{"id":2255,"date":"2019-09-12T13:33:00","date_gmt":"2019-09-12T13:33:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=2255"},"modified":"2026-02-19T19:17:16","modified_gmt":"2026-02-19T19:17:16","slug":"portfolio-standard-deviation","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/portfolio-management\/portfolio-standard-deviation\/","title":{"rendered":"Portfolio Standard Deviation"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Portfolio Risk and Return \u2013 Part I (2025 Level I CFA\u00ae Exam \u2013 Portfolio Management \u2013 Module 1)\",\n  \"description\": \"This lesson covers Portfolio Risk and Return \u2013 Part I for the 2025 CFA\u00ae Level I Portfolio Management curriculum. It explains how to calculate and interpret expected return, variance, standard deviation, covariance, correlation, and portfolio standard deviation. The video also examines diversification benefits, the efficient frontier, the global minimum variance portfolio, the role of a risk-free asset, the Capital Market Line, and investor risk preferences, with worked examples and calculator tips to support exam preparation.\",\n  \"uploadDate\": \"2023-11-07T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/DLKhsZvcD-c\/default.jpg\",\n  \"contentUrl\": \"https:\/\/youtu.be\/DLKhsZvcD-c\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/DLKhsZvcD-c\",\n  \"duration\": \"PT55M38S\"\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"Consider two assets in a portfolio. Asset A has an allocation of 80% and a standard deviation of 16%. Asset B has an allocation of 20% and a standard deviation of 25%. The correlation coefficient between asset A and asset B is 0.6. In this case, the portfolio standard deviation is closest to:\",\n    \"text\": \"Consider two assets in a portfolio. Asset A has an allocation of 80% and a standard deviation of 16%. Asset B has an allocation of 20% and a standard deviation of 25%. The correlation coefficient between asset A and asset B is 0.6. In this case, the portfolio standard deviation is closest to:\\n\\nA. 16.3%\\nB. 2.7%\\nC. 22%\",\n    \"answerCount\": 3,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is A.\\n\\nWe determine the portfolio variance as follows:\\n\\nPortfolio variance = (0.8)^2 * (0.16)^2 + (0.2)^2 * (0.25)^2 + 2(0.8)(0.2)(0.16)(0.25)(0.6)\\n\\nThen, we use the square root of the variance to get the standard deviation:\\n\\nPortfolio standard deviation = \u221a2.66% = 16.3%\"\n    }\n  }\n}\n<\/script>\n\n\n\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/DLKhsZvcD-c?si=IwatUfU71LjpJkAO\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n\n\n\n<p>The standard deviation of a portfolio of assets, or portfolio risk, is simply not the sum of the risk of the underlying securities. Due to the correlation between securities, the computation of portfolio risk must incorporate this correlation relationship.<\/p>\n\n\n\n<div style=\"margin:22px 0;\">\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\"\n     target=\"_blank\"\n     rel=\"noopener noreferrer\"\n     style=\"\n        display:block;\n        width:100%;\n        text-align:center;\n        padding:14px 0;\n        border:2px solid #2f5bea;\n        border-radius:40px;\n        text-decoration:none;\n        font-weight:500;\n        font-size:18px;\n        color:#2f5bea;\n        background-color:transparent;\n        box-sizing:border-box;\n     \">\n     Practice portfolio risk questions with our free trial.\n  <\/a>\n<\/div>\n\n\n\n<h2><strong>Computing Portfolio Standard Deviation<\/strong><\/h2>\n<p>The portfolio standard deviation and variance are important. They involve the variance of the assets and the covariance between asset pairs. For a portfolio with assets X and Y, the portfolio variance can be calculated as follows:<\/p>\n<p>$$ \\text{Portfolio variance} = w_X^2\\sigma_X^2 + w_Y^2\\sigma_Y^2 + 2 w_{X} w_{Y} \\sigma_{X} \\sigma_{Y} \\rho_{XY} $$<\/p>\n<p>Therefore,<\/p>\n<p>$$ \\text{Portfolio standard deviaton} = \\sqrt{w_X^2\\sigma_X^2 + w_Y^2\\sigma_Y^2 + 2 w_{X} w_{Y} \\sigma_{X} \\sigma_{Y} \\rho_{XY}} $$<\/p>\n<p>Where:<\/p>\n<p><em>w<\/em> = Weight of the asset within the portfolio.<\/p>\n<p>\\(\\sigma\\) = Standard deviation.<\/p>\n<p>\\( \\rho \\) = Correlation coefficient.<\/p>\n<p>Note that\u00a0\\( \\sigma_{X} \\sigma_{Y} \\rho_{XY} = \\text{Covariance}_{XY}\\)<\/p>\n<blockquote>\n<h2><strong>Question<\/strong><\/h2>\n<p>Consider two assets in a portfolio. Asset A has an allocation of 80% and a standard deviation of 16%. Asset B has an allocation of 20% and a standard deviation of 25%. The correlation coefficient between asset A and asset B is 0.6. In this case, the portfolio standard deviation is <em>closest to<\/em>:<\/p>\n<p>A. 16.3%.<\/p>\n<p>B. 2.7%.<\/p>\n<p>C. 22%.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is <strong>A<\/strong>.<\/p>\n<p>We determine the portfolio variance as follows:<\/p>\n<p>Portfolio variance = (0.8)^2 \\times (0.16)^2 + (0.2)^2 \\times (0.25)^2 + 2(0.8)(0.2)(0.16)(0.25)(0.6)<\/p>\n<p>Then, we use the square root of the variance to get the standard deviation:<\/p>\n<p>\\( \\text{Portfolio standard deviation} =\\sqrt{2.66\\%} = 16.3\\% \\)<\/p>\n<\/blockquote>\n\n\n<div style=\"text-align:center; margin:42px 0 10px;\">\n\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\"\n     target=\"_blank\"\n     rel=\"noopener noreferrer\"\n     style=\"\n        display:inline-block;\n        padding:16px 36px;\n        background-color:#3f78d7;\n        color:#ffffff;\n        text-decoration:none;\n        font-weight:600;\n        font-size:18px;\n        border-radius:40px;\n        line-height:1.1;\n     \">\n     Start Free Trial\n  <\/a>\n\n  <p style=\"\n        margin-top:18px;\n        max-width:720px;\n        margin-left:auto;\n        margin-right:auto;\n        font-size:17px;\n        line-height:1.6;\n     \">\n     Access AnalystPrep\u2019s free trial to solve CFA-style portfolio standard deviation problems and strengthen your understanding of diversification, covariance, and risk measurement.\n  <\/p>\n\n<\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>The standard deviation of a portfolio of assets, or portfolio risk, is simply not the sum of the risk of the underlying securities. Due to the correlation between securities, the computation of portfolio risk must incorporate this correlation relationship. Practice&#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-2255","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>Portfolio Standard Deviation | CFA Level 1<\/title>\n<meta name=\"description\" content=\"Portfolio standard deviation measures risk, considering asset correlations. 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