{"id":18808,"date":"2021-07-31T22:47:03","date_gmt":"2021-07-31T22:47:03","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=18808"},"modified":"2026-06-11T08:44:15","modified_gmt":"2026-06-11T08:44:15","slug":"define-arbitrage-opportunity-and-determine-whether-an-arbitrage-opportunity-exists","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/define-arbitrage-opportunity-and-determine-whether-an-arbitrage-opportunity-exists\/","title":{"rendered":"Arbitrage Opportunities"},"content":{"rendered":"<p><script type=\"application\/ld+json\">\r\n{\r\n  \"@context\": \"https:\/\/schema.org\",\r\n  \"@type\": \"QAPage\",\r\n  \"mainEntity\": {\r\n    \"@type\": \"Question\",\r\n    \"name\": \"Least likely true statement about portfolio MNO valuation\",\r\n    \"text\": \"An investment firm uses a single-factor model to evaluate assets. Consider portfolios ABC, XYZ, and MNO with comparable risk exposures.\\n\\nWhich of the following statements is least likely true about portfolio MNO?\\n\\nA. It is overvalued.\\n\\nB. It is undervalued.\\n\\nC. It is fairly valued.\",\r\n    \"answerCount\": 1,\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"The correct answer is B.\\n\\nA replicating portfolio using ABC and XYZ can match the risk exposures of MNO while delivering a higher expected return. This implies that MNO is overvalued. Therefore, the statement that it is undervalued is least likely to be true.\"\r\n    }\r\n  }\r\n}\r\n<\/script><\/p>\r\n\r\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/SGL5FhV5IUQ\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\r\n<h2>Arbitrage Opportunity<\/h2>\r\n<p>Arbitrage is risk-free trading that does not require an initial investment of money but earns an expected positive net return. An <strong>arbitrage opportunity<\/strong> exists if an investor can make a deal that would give an immediate profit, with zero initial cost, no risk of future loss, and a non-zero probability of future profit.<\/p>\r\n<h3>Characteristics of Arbitrage Opportunity<\/h3>\r\n<ul>\r\n\t<li>It neither costs anything today nor in any state in the future.<\/li>\r\n\t<li>It has a positive payoff either today or at a future date (or both).<\/li>\r\n<\/ul>\r\n<div style=\"text-align: center; margin: 30px 0;\"><a style=\"background: #2f6fdd; color: #ffffff; padding: 14px 28px; border-radius: 999px; text-decoration: none; font-weight: 600; font-size: 16px; display: inline-flex; align-items: center; justify-content: center; line-height: 1.4;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener\"> Practice detecting and exploiting arbitrage opportunities with our Free Trial <\/a><\/div>\r\n<h4>Example: Exploiting an Arbitrage Opportunity<\/h4>\r\n<p>Assume you are an investor in an investment firm that uses a two-factor model to evaluate assets. The following data for portfolios A, B, and C is provided:<\/p>\r\n<p>$$ \\begin{array}{c|c|c|c} \\textbf{Portfolio} &amp; \\textbf{Expected Return} &amp; \\bf{{\\beta}_{1}} &amp; \\bf{{\\beta}_{2}} \\\\ \\hline A &amp; 12\\% &amp; 1 &amp; 0.4 \\\\ \\hline B &amp; 16\\% &amp; 0.8 &amp; 0.8 \\\\ \\hline C &amp; 12\\% &amp; 0.9 &amp; 0.6 \\end{array} $$<\/p>\r\n<p>The arbitrage opportunity is <em>closest<\/em> to:<\/p>\r\n<h4>Solution<\/h4>\r\n<p>If we allocate 50% of funds to portfolio A and the remaining 50% to B, we can obtain a portfolio (D) with \\(\\beta_1\\) and \\(\\beta_2\\) equal to the Portfolio C betas.<\/p>\r\n<p>\\(\\beta_1\\) for portfolio D = 0.5(1.0) + 0.5(0.8) = 0.9<\/p>\r\n<p>\\(\\beta_2\\) for portfolio D = 0.5(0.4) + 0.5(0.8) = 0.6<\/p>\r\n<p>The expected return for portfolio D is 0.5(12%) + 0.5(16%) = 14% while that of C is 12%. Therefore, portfolios D and C have the same risk, but D has a higher expected return.<\/p>\r\n<p>Logically, by buying portfolio D and short-selling portfolio C, we expect to earn a 14% \u2212 12% = 2% return. Investors will exploit the arbitrage opportunity, which will lead to the depreciation of prices of assets in portfolio C, and the rise of the expected return for portfolio C to its equilibrium value.<\/p>\r\n<p>The APT assumes that there are no market irregularities that prevent investors from exploiting arbitrage opportunities. Therefore, investors can hold extremely long and short positions, making mispricing vanish immediately. This makes arbitrage opportunities to be exploited and eliminated immediately.<\/p>\r\n<blockquote>\r\n<h2>Question<\/h2>\r\n<p>An investment firm uses a single-factor model to evaluate assets. Consider the following data for portfolios ABC, XYZ, and MNO:<\/p>\r\n<p>$$ \\begin{array}{c|c|c|c} \\textbf{Portfolio} &amp; \\textbf{Expected Return} &amp; \\bf{{\\beta}_{1}} &amp; \\bf{{\\beta}_{2}} \\\\ \\hline ABC &amp; 20\\% &amp; 1.00 &amp; 0.50 \\\\ \\hline XYZ &amp; 15\\% &amp; 0.80 &amp; 0.40 \\\\ \\hline MNO &amp; 17\\% &amp; 0.92 &amp; 0.46 \\end{array} $$<\/p>\r\n<p>Which of the following statements is <em>least likely<\/em> true about portfolio MNO?<\/p>\r\n<ol type=\"A\">\r\n\t<li>It is overvalued.<\/li>\r\n\t<li>It is undervalued.<\/li>\r\n\t<li>It is fairly valued.<\/li>\r\n<\/ol>\r\n<h4>Solution<\/h4>\r\n<p><strong>The correct answer is B.<\/strong><\/p>\r\n<p>We construct a portfolio with ABC and XYZ portfolios having the same risks as the MNO portfolio. To do so, we solve the following equations simultaneously:<\/p>\r\n<p>$$ \\begin{align*} x+0.8y &amp; = 0.92 \\\\ 0.5x+0.4y &amp; = 0.46 \\\\ x = 0.6 &amp; \\text{and} y = 0.4. \\end{align*} $$<\/p>\r\n<p>Therefore a new portfolio, NEW, can be created by allocating \\(\\frac{0.6}{0.6+0.4}\\times100=60\\%\\) of funds to ABC and the remaining 40% to XYZ. This portfolio will have the same risks are MNO. However, the expected return for portfolio NEW is \\(0.6(20\\%) + 0.4(15\\%) = 18\\%\\).<\/p>\r\n<p>This implies that the MNO portfolio is overvalued, and thus, arbitrageurs will short sell MNO and buy the NEW portfolio.<\/p>\r\n<\/blockquote>\r\n<p>Reading 40: Using Multifactor Models<\/p>\r\n<p><em>LOS 40 (b) Define arbitrage opportunity and determine whether an arbitrage opportunity exists.<\/em><\/p>\r\n\r\n<div style=\"background: #f5f7fa; padding: 32px 24px; border-radius: 12px; text-align: center; margin: 40px 0;\"><a style=\"background: #2f6fdd; color: #ffffff; padding: 14px 30px; border-radius: 999px; text-decoration: none; font-weight: 600; font-size: 16px; display: inline-flex; align-items: center; justify-content: center;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener\"> Start Free Trial \u2192 <\/a>\r\n<p style=\"margin: 14px auto 0; max-width: 650px; color: #555; font-size: 15px; line-height: 1.6;\">Practice defining arbitrage, evaluating multi\u2011factor return datasets, and determining whether arbitrage opportunities exist using pricing and factor loadings as tested on CFA Level\u202fII finance topics.<\/p>\r\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Arbitrage Opportunity Arbitrage is risk-free trading that does not require an initial investment of money but earns an expected positive net return. An arbitrage opportunity exists if an investor can make a deal that would give an immediate profit, with&#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":[102,473],"tags":[216,564],"class_list":["post-18808","post","type-post","status-publish","format-standard","hentry","category-cfa-level-2","category-portfolio-management","tag-cfa-level-2","tag-portfolio-management","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Arbitrage Opportunities and Pricing Concepts<\/title>\n<meta name=\"description\" content=\"Learn what arbitrage opportunities are, how they arise, and how to identify risk-free profit situations in financial markets.\" \/>\n<meta name=\"robots\" content=\"index, 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