{"id":23554,"date":"2021-11-19T10:48:59","date_gmt":"2021-11-19T10:48:59","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=23554"},"modified":"2026-03-01T06:31:55","modified_gmt":"2026-03-01T06:31:55","slug":"pricing-equity-forwards-and-futures","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/pricing-equity-forwards-and-futures\/","title":{"rendered":"Pricing Equity Forwards and Futures"},"content":{"rendered":"<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 does a dividend announcement affect the value of an existing forward contract?\",\r\n    \"text\": \"Assume that a dividend payment is announced between the forward\u2019s valuation date and expiration date. If the announcement does not change the current underlying price, the forward value is most likely to:\\n\\nA. Remain the same.\\n\\nB. Decrease.\\n\\nC. Increase.\",\r\n    \"answerCount\": 1,\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"The correct answer is B. A dividend payment reduces the forward price because the underlying asset\u2019s value decreases when dividends are paid. As a result, the value of an existing forward contract declines when a dividend is announced, assuming all other factors remain constant.\"\r\n    }\r\n  }\r\n}\r\n<\/script>\r\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/4fFXI985hyE\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\r\n<p>A forward contract is a contract that promises to buy or sell an asset on a specific date in the future at a prearranged price. We need to construct a portfolio with cash flows equal to the forward to price forwards and futures. From there, we can use the law of one price to determine the value of the forwards. Investment managers use equity index futures and swaps to hedge equity risk on a low tax basis. This section will illustrate the carry arbitrage model with equity forward pricing and valuation for equity forward and futures contracts. We assume that futures and forward contracts are priced the same way and that interest rates are compounded annually.<\/p>\r\n<h4>Example 1: Equity Futures Contract Prices With Continuous Compounded Interest Rates<\/h4>\r\n<p>The dividend yield on the EURO STOXX 50 is 5%, and the current stock index level is 3,200. The continuously compounded annual interest rate is 0.2%. Based on the carry arbitrage model, the three-month futures price is <em>most likely<\/em> to be:<\/p>\r\n<h4>Solution<\/h4>\r\n<p>The formula we will be using is:<\/p>\r\n<p style=\"text-align: left;\">\u00a0$$ F_0=S_0e^{(r_c+CC-CB)T} $$<\/p>\r\n<p>Let us assume that the carry costs are 0 for the stock index. The carry benefit will be 5%, and the financing cost will be 0.2%. Since the dividend yield is greater than the financing cost, the future price will be lower than the spot price. The future value of the underlying adjusted carrying dividend payments over the next three months is:<\/p>\r\n<p>$$ F_0=3200e^{(0.002+0-0.5)3\/12} = 3,161.829 $$<\/p>\r\n<h4>Example 2: Equity Forward Pricing and Forward Valuation With Discrete Dividends<\/h4>\r\n<p>Kraft Heinz common stock trades for $36.40 and pays a $1.50 dividend in one month. Assume that the dollar one month risk-free is 1% on an annual compounding basis. Further, assume that the stock goes ex-dividend the same day the contract expires in one month. The one-month forward price for Kraft Heinz common stock will be <em>closest<\/em> to:<\/p>\r\n<h4>Solution<\/h4>\r\n<p>\\(S_0\\) = 36.4, \\(r\\) = 1.0% \\(T\\) = 1\/12 and \\(FV(CB_0)\\) = 1.5 = \\(CB_T\\)<\/p>\r\n<p>$$ \\begin{align} F_0\u00a0 &amp; =\u00a0 FV(S_0+CC_0-CB_0) \\\\ &amp; = 36.4(1+0.01)^{1\u204412}+0-1.5 \\\\ &amp; = $34.93 \\end{align} $$<\/p>\r\n<p>The value before the contract expires is the present value of the difference between the initial equity forward price and the current forward price.<\/p>\r\n<blockquote>\r\n<h2>Question\u00a0<\/h2>\r\n<p>Assume that a dividend payment is announced between the forward\u2019s valuation and expiration date. If the announcement remains unchanged the current underlying price, the forward value is <em>most likely<\/em> to:<\/p>\r\n<ol style=\"list-style-type: upper-alpha;\">\r\n\t<li>Remain the same.<\/li>\r\n\t<li>Decrease.<\/li>\r\n\t<li>Increase.<\/li>\r\n<\/ol>\r\n<h4>Solution<\/h4>\r\n<p><strong>The correct answer is B.<\/strong><\/p>\r\n<p>Payment of dividends is likely to reduce the forward price and therefore, lower the value of the initial forward contract.<\/p>\r\n<\/blockquote>\r\n<p>Reading 33: Pricing and Valuation of Forward Commitments<\/p>\r\n<p><em>LOS 33 (<\/em><em>b) Describe how equity forwards and futures are priced, and calculate and interpret their no-arbitrage value.<\/em><\/p>\r\n<p>&nbsp;<\/p>\r\n<!-- \/wp:post-content -->\r\n<!-- wp:tadv\/classic-paragraph \/-->","protected":false},"excerpt":{"rendered":"<p>A forward contract is a contract that promises to buy or sell an asset on a specific date in the future at a prearranged price. We need to construct a portfolio with cash flows equal to the forward to price&#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":[],"class_list":["post-23554","post","type-post","status-publish","format-standard","hentry","category-cfa-level-2","category-derivatives","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Pricing Equity Forwards &amp; Futures | CFA L2<\/title>\n<meta name=\"description\" content=\"Learn equity forward price formulas, futures valuation, dividend adjustments, and the difference between forward price and value in CFA Level 2.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, 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