{"id":18824,"date":"2021-08-01T06:56:31","date_gmt":"2021-08-01T06:56:31","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=18824"},"modified":"2026-06-04T06:14:03","modified_gmt":"2026-06-04T06:14:03","slug":"explain-sources-of-active-risk-and-interpret-tracking-risk-and-the-information-ratio","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/explain-sources-of-active-risk-and-interpret-tracking-risk-and-the-information-ratio\/","title":{"rendered":"Active Risk, Tracking Risk and Information Ratio"},"content":{"rendered":"<p><script type=\"application\/ld+json\">\r\n{\r\n  \"@context\": \"https:\/\/schema.org\",\r\n  \"@type\": \"QAPage\",\r\n  \"mainEntity\": {\r\n    \"@type\": \"Question\",\r\n    \"name\": \"Using the following data to calculate the manager\u2019s information ratio, which of the following is most likely correct about the portfolio in question relative to the benchmark?\",\r\n    \"answerCount\": 3,\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"The correct answer is B. It is volatile relative to the benchmark. The information ratio is calculated as IR = (Rp\u0304 \u2212 Rb\u0304) \/ S(Rp \u2212 Rb) = (0.0144 \u2212 0.0117) \/ 0.0041 = 0.6585, approximately 0.66. A relatively high information ratio indicates that the portfolio's active returns differ meaningfully from the benchmark, implying greater volatility relative to the benchmark.\"\r\n    },\r\n    \"suggestedAnswer\": [\r\n      {\r\n        \"@type\": \"Answer\",\r\n        \"text\": \"It is close to the benchmark.\"\r\n      },\r\n      {\r\n        \"@type\": \"Answer\",\r\n        \"text\": \"It is volatile relative to the benchmark.\"\r\n      },\r\n      {\r\n        \"@type\": \"Answer\",\r\n        \"text\": \"It has a low information ratio.\"\r\n      }\r\n    ]\r\n  }\r\n}\r\n<\/script><\/p>\r\n<p>&nbsp;<\/p>\r\n\r\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/SGL5FhV5IUQ\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\r\n<h2>Active Risk<\/h2>\r\n<p><strong>Active return<\/strong> refers to the return on the portfolio above the return on the benchmark. That is,<\/p>\r\n<p>$$ \\text{Active return} = R_P-R_b $$<\/p>\r\n<p><strong>Active risk<\/strong>, also known traditionally as <strong>tracking error <\/strong>or<strong> tracking risk<\/strong>, is a risk that a portfolio manager creates in an attempt to outperform benchmark returns against which it is compared. In addition, active risk helps a portfolio manager achieve higher returns for investors. In other words, it is the standard deviation of active returns.<\/p>\r\n<h3>Measuring Active Risk<\/h3>\r\n<p>$$ \\text{Active risk} = \\text{Tracking error (TE)} = s(R_P-R_b) $$<\/p>\r\n<p>Where:<\/p>\r\n<ul>\r\n\t<li>S is the sample standard deviation.<\/li>\r\n\t<li>\\(R_P\\) is the return of the portfolio.<\/li>\r\n\t<li>\\(R_b\\) is the benchmark return.<\/li>\r\n<\/ul>\r\n<div style=\"text-align: center; margin: 28px 0;\"><a style=\"display: inline-block; background: #1a73e8; color: #ffffff; padding: 12px 26px; border-radius: 40px; font-size: 16px; font-weight: 500; text-decoration: none; line-height: 1.4;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"> Measure active risk and tracking error with our free trial <\/a><\/div>\r\n<h2>Tracking Risk and Information Ratio (IR)<\/h2>\r\n<p>Information ratio (IR) is a measure of returns of a portfolio beyond the returns of a benchmark in comparison with the returns&#8217; volatility. Strictly speaking, a benchmark is typically an index representing the market or a particular sector.<\/p>\r\n<p>Information Ratio (IR) is used as a measure of a portfolio manager&#8217;s skills and ability to generate excess returns relative to a benchmark. It also identifies the consistency of performance by incorporating a tracking risk component into the calculation.<\/p>\r\n<p>Tracking risk identifies the level of consistency with which a portfolio follows the performance of a benchmark. A low tracking risk implies that a portfolio is closely following the benchmark. A high tracking error implies that a portfolio is volatile relative to the benchmark and that returns are drifting from the benchmark. Investors prefer a <strong>low tracking error<\/strong>.<\/p>\r\n<h3>Information Risk (IR) Formula<\/h3>\r\n<p>Although compared funds may be different, the information risk (IR) formula standardizes the returns by dividing the difference in their performances by their tracking risk.<\/p>\r\n<p>$$ {IR} =\\frac{\\bar{R_p}-\\bar{R_b}}{S(R_P-R_b) } $$<\/p>\r\n<p>where:<\/p>\r\n<ul>\r\n\t<li>\\(\\bar{R_p}\\) is the average of the portfolio returns for the chosen periods.<\/li>\r\n\t<li>\\(\\bar{R_b}\\) is the average of the benchmark returns for the chosen periods.<\/li>\r\n<\/ul>\r\n<blockquote>\r\n<h2>Question<\/h2>\r\n<p>Using the following data to calculate the manager\u2019s information ratio:<\/p>\r\n<p>$$ \\begin{array}{c|c|c} \\textbf{Period} &amp; \\bf{\\text{Portfolio Returns } ({R}_{p})} &amp; \\bf{\\text{Benchmark Returns }({R}_{b})} \\\\ \\hline 1 &amp; 0.0211 &amp; 0.0111 \\\\ \\hline 2 &amp; 0.0091 &amp; 0.0112 \\\\ \\hline 3 &amp; 0.0128 &amp; 0.0091 \\\\ \\hline 4 &amp; 0.0083 &amp; 0.0092 \\\\ \\hline 5 &amp; 0.0160 &amp; 0.0111 \\\\ \\hline 6 &amp; 0.0191 &amp; 0.0183 \\end{array} $$<\/p>\r\n<p>Which of the following is <em>most likely<\/em> correct about the portfolio in question relative to the benchmark?<\/p>\r\n<ol type=\"A\">\r\n\t<li>It is close to the benchmark.<\/li>\r\n\t<li>It is volatile relative to the benchmark.<\/li>\r\n\t<li>It has a low information ratio.<\/li>\r\n<\/ol>\r\n<h4>Solution<\/h4>\r\n<p><strong>The correct answer is B.<\/strong><\/p>\r\n<p>$$ \\begin{array}{c|c|c|c} \\textbf{Period} &amp; \\bf{\\text{Portfolio}} &amp; \\bf{\\text{Benchmark}} &amp; \\bf{{R}_{p}-{R}_{b}} \\\\ &amp; \\textbf{returns} &amp; \\textbf{returns} &amp; \\\\ &amp; \\bf{({R}_{p})} &amp; \\bf{({R}_{b})} &amp; \\\\ \\hline 1 &amp; 0.0211 &amp; 0.0111 &amp; 0.0100 \\\\ \\hline 2 &amp; 0.0091 &amp; 0.0112 &amp; (0.0021) \\\\ \\hline 3 &amp; 0.0128 &amp; 0.0091 &amp; 0.0037 \\\\ \\hline 4 &amp; 0.0083 &amp; 0.0092 &amp; (0.0009) \\\\ \\hline 5 &amp; 0.0160 &amp; 0.0111 &amp; 0.0049 \\\\ \\hline 6 &amp; 0.0191 &amp; 0.0183 &amp; 0.0008 \\\\ \\hline \\textbf{Average} &amp; \\bf{0.0144} &amp; \\bf{0.0117} &amp; \\bf{0.0027} \\\\ \\hline \\textbf{Standard} &amp; &amp; &amp; \\bf{0.0041} \\\\ \\textbf{Deviation} &amp; &amp; &amp; \\\\ \\end{array} $$<\/p>\r\n<p>$$ \\begin{align*} {IR} &amp;=\\frac{{\\bar{R}}_P-{\\bar{R}}_b}{S(R_P-R_b) } \\\\ &amp; =\\frac{0.0144-0.0117}{0.0041}=0.6585\\approx\\ 0.66 \\end{align*} $$<\/p>\r\n<p>The high information ratio implies that the portfolio is volatile relative to the benchmark.<\/p>\r\n<p><strong>A is incorrect.<\/strong>\u00a0The high information ratio shows that the portfolio is not closely following the benchmark.<\/p>\r\n<p><strong>C is incorrect.<\/strong>\u00a0Investors prefer a portfolio with a low information ratio.<\/p>\r\n<\/blockquote>\r\n<p>Reading 40: Using Multifactor Models<\/p>\r\n<p><em>LOS 40 (e) Explain sources of active risk and interpret tracking risk and the information ratio.<\/em><\/p>\r\n\r\n<div style=\"background: #f5f7fb; padding: 24px 18px; border-radius: 12px; text-align: center; margin: 36px 0 18px;\"><a style=\"display: inline-block; background: #1a73e8; color: #ffffff; padding: 10px 24px; border-radius: 40px; font-size: 16px; font-weight: bold; text-decoration: none; margin-bottom: 16px;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"> Start Free Trial \u2192 <\/a>\r\n<div style=\"font-size: 14px; color: #333333; max-width: 650px; margin: 0 auto; line-height: 1.6;\">Practice tracking error, information ratio, active return, and portfolio performance evaluation questions with CFA Level II Portfolio Management examples and guided explanations.<\/div>\r\n<\/div>","protected":false},"excerpt":{"rendered":"<p>&nbsp; Active Risk Active return refers to the return on the portfolio above the return on the benchmark. That is, $$ \\text{Active return} = R_P-R_b $$ Active risk, also known traditionally as tracking error or tracking risk, is a risk&#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-18824","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 v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Active Risk, Tracking Risk &amp; Information Ratio<\/title>\n<meta name=\"description\" content=\"Learn the sources of active risk, how tracking risk is measured, and how to interpret the information ratio in portfolio performance 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