{"id":1446,"date":"2016-12-08T14:37:00","date_gmt":"2016-12-08T14:37:00","guid":{"rendered":"https:\/\/nag.com\/?post_type=insights&#038;p=1243"},"modified":"2023-07-04T16:37:41","modified_gmt":"2023-07-04T16:37:41","slug":"index-tracking-portfolio-optimization-model","status":"publish","type":"insights","link":"https:\/\/nag.com\/insights\/index-tracking-portfolio-optimization-model\/","title":{"rendered":"Index-tracking Portfolio Optimization Model"},"content":{"rendered":"<div class=\"container content-area-default \">\n    <div class=\"row justify-content--center\">\n        <div class=\"col-12 col-md-10 col-lg-8 col-xl-6\">\n            <p>Index-tracking is a form of passive fund management. The index-tracking problem is the problem of reproducing the performance of a stock market index by considering a portfolio of assets comprised on the index. This approach differs from the full replication strategy, where a fund purchases all the stocks that make up a particular market index. A passively managed fund whose objective is to reproduce the return on an index is known as an index fund, or a tracker fund. The classical index-tracking approach represents the problem in a least square framework with errors computed using a sample of historical data. A new approach described in N. C. P. Edirisinghe &#8220;Index-tracking optimal portfolio selection&#8221; Quantitative Finance Letters, Vol. 1, 16-20, (2013), which this report is based on, replaces the classical risk measure of portfolio variance by the variance of tracking errors between stochastic index return and the return on the portfolio selection. In this report we formulate the index-tracking portfolio optimization model and present an illustrative example where we compare the presented model with the classical Markowitz mean-variance portfolio optimization model.<\/p>\n        <\/div>\n    <\/div>\n<\/div>\n\n\n<div class=\"gbc-title-banner tac tac-lg tac-xl\" style='border-radius: 0px; '>\n    <div class=\"container\" style='border-radius: 0px; '>\n        <div class=\"row justify-content--center\" >\n            <div class=\"col-12\"  >\n                <div class=\"wrap pv-4 \" style=\"0pxbackground-color: \">\n                                <div class=\"col-12 col-md-10 col-lg-8 col-xl-6  banner-content\"  >\n    \n                    \n                    <div class=\"mt-1 mb-1 content\"><\/div>\n\n                    \n                    <a href='https:\/\/support.nag.com\/doc\/techrep\/pdf\/tr1_16.pdf' style='background-color: #ff7d21ff; color: #ffffffff; border-radius: 30px; font-weight: 600; ' class='btn mr-1  ' target=\"_blank\">Read the report <i class='fas fa-angle-right'><\/i><\/a>                <\/div>\n                <\/div>\n            <\/div>\n        <\/div>\n    <\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>The index-tracking problem is the problem of reproducing the performance of a stock market index by considering a portfolio of assets comprised on the index.<\/p>\n","protected":false},"author":17,"featured_media":1246,"parent":0,"menu_order":0,"template":"","meta":{"content-type":"","footnotes":""},"post-tag":[21],"class_list":["post-1446","insights","type-insights","status-publish","has-post-thumbnail","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.8 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Index-tracking Portfolio Optimization Model - nAG<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/nag.com\/insights\/index-tracking-portfolio-optimization-model\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Index-tracking Portfolio Optimization Model - nAG\" \/>\n<meta property=\"og:description\" content=\"The index-tracking problem is the problem of reproducing the performance of a stock market index by considering a portfolio of assets comprised on the index.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/nag.com\/insights\/index-tracking-portfolio-optimization-model\/\" \/>\n<meta property=\"og:site_name\" content=\"nAG\" \/>\n<meta property=\"article:modified_time\" content=\"2023-07-04T16:37:41+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/nag.com\/wp-content\/uploads\/2016\/12\/sean-pollock-phyq704ffda-unsplash.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"2000\" \/>\n\t<meta property=\"og:image:height\" content=\"1000\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:site\" content=\"@NAGTalk\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/nag.com\/insights\/index-tracking-portfolio-optimization-model\/\",\"url\":\"https:\/\/nag.com\/insights\/index-tracking-portfolio-optimization-model\/\",\"name\":\"Index-tracking Portfolio Optimization Model - nAG\",\"isPartOf\":{\"@id\":\"https:\/\/nag.com\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/nag.com\/insights\/index-tracking-portfolio-optimization-model\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/nag.com\/insights\/index-tracking-portfolio-optimization-model\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/nag.com\/wp-content\/uploads\/2016\/12\/sean-pollock-phyq704ffda-unsplash.jpg\",\"datePublished\":\"2016-12-08T14:37:00+00:00\",\"dateModified\":\"2023-07-04T16:37:41+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/nag.com\/insights\/index-tracking-portfolio-optimization-model\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/nag.com\/insights\/index-tracking-portfolio-optimization-model\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/nag.com\/insights\/index-tracking-portfolio-optimization-model\/#primaryimage\",\"url\":\"https:\/\/nag.com\/wp-content\/uploads\/2016\/12\/sean-pollock-phyq704ffda-unsplash.jpg\",\"contentUrl\":\"https:\/\/nag.com\/wp-content\/uploads\/2016\/12\/sean-pollock-phyq704ffda-unsplash.jpg\",\"width\":2000,\"height\":1000,\"caption\":\"Index tracking\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/nag.com\/insights\/index-tracking-portfolio-optimization-model\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/nag.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Insights\",\"item\":\"https:\/\/nag.com\/insights\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Index-tracking Portfolio Optimization Model\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/nag.com\/#website\",\"url\":\"https:\/\/nag.com\/\",\"name\":\"NAG\",\"description\":\"Robust, trusted numerical software and computational expertise.\",\"publisher\":{\"@id\":\"https:\/\/nag.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/nag.com\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/nag.com\/#organization\",\"name\":\"Numerical Algorithms Group\",\"alternateName\":\"NAG\",\"url\":\"https:\/\/nag.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/nag.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/nag.com\/wp-content\/uploads\/2023\/11\/NAG-Logo.png\",\"contentUrl\":\"https:\/\/nag.com\/wp-content\/uploads\/2023\/11\/NAG-Logo.png\",\"width\":1244,\"height\":397,\"caption\":\"Numerical Algorithms Group\"},\"image\":{\"@id\":\"https:\/\/nag.com\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/x.com\/NAGTalk\",\"https:\/\/www.linkedin.com\/company\/nag\/\",\"https:\/\/www.youtube.com\/user\/NumericalAlgorithms\",\"https:\/\/github.com\/numericalalgorithmsgroup\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Index-tracking Portfolio Optimization Model - nAG","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/nag.com\/insights\/index-tracking-portfolio-optimization-model\/","og_locale":"en_US","og_type":"article","og_title":"Index-tracking Portfolio Optimization Model - nAG","og_description":"The index-tracking problem is the problem of reproducing the performance of a stock market index by considering a portfolio of assets comprised on the index.","og_url":"https:\/\/nag.com\/insights\/index-tracking-portfolio-optimization-model\/","og_site_name":"nAG","article_modified_time":"2023-07-04T16:37:41+00:00","og_image":[{"width":2000,"height":1000,"url":"https:\/\/nag.com\/wp-content\/uploads\/2016\/12\/sean-pollock-phyq704ffda-unsplash.jpg","type":"image\/jpeg"}],"twitter_card":"summary_large_image","twitter_site":"@NAGTalk","schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/nag.com\/insights\/index-tracking-portfolio-optimization-model\/","url":"https:\/\/nag.com\/insights\/index-tracking-portfolio-optimization-model\/","name":"Index-tracking Portfolio Optimization Model - nAG","isPartOf":{"@id":"https:\/\/nag.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/nag.com\/insights\/index-tracking-portfolio-optimization-model\/#primaryimage"},"image":{"@id":"https:\/\/nag.com\/insights\/index-tracking-portfolio-optimization-model\/#primaryimage"},"thumbnailUrl":"https:\/\/nag.com\/wp-content\/uploads\/2016\/12\/sean-pollock-phyq704ffda-unsplash.jpg","datePublished":"2016-12-08T14:37:00+00:00","dateModified":"2023-07-04T16:37:41+00:00","breadcrumb":{"@id":"https:\/\/nag.com\/insights\/index-tracking-portfolio-optimization-model\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/nag.com\/insights\/index-tracking-portfolio-optimization-model\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/nag.com\/insights\/index-tracking-portfolio-optimization-model\/#primaryimage","url":"https:\/\/nag.com\/wp-content\/uploads\/2016\/12\/sean-pollock-phyq704ffda-unsplash.jpg","contentUrl":"https:\/\/nag.com\/wp-content\/uploads\/2016\/12\/sean-pollock-phyq704ffda-unsplash.jpg","width":2000,"height":1000,"caption":"Index tracking"},{"@type":"BreadcrumbList","@id":"https:\/\/nag.com\/insights\/index-tracking-portfolio-optimization-model\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/nag.com\/"},{"@type":"ListItem","position":2,"name":"Insights","item":"https:\/\/nag.com\/insights\/"},{"@type":"ListItem","position":3,"name":"Index-tracking Portfolio Optimization Model"}]},{"@type":"WebSite","@id":"https:\/\/nag.com\/#website","url":"https:\/\/nag.com\/","name":"NAG","description":"Robust, trusted numerical software and computational expertise.","publisher":{"@id":"https:\/\/nag.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/nag.com\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/nag.com\/#organization","name":"Numerical Algorithms Group","alternateName":"NAG","url":"https:\/\/nag.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/nag.com\/#\/schema\/logo\/image\/","url":"https:\/\/nag.com\/wp-content\/uploads\/2023\/11\/NAG-Logo.png","contentUrl":"https:\/\/nag.com\/wp-content\/uploads\/2023\/11\/NAG-Logo.png","width":1244,"height":397,"caption":"Numerical Algorithms Group"},"image":{"@id":"https:\/\/nag.com\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/x.com\/NAGTalk","https:\/\/www.linkedin.com\/company\/nag\/","https:\/\/www.youtube.com\/user\/NumericalAlgorithms","https:\/\/github.com\/numericalalgorithmsgroup"]}]}},"_links":{"self":[{"href":"https:\/\/nag.com\/wp-json\/wp\/v2\/insights\/1446","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/nag.com\/wp-json\/wp\/v2\/insights"}],"about":[{"href":"https:\/\/nag.com\/wp-json\/wp\/v2\/types\/insights"}],"author":[{"embeddable":true,"href":"https:\/\/nag.com\/wp-json\/wp\/v2\/users\/17"}],"version-history":[{"count":3,"href":"https:\/\/nag.com\/wp-json\/wp\/v2\/insights\/1446\/revisions"}],"predecessor-version":[{"id":2925,"href":"https:\/\/nag.com\/wp-json\/wp\/v2\/insights\/1446\/revisions\/2925"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/nag.com\/wp-json\/wp\/v2\/media\/1246"}],"wp:attachment":[{"href":"https:\/\/nag.com\/wp-json\/wp\/v2\/media?parent=1446"}],"wp:term":[{"taxonomy":"post-tag","embeddable":true,"href":"https:\/\/nag.com\/wp-json\/wp\/v2\/post-tag?post=1446"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}