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Randomized Control in Performance Analysis and Empirical Asset Pricing

Published 14 Feb 2024 in q-fin.PM, cs.CG, and q-fin.CP | (2403.00009v1)

Abstract: The present article explores the application of randomized control techniques in empirical asset pricing and performance evaluation. It introduces geometric random walks, a class of Markov chain Monte Carlo methods, to construct flexible control groups in the form of random portfolios adhering to investor constraints. The sampling-based methods enable an exploration of the relationship between academically studied factor premia and performance in a practical setting. In an empirical application, the study assesses the potential to capture premias associated with size, value, quality, and momentum within a strongly constrained setup, exemplified by the investor guidelines of the MSCI Diversified Multifactor index. Additionally, the article highlights issues with the more traditional use case of random portfolios for drawing inferences in performance evaluation, showcasing challenges related to the intricacies of high-dimensional geometry.

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References (134)
  1. Measuring the investment performance of pension funds for the purpose of inter-fund comparison. Bank Administration Institute, 1968.
  2. H.M. Afshar and J. Domke. Reflection, refraction, and Hamiltonian Monte Carlo. In Advances in neural information processing systems, pages 3007–3015, 2015.
  3. M. M. Ali. Content of the frustum of a simplex. Pacific Journal of Mathematics, 49:313–322, 1973.
  4. K. M. Anstreicher. Improved complexity for maximum volume inscribed ellipsoids. SIAM Journal on Optimization, 13(2):309–320, 2002.
  5. The surprising alpha from malkiel’s monkey and upside-down strategies. The Journal of Portfolio Management, 4:91–105, 2013.
  6. Quality minus junk. Review of Accounting Studies, 24:34–112, 2019.
  7. C. Bachelard. On the geometry of the bootstrap. Unpublished Manuscript, 2024.
  8. Randomized geometric tools for anomaly detection in stock markets. In Francisco Ruiz, Jennifer Dy, and Jan-Willem van de Meent, editors, Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, volume 206 of Proceedings of Machine Learning Research, pages 9400–9416. PMLR, 25–27 Apr 2023.
  9. R. W. Banz. The relationship between return and market value of common stocks. Journal of Financial Economics, 9:3–18, 1981.
  10. Hit-and-run algorithms for the identification of nonredundant linear inequalities. Mathematical Programming, 37(2):184–207, Jun 1987.
  11. D. Bertsimas and S. Vempala. Solving convex programs by random walks. J. ACM, 51(4):540–556, July 2004.
  12. Resampling fewer than n observations. Statistica Sinica, 7:1–31, 1997.
  13. A cross-sectional score for the relative performance of an allocation. International Review of Applied Financial Issues and Economics, 3, 2011.
  14. G. P. Brinsan and N. Fachler. Measuring non-us. equity portfolio performance. 11:73–76, 1985.
  15. Determinants of portfolio performance. Financial Analysts Journal, 41:39–44, 1986.
  16. P. Burns. Random portfolios for performance measurement. In E. Kontoghiorghes and C. Gatu, editors, Optimisation, Econometric, and Financial Analysis, pages 227–249, New York, 2007. Springer.
  17. Hit-and-run algorithms for generating multivariate distributions. Mathematics of Operations Research, 18(2):255–266, 1993.
  18. On the cross-sectional distribution of portfolios’ returns. arXiv:2105.06573, 2021.
  19. Practical volume computation of structured convex bodies, and an application to modeling portfolio dependencies and financial crises. 2018.
  20. M. M. Carhart. On persistence in mutual fund performance. The Journal of Finance, 52:57–82, 1997.
  21. Modeling asset allocation strategies and a new portfolio performance score. Digital Finance, 3:333–371, 2021.
  22. A practical algorithm for volume estimation based on billiard trajectories and simulated annealing. ACM J. Exp. Algorithmics, 28, may 2023.
  23. Efficient sampling in spectrahedra and volume approximation. Linear Algebra and its Applications, 648:205–232, 2022.
  24. A. Chalkis and V. Fisikopoulos. volesti: Volume Approximation and Sampling for Convex Polytopes in R. The R Journal, 13(2):642–660, 2021.
  25. Truncated log-concave sampling for convex bodies with reflective hamiltonian monte carlo. ACM Trans. Math. Softw., 49(2), jun 2023.
  26. volesti. https://github.com/GeomScale/volesti, 2024.
  27. Geometric Algorithms for Sampling the Flux Space of Metabolic Networks. In Kevin Buchin and Éric Colin de Verdière, editors, 37th International Symposium on Computational Geometry (SoCG 2021), volume 189 of Leibniz International Proceedings in Informatics (LIPIcs), pages 21:1–21:16, Dagstuhl, Germany, 2021. Schloss Dagstuhl – Leibniz-Zentrum für Informatik.
  28. Hamiltonian Monte Carlo with boundary reflections, and application to polytope volume calculations. Research Report RR-9222, INRIA Sophia Antipolis, France, 2018.
  29. Portfolio selection with qualitative input. Journal of Banking & Finance, 36:489–496, 2012.
  30. An evaluation of alternative equity indices - part 2: Fundamental weighting schemes. Cass Consulting, March 2013, 2013.
  31. An empirical evaluation of alternative portfolio-selection models. The Journal of Business, 40:166–193, 1967.
  32. A near-optimal algorithm for approximating the john ellipsoid. In Alina Beygelzimer and Daniel Hsu, editors, Proceedings of the Thirty-Second Conference on Learning Theory, volume 99 of Proceedings of Machine Learning Research, pages 849–873. PMLR, 25–28 Jun 2019.
  33. B. Cousins. Efficient high-dimensional sampling and integration. PhD thesis, Georgia Institute of Technology, Georgia, U.S.A., 2017.
  34. B. Cousins and S. Vempala. Bypassing KLS: Gaussian cooling and an O*⁢(n3)superscript𝑂superscript𝑛3{O}^{*}(n^{3})italic_O start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT ( italic_n start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT ) volume algorithm. In Proc. ACM STOC, pages 539–548, 2015.
  35. B. Cousins and S. Vempala. A practical volume algorithm. Mathematical Programming Computation, 8:133–160, 2016.
  36. R. Dawson and R. Young. Near-uniformly distributed, stochastically generated portfolios. 2003.
  37. M. Lopez de Prado. Causal factor investing: Can factor investing become scientific? ADIA Research Lab, 2022.
  38. P. O. Dietz. Pension funds: Measuring investment performance. 1966.
  39. A random polynomial-time algorithm for approximating the volume of convex bodies. J. ACM, 38(1):1–17, 1991.
  40. B. Efron. The bootstrap: Another look at the jacknife. The Annals of Statistics, 7:1–26, 1979.
  41. I.Z. Emiris and V. Fisikopoulos. Practical polytope volume approximation. ACM Transactions of Mathematical Software, 2018, 44(4):38:1–38:21, 2014. Conf. version: Proc. Symp. Comp. Geometry, 2014.
  42. Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33:3–56, 1993.
  43. A five-factor asset pricing model. Journal of Financial Economics, 116:1–22, 2015.
  44. Risk, return, and equilibrium: Empirical tests. Journal of Political Economy, 81:607–636, 1973.
  45. Shadow dirichlet for restricted probability modeling. Advances in Neural Information Processing Systems 23, pages 613–621, 2010.
  46. Eigen v3, 2010.
  47. G. van Valkenhoef, T. Tervonen. hitandrun: ”Hit and Run” and ”Shake and Bake” for Sampling Uniformly from Convex Shapes. R Foundation for Statistical Computing, 2022.
  48. A. Gelman and D. B. Rubin. Inference from Iterative Simulation Using Multiple Sequences. Statistical Science, 7(4):457–472, 1992. Publisher: Institute of Mathematical Statistics.
  49. M. Girolami and B. Calderhead. Riemann manifold langevin and hamiltonian monte carlo methods. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 73(2):123–214, 2011.
  50. A kernel two-sample test. Journal of Machine Learning Research, 13(25):723–773, 2012.
  51. E. Gryazina and B. Polyak. Random sampling: Billiard walk algorithm. European Journal of Operational Research, 238:497–504, 2014.
  52. A. Gustafson and H. Narayanan. John’s walk. arXiv preprint arXiv:1803.02032, page NA, 2018.
  53. CHRR: coordinate hit-and-run with rounding for uniform sampling of constraint-based models. Bioinformatics, 33(11):1741–1743, 2017.
  54. W. K. Hastings. Monte carlo sampling methods using markov chains and their applications. Biometrika, 57(1):97–109, 1970.
  55. Creation and analysis of biochemical constraint-based models: The cobra toolbox v3.0. Nature Protocols, 14:639–702, 2019.
  56. M. D. Hoffman and A. Gelman. The no-u-turn sampler: Adaptively setting path lengths in hamiltonian monte carlo. J. Mach. Learn. Res., 15(1):1593–1623, January 2014.
  57. K-L. Huang and S. Mehrotra. An empirical evaluation of walk-and-round heuristics for mixed integer linear programs. Computational Optimization and Applications, 55:545–570, 2013.
  58. Fritz J. Extremum Problems with Inequalities as Subsidiary Conditions. In Giorgio Giorgi and Tinne Hoff Kjeldsen, editors, Traces and Emergence of Nonlinear Programming, pages 197–215. Springer, Basel, 2014.
  59. HOPS: high-performance library for (non-)uniform sampling of convex-constrained models. Bioinformatics, 37(12):1776–1777, 10 2020.
  60. N. Jegadeesh and S. Titman. Returns to buying winners and selling losers: Implications for stock market efficiency. The Journal of Finance, 48:65–91, 1993.
  61. Is there a replication crisisi in finance? The Journal of Finance, 78:2465–2518, 2023.
  62. Reducing isotropy and volume to KLS: An O*⁢(n3⁢ψ2)superscript𝑂superscript𝑛3superscript𝜓2{O}^{*}(n^{3}\psi^{2})italic_O start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT ( italic_n start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT italic_ψ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ) volume algorithm. In Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021, page 961–974, New York, NY, USA, 2021. Association for Computing Machinery.
  63. Performance hypothesis testing with the sharpe and treynor measures. The Journal of Finance, 36:889–908, 1981.
  64. A. T. Kalai and S. Vempala. Simulated annealing for convex optimization. Mathematics of Operations Research, 31(2):253–266, 2006.
  65. Random walks and an O(n5superscript𝑛5n^{5}italic_n start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT) volume algorithm for convex bodies. Random Structures and Algorithms, 11:1 – 50, 1997.
  66. R. Kannan and H. Narayanan. Random walks on polytopes and an affine interior point method for linear programming. Mathematics of Operations Research, 37:1 – 20, 2012.
  67. E. Kasak and W. Pohlmeier. Testing out-of-sample portfolio performance. International Journal of Forecasting, 35:540–554, 2019.
  68. Direction choice for accelerated convergence in hit-and-run sampling. Operations Research, 46(1):84–95, 1998.
  69. On the complexity of approximating the maximal inscribed ellipsoid for a polytope. Mathematical Programming, 61(1):137–159, August 1993.
  70. W. C. Kim and Y. Lee. A uniformly distributed random portfolio. Quantitative Finance, 16:297–307, 2016.
  71. Polytopesamplermatlab. https://github.com/ConstrainedSampler/PolytopeSamplerMatlab, 2021.
  72. Sampling with riemannian hamiltonian monte carlo in a constrained space. In S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh, editors, Advances in Neural Information Processing Systems, volume 35, pages 31684–31696. Curran Associates, Inc., 2022.
  73. Condition-number-independent convergence rate of riemannian hamiltonian monte carlo with numerical integrators. In Gergely Neu and Lorenzo Rosasco, editors, Proceedings of Thirty Sixth Conference on Learning Theory, volume 195 of Proceedings of Machine Learning Research, pages 4504–4569. PMLR, 12–15 Jul 2023.
  74. P. Kumar and E. A. Yildirim. Minimum-volume enclosing ellipsoids and core sets. Journal of Optimization Theory and Applications, 126(1):1–21, Jul 2005.
  75. Strong self-concordance and sampling. In Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2020, page 1212–1222, New York, NY, USA, 2020. Association for Computing Machinery.
  76. A. Laddha and S. Vempala. Convergence of gibbs sampling: Coordinate hit-and-run mixes fast. Discrete & Computational Geometry, Apr 2023.
  77. J. B. Lasserre. Volume of slices and sections of the simplex in closed form. Optimization Letters, 9:1263–1269, 2015.
  78. O. Ledoit and M. Wolf. Robust performance hypothesis testing with the sharpe ratio. Journal of Empirical Finance, 15:850–859, 2008.
  79. An alternative approach for portfolio performance evaluation: enabling fund evaluation relative to peer group via malkiel’s monkey. Applied Economics, 50:4318–4327, 2018.
  80. Y. T. Lee and A. Sidford. Path Finding Methods for Linear Programming: Solving Linear Programs in Õ(vrank) Iterations and Faster Algorithms for Maximum Flow. In 2014 IEEE 55th Annual Symposium on Foundations of Computer Science, pages 424–433, October 2014. ISSN: 0272-5428.
  81. Y. T. Lee and S. Vempala. Eldan’s stochastic localization and the KLS hyperplane conjecture: An improved lower bound for expansion. In 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS), pages 998–1007, Oct 2017.
  82. Y. T. Lee and S. Vempala. Geodesic walks in polytopes. In Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017, pages 927–940, New York, NY, USA, 2017. ACM.
  83. Y. T. Lee and S. Vempala. Convergence rate of riemannian hamiltonian monte carlo and faster polytope volume computation. In Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2018, page 1115–1121, New York, NY, USA, 2018. Association for Computing Machinery.
  84. Y. T. Lee and S. Vempala. The Kannan-Lovasz-Simonovits conjecture. arXiv preprint arXiv:1807.03465, page NA, 2018.
  85. B. Liang. Price pressure: Evidence from the dartboard column. The Journal of Business, 72:119–134, 1999.
  86. J. Lintner. Security prices, risk and maximal gains from diversification. The Journal of Finance, 20:587–615, 1965.
  87. F. Lisi. Dicing with the market: Randomized procedures for evaluation of mutual funds. Quantitative Finance, 11:163–172, 2009.
  88. L. Lovász and M. Simonovits. Mixing rate of markov chains, an isoperimetric inequality, and computing volume. Proceedings 31st Annual Symposium on Foundations of Computer Science, 22.-24. Oct. 1990, pages 346–355, 1990.
  89. L. Lovász and M. Simonovits. Random walks in a convex body and an improved volume algorithm. Random Structures and Algorithms, 4:359–412, 1993.
  90. L. Lovász and S. Vempala. Hit and run is fast and fun. Technical Report MSR-TR-2003-05, Microsoft Research, Redmond., page NA, 2003.
  91. L. Lovász and S. Vempala. Logconcave functions: geometry and efficient sampling algorithms. In 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings., pages 640–649, 2003.
  92. L. Lovász and S. Vempala. Fast algorithms for logconcave functions: Sampling, rounding, integration and optimization. Proceedings 47th Annual IEEE Symposium on Foundations of Computer Science, 21- 24. Oct 2006, 2006.
  93. L. Lovász and S. Vempala. Hit-and-run from a corner. SIAM J. Comp., 35(4):985–1005, 2006.
  94. L. Lovász and S. Vempala. Simulated annealing in convex bodies and an O(n4)*{}^{*}(n^{4})start_FLOATSUPERSCRIPT * end_FLOATSUPERSCRIPT ( italic_n start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT ) volume algorithms. J. Computer and System Sciences, 72:392–417, 2006.
  95. B. G. Malkiel. A random walk down wall street. 1973.
  96. O. Mangoubi and A. Smith. Rapid mixing of hamiltonian monte carlo on strongly log-concave distributions, 2017.
  97. O. Mangoubi and N.K. Vishnoi. Faster algorithms for polytope rounding, sampling, and volume computation via a sublinear ”ball walk”. In FOCS, 2019.
  98. J. Maurer and S. Watanabe. Boost random number library. Software, 2017.
  99. optgpsampler: An improved tool for uniformly sampling the solution-space of genome-scale metabolic networks. PLOS ONE, 9(2):1–8, 02 2014.
  100. C. Memmel. Performance hypothesis testing with the sharpe ratio. Finance Letters, 1:21–23, 2003.
  101. The wall street journal contests: the experts, the darts, and the efficient market hypothesis. Applied Financial Economics, 4:371–374, 1994.
  102. J. Mossin. Equilibrium in a capital asset market. Econometrica, 34:768–783, 1966.
  103. H. Narayanan. Randomized interior point methods for sampling and optimization. Annals of Applied Probability, 26(1):597–641, February 2016. Publisher: Institute of Mathematical Statistics.
  104. H. Narayanan and P. Srivastava. On the mixing time of coordinate hit-and-run, 2020.
  105. R. M. Neal. MCMC Using Hamiltonian Dynamics, chapter 5. CRC Press, 2011.
  106. A. Nemirovski. On self-concordant convex-concave functions. Optimization Methods & Software - OPTIM METHOD SOFTW, 11, 05 1999.
  107. S. P. Nielsen. ll-ACHRB: a Scalable Algorithm for Sampling the Feasible Solution Space of Metabolic Networks. Bioinformatics, 32:2330–2337, 2016.
  108. Estimating expected returns in an event study framework: Evidence from the dartboard column. Quarterly Journal of Business and Economics, 40:3–21, 2001.
  109. ersuasive evidence of market inefficiency. The Journal of Portfolio Management, 11:9–16, 1985.
  110. V. Roy. Convergence Diagnostics for Markov Chain Monte Carlo. Annual Review of Statistics and Its Application, 7(1):387–412, 2020.
  111. R. Rubin. The bayesian bootstrap. The Annals of Statistics, 9:130–134, 1981.
  112. M. Rudelson. Random vectors in the isotropic position. J. Funct. Anal, pages 60–72, 1999.
  113. ll-ACHRB: A Scalable Algorithm for Sampling the Feasible Solution Space of Metabolic Networks. Bioinformatics, 32(15):2330–2337, 03 2016.
  114. S. Sachdeva and N. K. Vishnoi. The mixing time of the dikin walk in a polytope—a simple proof. Operations Research Letters, 44(5):630–634, 2016.
  115. W. F. Sharpe. Capital asset prices: A theory of market equilibrium under conditions of risk. The Journal of Finance, 19:425–444, 1964.
  116. W. F. Sharpe. The arithmetic of active management. The Financial Analysts’ Journal, 47:7 – 9, 1991.
  117. R. L. Smith. Efficient monte carlo procedures for generating points uniformly distributed over bounded regions. Operations Research, 32(6):1296–1308, 1984.
  118. Faster algorithm for structured john ellipsoid computation, 2022.
  119. R. Stein. Not fooled by randomness: Using random portfolios to analyse investment funds. Investment Analysts Journal, 43:1–15, 2014.
  120. R. J. Surz. Portfolio opportunity distributions. The Journal of Investing, 3:36–41, 1994.
  121. R. J. Surz. A fresh look at investment performance evaluation: Unifying best practices to improve timeliness and reliability. The Journal of Portfolio Management, 32:54–65, 2006.
  122. Uniform distributions in a class of convex polyhedrons with applications to drug combination studies. Journal of Multivariate Analysis, 100:1854–1865, 2009.
  123. On khachiyan’s algorithm for the computation of minimum-volume enclosing ellipsoids. Discrete Applied Mathematics, 155(13):1731–1744, 2007.
  124. P. M. Vaidya. A new algorithm for minimizing convex functions over convex sets | SpringerLink, 1996.
  125. xsample(): An r function for sampling linear inverse problems. Journal of Statistical Software, Code Snippets, 30(1):1–15, 2009.
  126. G. Varsi. The multidimensional content of the frustum of the simplex. Pacific Journal of Mathematics, 46:303–314, 1973.
  127. S. Vempala. Geometric random walks: A survey. Combinatorial and Computational Geometry, 52:577–616, 2005.
  128. A. Yao. walkr. https://github.com/andyyao95/walkr, 2020.
  129. C. Yuansi. An almost constant lower bound of the isoperimetric coefficient in the KLS conjecture. Geometric and Functional Analysis, 31(1):34–61, Feb 2021.
  130. Vaidya walk: A sampling algorithm based on the volumetric barrier. In 2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pages 1220–1227, October 2017.
  131. Fast MCMC Sampling Algorithms on Polytopes. Journal of Machine Learning Research, 19(55):1–86, 2018.
  132. Polytopewalk. https://github.com/yuachen/polytopewalk, 2020.
  133. C. Yuansi and R. Eldan. Hit-and-run mixing via localization schemes, 2022.
  134. Y. Zhang and L. Gao. On numerical solution of the maximum volume ellipsoid problem. SIAM Journal on Optimization, 14(1):53–76, 2003.

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