{"id":218664,"date":"2025-05-24T07:29:44","date_gmt":"2025-05-24T07:29:44","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=218664"},"modified":"2025-05-24T07:30:12","modified_gmt":"2025-05-24T07:30:12","slug":"a-stock-has-an-expected-return-of-13-8-percent-the-risk-free-rate-is-4-5-percent-and-the-market-risk-premium-is-7-5-percent","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/24\/a-stock-has-an-expected-return-of-13-8-percent-the-risk-free-rate-is-4-5-percent-and-the-market-risk-premium-is-7-5-percent\/","title":{"rendered":"A stock has an expected return of 13.8 percent, the risk-free rate is 4.5 percent, and the market risk premium is 7.5 percent."},"content":{"rendered":"\n<p>A stock has an expected return of 13.8 percent, the risk-free rate is 4.5 percent, and the market risk premium is 7.5 percent. What must the beta of this stock be? (Round your answer to 2 decimal places. (e.g., 32.16)) Beta of stock=<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find the <strong>beta (\u03b2)<\/strong> of a stock, we use the <strong>Capital Asset Pricing Model (CAPM)<\/strong> formula: Expected&nbsp;Return=Rf+\u03b2\u00d7(Rm\u2212Rf)\\text{Expected Return} = R_f + \\beta \\times (R_m &#8211; R_f)<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>RfR_f is the <strong>risk-free rate<\/strong><\/li>\n\n\n\n<li>Rm\u2212RfR_m &#8211; R_f is the <strong>market risk premium<\/strong><\/li>\n\n\n\n<li>\u03b2\\beta is the <strong>beta of the stock<\/strong><\/li>\n\n\n\n<li><strong>Expected Return<\/strong> is the return investors expect from the stock<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Given:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Expected Return = <strong>13.8%<\/strong><\/li>\n\n\n\n<li>Risk-free rate (RfR_f) = <strong>4.5%<\/strong><\/li>\n\n\n\n<li>Market Risk Premium = <strong>7.5%<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Now plug the values into the CAPM formula and solve for beta (\u03b2\\beta): 13.8%=4.5%+\u03b2\u00d77.5%13.8\\% = 4.5\\% + \\beta \\times 7.5\\% 13.8%\u22124.5%=\u03b2\u00d77.5%13.8\\% &#8211; 4.5\\% = \\beta \\times 7.5\\% 9.3%=\u03b2\u00d77.5%9.3\\% = \\beta \\times 7.5\\% \u03b2=9.3%7.5%=1.24\\beta = \\frac{9.3\\%}{7.5\\%} = 1.24<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 Final Answer:<\/h3>\n\n\n\n<p><strong>Beta of stock = 1.24<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><\/h3>\n\n\n\n<p>The beta (\u03b2) of a stock is a measure of its sensitivity to movements in the overall market. A beta of 1.0 means the stock\u2019s price moves exactly with the market. A beta greater than 1 indicates that the stock is more volatile than the market, while a beta less than 1 means it is less volatile.<\/p>\n\n\n\n<p>In this case, we use the Capital Asset Pricing Model (CAPM) to determine the stock&#8217;s beta. CAPM is a widely-used model in finance that relates the expected return on a security to its systematic risk, measured by beta. The model assumes that investors require compensation for time value of money (captured by the risk-free rate) and risk (captured by the market risk premium).<\/p>\n\n\n\n<p>The expected return of the stock is 13.8%, the risk-free rate is 4.5%, and the market risk premium is 7.5%. The market risk premium represents the additional return investors expect for taking on the risk of investing in the stock market as a whole, above the risk-free rate.<\/p>\n\n\n\n<p>We rearranged the CAPM formula to isolate beta and solved: \u03b2=Expected&nbsp;Return\u2212RfMarket&nbsp;Risk&nbsp;Premium=13.8%\u22124.5%7.5%=1.24\\beta = \\frac{\\text{Expected Return} &#8211; R_f}{\\text{Market Risk Premium}} = \\frac{13.8\\% &#8211; 4.5\\%}{7.5\\%} = 1.24<\/p>\n\n\n\n<p>This tells us that the stock has a beta of 1.24, meaning it is 24% more volatile than the market. If the market increases by 1%, this stock is expected to increase by approximately 1.24%, and vice versa for decreases.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/05\/image-310.png\" alt=\"\" class=\"wp-image-218665\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>A stock has an expected return of 13.8 percent, the risk-free rate is 4.5 percent, and the market risk premium is 7.5 percent. What must the beta of this stock be? (Round your answer to 2 decimal places. (e.g., 32.16)) Beta of stock= The Correct Answer and Explanation is: To find the beta (\u03b2) of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-218664","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/218664","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=218664"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/218664\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=218664"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=218664"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=218664"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}