{"id":1467,"date":"2020-04-15T13:29:00","date_gmt":"2020-04-15T13:29:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=1467"},"modified":"2026-01-05T08:21:00","modified_gmt":"2026-01-05T08:21:00","slug":"concepts-arbitrage-replication-risk-neutrality","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/derivatives\/concepts-arbitrage-replication-risk-neutrality\/","title":{"rendered":"Concepts of Arbitrage, Replication and Risk Neutrality"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n\n  \"name\": \"Basics of Derivative Pricing and Valuation (2025 Level I CFA\u00ae Exam \u2013 Derivative \u2013 Module 2)\",\n\n  \"description\": \"This video lesson covers Topic 7 \u2013 Derivatives, Module 2 \u2013 Basics of Derivative Pricing and Valuation. It explores core concepts like arbitrage, replication, and risk neutrality in pricing derivatives. Key highlights include the valuation of forward and futures contracts, factors affecting options pricing, put\u2013call parity, and the binomial model. It also differentiates between European and American options and explains their respective value determinants.\",\n\n  \"uploadDate\": \"2022-06-29T00:00:00+00:00\",\n\n  \"thumbnailUrl\": \"https:\/\/analystprep.com\/path-to-thumbnail\/derivative-pricing-thumbnail.jpg\", \n\n  \"contentUrl\": \"https:\/\/youtu.be\/0Geaej45v7w\",\n\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/0Geaej45v7w\",\n\n  \"duration\": \"PT1H08M27S\",\n\n  \"publisher\": {\n    \"@type\": \"Organization\",\n    \"name\": \"AnalystPrep\",\n    \"logo\": {\n      \"@type\": \"ImageObject\",\n      \"url\": \"https:\/\/analystprep.com\/path-to-logo\/logo.jpg\",\n      \"width\": 600,\n      \"height\": 60\n    }\n  }\n}\n<\/script>\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"Market response to an arbitrage opportunity\",\n    \"text\": \"When an arbitrage opportunity presents itself, what is most likely to happen?\\n\\nA. Investors trade quickly and prices adjust to eliminate the opportunity.\\n\\nB. Clearinghouses will restrict the transactions that can be arbitraged.\\n\\nC. An investor has the opportunity to earn a risk premium in the short run.\",\n    \"answerCount\": 1,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"A. Investors trade quickly and prices adjust to eliminate the opportunity.\\n\\nArbitrage opportunities attract rapid buying and selling by market participants. Increased demand for the underpriced asset pushes its price up, while increased supply of the overpriced asset pushes its price down. This trading activity continues until the price discrepancy disappears, eliminating the arbitrage opportunity.\"\n    }\n  }\n}\n<\/script>\n\n\n\n\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/0Geaej45v7w?si=6jPi-bH_8EqdU4ZH\" 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<p>The concepts of arbitrage, replication, and risk neutrality are important to comprehend when pricing derivatives. We can use assumptions about arbitrage and investor risk preferences to determine derivative pricing.<\/p>\n<h2>Arbitrage<\/h2>\n<p>Arbitrage refers to exploiting a price imbalance in the same asset that exists between two or more markets. For derivatives, this is taking advantage of the differences in prices of a unique asset to make a risk-free profit. Arbitrage opportunities tend to be exploited very quickly, which forces the convergence of prices. This is why identical assets should have just one price giving rise to the law of one price. However, there are circumstances where the cost of exploiting the arbitrage opportunity may exceed the benefit, in which case, the price discrepancy (which tends to be small) will persist.<\/p>\n<p>Consider this simple example: Company ABC\u2019s stock trades on the New York Stock Exchange for $10.00, and the equivalent of $11.00 on the London Stock Exchange. This sets up a perfect, risk-free arbitrage opportunity. The \u2018arbitrageur\u2019 can buy ABC\u2019s stock on the New York Stock Exchange for $10.00 and simultaneously sell the stock on the London Stock Exchange for $11.00, making a $1 per share \u2018riskless\u2019 profit. This action by market participants would force the two prices to converge back to one price.<\/p>\n<h2><strong>Replication<\/strong><\/h2>\n<p>Replication creates an asset or portfolio using a combination of another asset, portfolio, and\/or derivative. The following combinations produce the equivalent single asset:<\/p>\n<p>$$ \\text{Long asset} + \\text{Short derivative} = \\text{Long risk free asset} $$<\/p>\n<p>For example, let\u2019s say an investor has just bought one troy ounce of gold at USD 1,500. Then, his short sell a futures contract on a troy ounce of gold at USD 1575 for one year so that he can sell his troy ounce of gold in twelve months at a higher price. This means that his return should be equivalent to the return he would earn on a risk-free asset:<\/p>\n<p>$$\u00a0USD 1500-USD 1575=USD 75$$<\/p>\n<p>In other words, if the investor were to buy a risk-free bond for the same amount of USD 1500 and sell it one year later, he would earn an equivalent risk-free profit of USD 75 (or USD 75\/USD 1500 = 5%).<\/p>\n<p>We can rearrange the same formula as:<\/p>\n<p>$$ \\text{Long asset}+\\text{Short risk free asset}=\\text{Long derivative}$$<\/p>\n<p>$$ \\text{Short derivative}+\\text{Short risk free asset}=\\text{Short asset}$$<\/p>\n<p>If assets are priced correctly to prohibit arbitrage, replication would seem to be a pointless exercise. However, if we relax the no-arbitrage assumption, we may identify opportunities where replication may be more profitable or lower transaction costs.<\/p>\n<h2><strong>Risk Neutrality<\/strong><\/h2>\n<p>Most investors are risk-averse and will not accept a risk without commensurate returns. However, as risk aversion is not relevant to the pricing of a derivative (unlike other assets), we can assume the investor is risk-neutral. This means the expected payoff of the derivative can be discounted at the risk-free rate rather than having to use the risk-free rate plus some premium.<\/p>\n<p>Risk neutrality, otherwise known as risk-neutral derivative pricing, uses the fact that arbitrage opportunities guarantee that a risk-free portfolio consisting of the underlying and the derivative must earn the risk-free rate. The overall process of pricing derivatives by arbitrage and risk neutrality is called arbitrage-free pricing. We effectively determine the price of the derivative by assuming the market is free of arbitrage opportunities, sometimes referred to as the principle of no-arbitrage.<\/p>\n<blockquote>\n<h2>Question<\/h2>\n<p>When an arbitrage opportunity presents itself, what is <em>most likely<\/em> to happen?<\/p>\n<p>A. Investors trade quickly and prices adjust to eliminate the opportunity<\/p>\n<p>B. Clearinghouses will restrict the transactions that can be arbitraged<\/p>\n<p>C. An investor has the opportunity to earn a risk premium in the short run<\/p>\n<h5 data-tadv-p=\"keep\">Solution<\/h5>\n<p>The correct answer is A.<\/p>\n<p>The increased buying and selling by traders will eventually adjust the price to eliminate any arbitrage. As demand for the cheaper asset goes up, so does the price. When selling this asset in another market, the supply of that asset goes up, and the price of the asset goes down. Increased arbitrage activity will eventually neutralize the opportunity to take advantage of any price discrepancy.<\/p>\n<\/blockquote>","protected":false},"excerpt":{"rendered":"<p>The concepts of arbitrage, replication, and risk neutrality are important to comprehend when pricing derivatives. We can use assumptions about arbitrage and investor risk preferences to determine derivative pricing. Arbitrage Arbitrage refers to exploiting a price imbalance in the same&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[10],"tags":[],"class_list":["post-1467","post","type-post","status-publish","format-standard","hentry","category-derivatives","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>Arbitrage, Replication &amp; Risk Neutrality | CFA Level 1<\/title>\n<meta name=\"description\" content=\"Understand arbitrage, replication, and risk neutrality\u2014key concepts for derivative pricing, ensuring no-arbitrage and effective portfolio strategies.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link 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