{"id":19155,"date":"2021-08-05T09:22:53","date_gmt":"2021-08-05T09:22:53","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=19155"},"modified":"2024-04-11T13:05:31","modified_gmt":"2024-04-11T13:05:31","slug":"describe-how-value-added-by-active-management-is-measured","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/describe-how-value-added-by-active-management-is-measured\/","title":{"rendered":"Value Added"},"content":{"rendered":"\r\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/jg7OkPKXBSs\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\r\n<p><strong>Value-added<\/strong>, also called <strong>active return<\/strong>, is the difference between the managed portfolio return and the benchmark portfolio return. It is calculated using the following equation:<\/p>\r\n<p>$$ R_A=R_P-R_B $$<\/p>\r\n<p>Where:<\/p>\r\n<ul>\r\n\t<li>\\(R_A\\) is the value-added.<\/li>\r\n\t<li>\\(R_P\\) is the investor\u2019s return.<\/li>\r\n\t<li>\\(R_B\\) is the benchmark portfolio return.<\/li>\r\n<\/ul>\r\n<p>Value added is positive if an investor outperforms the passive benchmark portfolio. On the other hand, it is negative if an investor underperforms the benchmark portfolio.<\/p>\r\n<p>The return of the benchmark portfolio, \\(R_B\\), is given by:<\/p>\r\n<p>$$ R_B=\\sum_{i=1}^{n}{w_{b,i}\\times R_i} &#8230;&#8230;&#8230;1 $$<\/p>\r\n<p>Where:<\/p>\r\n<ul>\r\n\t<li>\\(w_{b,i}\\) is the benchmark weight of security \\(i\\).<\/li>\r\n\t<li>\\(R_i\\) is the return on security \\(i\\).<\/li>\r\n<\/ul>\r\n<p>On the other hand, \\(R_P\\), the return on the managed portfolio is given by:<\/p>\r\n<p>$$ R_P=\\sum_{i=1}^{n}{w_{p,i}\\times R_i} &#8230;&#8230;&#8230;2 $$<\/p>\r\n<p>Where:<\/p>\r\n<ul>\r\n\t<li>\\(w_{p,i}\\) is the portfolio weight of security \\(i\\).<\/li>\r\n<\/ul>\r\n<p>Note that the value added is driven by differences in weights between the managed portfolio and the benchmark portfolio.<\/p>\r\n<p>Combining equation 1 and 2 gives:<\/p>\r\n<p>$$ R_A=\\sum_{i=1}^{n} \\Delta w_iR_i $$<\/p>\r\n<p>Where:<\/p>\r\n<ul>\r\n\t<li>\\(\\Delta w_i \\text{(active weight)} = w_{p,i}-w_{b,i}\\).<\/li>\r\n<\/ul>\r\n<p>Value-added can emerge from security selection, asset class allocation, and decompositions into economic sector weightings and geographic weights.<\/p>\r\n<h4>Example: Measuring Value Added<\/h4>\r\n<p>The following table shows the weights and the corresponding portfolio and benchmark returns of four securities of ABC, a hypothetical company.<\/p>\r\n<p>$$ \\begin{array}{c|c|c|c} \\textbf{Security} &amp; \\textbf{Portfolio weight} &amp; \\textbf{Benchmark weight} &amp; \\textbf{Return} \\\\ \\hline A &amp; 35\\% &amp; 30\\% &amp; 16\\% \\\\ \\hline B &amp; 30\\% &amp; 25\\% &amp; 18\\% \\\\ \\hline C &amp; 20\\% &amp; 25\\% &amp; 14\\% \\\\ \\hline D &amp; 15\\% &amp; 20\\% &amp; 10\\% \\end{array} $$<\/p>\r\n<p>Calculate the active return (value added) of ABC.<\/p>\r\n<h4>Solution<\/h4>\r\n<p>$$ R_A=\\sum_{i=1}^{n} \\Delta w_iR_i $$<\/p>\r\n<p>Where:<\/p>\r\n<ul>\r\n\t<li>\\(\\Delta w_i\\) is the active weight = \\(w_{p,i}-w_{b,i}\\).<\/li>\r\n<\/ul>\r\n<p>The following table shows the calculations of value added:<\/p>\r\n<p>$$ \\begin{array}{c|c|c|c|c|c} \\textbf{Security} &amp; \\textbf{Portfolio} &amp; \\textbf{Benchmark} &amp; \\textbf{Return} &amp; \\bf{ {w}_{{p},{i}}} &amp; \\bf{({w}_{{p},{i}}-{w}_{{b},{i}})}\\\\ {} &amp; \\textbf{weight} &amp; \\textbf{weight} &amp; {} &amp; \\bf{ &#8211; {w}_{{b},{i}}} &amp; {\\bf{\\times {R}_{i}}} \\\\ \\hline A &amp; 35\\% &amp; 30\\% &amp; 16\\% &amp; {5\\%}&amp; 0.8\\%\\\\ \\hline B &amp; 30\\% &amp; 25\\% &amp; 18\\% &amp; {5\\%} &amp; 0.9\\% \\\\ \\hline C &amp; 20\\% &amp; 25\\% &amp; 14\\% &amp; {-5\\%}&amp; -0.7\\% \\\\ \\hline D &amp; 15\\% &amp; 20\\% &amp; 10\\% &amp; {-5\\%} &amp; -0.5\\% \\end{array} $$<\/p>\r\n<p>Therefore,<\/p>\r\n<p>$$ R_A=0.8+0.9-0.7-0.5=0.5\\% $$<\/p>\r\n<blockquote>\r\n<h2>Question<\/h2>\r\n<p>XYZ is a hypothetical pension scheme with investments in various asset classes, as shown in the following table. The expected portfolio returns and the passive benchmark return is shown alongside each asset class.<\/p>\r\n<p>$$ \\begin{array}{c|c|c|c|c} \\textbf{Asset} &amp; \\textbf{Portfolio} &amp; \\textbf{Benchmark} &amp; \\textbf{Portfolio} &amp; \\textbf{Benchmark} \\\\ \\textbf{Class} &amp; \\textbf{weight} &amp; {\\textbf{weight } \\bf{(\\%)}} &amp; \\textbf{Return} &amp; \\textbf{Return} \\\\ \\hline \\text{Quoted} &amp; 20\\% &amp; 25\\% &amp; 20\\% &amp; 18\\% \\\\ \\text{equities} &amp; &amp; &amp; &amp; \\\\ \\hline \\text{Treasury} &amp; 50\\% &amp; 40\\% &amp; 15\\% &amp; 10\\% \\\\ \\text{bonds} &amp; &amp; &amp; &amp; \\\\ \\hline \\text{Offshore} &amp; 30\\% &amp; 35\\% &amp; 10\\% &amp; 4\\% \\\\ \\text{investments} &amp; &amp; &amp; &amp; \\\\ \\end{array} $$<\/p>\r\n<p>The ex-ante value added is <em>closest to<\/em>:<\/p>\r\n<ol type=\"A\">\r\n\t<li>-0.5%.<\/li>\r\n\t<li>0.0%.<\/li>\r\n\t<li>0.75%.<\/li>\r\n<\/ol>\r\n<h4>Solution<\/h4>\r\n<p><strong>The correct answer is B.<\/strong><\/p>\r\n<p>Ex-ante value added is the difference between the expected return of an actively managed portfolio and the expected return of its benchmark:<\/p>\r\n<p>$$ E(R_A)={E(R}_P)-{(R}_B) $$<\/p>\r\n<p>Return of the benchmark portfolio, \\(R_B\\), is given by:<\/p>\r\n<p>$$ \\begin{align*} E({R}_B) &amp;=\\sum_{i=1}^{n}{w_{b,i}\\times E(R_i)} \\\\ R_B &amp;=\\left(0.25\\times0.20\\right)+\\left(0.4\\times0.15\\right)+\\left(0.35\\times0.10\\right)=0.145 \\end{align*} $$<\/p>\r\n<p>Return on the managed portfolio is given by:<\/p>\r\n<p>$$ \\begin{align*} {E(R_P)} &amp; ={\\sum_{i=1}^{n}{w_{p,i}\\times E(R_i)} }\\\\ &amp;=\\left(0.20\\times0.20\\right)+\\left(0.50\\times0.15\\right)+\\left(0.30\\times0.10\\right)=0.145 \\\\ R_A &amp; =0.145-0.145=0.0\\% \\end{align*} $$<\/p>\r\n<\/blockquote>\r\n<p>Reading 44: Analysis of Active Portfolio Management<\/p>\r\n<p><em>LOS 44 (a) Describe how value added by active management is measured.<\/em><\/p>\r\n","protected":false},"excerpt":{"rendered":"<p>Value-added, also called active return, is the difference between the managed portfolio return and the benchmark portfolio return. It is calculated using the following equation: $$ R_A=R_P-R_B $$ Where: \\(R_A\\) is the value-added. \\(R_P\\) is the investor\u2019s return. \\(R_B\\) is&#8230;<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[102,473],"tags":[216,564],"class_list":["post-19155","post","type-post","status-publish","format-standard","hentry","category-cfa-level-2","category-portfolio-management","tag-cfa-level-2","tag-portfolio-management","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Value Added - CFA, FRM, and Actuarial Exams Study Notes<\/title>\n<meta name=\"description\" content=\"Value-added, also called active return, is the difference between the managed portfolio return and the benchmark portfolio return.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/describe-how-value-added-by-active-management-is-measured\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Value Added - 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