{"id":2834,"date":"2019-09-01T11:00:00","date_gmt":"2019-09-01T11:00:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=2834"},"modified":"2026-03-31T12:55:15","modified_gmt":"2026-03-31T12:55:15","slug":"beta-explained","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/portfolio-management\/beta-explained\/","title":{"rendered":"Beta Explained"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Portfolio Risk and Return \u2013 Part II (2025 Level I CFA\u00ae Exam \u2013 PM \u2013 Module 2)\",\n  \"description\": \"CFA\u00ae Level I Portfolio Management video lesson by AnalystPrep covering Portfolio Risk and Return \u2013 Part II (Module 2). This lecture connects the efficient frontier to the Capital Allocation Line (CAL) and Capital Market Line (CML), explains systematic versus nonsystematic risk, and builds intuition for beta. It applies the Capital Asset Pricing Model (CAPM) and the Security Market Line (SML) to security selection, and concludes with performance evaluation measures including the Sharpe ratio, Treynor ratio, M\u00b2, and Jensen\u2019s alpha, with exam-focused explanations and examples.\",\n  \"uploadDate\": \"2022-07-02T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/OCZddCJ_HwM\/default.jpg\",\n  \"contentUrl\": \"https:\/\/www.youtube.com\/watch?v=OCZddCJ_HwM\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/OCZddCJ_HwM\",\n  \"duration\": \"PT54M58S\"\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\": \"If the correlation between an asset and the market is 0.6, the standard deviation of the asset is 18%, and the standard deviation of the market is 14%, what is the asset beta?\",\n    \"text\": \"If the correlation between an asset and the market is 0.6, the standard deviation of the asset is 18%, and the standard deviation of the market is 14%, what is the asset beta?\",\n    \"answerCount\": 3,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"0.77.\"\n    },\n    \"suggestedAnswer\": [\n      {\n        \"@type\": \"Answer\",\n        \"text\": \"0.47.\"\n      },\n      {\n        \"@type\": \"Answer\",\n        \"text\": \"0.99.\"\n      }\n    ]\n  }\n}\n<\/script>\n\n\n\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/OCZddCJ_HwM?si=OXIKfRDUFGFUu2Lv\" 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<p>Beta is a measure of systematic risk. Statistically, it depends on the degree of correlation between a security and the market.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Calculating Beta<\/strong><\/h2>\n\n\n\n<p>We begin with the single index model using realized returns constructed as follows:<\/p>\n\n\n\n<p>$$ R_i \u2013 R_f = \\beta_i [R_i \u2013 R_f] + e_i $$<\/p>\n\n\n\n<p>Which we can also formulate as:<\/p>\n\n\n\n<p>$$ R_i = (1 \u2013 \\beta_i ) R_f + \\beta_i \u00d7 R_m + e_i $$<\/p>\n\n\n\n<p>Systematic risk depends on the correlation between the asset and the market. Therefore, beta can be measured by examining the covariance between <em>R<sub>i<\/sub><\/em> and <em>R<sub>m<\/sub><\/em>:<\/p>\n\n\n\n<p>$$ Cov(R_i, R_m) = Cov(\\beta_i \u00d7 R_m + e_i , R_m) $$<\/p>\n\n\n\n<p>$$ Cov(R_i, R_m) = \\beta_i Cov(R_m, R_m) + Cov(e_i , R_m) $$<\/p>\n\n\n\n<p>$$ Cov(R_i, R_m) = \\beta_i \\sigma_m^2 + 0 $$<\/p>\n\n\n\n<p>Note: <em>Cov(e<sub>i <\/sub>, R<sub>m<\/sub>) <\/em>= 0 because the error term is uncorrelated with the market. By rearranging the equation to solve beta, we have:<\/p>\n\n\n\n<p>$$ \\beta_i = \\frac { Cov(R_i, R_m )}{ \\sigma_m^2} $$<\/p>\n\n\n\n<p>Where \\(Cov(R_i, R_m) = \\rho_{ i,m} \\sigma_i \\sigma_m\\) which, when substituted into the equation, simplifies it to \\(\\beta_i= \\frac{\\rho_{ i,m} \\sigma_i } {\\sigma_m}\\).<\/p>\n\n\n\n<p>Beta provides a measurement of the sensitivity of the asset returns to the market as a whole. Aside from this, it captures the portion of the asset risk that cannot be diversified.<\/p>\n\n\n\n<div style=\"text-align: center; margin: 22px 0;\">\n  <div style=\"max-width: 680px; margin: 0 auto;\">\n    <a href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"\n       style=\"display: flex; align-items: center; justify-content: center;\n       width: 100%; padding: 10px 18px;\n       border: 2px solid #1e5bd8; color: #1e5bd8;\n       border-radius: 9999px; text-decoration: none; font-weight: 600;\">\n      Practice beta and systematic risk concepts with our free trial\n    <\/a>\n  <\/div>\n<\/div>\n\n\n<h2><strong>Estimating Beta<\/strong><\/h2>\n<p>The variances and correlations required to calculate beta are usually determined using the historical returns for the asset and market. A regression analysis can be performed. The analysis essentially plots the market returns on the x-axis and the security returns on the y-axis and then finds the &#8220;best fit&#8221; straight line through these points. The slope of the regression line is the measure of beta. Using return data over the prior 12 months tends to represent the security&#8217;s current level of systematic risk. However, this approach may be less accurate than a beta measured over 3 to 5 years, given that a short-term event may impact the data.<\/p>\n<p>It is important to recognize that irrespective of the data period, beta is an estimate of systematic risk based on historical data and may not represent future systematic risk.<\/p>\n<h2><strong>Interpreting Beta<\/strong><\/h2>\n<p>A positive beta indicates that the asset moves in the same direction as the market, whereas a negative beta indicates the opposite.<\/p>\n<p>The beta of a risk-free asset is zero because the covariance of the risk-free asset and the market is zero. The market&#8217;s beta is, by definition, 1, and most developed market stocks tend to exhibit high, positive betas.<\/p>\n<blockquote>\n<h2><strong>Question<\/strong><\/h2>\n<p>If the correlation between an asset and the market is 0.6, the standard deviation of the asset is 18%, and the standard deviation of the market is 14%, what is the asset beta?<\/p>\n<p>A. 0.77.<\/p>\n<p>B. 0.47.<\/p>\n<p>C. 0.99.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is <strong>A<\/strong>.<\/p>\n<p>\\(\\beta_i= \\frac{\\rho_{ i,m} \\sigma_i } {\\sigma_m}\\)<\/p>\n<p>\\(\\beta_i= \\frac{0.6 \u00d7 0.18 } {0.14}\\)<\/p>\n<p>\\(\\beta_i= 0.77\\)<\/p>\n<\/blockquote>\n\n\n<div style=\"text-align: center; margin: 30px 0;\">\n  <a style=\"display: inline-flex; align-items: center; justify-content: center; padding: 12px 26px; border-radius: 9999px; background: #1e5bd8; color: #ffffff; font-weight: bold; text-decoration: none;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\">\n    Start Free Trial \u2192\n  <\/a>\n  <p style=\"margin-top: 12px; font-size: 16px; line-height: 1.5;\">\n    Practice beta calculation, market risk interpretation, and CAPM concepts with CFA Level I exam-style questions.\n  <\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Beta is a measure of systematic risk. Statistically, it depends on the degree of correlation between a security and the market. Calculating Beta We begin with the single index model using realized returns constructed as follows: $$ R_i \u2013 R_f&#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-2834","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>Beta in Portfolio Management | CFA Level 1<\/title>\n<meta name=\"description\" content=\"Beta measures an asset&#039;s sensitivity to market movements. 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