{"id":23576,"date":"2021-11-19T15:30:38","date_gmt":"2021-11-19T15:30:38","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=23576"},"modified":"2026-01-19T16:11:42","modified_gmt":"2026-01-19T16:11:42","slug":"pricing-and-valuing-equity-swap-contracts","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/pricing-and-valuing-equity-swap-contracts\/","title":{"rendered":"Pricing and Valuing Equity Swap Contracts"},"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\": \"What is the value of the equity swap to the fixed-rate payer after 30 days?\",\r\n    \"text\": \"An equity swap has an annual swap rate of 4% and a notional principal of $2 million. The underlying index is currently trading at 2,000. After 30 days, the index trades at 2,200, and the LIBOR spot rates are: 60-day 3.90%, 150-day 4.55%, 240-day 5.20%, and 330-day 5.85%. The value of the equity swap to the fixed-rate payer is closest to which of the following?\",\r\n    \"answerCount\": 1,\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"The value of the equity swap to the fixed-rate payer is $223,980. Using the LIBOR spot rates, the discount factors are D60 = 0.9935, D150 = 0.9814, D240 = 0.9665, and D330 = 0.9491. The fixed-rate leg value is P(fixed) = (0.04\/4) \u00d7 (0.9935 + 0.9814 + 0.9665 + 0.9491) + 1 \u00d7 0.9491 = 0.98801. The index leg value is P(index) = 2200\/2000 = 1.1. Therefore, swap value = [P(index) \u2212 P(fixed)] \u00d7 notional = (1.1 \u2212 0.98801) \u00d7 2,000,000 = 223,980.\",\r\n      \"dateCreated\": \"2026-01-19\"\r\n    }\r\n  }\r\n}\r\n<\/script>\r\n\r\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/4fFXI985hyE\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\r\n<h2>Equity Swaps<\/h2>\r\n<p>An <em><strong>equity swap<\/strong> <\/em>is an OTC derivative contract in which two parties agree to exchange a series of cash flows. In this arrangement, one party pays a variable series determined by equity. The other party pays a variable series determined by different equity or rate or a fixed series.<\/p>\r\n<h3>Types of Equity Swaps<\/h3>\r\n<ul>\r\n\t<li>Pay a fixed rate and receive equity return.<\/li>\r\n\t<li>Pay floating rate and receive equity return.<\/li>\r\n\t<li>Pay one equity return and receive another equity return.<\/li>\r\n<\/ul>\r\n<p>We can look at an equity swap as a portfolio of an equity position and a bond.<\/p>\r\n<p>The equity swap cashflows are expressed as :<\/p>\r\n<ul>\r\n\t<li>NA(Equity return \u2013 Fixed rate) (for pay fixed, receive equity party)<\/li>\r\n\t<li>NA(Equity return \u2013 Floating rate) (for pay floating, receive equity)<\/li>\r\n\t<li>NA(Equity return X \u2013 Equity return Y) (for pay equity, receive equity) where X and Y denote different equities.<\/li>\r\n<\/ul>\r\n<h3>Pricing Equity Swaps<\/h3>\r\n<p>An equity swap is priced at the same rate as a comparable interest rate swap. Note, however, that the cashflows involved are very different.<\/p>\r\n<p>The fixed swap rate is:<\/p>\r\n<p>$$ r_{FIX}=\\frac{1-{PV}_{0,t_n}\\left(1\\right)}{\\sum_{i=1}^{n}{{PV}_{0,t_i}\\left(1\\right)}} $$<\/p>\r\n<h4>Example: Calculating the price of an Equity Swap<\/h4>\r\n<p>Consider a four-year annual reset Libor floating-rate bond trading at par. A comparable interest rate swap has a fixed rate of 1.117%. The information used to price the interest rate swap is given in the following table:<\/p>\r\n<p>$$ \\begin{array}{c|c} \\textbf{Year} &amp; \\textbf{Discount factor} \\\\ \\hline 1 &amp; 0.9723 \\\\ \\hline 2 &amp; 0.9667 \\\\ \\hline 3 &amp; 0.9625 \\\\ \\hline 4 &amp; 0.9569 \\end{array} $$<\/p>\r\n<p>Using the same data, the fixed interest rate for a 4-year pay fixed rate and receive equity return equity swap is <em>closest<\/em> to:<\/p>\r\n<h4>Solution<\/h4>\r\n<p>The fixed-rate on an equity swap is identical to the fixed rate on a comparable interest rate swap. This means that the fixed rate on the equity swap will be 1.117%, which is similar to the fixed rate on a comparable interest rate swap.<\/p>\r\n<h3>Valuing an Equity Swap<\/h3>\r\n<p>Valuing an equity swap after it is initiated is comparable to valuing an interest rate swap. However, instead of adjusting the floating-rate bond for the last floating rate observed (advanced set), the value of the notional amount of equity is adjusted.<\/p>\r\n<p>Therefore, the value of an equity swap is expressed as:<\/p>\r\n<p>$$ V_t = FB_t\\left(C_0\\right)- \\frac {S_t}{S_{t-}}NA_E &#8211; PV(Par &#8211; NA_E) $$<\/p>\r\n<p>Where:<\/p>\r\n<p>\\(FB_t(C_0)\\) = Time \\(t\\) value of a fixed-rate bond initiated with coupon C0 at time 0.<\/p>\r\n<p>\\(S_t\\) = Current equity price.<\/p>\r\n<p>\\(S_{t\u2013}\\) = Equity price observed at the last reset date.<\/p>\r\n<blockquote>\r\n<h2>Question\u00a0<\/h2>\r\n<p>An equity swap has an annual swap rate of 4% and a notional principal of $ 2 million. The underlying index is currently trading at 2,000.<\/p>\r\n<p>After 30 days, the index trades at 2,200, and the LIBOR spot rates are as given in the following table:<\/p>\r\n<p>$$ \\begin{array}{c|c} \\textbf{Year} &amp; \\textbf{Spot rates} \\\\ \\hline 60 -\\text{day Libor} &amp; 3.90\\% \\\\ \\hline 150-\\text{day Libor} &amp; 4.55\\% \\\\ \\hline 240-\\text{day Libor} &amp; 5.20\\% \\\\ \\hline 330-\\text{day Libor} &amp; 5.85\\% \\end{array} $$<\/p>\r\n<p>The value of the equity swap to the fixed-rate payer is closest to:<\/p>\r\n<ol type=\"A\">\r\n\t<li>$301,800.<\/li>\r\n\t<li>$23,980.<\/li>\r\n\t<li>$223,980.<\/li>\r\n<\/ol>\r\n<h4>Solution<\/h4>\r\n<p><strong>The correct answer is C.<\/strong><\/p>\r\n<p>The first step is to calculate the discount factors:<\/p>\r\n<p>$$ \\begin{align*} D_{60} &amp;=\\frac{1}{1+\\left(0.0390\\times\\frac{60}{360}\\right)}=0.9935 \\\\ D_{150} &amp;=\\frac{1}{1+\\left(0.0455\\times\\frac{150}{360}\\right)}=0.9814 \\\\ D_{240} &amp;=\\frac{1}{1+\\left(0.0520\\times\\frac{240}{360}\\right)}=0.9665 \\\\ D_{330} &amp;=\\frac{1}{1+\\left(0.0585\\times\\frac{330}{360}\\right)}=0.9491 \\end{align*} $$<\/p>\r\n<p>The value of the fixed-rate bond is then calculated as:<\/p>\r\n<p>$$ \\begin{align*} P(\\text {fixed}) &amp; =\\frac{\\left(4\\%\\right)}{4} \\times(0.9935+0.9814+0.9665+0.9491)+1\\times0.9491 \\\\ &amp; = 0.98801 \\end{align*} $$<\/p>\r\n<p>The value of the index investment :<\/p>\r\n<p>$$ P(\\text{Index}) =\\frac {2200}{2000} = 1.1 $$<\/p>\r\n<p>The swap value to the fixed-rate payer is, therefore:<\/p>\r\n<p>$$ \\begin{align*} V &amp; = [P(\\text{index}) -P(\\text{fixed})]\\times \\text{notional principal} \\\\ &amp; = (1.1-0.98801)\\times $2 \\text{ million} \\\\ &amp; =$223,980 \\end{align*} $$<\/p>\r\n<\/blockquote>\r\n<p>Reading 33: Pricing and Valuation of Forward Commitments<\/p>\r\n<p><em>LOS 33 (g) Describe how equity swaps are priced, and calculate and interpret their no-arbitrage value.<\/em><\/p>\r\n<p><\/p><!-- \/wp:post-content -->","protected":false},"excerpt":{"rendered":"<p>Equity Swaps An equity swap is an OTC derivative contract in which two parties agree to exchange a series of cash flows. In this arrangement, one party pays a variable series determined by equity. The other party pays a variable&#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-23576","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 v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Pricing and Valuing Equity Swap Contracts - CFA, FRM, and Actuarial Exams Study Notes<\/title>\n<meta name=\"description\" content=\"Learn about equity swaps, their types, pricing mechanisms using fixed swap rates, and valuation techniques.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/pricing-and-valuing-equity-swap-contracts\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Pricing and Valuing Equity Swap Contracts - 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