{"id":25525,"date":"2022-07-21T09:00:00","date_gmt":"2022-07-21T13:00:00","guid":{"rendered":"https:\/\/gestionderiesgo.org\/?p=25525"},"modified":"2026-10-12T21:14:51","modified_gmt":"2026-10-13T01:14:51","slug":"construccion-de-matrices-de-covarianza-robustas-marcenko-pastur","status":"publish","type":"post","link":"https:\/\/gestionderiesgo.org\/en\/construccion-de-matrices-de-covarianza-robustas-marcenko-pastur\/","title":{"rendered":"Construction of Robust Covariance Matrices for Investment Portfolio Optimization: An Application of the Marcenko-Pastur Theorem"},"content":{"rendered":"<div class=\"fusion-fullwidth fullwidth-box fusion-builder-row-1 fusion-flex-container nonhundred-percent-fullwidth non-hundred-percent-height-scrolling\" 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.cgp-cover.cgp-doc{aspect-ratio:4\/3}#cgr-pub .cgp-head{grid-template-columns:minmax(0,1fr);gap:26px}#cgr-pub .cgp-body{grid-template-columns:minmax(0,1fr);gap:30px}#cgr-pub .cgp-side{position:static}}\n@media(max-width:520px){#cgr-pub{font-size:16px}#cgr-pub .cgp-facts{grid-template-columns:minmax(0,1fr)}#cgr-pub .cgp-btn{width:100%;justify-content:center}}\n<\/style>\n<div id=\"cgr-pub\">\n<header class=\"cgp-head\">\n<figure class=\"cgp-cover cgp-doc\"><i style=\"background-image:url(https:\/\/gestionderiesgo.org\/wp-content\/uploads\/2026\/10\/pub-construccion-de-matrices-de-covarianza-robustas-marcenko-pastur.jpg?v=1791456467)\"><\/i><img fetchpriority=\"high\" src=\"https:\/\/gestionderiesgo.org\/wp-content\/uploads\/2026\/10\/pub-construccion-de-matrices-de-covarianza-robustas-marcenko-pastur.jpg?v=1791456467\" width=\"720\" height=\"1018\" alt=\"Primera p\u00e1gina del documento: Construcci\u00f3n de Matrices de Covarianza Robustas para Optimizaci\u00f3n de Portafolios de Inversi\u00f3n: Una Aplicaci\u00f3n del Teorema de Marcenko-Pastur\" loading=\"eager\" decoding=\"async\"><\/figure>\n<div class=\"cgp-intro\">\n<p class=\"cgp-kind\">Research \u00b7 Risk Management Club<\/p>\n<h2 class=\"cgp-title\">Construction of Robust Covariance Matrices for Investment Portfolio Optimization: An Application of the Marcenko-Pastur Theorem<\/h2>\n<p class=\"cgp-lead\">Covariance matrices estimated from historical data contain noise; random matrix theory makes it possible to separate it from the signal.<\/p>\n<dl class=\"cgp-facts\"><div><dt>Organization<\/dt><dd>Dominican Republic Risk Management Club (CGR)<\/dd><\/div><div><dt>Document date<\/dt><dd>21 July 2022<\/dd><\/div><div><dt>Type<\/dt><dd>Research<\/dd><\/div><div><dt>Language<\/dt><dd>Spanish<\/dd><\/div><div><dt>Scope<\/dt><dd>Dominican Republic<\/dd><\/div><div><dt>Length<\/dt><dd>14 pages<\/dd><\/div><div><dt>Authorship<\/dt><dd>Omar Bairan<\/dd><\/div><\/dl>\n<div class=\"cgp-actions\"><a class=\"cgp-btn\" href=\"https:\/\/gestionderiesgo.org\/wp-content\/uploads\/2022\/09\/Construcci_n_de_Matrices_de_Covarianza_Robustas_para_Optimizaci_n_de_Portafolios_de_Inversi_n__Una_Aplicaci_n_del_Teorema_de_Marcenko_Pastur_.pdf\" target=\"_blank\" rel=\"noopener noreferrer\"><svg viewbox=\"0 0 24 24\" aria-hidden=\"true\"><path d=\"M7 3h7l5 5v12a1 1 0 0 1-1 1H7a1 1 0 0 1-1-1V4a1 1 0 0 1 1-1z\"\/><path d=\"M14 3v5h5\"\/><path d=\"M9 14h6\"\/><path d=\"M9 17h4\"\/><\/svg>Open the research (PDF hosted on this site)<\/a><\/div>\n<\/div>\n<\/header>\n<div class=\"cgp-body\">\n<div class=\"cgp-main\">\n<h3>What it contains<\/h3>\n<p>The work starts from a classic problem of modern portfolio theory: Markowitz\u2019s mean-variance framework suffers from the instability of covariance matrices, which are estimated from financial time series that are neither deterministic nor stationary and therefore include noise. It proposes applying the Marcenko-Pastur probability distribution to separate the eigenvalues of the covariance matrix that correspond to noise from those that represent real signals.<\/p><p>The methodology generates random correlation matrices from time series, obtains their eigenvalues and eigenvectors and compares the resulting distribution with the expected Marcenko-Pastur one. It then applies a denoising procedure to the covariance matrix obtained from correlated random samples, using the Cholesky decomposition, and compares the minimum variance of three portfolios: one built with the true matrix, one with the matrix estimated from samples and one with the denoised matrix.<\/p><p>According to its conclusion, with the denoised matrix a considerable reduction in the portfolio\u2019s standard deviation is achieved, of more than 22\u00a0% relative to the portfolio built with the correlation matrix obtained from observed data. The data are simulated and the portfolio is synthetic, and the document includes at the end the Python code used.<\/p>\n<section class=\"cgp-importa\"><h3>Why it matters for risk management<\/h3><p>It is a technical reference for market risk and investment teams interested in the stability of covariance matrices. Because the data are simulated, the results illustrate the method and require validation with real data before they are used in investment decisions.<\/p><\/section>\n<p class=\"cgp-aviso\">Research published by the Club in its research library. No version on another site was found; the PDF hosted here is linked.<\/p><p class=\"cgp-note\">Summary prepared by the Dominican Republic Risk Management Club from a reading of the original document, with the source verified on 7 October 2026. It does not replace reading the official text and is not advice.<\/p>\n<p class=\"cgp-back\"><a href=\"\/en\/publicaciones\/\">See all publications<\/a><\/p>\n<\/div>\n<aside class=\"cgp-side\">\n<section class=\"cgp-card\"><h3>Key points<\/h3><ul class=\"cgp-points\"><li>Purpose: to reduce the noise of covariance matrices used in portfolio optimization.<\/li><li>Method: the Marcenko-Pastur distribution to separate noise eigenvalues from signal eigenvalues.<\/li><li>It compares three portfolios: with the true matrix, the estimated one and the denoised matrix.<\/li><li>Result: a reduction of more than 22\u00a0% of the standard deviation against the observed-data matrix.<\/li><li>It uses simulated data and a synthetic portfolio; it includes the Python code.<\/li><\/ul><\/section>\n<section class=\"cgp-card\"><h3>How to cite it<\/h3><p class=\"cgp-cite\">Bairan, O. (2022). Construction of Robust Covariance Matrices for Investment Portfolio Optimization: An Application of the Marcenko-Pastur Theorem. 21 July 2022. Document published by the Dominican Republic Risk Management Club.<\/p><\/section>\n<section class=\"cgp-card\"><h3>Topics<\/h3><ul class=\"cgp-chips\"><li><a href=\"\/en\/publicaciones\/?tema=riesgo-de-mercado-y-liquidez\">Market and liquidity risk<\/a><\/li><li><a href=\"\/en\/publicaciones\/?tema=innovacion-e-inteligencia-artificial\">Innovation and artificial intelligence<\/a><\/li><\/ul><\/section>\n<\/aside>\n<\/div>\n<\/div><link rel=\"stylesheet\" href=\"https:\/\/fonts.googleapis.com\/css2?family=Zilla+Slab:wght@500;600&display=swap\">\n<footer id=\"cgr-foot\" aria-label=\"Footer of the Risk Management Club\">\n<style>\n#main{padding-bottom:0!important}\n.fusion-fullwidth:has(#cgr-foot),.fusion-layout-column:has(#cgr-foot){padding-bottom:0!important;margin-bottom:0!important}\n#cgr-foot{--navy:#0E3351;--blue:#186392;--web:#1A80B6;--red:#E22A3A;--ink:#1C2632;--slate:#5B6775;--line:#D9E1EA;--mist:#F2F5F8;\n  position:relative;margin:96px 0 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All rights reserved.<\/p><\/div>\n  <nav class=\"cgf-pol\" aria-label=\"Policies\">\n    <a href=\"\/en\/politicasdeprivacidad\/\">Privacy<\/a><a href=\"\/en\/terminos-y-condiciones-2\/\">Terms and Conditions<\/a><a href=\"\/en\/politicas-de-entrega\/\">Delivery<\/a><a href=\"\/en\/politicas-de-cancelacion\/\">Cancellation<\/a><a href=\"\/en\/politicas-de-devolucion\/\">Returns<\/a><a href=\"\/en\/politicas-de-reembolso\/\">Refunds<\/a><a href=\"\/en\/politicas-de-seguridad\/\">Security<\/a><a href=\"\/en\/preguntas-frecuentes\/\">Frequently asked questions<\/a>\n  <\/nav>\n<\/div>\n<\/footer>\n\n<style>#cgr-foot .cgf-ct li a.cgf-wa{display:inline-flex;vertical-align:middle;margin-left:8px}#cgr-foot .cgf-ct li a.cgf-wa svg{width:18px;height:18px;margin:0;fill:#25D366;stroke:none}<\/style><\/div><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p>Research by Omar Bairan, from July 2022, that applies the Marcenko-Pastur distribution to remove noise from covariance matrices and reduce the variance of a synthetic portfolio by more than 22 %. It includes the Python code.<\/p>","protected":false},"author":1,"featured_media":25600,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":true,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"cgp_org":"Club de Gesti\u00f3n de Riesgos de la Rep\u00fablica Dominicana","cgp_siglas":"CGR","cgp_tipo":"Investigaci\u00f3n","cgp_fecha":"2022-07-21","cgp_url":"https:\/\/gestionderiesgo.org\/wp-content\/uploads\/2022\/09\/Construcci_n_de_Matrices_de_Covarianza_Robustas_para_Optimizaci_n_de_Portafolios_de_Inversi_n__Una_Aplicaci_n_del_Teorema_de_Marcenko_Pastur_.pdf","cgp_pdf":"","cgp_idioma":"Espa\u00f1ol","cgp_pais":"Rep\u00fablica Dominicana","cgp_temas":"Riesgo de mercado y liquidez,Innovaci\u00f3n e inteligencia artificial","cgp_portada":"https:\/\/gestionderiesgo.org\/wp-content\/uploads\/2026\/10\/pub-construccion-de-matrices-de-covarianza-robustas-marcenko-pastur.jpg","cgp_verificado":"2026-10-07","cgp_origen":"migrada","cgp_fuente":"Club de Gesti\u00f3n de Riesgos","cgp_paginas":"14","cgp_autores":"Omar Bairan","cgp_fecha_texto":"","cgp_portada_tipo":"doc","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[74],"tags":[],"class_list":["post-25525","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-publicaciones-del-sector"],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/gestionderiesgo.org\/wp-content\/uploads\/2026\/10\/pub-construccion-de-matrices-de-covarianza-robustas-marcenko-pastur.jpg","_links":{"self":[{"href":"https:\/\/gestionderiesgo.org\/en\/wp-json\/wp\/v2\/posts\/25525","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gestionderiesgo.org\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gestionderiesgo.org\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gestionderiesgo.org\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gestionderiesgo.org\/en\/wp-json\/wp\/v2\/comments?post=25525"}],"version-history":[{"count":5,"href":"https:\/\/gestionderiesgo.org\/en\/wp-json\/wp\/v2\/posts\/25525\/revisions"}],"predecessor-version":[{"id":26336,"href":"https:\/\/gestionderiesgo.org\/en\/wp-json\/wp\/v2\/posts\/25525\/revisions\/26336"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/gestionderiesgo.org\/en\/wp-json\/wp\/v2\/media\/25600"}],"wp:attachment":[{"href":"https:\/\/gestionderiesgo.org\/en\/wp-json\/wp\/v2\/media?parent=25525"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gestionderiesgo.org\/en\/wp-json\/wp\/v2\/categories?post=25525"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gestionderiesgo.org\/en\/wp-json\/wp\/v2\/tags?post=25525"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}