{"id":18729,"date":"2021-07-30T14:36:15","date_gmt":"2021-07-30T14:36:15","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=18729"},"modified":"2026-06-04T06:00:32","modified_gmt":"2026-06-04T06:00:32","slug":"describe-how-a-delta-hedge-is-executed","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/describe-how-a-delta-hedge-is-executed\/","title":{"rendered":"Describe How a Delta Hedge is Executed"},"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\": \"How can an investor create a delta-neutral hedge using call options?\",\r\n    \"text\": \"An investor owns a portfolio with 10,000 shares of Contagia Inc. common stock currently trading at $30 per share. The investor wants to delta hedge the portfolio using call options. A call option on the Contagia shares with a strike price of $30 has a delta of 0.5.\\n\\nThe strategy to create a delta-neutral hedge most likely involves:\\n\\nA. Selling 10,000 call options.\\n\\nB. Buying 20,000 call options.\\n\\nC. Selling 20,000 call options.\",\r\n    \"answerCount\": 1,\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"The correct answer is C.\\n\\nPortfolio delta = 10,000 (since each share has a delta of 1).\\n\\nCall option delta = 0.5.\\n\\nTo achieve delta neutrality:\\n\\nNumber of options = - (Portfolio delta \/ Option delta) = - (10,000 \/ 0.5) = -20,000.\\n\\nThe negative sign indicates selling options. Therefore, the investor must sell 20,000 call options to create a delta-neutral hedge.\"\r\n    }\r\n  }\r\n}\r\n<\/script><\/p>\r\n\r\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/rnMud0L9-g0\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\r\n<p><em><strong>Delta hedging<\/strong><\/em> involves adding up the deltas of the individual assets and options that make up a portfolio. A delta hedged portfolio is one for which the weighted sums of deltas of individual assets are zero. A position with a zero delta is referred to as a <em><strong>delta-neutral position<\/strong><\/em>.<\/p>\r\n<p>Denote the delta of a hedging instrument by \\(\\text{Delta}_H\\) and the optimal number of hedging units \\(N_H=-\\frac{\\text{Portfolio Delta}}{\\text{Delta}_H} \\).<\/p>\r\n<p>To achieve a delta hedged portfolio, short the hedging instrument if \\(N_{H }\\) is negative and long the hedging instrument if \\(N_H\\) is positive.<\/p>\r\n<p>A delta-neutral portfolio is one that does not change in value as a result of small changes in the underlying price. Delta neutral implies that:<\/p>\r\n<p>$$ \\text{Portfolio delta}+N_H {\\text{Delta}_H}=0 $$<\/p>\r\n<p>A portfolio should be rebalanced regularly to ensure that the sum of deltas remains close to zero. <em><strong>Static delta hedging<\/strong><\/em> involves the construction of an initial portfolio with a sum of deltas of zero, at time 0. In fact, the sum of deltas is never adjusted. <span style=\"font-size: 1rem;\">On the other hand, <\/span><em style=\"font-size: 1rem;\"><strong>dynamic delta hedging<\/strong><\/em><span style=\"font-size: 1rem;\"> involves continuously rebalancing the portfolio to maintain a constant total portfolio delta of zero.<\/span><\/p>\r\n<div style=\"text-align: center; margin: 28px 0;\"><a style=\"display: inline-block; background: #1a73e8; color: #ffffff; padding: 12px 26px; border-radius: 40px; font-size: 16px; font-weight: 500; text-decoration: none; line-height: 1.4;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"> Practice delta hedging and option risk management with our CFA Free Trial <\/a><\/div>\r\n<h4>Example: Delta Hedging #1<\/h4>\r\n<p>Consider a portfolio composed of 1,500 shares. Call options with a delta of +0.50 are used to hedge this portfolio. A delta hedge could be implemented by selling enough calls to make the portfolio delta neutral.<\/p>\r\n<p>The optimal number of hedging units is determined as follows:<\/p>\r\n<p>$$ N_H=-\\frac{\\text{Portfolio Delta}}{\\text{Delta}_H} $$<\/p>\r\n<p>Portfolio delta = 1,500<\/p>\r\n<p>\\(\\text{Delta}_{H}\\) = +0.50<\/p>\r\n<p>Therefore, \\(N_H =-\\frac{1,500}{0.50} =-3,000\\)<\/p>\r\n<p>This means that we must sell 3,000 calls to achieve delta neutrality.<\/p>\r\n<h4>Example: Delta Hedging #2<\/h4>\r\n<p>Given the following information:<\/p>\r\n<p>\\(S_0 = 60\\)<\/p>\r\n<p>\\(K = 50\\)<\/p>\r\n<p>\\(r = 2\\%\\)<\/p>\r\n<p>\\(T = 1\\)<\/p>\r\n<p>\\(\\sigma=20\\%\\)<\/p>\r\n<p>\\(\\text{Delta}_c=0.537\\)<\/p>\r\n<p>\\(\\text{Delta}_p= &#8211; 0.463\\)<\/p>\r\n<p>Assume that the underlying asset does not pay a dividend consider a short position of 5,000 shares of stock.<\/p>\r\n<p>Delta hedge this portfolio using call options and put options.<\/p>\r\n<h4>Hedging Using Call Options<\/h4>\r\n<p>The optimal number of hedging units,<\/p>\r\n<p>$$ N_H = -\\frac{\\text{Portfolio Delta}}{\\text{Delta}_H} $$<\/p>\r\n<p>Where:<\/p>\r\n<p>Portfolio Delta = -5,000<\/p>\r\n<p>\\(\\text{Delta}_H\\) = 0.537<\/p>\r\n<p>\\(N_H=-\\frac{-(-5,000)}{0.537}\\) = 9,311<\/p>\r\n<p>This means that we must buy 9,311 calls to make the portfolio delta neutral.<\/p>\r\n<h4>Hedging Using Put Options<\/h4>\r\n<p>We have portfolio delta = -5,000<\/p>\r\n<p>\\(\\text{Delta}_H\\) = -0.463<\/p>\r\n<p>\\(N_H=-\\frac{-5,000}{-0.463}=-10,799\\)<\/p>\r\n<p>This means that we must sell 10,799 put options.<\/p>\r\n<p><em><strong>Note to candidates:<\/strong> <\/em>The amount of call options to be bought is not the same amount as the number of put options to be sold.<\/p>\r\n<blockquote>\r\n<h2>Question<\/h2>\r\n<p>An investor owns a portfolio with 10,000 shares of Contagia Inc. common stock currently trading at $30 per share. The investor wants to delta hedge the portfolio using call options. A call option on the Contagia shares with a strike price of $30 has a delta of 0.5.<\/p>\r\n<p>The strategy to create a delta-neutral hedge <em>most likely<\/em> involves:<\/p>\r\n<ol type=\"A\">\r\n\t<li>Selling 10,000 call options.<\/li>\r\n\t<li>Buying 20,000 call options.<\/li>\r\n\t<li>Selling 20,000 call options.<\/li>\r\n<\/ol>\r\n<h4>Solution<\/h4>\r\n<p><strong>The correct answer is C.<\/strong><\/p>\r\n<p>Portfolio delta = 10,000<\/p>\r\n<p>\\(\\text{Delta}_H\\) = 0.5<\/p>\r\n<p>The optimal number of call options required to hedge against movements in the stock price is determined as:<\/p>\r\n<p>$$ \\begin{align*} N_H &amp;=-\\frac{\\text{Portfolio Delta}}{\\text{Delta}_H} \\\\ N_H &amp;=\\frac{-10,000}{0.5} =-20,000 \\end{align*} $$<\/p>\r\n<p>This means that the investor must sell 20,000 calls to achieve delta neutrality.<\/p>\r\n<\/blockquote>\r\n<p>Reading 34: Valuation of Contingent Claims<\/p>\r\n<p><em>LOS 34 (l) Describe how a delta hedge is executed.<\/em><\/p>\r\n\r\n<div style=\"background: #f5f7fb; padding: 24px 18px; border-radius: 12px; text-align: center; margin: 36px 0 18px;\"><a style=\"display: inline-block; background: #1a73e8; color: #ffffff; padding: 10px 24px; border-radius: 40px; font-size: 16px; font-weight: bold; text-decoration: none; margin-bottom: 16px;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"> Start Free Trial \u2192 <\/a>\r\n<div style=\"font-size: 14px; color: #333333; max-width: 650px; margin: 0 auto; line-height: 1.6;\">Practice delta hedging, option Greeks, and dynamic hedging strategies with CFA Level II derivatives questions and step-by-step explanations.<\/div>\r\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Delta hedging involves adding up the deltas of the individual assets and options that make up a portfolio. A delta hedged portfolio is one for which the weighted sums of deltas of individual assets are zero. A position with a&#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":[102,302],"tags":[216,304],"class_list":["post-18729","post","type-post","status-publish","format-standard","hentry","category-cfa-level-2","category-derivatives","tag-cfa-level-2","tag-derivatives","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>Delta Hedging Strategy and Execution Steps<\/title>\n<meta name=\"description\" content=\"Learn how delta hedging works, including delta-neutral positions, static vs dynamic hedging, and how to manage option risk.\" \/>\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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