{"id":18880,"date":"2021-08-02T22:45:47","date_gmt":"2021-08-02T22:45:47","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=18880"},"modified":"2026-04-06T06:54:41","modified_gmt":"2026-04-06T06:54:41","slug":"describe-extensions-of-var","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/describe-extensions-of-var\/","title":{"rendered":"Extensions of VaR"},"content":{"rendered":"<p><script type=\"application\/ld+json\">\r\n{\r\n  \"@context\": \"https:\/\/schema.org\",\r\n  \"@type\": \"ImageObject\",\r\n  \"@id\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/08\/Conditional-Value-at-Risk-1536x1214.jpg#image\",\r\n  \"url\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/08\/Conditional-Value-at-Risk-1536x1214.jpg\",\r\n  \"contentUrl\": \"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/08\/Conditional-Value-at-Risk-1536x1214.jpg\",\r\n  \"name\": \"Conditional Value at Risk (CVaR) Illustration\",\r\n  \"caption\": \"Illustration of Conditional Value at Risk (CVaR) showing expected loss beyond the VaR threshold.\",\r\n  \"description\": \"Graphical depiction of the Conditional Value at Risk (CVaR) concept, an extension of Value at Risk (VaR) that quantifies the average loss given that the VaR threshold has been exceeded, from the CFA Level II study notes on extensions of VaR risk measures. :contentReference[oaicite:0]{index=0}\",\r\n  \"encodingFormat\": \"image\/jpeg\",\r\n  \"width\": 1536,\r\n  \"height\": 1214,\r\n  \"creator\": {\r\n    \"@type\": \"Organization\",\r\n    \"name\": \"AnalystPrep\"\r\n  },\r\n  \"creditText\": \"AnalystPrep\",\r\n  \"copyrightNotice\": \"\u00a9 AnalystPrep\",\r\n  \"mainEntityOfPage\": {\r\n    \"@type\": \"WebPage\",\r\n    \"@id\": \"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/describe-extensions-of-var\/\"\r\n  },\r\n  \"isPartOf\": {\r\n    \"@type\": \"WebPage\",\r\n    \"@id\": \"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/describe-extensions-of-var\/\"\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  \"mainEntity\": {\r\n    \"@type\": \"Question\",\r\n    \"name\": \"Which of the following statements about the extensions of VaR is the most accurate?\",\r\n    \"text\": \"Which of the following statements about the extensions of VaR is the most accurate?\\n\\nA. Marginal VaR is a tail risk metric that quantifies the amount of expected losses beyond the VaR cutoff point.\\n\\nB. Conditional VaR is a measure of how removing a position from a portfolio may affect the overall VaR.\\n\\nC. Incremental VaR measures the impact on the VaR resulting from small changes caused by taking different positions of a portfolio.\",\r\n    \"answerCount\": 3,\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"Incremental VaR measures the impact on the VaR resulting from small changes caused by taking different positions of a portfolio.\",\r\n      \"commentary\": \"Incremental value at risk (IVaR) measures the impact on the portfolio VaR resulting from small changes in portfolio positions. It is calculated by comparing the portfolio VaR before and after a small change in a position. Marginal VaR instead measures the effect of removing an entire position, while Conditional VaR (CVaR) measures expected losses beyond the VaR cutoff point.\"\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<h2>Conditional Value at Risk (CVaR)<\/h2>\r\n<p>Rockafellar and Uryasev introduced <strong>conditional value-at-risk<\/strong> (CVaR) in 2000. CVaR is a tail risk metric that quantifies the amount of the expected losses beyond the VaR cutoff point at a specific confidence level. It is also known as the <strong>expected shortfall<\/strong> (ES), <strong>average value at risk<\/strong> (AVaR), or <strong>expected tail loss<\/strong> (ETL). CVaR is a weighted average of the losses in the tail of the return&#8217;s distribution beyond the VaR level.<\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-26662\" src=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/08\/Conditional-Value-at-Risk.jpg\" alt=\"Conditional Value at Risk\" width=\"1590\" height=\"1257\" srcset=\"https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/08\/Conditional-Value-at-Risk.jpg 1590w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/08\/Conditional-Value-at-Risk-300x237.jpg 300w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/08\/Conditional-Value-at-Risk-1024x810.jpg 1024w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/08\/Conditional-Value-at-Risk-768x607.jpg 768w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/08\/Conditional-Value-at-Risk-1536x1214.jpg 1536w, https:\/\/analystprep.com\/study-notes\/wp-content\/uploads\/2021\/08\/Conditional-Value-at-Risk-400x316.jpg 400w\" sizes=\"auto, (max-width: 1590px) 100vw, 1590px\" \/>CVaR is mathematically complex to obtain when the parametric method is used. This can be attributed to the fact that this method cannot be used in the determination of the magnitude of losses more magnificent than the VaR.<\/p>\r\n<div style=\"margin: 20px 0;\"><a style=\"display: block; width: 100%; text-align: center; padding: 10px; border: 2px solid #2f5bea; border-radius: 40px; font-size: 16px; color: #2f5bea; text-decoration: none;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener\"> Practice VaR extension questions with our free trial. <\/a><\/div>\r\n<h2>Incremental Value at Risk (IVaR)<\/h2>\r\n<p>Kevin Dowd introduced <strong>incremental value at risk<\/strong> in 1999. Incremental value at risk (IVaR) measures the impact of small changes as a result of taking different positions of the portfolio on the VaR. To obtain IVaR, VaR is repeatedly calculated considering different positions of the portfolio. The difference between the new VaR and the original is the IVaR.<\/p>\r\n<h2>Marginal VaR (MVaR)<\/h2>\r\n<p><strong>Marginal VaR<\/strong> is a measure of the impact of removing a position from a portfolio on the overall VaR. It is different from IVaR because it measures the impact of removing an entire portfolio holding rather than making small changes, in the portfolio position, on VaR.<\/p>\r\n<h2>Relative VaR<\/h2>\r\n<p><strong>Relative VaR<\/strong> measures the risk resulting from the underperformance of a portfolio relative to a benchmark portfolio. Assuming a 95% confidence level, a 1-day relative VaR of $5,000 for portfolio B implies that, on average, the portfolio would underperform only for five days in a hundred days, relative to the benchmark by more than $5,000 due to market changes.<\/p>\r\n<blockquote>\r\n<h2>Question<\/h2>\r\n<p>Which of the following statements about the extensions of VaR is the <em>most accurate<\/em> ?<\/p>\r\n<ol type=\"A\">\r\n\t<li>Marginal VaR is a tail risk metric that quantifies the amount of expected losses beyond the VaR cutoff point.<\/li>\r\n\t<li>Conditional VaR is a measure of how removing a position from a portfolio may affect the overall VaR.<\/li>\r\n\t<li>Incremental VaR measures the impact on the VaR resulting from small changes caused by taking different positions of a portfolio.<\/li>\r\n<\/ol>\r\n<h4>Solution<\/h4>\r\n<p><strong>The correct answer is C.<\/strong><\/p>\r\n<p>Incremental value at risk (IVaR) measures the impact on the VaR resulting from small changes caused by taking different positions of a portfolio. To obtain IVaR, VaR is repeatedly calculated considering the different positions of the portfolio. The difference between the new VaR and the original is the IVaR.<\/p>\r\n<p><strong>A is incorrect.<\/strong>\u00a0Marginal VaR is a measure of how the removal of a position from a portfolio may affect the overall VaR. It is different from IVaR because it measures the impact that the removal of an entire position rather than making small changes in a portfolio has on VaR.<\/p>\r\n<p><strong>B is incorrect.<\/strong>\u00a0Conditional value-at-risk (CVaR) is a tail risk metric that quantifies the amount of the expected losses beyond the VaR cutoff point at a specific confidence level.<\/p>\r\n<\/blockquote>\r\n<p>Reading 41: Measuring and Managing Market Risk<\/p>\r\n<p><em>LOS 41 (e) Describe extensions of VaR.<\/em><\/p>\r\n\r\n\r\n<div style=\"margin: 20px 0;\">\r\n<div style=\"text-align: center; margin: 40px 0;\"><a style=\"display: inline-block; padding: 10px 26px; background: #3f78d7; color: #fff; border-radius: 40px; font-size: 16px; text-decoration: none;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener\"> Start Free Trial \u2192 <\/a>\r\n<p style=\"margin-top: 10px; max-width: 600px; margin-left: auto; margin-right: auto; font-size: 14px;\">Solve CFA Level II questions on incremental VaR, marginal VaR, and portfolio risk decomposition.<\/p>\r\n<\/div>\r\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Conditional Value at Risk (CVaR) Rockafellar and Uryasev introduced conditional value-at-risk (CVaR) in 2000. CVaR is a tail risk metric that quantifies the amount of the expected losses beyond the VaR cutoff point at a specific confidence level. It is&#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-18880","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 v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Extensions of VaR | CFA Level II Notes<\/title>\n<meta name=\"description\" content=\"Learn key extensions of VaR, including Conditional VaR, Incremental VaR, Marginal VaR, and Relative VaR in risk measurement.\" \/>\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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