{"id":354,"date":"2019-08-17T13:28:00","date_gmt":"2019-08-17T13:28:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=354"},"modified":"2026-01-09T10:49:17","modified_gmt":"2026-01-09T10:49:17","slug":"coefficient-of-variation-sharpe-ratio","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/coefficient-of-variation-sharpe-ratio\/","title":{"rendered":"Coefficient of Variation"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Statistical Concepts and Market Returns (2021 Level I CFA\u00ae Exam \u2013 Reading 7)\",\n  \"description\": \"This video lesson covers statistical concepts and market returns, distinguishing between descriptive and inferential statistics. It explains populations vs. samples, types of measurement scales, frequency distributions, measures of central tendency, dispersion, skewness, and kurtosis. The lesson also introduces statistical applications in finance for decision-making and risk assessment.\",\n  \"uploadDate\": \"2020-07-20T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/alD9eAT2lQU\/maxresdefault.jpg\",\n  \"contentUrl\": \"https:\/\/youtu.be\/alD9eAT2lQU\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/alD9eAT2lQU\",\n  \"duration\": \"PT31M21S\"\n}\n<\/script>\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"@id\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/coefficient-of-variation-sharpe-ratio\/#qapage-question-1\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"@id\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/coefficient-of-variation-sharpe-ratio\/#question-1\",\n    \"name\": \"If a security has a mean expected return of 10% and a standard deviation of 5%, what is its coefficient of variation?\",\n    \"text\": \"If a security has a mean expected return of 10% and a standard deviation of 5%, its coefficient of variation is closest to which of the following?\\nA. 0.005\\nB. 0.5\\nC. 2\",\n    \"answerCount\": 1,\n    \"author\": {\n      \"@type\": \"Organization\",\n      \"name\": \"AnalystPrep\"\n    },\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"@id\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/coefficient-of-variation-sharpe-ratio\/#answer-1\",\n      \"text\": \"B. 0.5. The coefficient of variation is calculated as the standard deviation divided by the mean expected return. Here, 0.05 divided by 0.10 equals 0.5.\",\n      \"author\": {\n        \"@type\": \"Organization\",\n        \"name\": \"AnalystPrep\"\n      }\n    }\n  }\n}\n<\/script>\n\n\n\n<iframe loading=\"lazy\" width=\"611\" height=\"344\"\n  src=\"https:\/\/www.youtube.com\/embed\/alD9eAT2lQU\"\n  title=\"YouTube video player\"\n  frameborder=\"0\"\n  allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\"\n  referrerpolicy=\"strict-origin-when-cross-origin\"\n  allowfullscreen>\n<\/iframe>\n\n\n\n\n<p>The coefficient of variation, CV, is a measure of spread that describes the amount of variability of data relative to<br class=\"clear\" \/>its mean. It has <strong>no units<\/strong>, and as such, we can use it as an alternative to the <a href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/uncategorized\/measures-dispersion-examples\/\">standard deviation<\/a> to compare the variability of data sets that have different means.<\/p>\n<p><!--more--><\/p>\n<h2><strong>Coefficient of Variation Formula<\/strong><\/h2>\n<p>$$ \\text{CV} = \\cfrac {S}{\\text x\u0304} $$<\/p>\n<p>Where S is the standard deviation of a sample<\/p>\n<p>And x\u0304 is the mean of the sample.<\/p>\n<p><em>Note: the formula can be replaced with \u03c3\/\u03bc when dealing with a population.<\/em><\/p>\n<p>Below is the procedure to follow\u00a0 when calculating the coefficient of variation:<\/p>\n<ol>\n<li>compute the mean of the data;<\/li>\n<li>calculate the sample standard deviation of the data set, S; and<\/li>\n<li>find the ratio of S to the mean, x\u0304.<\/li>\n<\/ol>\n<h3>Example: Calculating the Coefficient of Variation<\/h3>\n<p>Calculate the relative variability for the samples 40, 46, 34, 35, and 45 of a population.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p><strong>Step 1:<\/strong> calculate the mean.<\/p>\n<p>$$ \\text{Mean} =\\cfrac {(40 + 46 + 34 + 35 + 45)}{5} =\\cfrac {200}{5} = 40 $$<\/p>\n<p><strong>Step 2:<\/strong> calculate the sample standard deviation. (Start with the variance, \\(S^2\\).)<\/p>\n<p>$$ \\begin{align*} S^2 &amp; =\\cfrac {{(40 \u2013 40)^2 + &#8230; + (45 \u2013 40)^2 }}{4} \\\\ &amp;=\\cfrac {122}{4} \\\\ &amp; = 30.5 \\\\ \\end{align*} $$<\/p>\n<p><em>Note: since it is the sample standard deviation, and not the population standard deviation, we use n &#8211; 1 as the denominator.<\/em><\/p>\n<p>Therefore,<\/p>\n<p>$$ S = \\sqrt{30.5} = 5.52268 $$<\/p>\n<p><strong>Step 3<\/strong>: calculate the ratio.<\/p>\n<p>$$ \\text{Ratio} =\\cfrac {5.52268}{40} = 0.13806 \\text{ or } 13.81\\% $$<\/p>\n<p><em>(You can use these links to refresh your memory on calculation of the <a href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/measures-of-central-tendency\/\">mean<\/a> and <a href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/uncategorized\/measures-dispersion-examples\/\">standard deviation<\/a>)<\/em><\/p>\n<h3><strong>Interpreting the Coefficient of Variation<\/strong><\/h3>\n<p>In finance, the coefficient of variation is used to measure the <strong>risk per unit of return<\/strong>. For example, assume that the mean monthly return on a T-Bill is 0.5% with a standard deviation of 0.58%. Suppose we have another investment, say, Y with a 1.5% mean monthly return and standard deviation of 6%. Then,<\/p>\n<p>$$ \\text{CV}_{\\text T-\\text {Bill}} =\\cfrac {0.58}{0.5} = 1.16 $$<\/p>\n<p>$$ \\text{CV}_\\text{Y} =\\cfrac {6}{1.5} = 4 $$<\/p>\n<p>Interpretation: the dispersion per unit monthly return of T-Bills is less than that of Y. Therefore, investment Y is riskier than an investment on T-Bills.<\/p>\n<blockquote>\n<h2><strong>Question<\/strong><\/h2>\n<p>If a security has a mean expected return of 10% and a standard deviation of 5%, its coefficient of variation is <em>closest<\/em> to:<\/p>\n<ol style=\"list-style-type: upper-alpha;\">\n<li>0.005<\/li>\n<li>0.5<\/li>\n<li>2<\/li>\n<\/ol>\n<p><strong>Solution<\/strong><\/p>\n<p>$$ \\text{CV} = \\cfrac {S}{\\text x\u0304} = \\cfrac {0.05}{0.10} = 0.5$$<\/p>\n<p>Where S is the standard deviation of a sample<\/p>\n<p>And x\u0304 is the mean of the sample.<\/p>\n<\/blockquote>\n<div class=\"notes_inv\"><hr \/>\n<p>\u00a0<\/p>\n<\/div>\n<p>\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The coefficient of variation, CV, is a measure of spread that describes the amount of variability of data relative toits mean. It has no units, and as such, we can use it as an alternative to the standard deviation to&#8230;<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[2],"tags":[],"class_list":["post-354","post","type-post","status-publish","format-standard","hentry","category-quantitative-methods","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Coefficient of Variation &amp; Sharpe Ratio | CFA Level 1<\/title>\n<meta name=\"description\" content=\"The coefficient of variation measures risk relative to return, while the Sharpe ratio evaluates risk-adjusted performance in investments.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" 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