{"id":34317,"date":"2023-11-06T06:09:25","date_gmt":"2023-11-06T06:09:25","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=34317"},"modified":"2026-03-09T20:48:06","modified_gmt":"2026-03-09T20:48:06","slug":"risk-budgeting-concepts-in-portfolio-construction","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-iii\/risk-budgeting-concepts-in-portfolio-construction\/","title":{"rendered":"Risk Budgeting Concepts in Portfolio Construction"},"content":{"rendered":"<p><script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"Based on the table, what is asset B's relative contribution to portfolio variance?\",\n    \"text\": \"Based on the table below, what is asset B's relative contribution to portfolio variance?\\n\\nAsset | Absolute Contribution to Portfolio Variance\\nA | 0.0434\\nB | 0.0019\\nC | 0.0355\\n\\nA. 0.0808\\nB. 0.0019\\nC. 0.0235\",\n    \"answerCount\": 1,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is C (0.0235). Step 1: Calculate the total portfolio variance by summing the absolute contributions: 0.0434 + 0.0019 + 0.0355 = 0.0808. Step 2: Calculate asset B\u2019s relative contribution: 0.0019 \u00f7 0.0808 = 0.0235. The relative contribution is low because asset B\u2019s absolute contribution to portfolio variance is small.\"\n    }\n  }\n}\n<\/script><br \/>\n<iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/cRk9eEBC0kg\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Risk budgeting involves distributing the total portfolio risk efficiently among its components. It&apos;s a crucial element of a robust risk management process, which consists of these four steps:<\/p>\n<ol type=\"1\">\n<li>Define the relevant risk metrics based on the fund&apos;s mandate:\n<ul>\n<li>Should you use absolute or relative measures?<\/li>\n<\/ul>\n<\/li>\n<li>Evaluate the risk associated with various aspects of the strategy:\n<ul>\n<li>Are you exposed to rewarded factors, or is it about allocations to sectors and securities?<\/li>\n<\/ul>\n<\/li>\n<li>Set the appropriate risk budget:\n<ul>\n<li>Establish an overall risk target for the portfolio.<\/li>\n<\/ul>\n<\/li>\n<li>Allocate the risk across individual factors or components.<\/li>\n<\/ol>\n<h2>Causes and Sources of Absolute Risk <\/h2>\n<p>Absolute risk in a portfolio arises from its variance, which is only relative to the portfolio itself, not compared to a benchmark. To calculate the contribution of a specific asset (i) to the portfolio&apos;s variance, we use this equation:<\/p>\n<p>$$ Cv_i = \\sum(W_iW_jC_{ij}) = w_iC_{ip} $$<\/p>\n<p>Where:<\/p>\n<ul>\n<li>\\(W_j\\) = Asset j&apos;s weight in the portfolio.<\/li>\n<li>\\(C_{ij}\\) = The covariance of returns between asset j and asset i.<\/li>\n<li>\\(C_{ip}\\) = The covariance of returns between asset I and the portfolio.<\/li>\n<\/ul>\n<p>This formula is multiplicative, meaning that each variable&apos;s increase leads to a higher contribution to portfolio variance. So, if an asset has a higher weight in the portfolio or tends to move closely with the portfolio, it contributes more to the portfolio&apos;s variance.<\/p>\n<h2>Causes and Sources of Relative\/Active Risk <\/h2>\n<p>The contribution of asset i to portfolio active variance can be determined using the following equation:<\/p>\n<p>$$ CAV_i = (W_{pi} -W_{bi}) rC_{ip} $$<\/p>\n<p><em>Where:<\/em><\/p>\n<ul>\n<li>\\(W_{pi}\\) = Weight of asset i in the portfolio.<\/li>\n<li>\\(W_{bi}\\) = Weight of asset i in the benchmark.<\/li>\n<li>\\(rC_{ip}\\) = Covariance between the active returns of asset i and the active returns of the portfolio, considering the covariances with all n assets in the portfolio.<\/li>\n<\/ul>\n<p>The sum of individual CAVs provides the portfoli&apos;s active return variance.<\/p>\n<h2>Determining the Appropriate Level of Risk <\/h2>\n<p>When customizing portfolios for clients, financial professionals should consider the following factors to align risk with individual needs:<\/p>\n<ul>\n<li><strong>Implementation constraints:<\/strong> Some portfolios come with explicit limitations on what can be included, directly impacting a manager&apos;s choices.<\/li>\n<li><strong>Limited diversification opportunities:<\/strong> As risk increases, the benefits to portfolio performance diminish, emphasizing the importance of considering risk-adjusted returns.<\/li>\n<li><strong>Leverage and its implications for risk:<\/strong> While leverage can enhance returns, it also introduces higher volatility and trading costs, prompting portfolio managers to conduct a cost-benefit analysis before implementing it.<\/li>\n<\/ul>\n<p>For those curious about the mathematical aspect of the last point, this formula illustrates the connection between geometric and arithmetic returns. When leverage is increased, both \\(R_a\\) and \\(\\sigma\\) go up. However, the negative relationship between standard deviation and the exponent means that continually escalating leverage will eventually outweigh the augmented returns.<\/p>\n<p>$$ R_g = R_a \u2013 \\left(\\frac {\\sigma^2}{2} \\right) $$<\/p>\n<p>Where:<\/p>\n<p>\\(R_g\\) = Geometric compound returns. \\(R_a\\) = Arithmetic return. \\(\\sigma^2\\) = Portfolio standard deviation.<\/p>\n<blockquote>\n<h2>Question<\/h2>\n<p>Based on the table below, what is asset b&apos;s relative contribution to portfolio variance?<\/p>\n<p>$$ \\begin{array}{c|c}<br \/>\n\\textbf{Asset} &#038;\t{\\textbf{Absolute Contribution} \\\\ \\textbf{to Portfolio Variance}} \\\\ \\hline<br \/>\nA &#038;\t0.0434 \\\\ \\hline<br \/>\nB &#038;\t0.0019 \\\\ \\hline<br \/>\nC &#038;\t0.0355<br \/>\n\\end{array} $$<\/p>\n<ol type=\"A\">\n<li>0.0808.<\/li>\n<li>0.0019.<\/li>\n<li>0.0235.<\/li>\n<\/ol>\n<p><strong>Solution<\/strong><\/p>\n<p><strong>The correct answer is C.<\/strong><\/p>\n<p><strong>Step 1:<\/strong> Calculate the overall portfolio variance by summing the absolute contributions:<\/p>\n<p>$$ 0.0434 + 0.0019 + 0.0355 = 0.0808 $$<\/p>\n<p><strong>Step 2:<\/strong> Calculate the relative contribution from asset B:<\/p>\n<p>$$  \\frac {0.0019}{0.0808} = 0.0235 $$<\/p>\n<p>The relative contribution from asset B is relatively low because its absolute contribution to portfolio variance is low.<\/p>\n<p><strong>A and B are incorrect.<\/strong> From the calculation the correct value is 0.0235<\/p>\n<\/blockquote>\n<p>Reading 26: Active Equity Investing: Portfolio Construction<\/p>\n<p>Los 26 (d) Discuss the application of risk budgeting concepts in portfolio construction<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Risk budgeting involves distributing the total portfolio risk efficiently among its components. It&apos;s a crucial element of a robust risk management process, which consists of these four steps: Define the relevant risk metrics based on the fund&apos;s mandate: Should you&#8230;<\/p>\n","protected":false},"author":3,"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-34317","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 v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Risk Budgeting in Portfolio Construction<\/title>\n<meta name=\"description\" content=\"Learn how risk budgeting works in portfolio construction and how contribution to variance helps allocate risk across assets.\" \/>\n<meta name=\"robots\" content=\"index, follow, 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