{"id":18848,"date":"2021-08-01T22:15:46","date_gmt":"2021-08-01T22:15:46","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=18848"},"modified":"2026-03-02T14:28:43","modified_gmt":"2026-03-02T14:28:43","slug":"explain-the-use-of-value-at-risk-var-in-measuring-portfolio-risk","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/explain-the-use-of-value-at-risk-var-in-measuring-portfolio-risk\/","title":{"rendered":"Value at Risk (VaR)"},"content":{"rendered":"<p><script type=\"application\/ld+json\">\r\n{\r\n  \"@context\": \"https:\/\/schema.org\",\r\n  \"@type\": \"ImageObject\",\r\n  \"url\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/08\/5-VaR-1536x1020.jpg\",\r\n  \"caption\": \"Value at Risk (VaR) illustration for measuring portfolio risk\",\r\n  \"width\": 1536,\r\n  \"height\": 1020,\r\n  \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\r\n  \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\r\n  \"creditText\": \"AnalystPrep Design Team\",\r\n  \"creator\": {\r\n    \"@type\": \"Organization\",\r\n    \"name\": \"AnalystPrep\"\r\n  }\r\n}\r\n<\/script> <script type=\"application\/ld+json\">\r\n{\r\n  \"@context\": \"https:\/\/schema.org\",\r\n  \"@type\": \"QAPage\",\r\n  \"@id\": \"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/explain-the-use-of-value-at-risk-var-in-measuring-portfolio-risk\/#q1\",\r\n  \"mainEntity\": {\r\n    \"@type\": \"Question\",\r\n    \"name\": \"Interpreting an annual 1% VaR of $45,000\",\r\n    \"text\": \"A hypothetical portfolio B has an annual 1% VaR of $45,000. Which of the following statements is most likely true about the portfolio?\\n\\nA. The expected minimum loss over one year, 1% of the time, is $45,000.\\nB. There is a 99% probability that the expected loss over the next year is more than $45,000.\\nC. The likelihood of losing $45,000 over the next year is 1%.\",\r\n    \"answerCount\": 3,\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"A. The expected minimum loss over one year, 1% of the time, is $45,000.\"\r\n    },\r\n    \"suggestedAnswer\": [\r\n      {\r\n        \"@type\": \"Answer\",\r\n        \"text\": \"A. The expected minimum loss over one year, 1% of the time, is $45,000.\"\r\n      },\r\n      {\r\n        \"@type\": \"Answer\",\r\n        \"text\": \"B. There is a 99% probability that the expected loss over the next year is more than $45,000.\"\r\n      },\r\n      {\r\n        \"@type\": \"Answer\",\r\n        \"text\": \"C. The likelihood of losing $45,000 over the next year is 1%.\"\r\n      }\r\n    ]\r\n  }\r\n}\r\n<\/script><\/p>\r\n\r\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/Q_AYzGoaFUA\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\r\n<p><strong>Value at Risk (VaR)<\/strong> measures the probability of underperformance by providing a statistical measure of downside risk.<\/p>\r\n<p>In the case of a continuous random variable, VaR can be computed as follows:<\/p>\r\n<p>$$ VaR\\left(X\\right)=-t \\text{ where } P\\left(X &lt; t\\right)=p $$<\/p>\r\n<p>VaR represents the maximum possible loss on a portfolio over a given period in the future, with a given degree of confidence. The degree of confidence is typically expressed as \\(1-p\\).<\/p>\r\n<div style=\"background: #f3f4f6; padding: 16px 14px; border-radius: 12px; margin: 20px 0; text-align: center;\"><a style=\"display: inline-flex; align-items: center; justify-content: center; padding: 12px 18px; border: 2px solid #1d4ed8; border-radius: 999px; color: #1d4ed8; text-decoration: none; font-weight: 600; font-size: 16px; line-height: 1; background: #ffffff; white-space: nowrap;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"> Apply VaR concepts to realistic Level II portfolio questions <\/a><\/div>\r\n<p>For instance, if an asset has a one-day 5% VaR of $7,500, then there is a 5% probability that the asset will fall in value by at least $7,500 over one day under normal market conditions. This can also be given in terms of a confidence level, that is, we are 95% (100% \u2212 5%) confident that the asset will experience a loss of at most $7,500 in one day.<\/p>\r\n<p>The following is an illustration of the 5% VaR of a hypothetical portfolio:<\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-26656\" src=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/08\/5-VaR.jpg\" alt=\"5% VaR\" width=\"1590\" height=\"1056\" srcset=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/08\/5-VaR.jpg 1590w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/08\/5-VaR-300x199.jpg 300w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/08\/5-VaR-1024x680.jpg 1024w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/08\/5-VaR-768x510.jpg 768w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/08\/5-VaR-1536x1020.jpg 1536w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/08\/5-VaR-400x266.jpg 400w\" sizes=\"auto, (max-width: 1590px) 100vw, 1590px\" \/>The above illustration shows that the portfolio&#8217;s expected return is $50m. Additionally, the probability of realizing a return of less than $42m is 5%.<\/p>\r\n<blockquote style=\"font: normal;\">\r\n<h2>Question<\/h2>\r\n<p>A hypothetical portfolio B has an annual 1% VaR of $45,000. Which of the following statements is <em>most likely<\/em> true about the portfolio?<\/p>\r\n<ol type=\"A\">\r\n\t<li>The expected minimum loss over one year, 1% of the time, is $45,000.<\/li>\r\n\t<li>There is a 99% probability that the expected loss over the next year is more than $45,000.<\/li>\r\n\t<li>The likelihood of losing $45,000 over the next year is 1%.<\/li>\r\n<\/ol>\r\n<h4>Solution<\/h4>\r\n<p><strong>The correct answer is A.<\/strong><\/p>\r\n<p>An annual 1% VaR of $45,000 means that there is a 1% probability of a loss greater than $45,000.<\/p>\r\n<p><strong>B is incorrect.<\/strong>\u00a0An annual 1% VaR of $45,000 means that there is a 99% probability that the portfolio will experience a loss of not more than $45,000 in one year.<\/p>\r\n<p><strong>C is incorrect.<\/strong>\u00a0VaR does not specify the probability of losing a particular amount.<\/p>\r\n<\/blockquote>\r\n<p>Reading 41: Measuring and Managing Market Risk<\/p>\r\n<p><em>LOS 41 (a) Explain the use of value at risk (VaR) in measuring portfolio risk.<\/em><\/p>\r\n<p>\r\n<\/p>\r\n<div style=\"background: #f3f4f6; padding: 22px 18px; border-radius: 14px; margin: 30px 0; text-align: center;\">\r\n<div style=\"font-size: 17px; line-height: 1.4; margin-bottom: 14px; color: #111827; font-weight: 600;\">Ready to calculate, interpret, and compare VaR under different confidence levels and time horizons?<\/div>\r\n<a style=\"display: inline-flex; align-items: center; justify-content: center; padding: 14px 24px; border-radius: 999px; background: #1d4ed8; color: #ffffff; text-decoration: none; font-weight: bold; font-size: 17px; line-height: 1;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"> Start Free Trial \u2192 <\/a>\r\n<div style=\"margin-top: 12px; font-size: 16px; color: #333333;\">Drill portfolio risk questions and master key formulas.<\/div>\r\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Value at Risk (VaR) measures the probability of underperformance by providing a statistical measure of downside risk. In the case of a continuous random variable, VaR can be computed as follows: $$ VaR\\left(X\\right)=-t \\text{ where } P\\left(X &lt; t\\right)=p $$&#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-18848","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 v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Using Value at Risk (VaR) | CFA Level II<\/title>\n<meta name=\"description\" content=\"Learn how Value at Risk (VaR) is used to measure portfolio downside risk and interpret potential losses at a given confidence level.\" 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