{"id":553,"date":"2019-10-10T13:27:00","date_gmt":"2019-10-10T13:27:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=553"},"modified":"2025-04-18T11:14:26","modified_gmt":"2025-04-18T11:14:26","slug":"conditional-expectations-investments","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/conditional-expectations-investments\/","title":{"rendered":"Application of Conditional Expectations in Investments"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Probability Concepts (2021 Level I CFA\u00ae Exam \u2013 Reading 8)\",\n  \"description\": \"This video lesson covers the foundational concepts of probability for CFA candidates, including random variables, events, probability rules, odds, conditional probabilities, and Bayes\u2019 theorem. It also explores portfolio analysis, expected values, covariance, correlation, and counting techniques such as permutations and combinations, all with real-world finance and investment applications.\",\n  \"uploadDate\": \"2020-10-01T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/i.ytimg.com\/vi\/hu47ZbsskEw\/hqdefault.jpg\",\n  \"contentUrl\": \"https:\/\/www.youtube.com\/watch?v=hu47ZbsskEw\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/hu47ZbsskEw\",\n  \"duration\": \"PT48M33S\"\n}\n<\/script>\n\n\n\n<p>[vsw id=&#8221;hu47ZbsskEw&#8221; source=&#8221;youtube&#8221; width=&#8221;611&#8243; height=&#8221;344&#8243; autoplay=&#8221;no&#8221;]<\/p>\n<p>The conditional expectation, in the context of investments, refers to the expected value of an investment <strong>given<\/strong> a certain set of real world events that are relevant to that particular investment. This means that analysts calculate and predict the expected value of an investment, taking the events likely to occur in the future and their probabilities into account. Competitors, governments, and financial institutions keep on releasing new pieces of information. Such pieces of information may have a positive or negative impact on an investment. This means that a project\u2019s expected value must be based on real world dynamics, events or scenarios.<\/p>\n<p><!--more--><\/p>\n<p>It beats financial logic to stick to the initially predicted returns from an investment if an investor believes that the post-initial assessment events can significantly impact earnings. For example, let&#8217;s consider a sugar importer who calculates their expected return assuming the government won&#8217;t impose import tariff. If the government is planning to introduce a tariff in the coming months, then the investor will have to estimate the expected returns considering the possibility of a tariff.<\/p>\n<p>The total probability rule is very useful when determining the unconditional expected value of an investment. The <strong>unconditional <\/strong>expected value, E(X), is the sum of conditional expected values. Therefore,<\/p>\n<p>$$ E\\left( X \\right) =\\sum { \\left\\{ E\\left( X|{ S }_{ i } \\right) P\\left( { S }_{ i } \\right) \\right\\} } $$<\/p>\n<h2><strong>Example<\/strong><\/h2>\n<p>The probability of relaxed trade restrictions in a given country is 40%. Therefore, shareholders of XYZ Company Limited expect their shares to return 5% if trade restrictions are maintained. On the other hand, they expect an 8% loss if trade restrictions are relaxed. Compute the expected change in return.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>We must take every possibility into account. In this case, we have a 40% chance of relaxed trade restrictions. Intuitively, this means there is a 60% chance that the current restrictions will be maintained. Therefore:<\/p>\n<p>$$ \\begin{align*}<br \/>\nE\\left( X \\right) &amp; =\\sum { \\left\\{ E\\left( X|{ S }_{ i } \\right) P\\left( { S }_{ i } \\right) \\right\\} } \\\\<br \/>\n&amp; = 0.6(0.05) + 0.4(-0.08) \\\\<br \/>\n&amp; = -0.002 \\\\<br \/>\n\\end{align*} $$<\/p>\n<h3><strong>Question<\/strong><\/h3>\n<blockquote>\n<p>There is a 20% chance that the government will impose a tariff on imported cars. A company that assembles cars locally expects returns of 14% if the tariff is imposed and returns of 11% if the tariff is not imposed. Determine the (unconditional) expected return.<\/p>\n<p>A. 11.6%<\/p>\n<p>B. 12.8%<\/p>\n<p>C. 12.5%<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is A.<\/p>\n<p>The unconditional expected return will be the sum of:<\/p>\n<p>(1) The expected return <strong>given<\/strong> no tariff times the probability that a tariff will not be imposed, and<\/p>\n<p>(2) The expected return <strong>given<\/strong> tariff times the probability that the tariff will be imposed. Thus,<\/p>\n<p>$$ \\begin{align*}<br \/>\nE\\left( X \\right) &amp; =\\sum { \\left\\{ E\\left( X|{ S }_{ i } \\right) P\\left( { S }_{ i } \\right) \\right\\} } \\\\<br \/>\n&amp; = 0.11(0.8) + 0.14(0.2) \\\\<br \/>\n&amp; = 0.116 \\text{ or } 11.6\\% \\\\<br \/>\n\\end{align*} $$<\/p>\n<p><em>Note to Candidates: Focus should be on the calculations.<\/em><\/p>\n<\/blockquote>\n<p><em>Reading 8 LOS 8i<\/em><\/p>\n<p><em>Explain the use of conditional expectation in investment applications.<\/em><\/p>\n<div class=\"notes_inv\">\n<hr \/>\n<p><a href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/learning-sessions-curriculum-quantitative-methods\/\"><em>Quantitative Methods \u2013 Learning Sessions<\/em><\/a><\/p>\n<\/div>\n<p><em>\u00a0<\/em><\/p>","protected":false},"excerpt":{"rendered":"<p>[vsw id=&#8221;hu47ZbsskEw&#8221; source=&#8221;youtube&#8221; width=&#8221;611&#8243; height=&#8221;344&#8243; autoplay=&#8221;no&#8221;] The conditional expectation, in the context of investments, refers to the expected value of an investment given a certain set of real world events that are relevant to that particular investment. This means that&#8230;<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[2],"tags":[],"class_list":["post-553","post","type-post","status-publish","format-standard","hentry","category-quantitative-methods","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>Conditional Expectations in Investments | CFA Level 1<\/title>\n<meta name=\"description\" content=\"Learn how conditional expectations impact investment decisions by assessing expected values based on real-world events and market conditions.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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