3

13.6 ECOS (Embedded Conic Solver)

13.7 OSQP (Operator-Splitting QP)

  • Stellato, B., Banjac, G., Goulart, P., Bemporad, A., & Boyd, S. (2020). OSQP: An Operator Splitting Solver for Quadratic Programs. Mathematical Programming Computation, 12(4), 637-672. https://doi.org/10.1007/s12532-020-00179-2

14. Data Processing and Numerical Conventions

14.1 Freedman-Diaconis Histogram Bin-Width Rule

  • Freedman, D., & Diaconis, P. (1981). On the Histogram as a Density Estimator: L2 Theory. Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete, 57(4), 453-476. https://doi.org/10.1007/BF01025868

14.2 Spectral Decomposition / PCA Risk Attribution

14.3 Risk Decomposition (Marginal and Component Risk Contribution)

  • Litterman, R. (1996). Hot Spots and Hedges. The Journal of Portfolio Management, 22(5), 52-75. https://doi.org/10.3905/jpm.1996.052
  • Qian, E. (2006). On the Financial Interpretation of Risk Contribution: Risk Budgets Do Add Up. Journal of Investment Management, 4(4), 41-51.

15. Foundational Textbooks

These textbooks provide background context across multiple sections.

Reference Works

  • Boyd, S., & Vandenberghe, L. (2004). Convex Optimization. Cambridge University Press.
  • Bodie, Z., Kane, A., & Marcus, A. J. (2021). Investments (12th ed.). McGraw-Hill.
  • Hull, J. C. (2022). Options, Futures, and Other Derivatives (11th ed.). Pearson.
  • Jorion, P. (2006). Value at Risk: The New Benchmark for Managing Financial Risk (3rd ed.). McGraw-Hill.
  • Lopez de Prado, M. (2018). Advances in Financial Machine Learning. John Wiley & Sons.
  • Lopez de Prado, M. (2020). Machine Learning for Asset Managers. Cambridge University Press.
  • Roncalli, T. (2013). Introduction to Risk Parity and Budgeting. Chapman & Hall/CRC.
  • Bacon, C. R. (2013). Practical Risk-Adjusted Performance Measurement. John Wiley & Sons.
  • Cover, T. M., & Thomas, J. A. (2006). Elements of Information Theory (2nd ed.). Wiley-Interscience.
  • Casella, G., & Berger, R. L. (2002). Statistical Inference (2nd ed.). Duxbury.
  • Alexander, C. (2008). Market Risk Analysis (4 vols). John Wiley & Sons.

16. Related Work (Cited but Not Actively Implemented)

These references are foundational context for techniques the platform discusses or builds upon, but are not currently executed by the optimizer engine. They are listed for completeness and intellectual honesty.

GARCH-Conditional Beta

Declared in the data schema but the computation is currently commented out and not produced by the live performance engine.

Deflated Sharpe Ratio

Foundational context for the Sharpe-inference work; no DSR implementation exists in the repo.

  • Bailey, D. H., & Lopez de Prado, M. (2014). The Deflated Sharpe Ratio: Correcting for Selection Bias, Backtest Overfitting, and Non-Normality. The Journal of Portfolio Management, 40(5), 94-107. https://doi.org/10.3905/jpm.2014.40.5.094

Other Foundational References Not Actively Executed

  • Konno, H., & Yamazaki, H. (1991). Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market. Management Science, 37(5), 519-531. https://doi.org/10.1287/mnsc.37.5.519
  • Han, C. (2017). Turnover Minimization: A Versatile Shrinkage Portfolio Estimator. Frontiers of Finance and Economics, 14(2). SSRN Working Paper. https://doi.org/10.2139/ssrn.2840422
  • Bodnar, T., Okhrin, O., & Parolya, N. (2019). Optimal Shrinkage Estimator for High-Dimensional Mean Vector. Journal of Multivariate Analysis, 170, 63-79. https://doi.org/10.1016/j.jmva.2018.07.004
  • Feng, Y., & Palomar, D. P. (2016). A Signal Processing Perspective on Financial Engineering. Foundations and Trends in Signal Processing, 9(1-2), 1-231. https://doi.org/10.1561/2000000072
  • Barfuss, W., Massara, G. P., Di Matteo, T., & Aste, T. (2016). Parsimonious Modeling with Information Filtering Networks. Physical Review E, 94(6), 062306. https://doi.org/10.1103/PhysRevE.94.062306
  • Gerber, S., Markowitz, H. M., Ernst, P. A., Miao, Y., Javid, B., & Sargen, P. (2022). The Gerber Statistic: A Robust Co-Movement Measure for Portfolio Optimization. The Journal of Portfolio Management, 48(3), 87-102. https://doi.org/10.3905/jpm.2021.1.316
  • Sjostrand, D., & Behnejad, N. (2020). Exploration of hierarchical clustering in long-only equity portfolios. Master's thesis.

17. Software Libraries

The engine wraps the following open-source libraries; their authors are credited here.

Open-Source Libraries

  • Martin, R. A. (2021). PyPortfolioOpt: portfolio optimization in Python. Journal of Open Source Software, 6(61), 3066. https://doi.org/10.21105/joss.03066
  • Cajas, D. (2024). Riskfolio-Lib: Portfolio Optimization and Quantitative Strategic Asset Allocation in Python. https://github.com/dcajasn/Riskfolio-Lib
  • Delatte, H., & Nicolini, C. (2024). skfolio: Python library for portfolio optimization built on top of scikit-learn. https://github.com/skfolio/skfolio
  • Diamond, S., & Boyd, S. (2016). CVXPY: A Python-Embedded Modeling Language for Convex Optimization. JMLR, 17(83), 1-5.
  • Seabold, S., & Perktold, J. (2010). Statsmodels: Econometric and Statistical Modeling with Python. Proceedings of the 9th Python in Science Conference.
  • Pedregosa, F., et al. (2011). Scikit-learn: Machine Learning in Python. Journal of Machine Learning Research, 12, 2825-2830.

Corrections

If you spot a missing reference, an incorrect attribution, or a more authoritative primary source for any technique listed here, please open an issue on the project repository. We treat citation accuracy as a publication-grade obligation.