{"id":2823,"date":"2019-09-01T11:00:00","date_gmt":"2019-09-01T11:00:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=2823"},"modified":"2026-01-05T12:57:24","modified_gmt":"2026-01-05T12:57:24","slug":"portfolio-risk-free-risky-assets","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/portfolio-management\/portfolio-risk-free-risky-assets\/","title":{"rendered":"Portfolio of Risk-free and Risky Assets"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"Effect of negative correlation on portfolio risk\",\n    \"text\": \"If two underlying assets are negatively correlated, combining them to form a portfolio will make the portfolio risk:\",\n    \"answerCount\": 3,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Decrease.\",\n      \"dateCreated\": \"2026-01-05\",\n      \"upvoteCount\": 1,\n      \"url\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/portfolio-management\/portfolio-risk-free-risky-assets\/\"\n    },\n    \"suggestedAnswer\": [\n      {\n        \"@type\": \"Answer\",\n        \"text\": \"Increase.\",\n        \"upvoteCount\": 0\n      },\n      {\n        \"@type\": \"Answer\",\n        \"text\": \"Remain constant.\",\n        \"upvoteCount\": 0\n      }\n    ]\n  }\n}\n<\/script>\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"ImageObject\",\n  \"@id\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/09\/Capital-Allocation-Line-CAL-given-Investor-Preferences1.png#image\",\n  \"url\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/09\/Capital-Allocation-Line-CAL-given-Investor-Preferences1.png\",\n  \"contentUrl\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/09\/Capital-Allocation-Line-CAL-given-Investor-Preferences1.png\",\n  \"name\": \"Capital Allocation Line (CAL) given Investor Preferences\",\n  \"caption\": \"Capital allocation line (CAL) illustrating combinations of a risk-free asset and a risky portfolio based on investor risk preferences.\",\n  \"description\": \"Diagram showing the Capital Allocation Line (CAL) representing all possible combinations of expected return and standard deviation when combining a risk-free asset with a risky portfolio, reflecting how different investor risk preferences shape allocations between risk-free and risky assets. The CAL connects the risk-free return with the risky portfolio\u2019s expected return and illustrates the risk-return trade-off. ([analystprep.com](https:\/\/analystprep.com\/cfa-level-1-exam\/portfolio-management\/portfolio-risk-free-risky-assets\/))\",\n  \"encodingFormat\": \"image\/png\",\n  \"width\": 974,\n  \"height\": 668,\n  \"creator\": {\n    \"@type\": \"Organization\",\n    \"name\": \"AnalystPrep\"\n  },\n  \"creditText\": \"AnalystPrep\",\n  \"copyrightNotice\": \"\u00a9 AnalystPrep\",\n  \"mainEntityOfPage\": {\n    \"@type\": \"WebPage\",\n    \"@id\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/portfolio-management\/portfolio-risk-free-risky-assets\/\"\n  },\n  \"isPartOf\": {\n    \"@type\": \"WebPage\",\n    \"@id\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/portfolio-management\/portfolio-risk-free-risky-assets\/\"\n  }\n}\n<\/script>\n\n\n\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/OCZddCJ_HwM\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\nBy combining a portfolio of risky assets with a risk-free asset, we can improve the return-risk characteristics of the portfolio and realize a better trade-off. This combination is called the capital allocation line (CAL). The proportion of allocation to risky assets versus allocation to risk-free assets will be dependent on the risk preferences of the investor.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-16808\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/09\/Capital-Allocation-Line-CAL-given-Investor-Preferences1.png\" alt=\"Capital-Allocation-Line-CAL-given-Investor-Preferences\" width=\"974\" height=\"668\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/09\/Capital-Allocation-Line-CAL-given-Investor-Preferences1.png 974w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/09\/Capital-Allocation-Line-CAL-given-Investor-Preferences1-300x206.png 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/09\/Capital-Allocation-Line-CAL-given-Investor-Preferences1-768x527.png 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/09\/Capital-Allocation-Line-CAL-given-Investor-Preferences1-400x274.png 400w\" sizes=\"auto, (max-width: 974px) 100vw, 974px\" \/><\/p>\n<h2><strong>Combined Portfolios<\/strong><\/h2>\n<p>We calculate the expected return of a mixed portfolio by adding up the expected returns of its components. To assess the portfolio&#8217;s risk, we need the allocation to each component, the standard deviation of each, and the correlation between them. When the assets aren&#8217;t perfectly correlated, the portfolio&#8217;s variance will be lower than that of its individual assets.<\/p>\n<p>Each investor will have their own risky portfolio, dependent on the assumptions they make on the likely performance of the underlying assets. Since every investor makes their own unique assumptions about the underlying assets, there is no one optimal risk portfolio. We need to make a simplifying assumption that investor expectations are homogenous in order to derive what would be the optimal market portfolio.<\/p>\n<blockquote>\n<h2><strong>Question<\/strong><\/h2>\n<p>If two underlying assets are negatively correlated, combining them to form a portfolio will make the portfolio risk:<\/p>\n<p>A. Increase.<\/p>\n<p>B. Decrease.<\/p>\n<p>C. Remain constant.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is <strong>B<\/strong>.<\/p>\n<p>When uncorrelated assets are combined to form a portfolio, a lack of correlation will reduce the overall portfolio volatility.<\/p><\/blockquote>","protected":false},"excerpt":{"rendered":"<p>By combining a portfolio of risky assets with a risk-free asset, we can improve the return-risk characteristics of the portfolio and realize a better trade-off. This combination is called the capital allocation line (CAL). The proportion of allocation to risky&#8230;<\/p>\n","protected":false},"author":18,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[7],"tags":[],"class_list":["post-2823","post","type-post","status-publish","format-standard","hentry","category-portfolio-management","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>Portfolio of Risk-Free &amp; Risky Assets | CFA Level 1<\/title>\n<meta name=\"description\" content=\"Learn how to combine risky and risk-free assets to construct a Capital Allocation Line (CAL), optimizing risk and return in portfolio management.\" \/>\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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