{"id":2825,"date":"2019-09-01T11:00:00","date_gmt":"2019-09-01T11:00:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=2825"},"modified":"2026-04-06T12:31:29","modified_gmt":"2026-04-06T12:31:29","slug":"cal-cml","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/portfolio-management\/cal-cml\/","title":{"rendered":"Capital Allocation Line (CAL) and Capital Market Line (CML)"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"@id\": \"https:\/\/analystprep.com\/#video-OCZddCJ_HwM\",\n  \"name\": \"Portfolio Risk and Return \u2013 Part II (2025 Level I CFA\u00ae Exam \u2013 Portfolio Management \u2013 Module 2)\",\n  \"description\": \"Topic 9 \u2013 Portfolio Management. Module 2 \u2013 Portfolio Risk and Return \u2013 Part II. This lesson covers: introduction and Learning Outcome Statements (0:00); implications of combining a risk-free asset with a portfolio of risky assets (4:45); the capital allocation line (CAL) and capital market line (CML) (6:49); systematic vs nonsystematic risk and why investors are not compensated for bearing nonsystematic risk (12:08); return-generating models, including the market model, and their uses (16:00); calculating and interpreting beta (24:32); the capital asset pricing model (CAPM), its assumptions, and the security market line (SML) (29:31); calculating expected return using the CAPM (39:43); applications of the CAPM and SML (41:04); and calculating and interpreting the Sharpe ratio, Treynor ratio, M\u00b2, and Jensen\u2019s alpha (48:18).\",\n  \"uploadDate\": \"2022-07-02T00:00:00+00:00\",\n  \"thumbnailUrl\": [\n    \"https:\/\/img.youtube.com\/vi\/OCZddCJ_HwM\/maxresdefault.jpg\",\n    \"https:\/\/img.youtube.com\/vi\/OCZddCJ_HwM\/hqdefault.jpg\"\n  ],\n  \"contentUrl\": \"https:\/\/www.youtube.com\/watch?v=OCZddCJ_HwM\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/OCZddCJ_HwM\",\n  \"duration\": \"PT54M58S\",\n  \"publisher\": {\n    \"@type\": \"Organization\",\n    \"name\": \"AnalystPrep\",\n    \"logo\": {\n      \"@type\": \"ImageObject\",\n      \"url\": \"https:\/\/analystprep.com\/default-logo.jpg\",\n      \"width\": 600,\n      \"height\": 60\n    }\n  }\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"What happens to portfolio risk and return as an investor moves up the CML?\",\n    \"text\": \"What happens to the portfolio risk and return, respectively, as an investor moves up the Capital Market Line (CML)? A. Risk decreases, return decreases. B. Risk increases, return decreases. C. Risk increases, return increases.\",\n    \"answerCount\": 1,\n    \"upvoteCount\": 0,\n    \"author\": {\n      \"@type\": \"Organization\",\n      \"name\": \"AnalystPrep\"\n    },\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is C. As an investor moves up the Capital Market Line (CML), both portfolio risk and expected return increase.\",\n      \"upvoteCount\": 0,\n      \"url\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/portfolio-management\/cal-cml\/\",\n      \"author\": {\n        \"@type\": \"Organization\",\n        \"name\": \"AnalystPrep\"\n      }\n    }\n  }\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"ImageObject\",\n  \"url\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/09\/cfa-level-1-efficient-frontier.png\",\n  \"caption\": \"Efficient frontier and portfolio optimization\",\n  \"width\": 974,\n  \"height\": 668,\n  \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\n  \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\n  \"creditText\": \"AnalystPrep Design Team\",\n  \"creator\": {\n    \"@type\": \"Organization\",\n    \"name\": \"AnalystPrep\"\n  }\n}\n<\/script>\n\n\n\n<iframe loading=\"lazy\"\n  width=\"611\"\n  height=\"344\"\n  src=\"https:\/\/www.youtube.com\/embed\/OCZddCJ_HwM\"\n  title=\"YouTube video player\"\n  frameborder=\"0\"\n  allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\"\n  referrerpolicy=\"strict-origin-when-cross-origin\"\n  allowfullscreen>\n<\/iframe>\n\n\n\n<p>We form a capital allocation line when we combine a risky asset portfolio with a risk-free asset. This represents the allocation between risk-free and risky assets based on investor risk preferences. The capital market line is a special case of the CAL, where the portfolio of risky assets is the market portfolio.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Passive and Active Portfolios<\/strong><\/h2>\n\n\n\n<p>A market can be informationally efficient. In such a case, the quoted security price in the market is an unbiased estimate of all the future discounted cash flows and reflects all publicly known information about the security. If all security prices reflect all publicly available information, then, in theory, there is no way to outperform the market. If this is the investor&#8217;s belief, then investing in a passive portfolio is the simplest and most convenient approach. A passive portfolio will track and replicate the market.<\/p>\n\n\n\n<p>Many investors do not believe the market price accurately reflects valuations. They have confidence in their ability to determine these mispricings based on their evaluation models. Such investors take an active approach to investing and overweighting undervalued assets and underweighting (or shorting, if allowed) overvalued assets. This style of investing is called active management.<\/p>\n\n\n\n<div style=\"width:100%; margin:30px 0; box-sizing:border-box;\">\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"\n     style=\"display:block;\n            width:100%;\n            max-width:100%;\n            box-sizing:border-box;\n            padding:16px 20px;\n            border:2px solid #2f6fed;\n            border-radius:999px;\n            background:#f2f4f8;\n            color:#2f6fed;\n            font-size:16px;\n            font-weight:500;\n            text-decoration:none;\n            text-align:center;\n            line-height:1.2;\">\n    Access our CFA free trial for CAL and CML practice\n  <\/a>\n<\/div>\n\n\n<h2><strong>The Market<\/strong><\/h2>\n<p>The market includes all risky assets or anything that has value \u2013 stocks, bonds, real estate, human capital, and commodities. These assets are all defined in &#8220;the market.&#8221; Not all market assets are tradable or investable. If global assets are considered, hundreds of thousands of individual securities make up the market and are considered tradable and investable. A typical investor is likely to rely on their local or regional stock market as a measure of &#8220;the market&#8221;.<\/p>\n<h2><strong>The Capital Market Line (CML)<\/strong><\/h2>\n<p>The Capital Market Line (CML) is a special case of the CAL, that is, the line that makes up the allocation between a risk-free asset and a risky portfolio for an investor. In the case of the CML, the risk portfolio is the market portfolio. Where an investor has defined &#8220;the market&#8221; to be their domestic stock market index, the expected return of the market is expressed as the expected return of that index. The risk-return characteristics for the potential risk asset portfolios can be plotted to generate a Markowitz efficient frontier. The point at which the line from the risk-free asset touches or is tangential to the Markowitz portfolio is defined as the market portfolio. The line connecting the risk-free asset with the market portfolio is the CML.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" width=\"974\" height=\"668\" class=\"aligncenter size-full wp-image-39438\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/09\/cfa-level-1-efficient-frontier.png\" alt=\"\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/09\/cfa-level-1-efficient-frontier.png 974w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/09\/cfa-level-1-efficient-frontier-300x206.png 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/09\/cfa-level-1-efficient-frontier-768x527.png 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/09\/cfa-level-1-efficient-frontier-400x274.png 400w\" sizes=\"auto, (max-width: 974px) 100vw, 974px\" \/><\/p>\n<p>The expected return and variance for the portfolio can be represented as follows:<\/p>\n<p>$$ \\text{Expected\u00a0return} = E(R_P) = wR_f + (1-w)E(R_m) $$<\/p>\n<p>$$ \\text{Variance} =\u00a0\\sigma_P^2 = w^2\\sigma_f^2 + (1-w)^2\\sigma_m^2 + 2w(1-w)Cov(R_f,R_m) $$<\/p>\n<p>Where:<\/p>\n<p>\\(R_f\\) is the return on the risk-free asset.<\/p>\n<p>\\(R_m\\) is the return on the market.<\/p>\n<p>\\(w\\) is the weight of the risk-free asset in the portfolio.<\/p>\n<p>\\(1-w\\)\u00a0is the weight of the market asset in the portfolio.<\/p>\n<p>Theoretically, the standard deviation of the risk-free asset is zero, and the term, \\(w^2\\sigma_f^2\\) falls out of the equation. Equally, the risk-free asset is assumed to have no covariance with the market portfolio. This means that the portfolio standard deviation is written as:<\/p>\n<p>$$ \\sigma_p = (1 &#8211; w)\\sigma_m $$<\/p>\n<p>By substitution, we can write:<\/p>\n<p>$$ E(R_p) = R_f +\u00a0 \\frac {E(R_m) &#8211; R_f}{\\sigma_m}\u00a0\u00d7\u00a0\\sigma_p $$<\/p>\n<p>This is in the form of an equation of a straight line where the intercept is\u00a0R<sub>f,<\/sub> and the slope is \\(\\frac {E(R_m) &#8211; R_f}{\\sigma_m}\\). This is the CML line which has a positive slope as the market return is greater than the risk-free return.<\/p>\n<blockquote>\n<h2><strong>Question<\/strong><\/h2>\n<p>What happens to the portfolio risk and return, respectively, as an investor moves up the CML?<\/p>\n<p>A. Risk decreases, return decreases.<\/p>\n<p>B. Risk increases, return decreases.<\/p>\n<p>C. Risk increases, return increases.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is <strong>C<\/strong>.<\/p>\n<p>The overall portfolio risk and return increase as an investor moves up the CML.<\/p>\n<\/blockquote>\n\n\n<div style=\"background:#f2f4f8; border-radius:16px; padding:32px 20px; text-align:center; margin:40px 0;\">\n  \n  <a href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"\n     style=\"display:inline-block;\n            background:#4a74c9;\n            color:#ffffff;\n            font-size:16px;\n            font-weight:600;\n            text-decoration:none;\n            padding:14px 34px;\n            border-radius:999px;\n            margin-bottom:16px;\">\n    Start Free Trial\n  <\/a>\n\n  <p style=\"margin:0 auto; max-width:520px; font-size:16px; line-height:1.6; color:#1f2937;\">\n    Understand CAL and CML with clear risk-return and portfolio practice\n  <\/p>\n\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>We form a capital allocation line when we combine a risky asset portfolio with a risk-free asset. This represents the allocation between risk-free and risky assets based on investor risk preferences. The capital market line is a special case of&#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-2825","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>Capital Market &amp; Allocation Lines | CFA Level 1<\/title>\n<meta name=\"description\" content=\"Understand the Capital Market Line (CML) and Capital Allocation Line (CAL), including their formulas and roles in optimal risk-return trade-offs. 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