{"id":195376,"date":"2025-02-28T07:57:53","date_gmt":"2025-02-28T07:57:53","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=195376"},"modified":"2025-02-28T07:57:56","modified_gmt":"2025-02-28T07:57:56","slug":"the-security-market-line-sml-is-an-equation-that-shows-the-relationship-between-risk-as-measured-by-beta-and-the-required-rate-securities","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/28\/the-security-market-line-sml-is-an-equation-that-shows-the-relationship-between-risk-as-measured-by-beta-and-the-required-rate-securities\/","title":{"rendered":"The security market line (SML) is an equation that shows the relationship between risk as measured by beta and the required rate securities"},"content":{"rendered":"\n<p>The security market line (SML) is an equation that shows the relationship between risk as measured by beta and the required rate securities. The SML equation is given below: Required return on Stock Risk-free return + (Market risk premium) (Stock&#8217;s beta) W If a stock&#8217;s expected return plots on or above the SML, then the stock&#8217;s return is -Select- expected return plots below the SML, the stock&#8217;s return is-select- to compensate the investor for r to compensate the investor for risk. The SML line can change due to expected inflation and risk aversion. If inflation changes, then the SML plotted on a graph will shi the old SML. If risk aversion changes, then the SML plotted on a graph will rotate up or down becoming more or less steep if invo less risk averse. A firm can influence market risk (hence its beta coefficient) through changes in the composition of its assets and amount of debt it uses. Quantitative Problem: You are given the following information for Wine and Cork Enterprises (WCE): TRF-4%; TM 8% ; RPM = 4%, and beta = 1.2 What is WCE&#8217;s required rate of return? Do not round intermediate calculations. Round your answer to two decimal places. % If inflation increases by 2% but there is no change in investors&#8217; risk aversion, what is WCE&#8217;s required rate of return now? Do no calculations. Round your answer to two decimal places. % Assume now that there is no change in inflation, but risk aversion increases by 1 What is WCE&#8217;s required rate of return now? intermediate calculations. Round your answer to two decimal places<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>The Security Market Line (SML) equation is given by:<\/p>\n\n\n\n<p>[<br>\\text{Required Return} = \\text{Risk-free Rate} + (\\text{Market Risk Premium} \\times \\text{Beta})<br>]<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Step 1: Calculating WCE\u2019s Required Rate of Return<\/strong><\/h4>\n\n\n\n<p>Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Risk-free rate (TRF) = 4%<\/li>\n\n\n\n<li>Market return (TM) = 8%<\/li>\n\n\n\n<li>Market risk premium (RPM) = 4% (since RPM = TM &#8211; TRF)<\/li>\n\n\n\n<li>Beta = 1.2<\/li>\n<\/ul>\n\n\n\n<p>[<br>\\text{Required Return} = 4\\% + (4\\% \\times 1.2)<br>]<\/p>\n\n\n\n<p>[<br>= 4\\% + 4.8\\% = 8.8\\%<br>]<\/p>\n\n\n\n<p>So, WCE\u2019s required rate of return is <strong>8.8%<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Step 2: Impact of Inflation Increase by 2%<\/strong><\/h4>\n\n\n\n<p>When inflation increases by 2%, both the risk-free rate and the market return increase by 2%. The new values are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>New risk-free rate = 4% + 2% = 6%<\/li>\n\n\n\n<li>New market return = 8% + 2% = 10%<\/li>\n\n\n\n<li>New market risk premium = 10% &#8211; 6% = 4%<\/li>\n<\/ul>\n\n\n\n<p>Using the SML formula:<\/p>\n\n\n\n<p>[<br>\\text{New Required Return} = 6\\% + (4\\% \\times 1.2)<br>]<\/p>\n\n\n\n<p>[<br>= 6\\% + 4.8\\% = 10.8\\%<br>]<\/p>\n\n\n\n<p>Thus, WCE\u2019s required return increases to <strong>10.8%<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Step 3: Impact of Increase in Risk Aversion by 1%<\/strong><\/h4>\n\n\n\n<p>When risk aversion increases, the market risk premium increases by 1%, making it:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>New market risk premium = 4% + 1% = 5%<\/li>\n<\/ul>\n\n\n\n<p>Applying the SML equation:<\/p>\n\n\n\n<p>[<br>\\text{New Required Return} = 4\\% + (5\\% \\times 1.2)<br>]<\/p>\n\n\n\n<p>[<br>= 4\\% + 6\\% = 10.0\\%<br>]<\/p>\n\n\n\n<p>Thus, WCE\u2019s required return increases to <strong>10.0%<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Key Insights<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If a stock&#8217;s expected return plots <strong>on or above the SML<\/strong>, it is considered <strong>fairly or undervalued<\/strong>.<\/li>\n\n\n\n<li>If a stock\u2019s expected return <strong>falls below the SML<\/strong>, it is <strong>overvalued<\/strong> as it does not sufficiently compensate for risk.<\/li>\n\n\n\n<li>An <strong>increase in inflation<\/strong> shifts the entire SML <strong>upward<\/strong>, increasing required returns.<\/li>\n\n\n\n<li>An <strong>increase in risk aversion<\/strong> makes the SML <strong>steeper<\/strong>, raising required returns for risky stocks.<\/li>\n<\/ul>\n\n\n\n<p>These factors affect investment decisions, portfolio risk, and corporate finance strategies.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Final Answers<\/strong><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>WCE\u2019s Required Rate of Return<\/strong> = <strong>8.8%<\/strong><\/li>\n\n\n\n<li><strong>After 2% Inflation Increase<\/strong> = <strong>10.8%<\/strong><\/li>\n\n\n\n<li><strong>After 1% Increase in Risk Aversion<\/strong> = <strong>10.0%<\/strong><\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>Now, I&#8217;ll generate an image illustrating the changes in the SML graph.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/02\/image-1614-1024x682.png\" alt=\"\" class=\"wp-image-195377\"\/><\/figure>\n\n\n\n<p>Here is a visual representation of the Security Market Line (SML) and how it shifts due to changes in inflation and risk aversion. The key takeaways from the graph:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Original SML (Blue Line)<\/strong> \u2013 Represents the initial relationship between risk (beta) and the required return.<\/li>\n\n\n\n<li><strong>After a 2% Inflation Increase (Red Dashed Line)<\/strong> \u2013 The entire SML shifts <strong>upward<\/strong>, increasing the required return for all levels of beta.<\/li>\n\n\n\n<li><strong>After a 1% Increase in Risk Aversion (Green Dash-Dot Line)<\/strong> \u2013 The SML rotates <strong>upward<\/strong>, making it steeper, meaning riskier stocks (higher beta) now require an even higher return.<\/li>\n<\/ol>\n\n\n\n<p>The points marked on the graph indicate WCE\u2019s required return under different scenarios, showing how market conditions affect investment decisions. Let me know if you need further clarifications! <\/p>\n","protected":false},"excerpt":{"rendered":"<p>The security market line (SML) is an equation that shows the relationship between risk as measured by beta and the required rate securities. The SML equation is given below: Required return on Stock Risk-free return + (Market risk premium) (Stock&#8217;s beta) W If a stock&#8217;s expected return plots on or above the SML, then the [&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-195376","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/195376","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=195376"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/195376\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=195376"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=195376"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=195376"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}