{"id":62320,"date":"2026-07-28T22:48:43","date_gmt":"2026-07-28T22:48:43","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=62320"},"modified":"2026-08-03T16:38:32","modified_gmt":"2026-08-03T16:38:32","slug":"portfolio-standard-deviation-2","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/uncategorized\/portfolio-standard-deviation-2\/","title":{"rendered":"Portfolio Standard Deviation"},"content":{"rendered":"\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\": \"Options:\\nA. 16.3%.\\nB. 2.7%.\\nC. 22%.\",\n    \"answerCount\": 1,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is A. The portfolio variance is calculated as: (0.8)\u00b2 \u00d7 (0.16)\u00b2 + (0.2)\u00b2 \u00d7 (0.25)\u00b2 + 2(0.8)(0.2)(0.16)(0.25)(0.6). The resulting portfolio variance is approximately 2.66%. Taking the square root of the variance gives a portfolio standard deviation of approximately 16.3%.\"\n    }\n  }\n}\n<\/script>\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<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)\u00b2 \u00d7 (0.16)\u00b2 + (0.2)\u00b2 \u00d7 (0.25)\u00b2 + 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><\/blockquote>\n\n\n<div style=\"text-align: center; margin: 30px 0;\"><a style=\"display: inline-flex; align-items: center; justify-content: center; padding: 12px 26px; border-radius: 9999px; background: #1e5bd8; color: #ffffff; font-weight: bold; text-decoration: none;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"> Start Free Trial \u2192 <\/a> <p style=\"margin-top: 12px; font-size: 16px; line-height: 1.5;\">Strengthen your understanding of monopolistic competition, market structures, firm behavior, and pricing strategies with CFA Level I study notes, practice questions, and mock exams.\n<\/p>\n <\/div>\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. Computing&#8230;<\/p>\n","protected":false},"author":15,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-62320","post","type-post","status-publish","format-standard","hentry","category-uncategorized","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>Portfolio Standard Deviation | CFA Level I<\/title>\n<meta name=\"description\" content=\"Learn how to calculate portfolio standard deviation, including the two-asset portfolio formula and its role in measuring investment risk.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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