{"id":46287,"date":"2023-09-06T13:45:34","date_gmt":"2023-09-06T13:45:34","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=46287"},"modified":"2026-03-10T19:28:21","modified_gmt":"2026-03-10T19:28:21","slug":"spot-curve-par-curve-and-forward-curve","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/fixed-income\/spot-curve-par-curve-and-forward-curve\/","title":{"rendered":"Spot Curve, Par curve and Forward Curve"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"The Term Structure of Interest Rates: Spot, Par, and Forward Curves (2025 CFA\u00ae Level I Exam \u2013 Fixed Income \u2013 Module 9)\",\n  \"description\": \"This lesson covers the term structure of interest rates for the 2025 CFA\u00ae Level I Fixed Income curriculum. It explains spot rates and the spot curve and demonstrates how to price bonds using spot rates. The video also defines par and forward rates, shows how to calculate par rates and forward rates from spot rates and vice versa, and compares the spot curve, par curve, and forward curve with exam-focused examples.\",\n  \"uploadDate\": \"2023-11-23T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/6C48PLyxNaU\/default.jpg\",\n  \"contentUrl\": \"https:\/\/youtu.be\/6C48PLyxNaU\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/6C48PLyxNaU\",\n  \"duration\": \"PT23M19S\"\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"ImageObject\",\n  \"url\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/09\/Img_2-12.jpg\",\n  \"caption\": \"Image showing Spot Curve, Par Curve & Forward Curve\",\n  \"width\": 1590,\n  \"height\": 1058,\n  \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\n  \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\n  \"creditText\": \"AnalystPrep Design Team\",\n  \"creator\": {\n    \"@type\": \"Organization\",\n    \"name\": \"AnalystPrep\"\n  }\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"When the spot curve is upward-sloping, how do the par rates typically compare to the spot rates?\",\n    \"text\": \"When the spot curve is upward-sloping, how do the par rates typically compare to the spot rates?\",\n    \"answerCount\": 1,\n    \"upvoteCount\": 0,\n    \"dateCreated\": \"2025-12-16T00:00:00+00:00\",\n    \"author\": {\n      \"@type\": \"Organization\",\n      \"name\": \"AnalystPrep\"\n    },\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is C. When the spot curve is upward-sloping, par rates tend to be close to, but slightly below, the corresponding spot rates because par rates are averages of spot rates over the life of the bond.\",\n      \"dateCreated\": \"2025-12-16T00:00:00+00:00\",\n      \"upvoteCount\": 0,\n      \"url\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/fixed-income\/spot-curve-par-curve-and-forward-curve\/\",\n      \"author\": {\n        \"@type\": \"Organization\",\n        \"name\": \"AnalystPrep\"\n      }\n    }\n  }\n}\n<\/script>\n\n\n\n<iframe loading=\"lazy\"\n  width=\"611\"\n  height=\"344\"\n  src=\"https:\/\/www.youtube.com\/embed\/6C48PLyxNaU\"\n  title=\"YouTube video player\"\n  frameborder=\"0\"\n  allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\"\n  referrerpolicy=\"strict-origin-when-cross-origin\"\n  allowfullscreen>\n<\/iframe>\n\n\n\n<p>Yields-to-maturity for zero-coupon government bonds could be analyzed for a full range of maturities called the government bond spot curve (or zero curves). Government spot rates are assumed to be risk-free.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Spot Curve<\/h3>\n\n\n\n<p>The spot curve is upward-sloping and flattens for longer times-to-maturity. As a result, longer-term government bonds usually have higher yields than shorter-term bonds. The hypothetical spot curve is ideal for analyzing the maturity structure because it meets the \u201call other things being equal\u201d assumption. The spot curve can also be inverted. This implies that one-year rates are expected to be lower in the future.<\/p>\n\n\n\n<div style=\"margin:24px 0;\">\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\"\n     target=\"_blank\"\n     rel=\"noopener noreferrer\"\n     style=\"\n       display:block;\n       width:100%;\n       text-align:center;\n       padding:16px 20px;\n       border:2px solid #2f5bff;\n       border-radius:50px;\n       background-color:#f5f7ff;\n       color:#2f5bff;\n       font-size:18px;\n       font-weight:500;\n       text-decoration:none;\n       line-height:1.3;\n     \">\n     Practice spot, par, and forward curve questions in our free trial.\n  <\/a>\n<\/div>\n\n\n<h3 id=\"par-curve\">Par Curve<\/h3>\n<p>The par curve differs from the spot curve because it is a sequence of yields-to-maturity, and each bond is priced at a par value. The par curve is obtained from the spot curve. All bonds on the par curve are supposed to have the same credit risk, periodicity, currency, liquidity, tax status, and annual yields. Between coupon payment dates, the flat price (not full price) is equal to the par value.<\/p>\n<h3 id=\"forward-curve\">Forward Curve<\/h3>\n<p>The forward curve is a series of forward rates, each of which has the same time frame.<\/p>\n<p>The following diagram demonstrates a comparison of the Spot curve, Par Curve, and Forward Curve for the Canadian Government Bonds.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-52753 size-full\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/09\/Img_2-12.jpg\" alt=\"Image showing Spot Curve, Par Curve &amp; Forward Curve\" width=\"1590\" height=\"1058\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/09\/Img_2-12.jpg 1590w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/09\/Img_2-12-300x200.jpg 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/09\/Img_2-12-1024x681.jpg 1024w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/09\/Img_2-12-768x511.jpg 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/09\/Img_2-12-1536x1022.jpg 1536w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2023\/09\/Img_2-12-400x266.jpg 400w\" sizes=\"auto, (max-width: 1590px) 100vw, 1590px\" \/><\/p>\n<p>We can deduce the following from the figure above:<\/p>\n<ol type=\"1\">\n<li>The spot rates exhibit a positive trend, leading to an upward-sloping spot curve.<\/li>\n<li>The spot and par curves closely align; however, par rates are a bit lower than spot rates. This difference becomes more pronounced for longer maturities.<\/li>\n<li>Forward rates are greater than both spot and par rates.<\/li>\n<\/ol>\n<p>These insights are rooted in the inherent relationships between curve patterns. When the spot curve trends upwards, par rates tend to be close to, but slightly beneath, spot rates, especially towards the long end of the curve. This is attributed to the influence of lower short-term spot rates, which increase the bond prices, especially for bonds with longer-term maturities. This increase, in turn, results in reduced par rates when calculations are based on a price equivalent to 100% of the par value.<\/p>\n<p>The following table summarizes the relationship between spot, par, and forward curves.<\/p>\n<p>$$<br \/>\\begin{array}{l|c|c}<br \/>\\textbf{Spot Curve Shape} &amp; \\textbf{Par Curve} &amp; \\textbf{Forward Curve} \\\\<br \/>\\hline<br \/>\\text{Upward Sloping} &amp; \\text{Below spot curve} &amp; \\text{Above spot curve} \\\\<br \/>\\hline<br \/>\\text{Flat} &amp; \\text{Equal to spot curve} &amp; \\text{Equal to spot curve} \\\\<br \/>\\hline<br \/>\\text{Downward Sloping (Inverted)} &amp; \\text{Above spot curve} &amp; \\text{Below spot curve} \\\\<br \/>\\end{array}<br \/>$$<\/p>\n<blockquote>\n<h3 id=\"question\">Question<\/h3>\n<p>When the spot curve is upward-sloping, how do the par rates typically compare to the spot rates?<\/p>\n<ol style=\"list-style-type: upper-alpha; text-align: left;\">\n<li>Par rates are above spot rates.<\/li>\n<li>Par rates are equal to spot rates.<\/li>\n<li>Par rates are below spot rates.<\/li>\n<\/ol>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is<strong> C<\/strong>.<\/p>\n<p>When the spot curve is upward-sloping, par rates tend to be close to, but slightly beneath, spot rates.<\/p>\n<p><strong>A is incorrect<\/strong>: Par rates are not typically above spot rates when the spot curve is upward-sloping.<\/p>\n<p><strong>B is incorrect<\/strong>: Par rates are not typically equal to spot rates; they are slightly below.<\/p>\n<\/blockquote>\n\n\n<div style=\"text-align:center;margin:50px 0 30px;\">\n\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\"\n     target=\"_blank\"\n     rel=\"noopener noreferrer\"\n     style=\"\n       display:inline-block;\n       padding:14px 34px;\n       background:linear-gradient(135deg,#4a74d1,#3b66c4);\n       color:#ffffff;\n       font-size:18px;\n       font-weight:600;\n       text-decoration:none;\n       border-radius:50px;\n       box-shadow:0 6px 18px rgba(59,102,196,0.25);\n     \">\n     Start Free Trial\n  <\/a>\n\n  <p style=\"\n       margin:18px auto 0;\n       max-width:620px;\n       font-size:16px;\n       line-height:1.6;\n       color:#333333;\n     \">\n     Master term structure concepts including spot rates, par yields, and forward rates with CFA Level I exam-style practice questions.\n  <\/p>\n\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Yields-to-maturity for zero-coupon government bonds could be analyzed for a full range of maturities called the government bond spot curve (or zero curves). Government spot rates are assumed to be risk-free. Spot Curve The spot curve is upward-sloping and flattens&#8230;<\/p>\n","protected":false},"author":12,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[9],"tags":[],"class_list":["post-46287","post","type-post","status-publish","format-standard","hentry","category-fixed-income","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>Spot Curve, Par Curve, and Forward Curve | CFA Level 1<\/title>\n<meta name=\"description\" content=\"The spot curve, par curve, and forward curve represent key yield relationships in fixed-income analysis. 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