{"id":2844,"date":"2019-09-01T11:00:00","date_gmt":"2019-09-01T11:00:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=2844"},"modified":"2026-03-08T11:11:32","modified_gmt":"2026-03-08T11:11:32","slug":"calculating-returns-using-capm","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/portfolio-management\/calculating-returns-using-capm\/","title":{"rendered":"Calculating Returns Using CAPM"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"ImageObject\",\n  \"url\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/09\/The-Security-Market-Line-SML1.png\",\n  \"caption\": \"The Security Market Line\",\n  \"width\": 974,\n  \"height\": 668,\n  \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\n  \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\n  \"creditText\": \"AnalystPrep Design Team\",\n  \"creator\": {\n    \"@type\": \"Organization\",\n    \"name\": \"AnalystPrep\"\n  }\n}\n<\/script>\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"Assume the risk-free rate is 2%, a security has a correlation of 0.8 with the market index and a standard deviation of 16%, while the standard deviation of the market is 12%. If the market expected return is 8%, what is the security\u2019s expected return?\",\n    \"text\": \"Assume the risk-free rate is 2%, a security has a correlation of 0.8 with the market index and a standard deviation of 16%, while the standard deviation of the market is 12%. If the market expected return is 8%, what is the security\u2019s expected return?\\n\\nA. 10.56%.\\n\\nB. 5.60%.\\n\\nC. 8.42%.\",\n    \"answerCount\": 1,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is C. The expected return is calculated using the Capital Asset Pricing Model (CAPM): E(Ri) = Rf + \u03b2i[E(Rm) \u2212 Rf]. First compute beta using \u03b2i = \u03c1i,m(\u03c3i\/\u03c3m). Substituting the values gives \u03b2i = (0.8 \u00d7 0.16) \/ 0.12 = 1.07. Then calculate the expected return: E(Ri) = 2% + 1.07 \u00d7 (8% \u2212 2%) = 8.42%.\"\n    }\n  }\n}\n<\/script>\n\n\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/OCZddCJ_HwM\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\nGiven as asset systematic risk, the expected return can be computed using the capital asset pricing model. The CAPM result is usually used as a first estimate of return. In addition, it is used in capital budgeting and the determination of economic feasibility. Besides providing security expected returns, CAPM can be used for estimating the cost of capital and setting insurance premiums.<\/p>\n<h2><strong>Calculating Expected Returns<\/strong><\/h2>\n<p>The Security Market Line (SML) is the graphical representation of the CAPM with beta reflecting systematic risk on the x-axis and expected return on the y-axis. The SML intersects the y-axis at the risk-free rate, and the slope of the line is the market risk premium, R<sub>m<\/sub> &#8211; R<sub>f<\/sub>.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-16836\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/09\/The-Security-Market-Line-SML1.png\" alt=\"The-Security-Market-Line-SML1\" width=\"974\" height=\"668\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/09\/The-Security-Market-Line-SML1.png 974w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/09\/The-Security-Market-Line-SML1-300x206.png 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/09\/The-Security-Market-Line-SML1-768x527.png 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/09\/The-Security-Market-Line-SML1-400x274.png 400w\" sizes=\"auto, (max-width: 974px) 100vw, 974px\" \/><\/p>\n<p>The SML is formulated as follows:<\/p>\n<p>$$E(R_i) = R_f + \\beta_i [E(R_m) \u2013 R_f]$$<\/p>\n<p>Where \\(\\beta_i= \\frac{\\rho_{ i,m} \\sigma_i } {\\sigma_m}\\)<\/p>\n<p>With data for the risk-free rate, the market expected return, the beta of a security (or its correlation with the market), and the standard deviations of the security and the market, we can calculate the expected return using CAPM.<\/p>\n<blockquote>\n<h2><strong>Question<\/strong><\/h2>\n<p>Assume the risk-free rate is 2%, a security has a correlation of 0.8 with the market index and a standard deviation of 16%, while the standard deviation of the market is 12%. If the market expected return is 8%, what is the security&#8217;s expected return?<\/p>\n<p>A. 10.56%.<\/p>\n<p>B. 5.60%.<\/p>\n<p>C. 8.42%.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is <strong>C<\/strong>.<\/p>\n<p>\\(E(R_i) = R_f + \\beta_i [E(R_m) \u2013 R_f]\\)<\/p>\n<p>Where \\(\\beta_i= \\frac{\\rho_{ i,m} \\sigma_i } {\\sigma_m}\\)<\/p>\n<p><em>Step 1: Find the Beta<\/em><\/p>\n<p>\\beta<sub>i <\/sub> = (0.8 \u00d7 0.16) \/ 0.12 = 1.07<\/p>\n<p>Step 2: Find the expected return<\/p>\n<p>E(<em>R<sub>i<\/sub><\/em>) = 2% + 1.07 \u00d7 (8% &#8211; 2%) = 8.42%<\/p><\/blockquote>","protected":false},"excerpt":{"rendered":"<p>Given as asset systematic risk, the expected return can be computed using the capital asset pricing model. The CAPM result is usually used as a first estimate of return. In addition, it is used in capital budgeting and the determination&#8230;<\/p>\n","protected":false},"author":18,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[7],"tags":[],"class_list":["post-2844","post","type-post","status-publish","format-standard","hentry","category-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>Calculating Expected Returns with CAPM | CFA Level 1<\/title>\n<meta name=\"description\" content=\"Learn how to use the Capital Asset Pricing Model (CAPM) to calculate expected returns and assess investment risk with the Security Market Line (SML).\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link 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