{"id":27672,"date":"2023-06-25T10:37:40","date_gmt":"2023-06-25T10:37:40","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=27672"},"modified":"2026-03-05T20:05:35","modified_gmt":"2026-03-05T20:05:35","slug":"absolute-and-relative-risk-budgets","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-iii\/absolute-and-relative-risk-budgets\/","title":{"rendered":"Absolute and Relative Risk Budgets"},"content":{"rendered":"<p><script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"When is a risk budget most likely to be optimal?\",\n    \"text\": \"A risk budget is most likely optimal when which of the following occurs? A) The ratio of absolute contribution to total risk is the same for all assets. B) The ratio of marginal contribution to total risk is higher than the portfolio Sharpe ratio. C) The ratio of excess return to marginal contribution to total risk is the same for all assets.\",\n    \"answerCount\": 1,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"A risk budget is optimal when the ratio of excess return to marginal contribution to total risk is the same for all assets in the portfolio. This condition ensures that each asset contributes equally to risk-adjusted performance at the margin.\",\n      \"dateCreated\": \"2026-01-19\"\n    }\n  }\n}\n<\/script><\/p>\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/vyLJwRncCBw\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p><em>Risk budgeting<\/em> is a means of making optimal use of risk to pursue return. A risk budget is optimal when the ratio of excess return to marginal contribution to total risk (MCTR) is the same for all assets in the portfolio. The following formulas help quantify and analyze portfolio allocation decisions:<\/p>\n<p><strong><u>Marginal Contribution to Total Risk <\/u><\/strong><u>&#8220;<\/u><strong><u>MCTR<\/u><\/strong><u>&#8220;<\/u><\/p>\n<p>$$ MCTR = \\text{Beta of asset class} \\times \\text{Portfolio standard deviation} $$<\/p>\n<p><u><strong>Absolute Contribution to Total Risk <\/strong>&#8220;<strong>ACTR<\/strong>&#8220;<\/u><\/p>\n<p>$$ {ACTR}=\\text{Asset weight} \\times {MCTR} $$<\/p>\n<p><u><strong>% of Risk Contributed by a Position<\/strong><\/u><\/p>\n<p>$$ \\% \\text{ of risk contributed by a position} =\\frac {ACTR}{\\text{(Total portfolio risk)}} $$<\/p>\n<p><u><strong>Ratio of Excess Return<\/strong><\/u><\/p>\n<p>$$ \\text{Ratio of excess return to MCTR} =\\frac {\\text{Expected return}-\\text{Risk free rate}}{{MCTR}} $$<\/p>\n<p>The optimal allocation to any asset class appears when the excess return to MCTR ratio is equal for all assets and the portfolio Sharpe Ratio.<\/p>\n<p>$$ \\small{\\begin{array}{c|c|c|c|c|c|c|c} &amp; \\textbf{Weight} &amp; {\\textbf{Excess}} &amp; \\textbf{Beta} &amp; \\textbf{MCTR} &amp; \\textbf{ACTR} &amp; \\bf{\\%} &amp; { \\textbf{Ratio of}} \\\\ &amp; &amp;{\\textbf{Return}} &amp; &amp; &amp; &amp; \\textbf{Contribution} &amp; \\textbf{Excess} \\\\ &amp; &amp; &amp; &amp; &amp; &amp; {\\textbf{to Risk}} &amp; \\textbf{Return} \\\\ &amp; &amp; &amp; &amp; &amp; &amp; &amp; \\textbf{to} \\\\ &amp; &amp; &amp; &amp; &amp; &amp; &amp; {\\textbf{MCTR} } \\\\ \\hline \\textbf{Equity} &amp; 52\\% &amp; 6.57\\% &amp; 1.5 &amp; 19.50\\% &amp; 10.10\\% &amp; 77.67\\% &amp; \\bf{0.337} \\\\ \\hline \\textbf{Bond} &amp; 34\\% &amp; 2.85\\% &amp; 0.65 &amp; 8.45\\% &amp; 2.90\\% &amp; 22.33\\% &amp; \\bf{0.337} \\\\ \\hline \\textbf{Cash} &amp; 14\\% &amp; 0 &amp; 0 &amp; 0.00\\% &amp; 0.00\\% &amp; 0.00\\% &amp; \\\\ \\hline \\textbf{Total} &amp; 100\\% &amp; 4.38\\% &amp; 1 &amp; &amp; 13.00\\% &amp; 100\\% &amp; \\end{array}} $$<\/p>\n<p>*Calculated values are subject to rounding errors.<\/p>\n<p>The portfolio standard deviation is 13%<\/p>\n<p>The calculation for bonds is as follows:<\/p>\n<p>$$ \\text{MCTR}_\\text{Bonds}=0.65 \\times 13= 8.45\\% $$<\/p>\n<p>$$ \\text{ACTR}_\\text{Bonds} =(0.34) \\times 8.45\\% \\approx 2.90\\% $$<\/p>\n<p>$$ \\% \\text{ Contribution to total } {\\text{risk}_\\text{Bonds}} = \\frac {(2.90\\%)}{(13\\%)} \\approx 22.31\\% $$<\/p>\n<p>Ratio of excess return to \\(\\text{ MCTR}_\\text{Bonds}=\\left(\\frac {(6.57\\%)}{(8.45\\%)} \\right)=77.75\\% \\)<\/p>\n<ul>\n<li>\\(\\text{Portfolio Sharpe ratio} =\\frac {(4.38\\%)}{(13\\%)} = 0.337\\)<\/li>\n<li>The Portfolio Sharpe ratio is <strong>equal<\/strong> to the ratio of excess return to MCTR for both equities and bonds.<\/li>\n<\/ul>\n<p>Therefore, the <strong>52\/34\/14 allocation<\/strong> is <strong>optimal<\/strong> from a <strong>risk-budgeting perspective<\/strong>.<\/p>\n<blockquote>\n<h2>Question<\/h2>\n<p>A risk budget is <em>most likely<\/em> optimal when which of the following occurs?<\/p>\n<ol type=\"A\">\n<li>The ratio of absolute contribution to total risk is the same for all assets in the portfolio.<\/li>\n<li>The ratio of marginal contribution to total risk is higher than the portfolio Sharpe ratio.<\/li>\n<li>The ratio of excess return to marginal contribution to total risk is the same for all assets in the portfolio.<\/li>\n<\/ol>\n<h4>Solution<\/h4>\n<p><strong>The correct answer is C:<\/strong><\/p>\n<p>A risk budget is optimal when the ratio of excess return to marginal contribution to total risk is the same for all assets in the portfolio.<\/p>\n<p><strong>A is incorrect.<\/strong> It refers to the ratio of absolute contribution to total risk rather than the ratio of excess return to marginal contribution to total risk. Absolute contribution to total risk does not consider an asset&#8217;s expected return. It, therefore, does not provide a complete picture of the trade-off between risk and return.<\/p>\n<p><strong>B is incorrect.<\/strong> It refers to the ratio of marginal contribution to total risk being higher than the portfolio Sharpe ratio. The Sharpe ratio measures risk-adjusted performance, calculated as the excess return of an investment over a risk-free rate, divided by the standard deviation of its returns. The relationship between the Sharpe ratio and the ratio of marginal contribution to total risk is irrelevant in determining whether a risk budget is optimal. Instead, what matters is whether the ratio of excess return to marginal contribution to total risk is the same for all assets in the portfolio.<\/p>\n<\/blockquote>\n<p>Reading 5: Principles of Asset Allocation<\/p>\n<p>Los 5 (g) Explain absolute and relative risk budgets and their use in determining and implementing an asset allocation<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Risk budgeting is a means of making optimal use of risk to pursue return. A risk budget is optimal when the ratio of excess return to marginal contribution to total risk (MCTR) is the same for all assets in the&#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":[571],"tags":[],"class_list":["post-27672","post","type-post","status-publish","format-standard","hentry","category-cfa-level-iii","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>Absolute and Relative Risk Budgets | CFA Level III<\/title>\n<meta name=\"description\" content=\"Learn how absolute and relative risk budgets guide portfolio allocation, including marginal contribution to risk and total risk concepts.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/analystprep.com\/study-notes\/cfa-level-iii\/absolute-and-relative-risk-budgets\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Absolute and Relative Risk Budgets | CFA Level III\" \/>\n<meta property=\"og:description\" content=\"Learn how absolute and relative risk budgets guide portfolio allocation, including marginal contribution to risk and total risk concepts.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/analystprep.com\/study-notes\/cfa-level-iii\/absolute-and-relative-risk-budgets\/\" \/>\n<meta property=\"og:site_name\" content=\"CFA, FRM, and Actuarial Exams Study Notes\" \/>\n<meta property=\"article:published_time\" content=\"2023-06-25T10:37:40+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-03-05T20:05:35+00:00\" \/>\n<meta name=\"author\" content=\"AnalystPrep Team\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"AnalystPrep Team\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/cfa-level-iii\\\/absolute-and-relative-risk-budgets\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/cfa-level-iii\\\/absolute-and-relative-risk-budgets\\\/\"},\"author\":{\"name\":\"AnalystPrep Team\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/#\\\/schema\\\/person\\\/ed0c939f3f12a02c5a193708b713d89e\"},\"headline\":\"Absolute and Relative Risk Budgets\",\"datePublished\":\"2023-06-25T10:37:40+00:00\",\"dateModified\":\"2026-03-05T20:05:35+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/cfa-level-iii\\\/absolute-and-relative-risk-budgets\\\/\"},\"wordCount\":627,\"articleSection\":[\"Level III of the CFA\u00ae Program\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/cfa-level-iii\\\/absolute-and-relative-risk-budgets\\\/\",\"url\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/cfa-level-iii\\\/absolute-and-relative-risk-budgets\\\/\",\"name\":\"Absolute and Relative Risk Budgets | CFA Level III\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/#website\"},\"datePublished\":\"2023-06-25T10:37:40+00:00\",\"dateModified\":\"2026-03-05T20:05:35+00:00\",\"author\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/#\\\/schema\\\/person\\\/ed0c939f3f12a02c5a193708b713d89e\"},\"description\":\"Learn how absolute and relative risk budgets guide portfolio allocation, including marginal contribution to risk and total risk concepts.\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/cfa-level-iii\\\/absolute-and-relative-risk-budgets\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/cfa-level-iii\\\/absolute-and-relative-risk-budgets\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/cfa-level-iii\\\/absolute-and-relative-risk-budgets\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Absolute and Relative Risk Budgets\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/#website\",\"url\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/\",\"name\":\"CFA, FRM, and Actuarial Exams Study Notes\",\"description\":\"Question Bank and Study Notes for the CFA, FRM, and Actuarial exams\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/#\\\/schema\\\/person\\\/ed0c939f3f12a02c5a193708b713d89e\",\"name\":\"AnalystPrep Team\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/0828fe7fdfdcf636b2061b4c563e20cc9b7453f7cd1641b4c43edbfba896727a?s=96&d=mm&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/0828fe7fdfdcf636b2061b4c563e20cc9b7453f7cd1641b4c43edbfba896727a?s=96&d=mm&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/0828fe7fdfdcf636b2061b4c563e20cc9b7453f7cd1641b4c43edbfba896727a?s=96&d=mm&r=g\",\"caption\":\"AnalystPrep Team\"},\"url\":\"https:\\\/\\\/analystprep.com\\\/study-notes\\\/author\\\/analystprep-team\\\/\"}]}<\/script>\n<meta property=\"og:video\" content=\"https:\/\/www.youtube.com\/embed\/vyLJwRncCBw\" \/>\n<meta property=\"og:video:type\" content=\"text\/html\" \/>\n<meta property=\"og:video:duration\" content=\"4457\" \/>\n<meta property=\"og:video:width\" content=\"480\" \/>\n<meta property=\"og:video:height\" content=\"270\" \/>\n<meta property=\"ya:ovs:adult\" content=\"false\" \/>\n<meta property=\"ya:ovs:upload_date\" content=\"2023-06-25T10:37:40+00:00\" \/>\n<meta property=\"ya:ovs:allow_embed\" content=\"true\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Absolute and Relative Risk Budgets | CFA Level III","description":"Learn how absolute and relative risk budgets guide portfolio allocation, including marginal contribution to risk and total risk concepts.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/analystprep.com\/study-notes\/cfa-level-iii\/absolute-and-relative-risk-budgets\/","og_locale":"en_US","og_type":"article","og_title":"Absolute and Relative Risk Budgets | CFA Level III","og_description":"Learn how absolute and relative risk budgets guide portfolio allocation, including marginal contribution to risk and total risk concepts.","og_url":"https:\/\/analystprep.com\/study-notes\/cfa-level-iii\/absolute-and-relative-risk-budgets\/","og_site_name":"CFA, FRM, and Actuarial Exams Study Notes","article_published_time":"2023-06-25T10:37:40+00:00","article_modified_time":"2026-03-05T20:05:35+00:00","author":"AnalystPrep Team","twitter_card":"summary_large_image","twitter_misc":{"Written by":"AnalystPrep Team","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/analystprep.com\/study-notes\/cfa-level-iii\/absolute-and-relative-risk-budgets\/#article","isPartOf":{"@id":"https:\/\/analystprep.com\/study-notes\/cfa-level-iii\/absolute-and-relative-risk-budgets\/"},"author":{"name":"AnalystPrep Team","@id":"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/ed0c939f3f12a02c5a193708b713d89e"},"headline":"Absolute and Relative Risk Budgets","datePublished":"2023-06-25T10:37:40+00:00","dateModified":"2026-03-05T20:05:35+00:00","mainEntityOfPage":{"@id":"https:\/\/analystprep.com\/study-notes\/cfa-level-iii\/absolute-and-relative-risk-budgets\/"},"wordCount":627,"articleSection":["Level III of the CFA\u00ae Program"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/analystprep.com\/study-notes\/cfa-level-iii\/absolute-and-relative-risk-budgets\/","url":"https:\/\/analystprep.com\/study-notes\/cfa-level-iii\/absolute-and-relative-risk-budgets\/","name":"Absolute and Relative Risk Budgets | CFA Level III","isPartOf":{"@id":"https:\/\/analystprep.com\/study-notes\/#website"},"datePublished":"2023-06-25T10:37:40+00:00","dateModified":"2026-03-05T20:05:35+00:00","author":{"@id":"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/ed0c939f3f12a02c5a193708b713d89e"},"description":"Learn how absolute and relative risk budgets guide portfolio allocation, including marginal contribution to risk and total risk concepts.","breadcrumb":{"@id":"https:\/\/analystprep.com\/study-notes\/cfa-level-iii\/absolute-and-relative-risk-budgets\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/analystprep.com\/study-notes\/cfa-level-iii\/absolute-and-relative-risk-budgets\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/analystprep.com\/study-notes\/cfa-level-iii\/absolute-and-relative-risk-budgets\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/analystprep.com\/study-notes\/"},{"@type":"ListItem","position":2,"name":"Absolute and Relative Risk Budgets"}]},{"@type":"WebSite","@id":"https:\/\/analystprep.com\/study-notes\/#website","url":"https:\/\/analystprep.com\/study-notes\/","name":"CFA, FRM, and Actuarial Exams Study Notes","description":"Question Bank and Study Notes for the CFA, FRM, and Actuarial exams","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/analystprep.com\/study-notes\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/analystprep.com\/study-notes\/#\/schema\/person\/ed0c939f3f12a02c5a193708b713d89e","name":"AnalystPrep Team","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/secure.gravatar.com\/avatar\/0828fe7fdfdcf636b2061b4c563e20cc9b7453f7cd1641b4c43edbfba896727a?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/0828fe7fdfdcf636b2061b4c563e20cc9b7453f7cd1641b4c43edbfba896727a?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/0828fe7fdfdcf636b2061b4c563e20cc9b7453f7cd1641b4c43edbfba896727a?s=96&d=mm&r=g","caption":"AnalystPrep Team"},"url":"https:\/\/analystprep.com\/study-notes\/author\/analystprep-team\/"}]},"og_video":"https:\/\/www.youtube.com\/embed\/vyLJwRncCBw","og_video_type":"text\/html","og_video_duration":"4457","og_video_width":"480","og_video_height":"270","ya_ovs_adult":"false","ya_ovs_upload_date":"2023-06-25T10:37:40+00:00","ya_ovs_allow_embed":"true"},"_links":{"self":[{"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/posts\/27672","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/comments?post=27672"}],"version-history":[{"count":32,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/posts\/27672\/revisions"}],"predecessor-version":[{"id":42002,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/posts\/27672\/revisions\/42002"}],"wp:attachment":[{"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/media?parent=27672"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/categories?post=27672"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/analystprep.com\/study-notes\/wp-json\/wp\/v2\/tags?post=27672"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}