{"id":1893,"date":"2019-09-27T13:33:00","date_gmt":"2019-09-27T13:33:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=1893"},"modified":"2026-04-29T19:51:02","modified_gmt":"2026-04-29T19:51:02","slug":"matrix-pricing","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/fixed-income\/matrix-pricing\/","title":{"rendered":"Matrix Pricing"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Introduction to Fixed Income Valuation (2025 Level I CFA\u00ae Exam \u2013 Fixed Income \u2013 Module 3)\",\n  \"description\": \"This video covers key concepts in fixed income valuation, including calculating bond prices, understanding relationships between bond characteristics and yields, defining spot rates, and analyzing yield curves. It also explains matrix pricing, accrued interest, forward rates, and yield measures for bonds, floating-rate notes, and money market instruments, along with interpreting yield spreads.\",\n  \"uploadDate\": \"2022-05-21T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/lEbeibhvCzM\/default.jpg\",\n  \"contentUrl\": \"https:\/\/www.youtube.com\/watch?v=lEbeibhvCzM\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/lEbeibhvCzM\",\n  \"duration\": \"PT56M17S\"\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\": \"Matrix pricing allows investors to estimate:\",\n    \"text\": \"Matrix pricing allows investors to estimate:\",\n    \"answerCount\": 3,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is B. Matrix pricing is a price estimation process that uses market discount rates inferred from the quoted prices of similar bonds with comparable maturity, coupon rates, and credit quality. It allows investors to estimate both market discount rates and prices for bonds that are not actively traded or do not have observable market prices.\"\n    }\n  }\n}\n<\/script>\n\n\n\n<iframe loading=\"lazy\" width=\"611\" height=\"344\"\n  src=\"https:\/\/www.youtube.com\/embed\/lEbeibhvCzM\"\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>When fixed-rate bonds are not actively traded, or there is no market price to calculate the rate of return required by investors, it is common practice to estimate the market discount rate and price based on quoted or flat prices of more frequently traded comparable bonds with similar credit quality, maturity, and coupon rates. This estimation process is called <em><strong>matrix pricing<\/strong><\/em>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Illustrative Example<\/strong><\/h2>\n\n\n\n<p>Assume that an analyst needs to value a 4-year, 5% annual coupon payment bond, Bond-K, which is not actively traded. The analyst could find some other bonds with comparable credit quality:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>bond-L: 3-year, 5.5% annual coupon payment bond at a price of 108; and<\/li>\n\n\n\n<li>bond-M: 5-year, 4.5% annual coupon payment bond at a price of 105.<\/li>\n<\/ul>\n\n\n\n<p>Therefore, we start with the following matrix:<\/p>\n\n\n\n<p>$$<br>\\begin{array}{l|c|c|c}<br>\\text{} &amp; \\begin{array}{c} \\text{4.5%-coupon} \\\\ \\text{Bond} \\end{array} &amp; \\begin{array}{c} \\text{5%-coupon} \\\\ \\text{Bond} \\end{array} &amp; \\text{5.5%-coupon Bond} \\\\<br>\\hline<br>\\text{3-year Bond} &amp; \\text{} &amp; \\text{} &amp; \\begin{array}{c} \\text{Price = 108} \\\\ \\text{YTM = ?} \\end{array} \\\\<br>\\hline<br>\\text{4-year Bond} &amp; \\text{} &amp; \\begin{array}{c} \\text{Price = ?} \\\\ \\text{YTM = ?} \\end{array} &amp; \\text{} \\\\<br>\\hline<br>\\text{5-year Bond} &amp; \\begin{array}{c} \\text{Price = 105} \\\\ \\text{YTM = ?} \\end{array} &amp; \\text{} &amp; \\text{} \\\\<br>\\end{array}<br>$$<\/p>\n\n\n\n<div style=\"margin: 30px 0;\">\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"\n     style=\"display:block;\n            width:100%;\n            padding:16px 20px;\n            border:2px solid #2f6fed;\n            border-radius:999px;\n            background:#f2f4f8;\n            color:#2f6fed;\n            font-size:16px;\n            font-weight:500;\n            text-decoration:none;\n            text-align:center;\n            line-height:1.2;\">\n    Access our CFA free trial for bond pricing practice\n  <\/a>\n<\/div>\n\n\n<h3><strong>Step 1: Find the Yield-to-Maturity of Observed Bonds<\/strong><\/h3>\n<p>Using the financial calculator for Bond-L: N=3; PV=-108; PMT=5.5; FV=100; CPT =&gt; I\/Y = 2.6887. The required yield on Bond-L is 2.69%.<\/p>\n<p>For Bond-M: N=5; PV=-105; PMT=4.5; FV=100; CPT =&gt; I\/Y = 3.3959. The required yield on Bond-M is 3.40%.<\/p>\n<p>We now have two more data points in our matrix:<\/p>\n<p>$$<br \/>\\begin{array}{l|c|c|c}<br \/>\\text{} &amp; \\begin{array}{c} \\text{4.5%-coupon} \\\\ \\text{Bond} \\end{array} &amp; \\begin{array}{c} \\text{5%-coupon} \\\\ \\text{Bond} \\end{array} &amp; \\text{5.5%-coupon Bond} \\\\<br \/>\\hline<br \/>\\text{3-year Bond} &amp; \\text{} &amp; \\text{} &amp; \\begin{array}{c} \\text{Price = 108} \\\\ \\text{YTM = 2.69%} \\end{array} \\\\<br \/>\\hline<br \/>\\text{4-year Bond} &amp; \\text{} &amp; \\begin{array}{c} \\text{Price = ?} \\\\ \\text{YTM = ?} \\end{array} &amp; \\text{} \\\\<br \/>\\hline<br \/>\\text{5-year Bond} &amp; \\begin{array}{c} \\text{Price = 105} \\\\ \\text{YTM = 3.4%} \\end{array} &amp; \\text{} &amp; \\text{} \\\\<br \/>\\end{array}<br \/>$$<\/p>\n<h3><strong>Step 2: Find the Yield-to-Maturity of the Non-Actively Traded Bond<\/strong><\/h3>\n<p>The estimated market discount rate for a 4-year bond that has the same credit quality is the average of two required yields:<\/p>\n<p>$$ YTM_{Bond-K} = \\frac{2.69\\% + 3.40\\%}{2} = 3.045\\% $$<\/p>\n<p>We now have the following matrix:<\/p>\n<p>$$<br \/>\\begin{array}{l|c|c|c}<br \/>\\text{} &amp; \\begin{array}{c} \\text{4.5%-coupon} \\\\ \\text{Bond} \\end{array} &amp; \\begin{array}{c} \\text{5%-coupon} \\\\ \\text{Bond} \\end{array} &amp; \\text{5.5%-coupon Bond} \\\\<br \/>\\hline<br \/>\\text{3-year Bond} &amp; \\text{} &amp; \\text{} &amp; \\begin{array}{c} \\text{Price = 108} \\\\ \\text{YTM = 2.69%} \\end{array} \\\\<br \/>\\hline<br \/>\\text{4-year Bond} &amp; \\text{} &amp; \\begin{array}{c} \\text{Price = ?} \\\\ \\text{YTM = 3.045%} \\end{array} &amp; \\text{} \\\\<br \/>\\hline<br \/>\\text{5-year Bond} &amp; \\begin{array}{c} \\text{Price = 105} \\\\ \\text{YTM = 3.4%} \\end{array} &amp; \\text{} &amp; \\text{} \\\\<br \/>\\end{array}<br \/>$$<\/p>\n<h3><strong>Step 3: Find the Price of the Non-Actively Traded Bond<\/strong><\/h3>\n<p>Given an estimated yield-to-maturity of 3.045%, the estimated price of the 4-year 5% illiquid bond is 107.26 per 100 of each par value. To find this value, we need to plug in the following variables into the financial calculator: N=4; I\/Y=3.045; PMT=5; FV=100; CPT =&gt; PV = -107.26<\/p>\n<p>Alternatively, we could use a timeline to find the same value:<\/p>\n<p>$$<br \/>\\begin{array}{l|ccccc}<br \/>\\text{Time Period} &amp; 1 &amp; 2 &amp; 3 &amp; 4\\\\<br \/>\\hline<br \/>\\text{Calculation} &amp; \\frac {\\$5}{{\\left(1+3.045\\%\\right)}^{ 1 } } &amp; \\frac { \\$5 }{ { \\left( 1+3.045\\% \\right) }^{ 2 } } &amp; \\frac { \\$5 }{ { \\left( 1+3.045\\% \\right) }^{ 3 } } &amp; \\frac { \\$105 }{ { \\left( 1+3.045\\% \\right) }^{ 4 } } \\\\<br \/>\\hline<br \/>\\text{Cash Flow} &amp; \\$4.85 &amp; +\\$4.70 &amp; +\\$4.56 &amp; +\\$92.92 &amp; =\\$107.03 \\\\<br \/>\\end{array}<br \/>$$<\/p>\n<h3><strong>Benefits of Matrix Pricing<\/strong><\/h3>\n<p>Matrix pricing is also used during the underwriting process to estimate the required yield spread over the benchmark rate. In this context, the benchmark rate is the yield-to-maturity of a similar government bond. Yield spreads are often stated in terms of basis points (bps). For example, if we have a yield-to-maturity of 3.75% and the comparable government bond yield (or benchmark rate) is 2.5%, the yield-spread will be 1.25% or 125 bps.<\/p>\n<blockquote>\n<h3><strong>Question<\/strong><\/h3>\n<p>Matrix pricing allows investors to estimate:<\/p>\n<ol style=\"list-style-type: upper-alpha;\">\n<li data-tadv-p=\"keep\">The bond coupon rates for bonds that are comparable to government bonds.<\/li>\n<li data-tadv-p=\"keep\">The market discount rates as well as the prices for bonds that are not actively traded.<\/li>\n<li data-tadv-p=\"keep\">The required yield spread as well as prices for bonds that become substantially risky after initial issuance of a bond.<\/li>\n<\/ol>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is <strong>B<\/strong>.<\/p>\n<p>Matrix pricing is a price estimation process that uses market discount rates based on the quoted prices of similar bonds (similar maturity, coupon rates, and credit quality) when a fixed-rate bond is not actively traded or there is no market price.<\/p>\n<\/blockquote>\n\n\n<h2>Why Matrix Pricing Matters in CFA Level I<\/h2>\n\n<p>Matrix pricing is a core CFA Level I Fixed Income concept. Candidates may be tested on estimating bond values using comparable securities, yield spreads, maturity matching, and pricing thinly traded bonds when direct market quotes are unavailable.<\/p>\n\n<p>Build confidence with the <a href=\"https:\/\/analystprep.com\/cfa-level-1\/\" target=\"_blank\">CFA Level I prep course<\/a> featuring guided lessons, practice questions, and full mock exams.<\/p>\n\n\n\n<div style=\"text-align:center; margin:32px 0 10px;\">\n\n<a href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\" style=\"display:inline-flex; align-items:center; justify-content:center; padding:12px 24px; border-radius:9999px; background:#1e5bd8; color:#ffffff; font-weight:700; text-decoration:none;\">\nStart Free Trial \u2192\n<\/a>\n\n<p style=\"margin-top:12px; font-size:16px; line-height:1.5;\">\nStrengthen your fixed-income analysis skills with targeted CFA practice questions.\n<\/p>\n\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>When fixed-rate bonds are not actively traded, or there is no market price to calculate the rate of return required by investors, it is common practice to estimate the market discount rate and price based on quoted or flat prices&#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":[9],"tags":[],"class_list":["post-1893","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 v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Matrix Pricing Explained | CFA Level 1<\/title>\n<meta name=\"description\" content=\"Learn matrix pricing methods to estimate market 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