{"id":8603,"date":"2020-12-21T14:02:07","date_gmt":"2020-12-21T14:02:07","guid":{"rendered":"https:\/\/analystprep.com\/blog\/?p=8603"},"modified":"2026-02-06T09:12:44","modified_gmt":"2026-02-06T09:12:44","slug":"evolution-of-portfolio-theory-efficient-frontier-to-sml","status":"publish","type":"post","link":"https:\/\/analystprep.com\/blog\/evolution-of-portfolio-theory-efficient-frontier-to-sml\/","title":{"rendered":"Evolution of Portfolio Theory Efficient Frontier to SML (Calculations for CFA\u00ae and FRM\u00ae Exams)"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"ImageObject\",\n  \"url\": \"https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/image-1.png\",\n  \"caption\": \"FRM Part I 2026 Time Series Update\",\n  \"width\": 320,\n  \"height\": 602,\n  \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\n  \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\n  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\"@type\": \"Organization\",\n    \"name\": \"AnalystPrep\"\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\/blog\/wp-content\/uploads\/2020\/12\/capture-3rd-pic.png\",\n  \"caption\": \"FRM Part I 2026 Time Series Update\",\n  \"width\": 425,\n  \"height\": 308,\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<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"What does the efficient frontier represent in portfolio theory?\",\n    \"text\": \"What does the efficient frontier represent in portfolio theory?\",\n    \"answerCount\": 1,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The efficient frontier represents the set of portfolios that deliver the highest expected return for each level of risk or the lowest risk for a given expected return. Portfolios below the frontier are considered inefficient because an investor can achieve a better risk-return balance with a portfolio on the frontier.\"\n    }\n  }\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [\n    {\n      \"@type\": \"Question\",\n      \"name\": \"What is the minimum-variance frontier?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"The minimum-variance frontier is the curve that plots all possible portfolios with the lowest variance for each level of expected return. It is generated by combining risky assets in different proportions to produce portfolios that minimize risk. The lower portion of the curve is inefficient, while the upper portion forms the efficient frontier. Only portfolios on the upper segment are considered optimal choices.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"What is the global minimum-variance portfolio?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"The global minimum-variance portfolio is the portfolio with the absolute lowest risk among all possible combinations of risky assets. It sits at the very bottom of the minimum-variance frontier. All other portfolios on the efficient frontier have higher risk but potentially higher expected returns. It is a key reference point when constructing portfolios along the frontier.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"What does the Capital Market Line (CML) represent?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"The Capital Market Line shows the relationship between expected return and total risk for efficient portfolios that combine the risk-free asset and the market portfolio. It represents the highest possible Sharpe ratio available to investors. Portfolios on the CML dominate all risky portfolios on the efficient frontier. Investors choose a point on the CML based on their risk preference by lending or borrowing at the risk-free rate.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"What is the Security Market Line (SML)?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"The Security Market Line illustrates the relationship between expected return and systematic risk, measured by beta, under the CAPM framework. It applies to individual assets and portfolios, unlike the CML, which applies only to efficient portfolios. Assets above the SML are undervalued because they offer higher-than-required returns for their level of risk. Assets below the SML are overvalued.\"\n      }\n    }\n  ]\n}\n<\/script>\n\n\n\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/en-0ZtZnTTk?si=L2u_Khv5g5i2L1HI\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_80 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/analystprep.com\/blog\/evolution-of-portfolio-theory-efficient-frontier-to-sml\/#Evolution_of_Portfolio_Theory\" >Evolution of Portfolio Theory<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/analystprep.com\/blog\/evolution-of-portfolio-theory-efficient-frontier-to-sml\/#Minimum-variance_Frontier\" >Minimum-variance Frontier<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/analystprep.com\/blog\/evolution-of-portfolio-theory-efficient-frontier-to-sml\/#Global_Minimum-variance_Portfolio\" >Global Minimum-variance Portfolio<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/analystprep.com\/blog\/evolution-of-portfolio-theory-efficient-frontier-to-sml\/#Efficient_Frontier\" >Efficient Frontier<\/a><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/analystprep.com\/blog\/evolution-of-portfolio-theory-efficient-frontier-to-sml\/#Example_1\" >Example 1<\/a><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/analystprep.com\/blog\/evolution-of-portfolio-theory-efficient-frontier-to-sml\/#Solution\" >Solution<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/analystprep.com\/blog\/evolution-of-portfolio-theory-efficient-frontier-to-sml\/#The_Two-Fund_Separation_Theorem\" >The Two-Fund Separation Theorem<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/analystprep.com\/blog\/evolution-of-portfolio-theory-efficient-frontier-to-sml\/#Capital_Allocation_Line_CAL\" >Capital Allocation Line (CAL)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/analystprep.com\/blog\/evolution-of-portfolio-theory-efficient-frontier-to-sml\/#Utility_and_Indifference_Curves\" >Utility and Indifference Curves<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/analystprep.com\/blog\/evolution-of-portfolio-theory-efficient-frontier-to-sml\/#The_Market\" >The Market<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/analystprep.com\/blog\/evolution-of-portfolio-theory-efficient-frontier-to-sml\/#The_Capital_Market_Line_CML\" >The Capital Market Line (CML)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/analystprep.com\/blog\/evolution-of-portfolio-theory-efficient-frontier-to-sml\/#Security_Market_Line_CAPM\" >Security Market Line &amp; CAPM<\/a><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/analystprep.com\/blog\/evolution-of-portfolio-theory-efficient-frontier-to-sml\/#Example_2\" >Example 2<\/a><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/analystprep.com\/blog\/evolution-of-portfolio-theory-efficient-frontier-to-sml\/#Solution-2\" >Solution<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Evolution_of_Portfolio_Theory\"><\/span>Evolution of Portfolio Theory<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>In theory, we could form a portfolio made up of all investable assets, however, this is not practical and we must find a way of filtering the investable universe. A risk-averse investor wants to find the combination of portfolio assets that minimizes risk for a given level of return.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Minimum-variance_Frontier\"><\/span>Minimum-variance Frontier<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>As we form a portfolio of assets, we can determine the portfolio return-risk characteristics that are a function of the characteristics of the underlying portfolio holdings and the correlation between the holdings. By varying the allocation to the underlying assets, we derive an investment opportunity set of different portfolio compositions. This is made up of the various combinations of risky assets that lead to specific portfolio risk-return characteristic which can be graphically plotted with portfolio expected return as the y-axis and portfolio standard deviation as the x-axis.<\/p>\n\n\n\n<p>For each level of return, the portfolio with the minimum risk will be selected by a risk-averse investor. This minimization of risk for each level of return creates a minimum-variance frontier \u2013 <em>a collection of all the minimum-variance (minimum-standard deviation) portfolios<\/em>. At a point along this minimum-variance frontier curve, there exists a minimum-variance portfolio which produces the highest returns per unit of risk.<\/p>\n\n\n\n<!-- TOP CTA \u2013 Full Width Outline Button -->\n<div style=\"margin:24px 0;\">\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\"\n     target=\"_blank\"\n     rel=\"noopener noreferrer\"\n     style=\"\n       display:block;\n       width:100%;\n       padding:14px 0;\n       border:2px solid #3b6fd8;\n       border-radius:50px;\n       font-size:18px;\n       font-weight:500;\n       text-align:center;\n       text-decoration:none;\n       color:#3b6fd8;\n       background-color:#f4f6f9;\n       box-sizing:border-box;\n     \">\n     Practice CFA portfolio theory questions now.\n  <\/a>\n<\/div>\n\n\n\n<h3><span class=\"ez-toc-section\" id=\"Global_Minimum-variance_Portfolio\"><\/span><span class=\"primary-color\">Global Minimum-variance Portfolio<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">Along the minimum-variance frontier, <em>the left-most point is a portfolio with minimum variance when compared to all possible portfolios of risky assets<\/em>. This is known as the global minimum-variance portfolio. An investor cannot hold a portfolio of risky (note: risk-free assets are excluded at this point) assets with a lower risk than the global minimum-variance portfolio.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Efficient_Frontier\"><\/span><span class=\"primary-color\">Efficient Frontier<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">The portion of the minimum-variance curve that lies above and to the right of the global minimum variance portfolio is known as the Markowitz efficient frontier as it contains all portfolios that rational, risk-averse investors would choose. We can also monitor the slope of the efficient frontier, the change in units of return per units of risk. As we move to higher levels of risk, the resulting increase in return begins to diminish. The slope begins to flatten. This means we cannot achieve ever-increasing returns as we take on more risk, quite the opposite. Investors experience a diminishing increase in potential returns as portfolio risk is increased. The developments can be explained using the slope of the efficient frontier:<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-8649 aligncenter\" src=\"https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/image-1-300x191.png\" alt=\"\" width=\"580\" height=\"369\" srcset=\"https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/image-1-300x191.png 300w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/image-1-400x255.png 400w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/image-1-484x308.png 484w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/image-1.png 515w\" sizes=\"auto, (max-width: 580px) 100vw, 580px\" \/><\/p>\n<h5><span class=\"ez-toc-section\" id=\"Example_1\"><\/span><span class=\"primary-color\">Example 1<\/span><span class=\"ez-toc-section-end\"><\/span><\/h5>\n<p>Which statement best describes the global minimum-variance portfolio?<\/p>\n<p>A. The global minimum variance portfolio gives investors the highest levels of returns<\/p>\n<p>B. The global minimum variance portfolio gives investors the lowest risk portfolio made up of risky assets<\/p>\n<p>C. The global minimum variance portfolio lies to the right of the efficient frontier<\/p>\n<h6><span class=\"ez-toc-section\" id=\"Solution\"><\/span><span class=\"primary-color\">Solution<\/span><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p>The correct answer is <strong>B<\/strong>.<\/p>\n<p>The global minimum variance portfolio lies to the far left of the efficient frontier and is made up of the portfolio of risky assets that produces the minimum risk for an investor.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"The_Two-Fund_Separation_Theorem\"><\/span><span class=\"primary-color\">The Two-Fund Separation Theorem<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">The two-fund separation theorem states that all investors regardless of taste, risk preference\u00a0and initial wealth will hold a combination of two portfolios or funds: a risk-free asset and an optimal portfolio of risky assets. This allows us to break the portfolio construction problem into two distinct steps: an investment decision and a financing decision. Firstly, the optimal risky asset portfolio using the risk, return and correlation characteristics of the underlying assets dictate the investment decision. Secondly, considering an investor\u2019s risk preference, a determination is made on the allocation to the risk-free asset. \u00a0Plotting graphically the risk-free asset with the risky portfolio creates the capital allocation line (CAL).<\/span><\/p>\n<h4><span class=\"ez-toc-section\" id=\"Capital_Allocation_Line_CAL\"><\/span><span class=\"primary-color\">Capital Allocation Line (CAL)<\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Capital allocation line (CAL) is a graph created by investors to measure the risk of a risk-free asset and risky asset (the risky asset represents multiple portfolios available to the investor). It is a line created on a graph of all possible combinations of risk-free and risky assets. Illustrated as follows:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-8652 aligncenter\" src=\"https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Snip-next-300x159.png\" alt=\"\" width=\"593\" height=\"314\" srcset=\"https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Snip-next-300x159.png 300w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Snip-next-400x213.png 400w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Snip-next-484x257.png 484w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Snip-next-570x303.png 570w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Snip-next.png 602w\" sizes=\"auto, (max-width: 593px) 100vw, 593px\" \/><\/p>\n<h4><span class=\"ez-toc-section\" id=\"Utility_and_Indifference_Curves\"><\/span><span class=\"primary-color\">Utility and Indifference Curves<\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><span style=\"font-weight: 400;\">Utility is a measure of relative satisfaction that an investor derives from different portfolios. We can generate a mathematical function to represent this utility that is a function of the portfolio expected return, the portfolio variance and a measure of risk aversion.<\/span><\/p>\n<p>$$U=E(r)-\\frac{1}{2}A\\sigma^2$$<\/p>\n<p>Where:<\/p>\n<p>\\(U\\)= utility<\/p>\n<p>\\(E(r)\\)= portfolio expected return<\/p>\n<p>\\(A\\)= risk aversion coefficient<\/p>\n<p>\\(\\sigma^2\\)= portfolio variance<\/p>\n<p><span style=\"font-weight: 400;\">In determining the risk aversion (A), we measure the marginal reward an investor needs in order to take on more risk. A risk-averse investor will need a high margin reward for taking on more risk. The utility equation shows the following:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Utility can be positive or negative \u2013 it is unbounded.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">High returns add to utility.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">High variance reduces utility.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Utility does not measure satisfaction but can be used to rank portfolios.<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">The risk aversion coefficient, A, is positive for risk-averse investors (any increase in risk reduces utility), it is 0 for risk-neutral investors (changes in risk do not affect utility) and negative for risk-seeking investors (additional risk increases utility).<\/span><\/p>\n<p>To get the optimal portfolio, combine the indifference curves with the CAL:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-8651 aligncenter\" src=\"https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/snip-222-300x185.png\" alt=\"\" width=\"589\" height=\"363\" srcset=\"https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/snip-222-300x185.png 300w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/snip-222-400x246.png 400w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/snip-222-484x298.png 484w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/snip-222-570x351.png 570w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/snip-222.png 634w\" sizes=\"auto, (max-width: 589px) 100vw, 589px\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"The_Market\"><\/span><span class=\"primary-color\">The Market<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">The market includes all risky assets or anything that has value \u2013 stocks, bonds, real estate, human capital, commodities \u2013 these are all assets defined in \u201cthe market.\u201d Not all market assets are tradeable or investable. If global assets are considered, there are hundreds of thousands of individual securities that make up the market that are\u00a0considered tradable and investable. A typical investor is likely to be more concerned with their local or regional stock market as a measure of \u201cthe market\u201d.<\/span><\/p>\n<p><blockquote class=\"wp-embedded-content\" data-secret=\"4UjZNXbjV9\"><a href=\"https:\/\/analystprep.com\/shop\/frm-part-1-and-part-2-complete-course-by-analystprep\/\">FRM Part 1 and Part 2 Complete Online Course<\/a><\/blockquote><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"&#8220;FRM Part 1 and Part 2 Complete Online Course&#8221; &#8212; AnalystPrep\" src=\"https:\/\/analystprep.com\/shop\/frm-part-1-and-part-2-complete-course-by-analystprep\/embed\/#?secret=XJ0HYQuIth#?secret=4UjZNXbjV9\" data-secret=\"4UjZNXbjV9\" width=\"600\" height=\"338\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe><\/p>\n<h3><span class=\"ez-toc-section\" id=\"The_Capital_Market_Line_CML\"><\/span><span class=\"primary-color\">The Capital Market Line (CML)<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">The Capital Market Line (CML) is a special case of the CAL \u2013 the line which 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 \u201cthe market\u201d 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. Where the line from the risk-free asset touches, or is tangential, to the Markowitz portfolio, this is defined as the market portfolio. The line connecting the risk-free asset with the market portfolio is the CML, illustrated in the graph below:<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-8654 aligncenter\" src=\"https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/snippppppy-300x164.png\" alt=\"\" width=\"585\" height=\"320\" srcset=\"https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/snippppppy-300x164.png 300w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/snippppppy-400x219.png 400w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/snippppppy-484x264.png 484w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/snippppppy-570x311.png 570w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/snippppppy.png 571w\" sizes=\"auto, (max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>$$E(R_p)=R_f+\\frac{E(R_m)-R_f}{\\sigma_m}\\times\\sigma_p$$<\/p>\n<p>This is the form of an equation of a straight line where the intercept is \\(R_f\\) and the slope is \\(\\frac{E(R_m)-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<h3><span class=\"ez-toc-section\" id=\"Security_Market_Line_CAPM\"><\/span><span class=\"primary-color\">Security Market Line &amp; CAPM<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">The Security Market Line (SML) is the graphical representation of the CAPM with beta reflecting systematic risk on the x-axis and expected return on the y-axis. The SML intersects the y-axis at the risk-free rate and the slope of the line is the market risk premium, \\(R_m-R_f\\).<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-8653 aligncenter\" src=\"https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/formula-300x138.png\" alt=\"\" width=\"589\" height=\"271\" srcset=\"https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/formula-300x138.png 300w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/formula-400x184.png 400w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/formula-484x222.png 484w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/formula-570x262.png 570w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/formula.png 694w\" sizes=\"auto, (max-width: 589px) 100vw, 589px\" \/><\/p>\n<h5><span class=\"ez-toc-section\" id=\"Example_2\"><\/span><span class=\"primary-color\">Example 2<\/span><span class=\"ez-toc-section-end\"><\/span><\/h5>\n<p>An over valued security would most likely plot:<\/p>\n<p>A. Below the Security Market Line (SML)<\/p>\n<p>B. On the Security Market Line (SML)<\/p>\n<p>C. Above the Security Market Line (SML)<\/p>\n<h6><span class=\"ez-toc-section\" id=\"Solution-2\"><\/span><span class=\"primary-color\">Solution<\/span><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p>The correct answer is <strong>A<\/strong>.<\/p>\n<p>If the security lies above the SML, it is underpriced (go long).<\/p>\n<p>If the security lies below the SML, it is overpriced (go short).<\/p>\n<p>This is illustrated by the security market line (SML) as follows:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-8656 aligncenter\" src=\"https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/capture-3rd-pic-300x217.png\" alt=\"\" width=\"513\" height=\"371\" srcset=\"https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/capture-3rd-pic-300x217.png 300w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/capture-3rd-pic-400x290.png 400w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/capture-3rd-pic.png 425w\" sizes=\"auto, (max-width: 513px) 100vw, 513px\" \/><\/p>\n\n\n<!-- BOTTOM CTA \u2013 Refined Version -->\n<div style=\"text-align:center; background-color:#f4f6f9; padding:35px 20px; border-radius:12px; margin-top:40px;\">\n\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\"\n     target=\"_blank\"\n     rel=\"noopener noreferrer\"\n     style=\"\n       display:inline-block;\n       padding:14px 34px;\n       background-color:#3b6fd8;\n       color:#ffffff;\n       border-radius:50px;\n       font-size:16px;\n       font-weight:600;\n       text-decoration:none;\n       margin-bottom:18px;\n     \">\n     Start Free Trial\n  <\/a>\n\n  <p style=\"max-width:700px; margin:0 auto; font-size:16px; line-height:1.6; color:#333;\">\n    Master the efficient frontier, CAPM, and the Security Market Line with exam-style practice questions, detailed explanations, and full mock exams inside AnalystPrep\u2019s free trial.\n  <\/p>\n\n<\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Evolution of Portfolio Theory In theory, we could form a portfolio made up of all investable assets, however, this is not practical and we must find a way of filtering the investable universe. A risk-averse investor wants to find 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":[70,71],"tags":[78,97,96,83,98],"class_list":["post-8603","post","type-post","status-publish","format-standard","hentry","category-cfa","category-frm","tag-cfa","tag-efficient-frontier","tag-evolution-of-portfolio-theory","tag-frm","tag-sml","blog-post","no-post-thumbnail","animate"],"acf":[],"post_mailing_queue_ids":[],"_links":{"self":[{"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/posts\/8603","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/comments?post=8603"}],"version-history":[{"count":31,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/posts\/8603\/revisions"}],"predecessor-version":[{"id":13918,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/posts\/8603\/revisions\/13918"}],"wp:attachment":[{"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/media?parent=8603"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/categories?post=8603"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/tags?post=8603"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}