{"id":3418,"date":"2019-10-08T13:33:00","date_gmt":"2019-10-08T13:33:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=3418"},"modified":"2026-04-20T09:43:40","modified_gmt":"2026-04-20T09:43:40","slug":"key-rate-duration","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/fixed-income\/key-rate-duration\/","title":{"rendered":"Key Rate Duration"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n\n  \"name\": \"Understanding Fixed-Income Risk and Return (2025 Level I CFA\u00ae Exam \u2013 Fixed Income \u2013 Module 5)\",\n\n  \"description\": \"This CFA video lesson covers fixed-income risk and return, detailing return sources for fixed-rate bonds, and key measures like Macaulay, modified, and effective durations. It explains bond sensitivity to yield curve shifts, portfolio duration, money duration, and convexity. Additionally, it explores how credit spreads, liquidity, and term structure affect bond yield and price changes.\",\n\n  \"uploadDate\": \"2022-06-01T00:00:00+00:00\",\n\n  \"thumbnailUrl\": \"https:\/\/analystprep.com\/path-to-thumbnail\/fixed-income-thumbnail.jpg\", \n\n  \"contentUrl\": \"https:\/\/youtu.be\/ys7hMfL_EIs\",\n\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/ys7hMfL_EIs\",\n\n  \"duration\": \"PT1H01M\",\n\n  \"publisher\": {\n    \"@type\": \"Organization\",\n    \"name\": \"AnalystPrep\",\n    \"logo\": {\n      \"@type\": \"ImageObject\",\n      \"url\": \"https:\/\/analystprep.com\/path-to-logo\/logo.jpg\",\n      \"width\": 600,\n      \"height\": 60\n    }\n  }\n}\n<\/script>\n\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\/2019\/10\/54b-d.png\",\n  \"caption\": \"Image showing key rate duration\",\n  \"width\": 974,\n  \"height\": 641,\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<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"The key rate duration formula is similar to which duration measure?\",\n    \"text\": \"The key rate duration formula is similar to which of the following formulas?\\n\\nA. Effective duration.\\nB. Modified duration.\\nC. Macaulay duration.\",\n    \"answerCount\": 1,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Effective duration.\\n\\nThe key rate duration formula is structurally similar to the effective duration formula. The primary difference is that key rate duration measures the sensitivity of a bond\u2019s price to a 1% change in yield at a specific point on the yield curve, using 0.01 in the denominator to reflect that targeted yield shift.\\n\\nModified and Macaulay duration do not isolate yield changes at individual maturities on the yield curve.\",\n      \"dateCreated\": \"2026-01-02\"\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\/ys7hMfL_EIs\"\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<p class=\"Text001\">The effective duration calculates expected changes in price for a bond or portfolio of bonds given a basis point change in yield. This, however, is only valid for parallel shifts in the yield curve. The key rate duration presents an improvement to the effective duration because it gives the expected changes in price when the yield curve shifts in a manner that is not perfectly parallel. In other words, it measures a security\u2019s sensitivity to shifts at \u201ckey\u201d points along the yield curve.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-10082 size-full\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/10\/54b-d.png\" alt=\"Image showing key rate duration\" width=\"974\" height=\"641\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/10\/54b-d.png 974w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/10\/54b-d-300x197.png 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/10\/54b-d-768x505.png 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/10\/54b-d-400x263.png 400w\" sizes=\"auto, (max-width: 974px) 100vw, 974px\" \/><\/p>\n<p>The key rate formula is similar to the effective duration formula, except that it uses 0.01 in the denominator to reflect a 1% (100 basis points) change in the yield at a specific point on the yield curve:<\/p>\n<p>$$ \\text{Key rate duration} =\\frac { { PV }_{ &#8211; }-{ { PV }_{ + } } }{ 2\\times 0.01 \\times { PV }_{ 0 } } $$<\/p>\n<p>Where:<\/p>\n<p>\\({ PV }_{ &#8211; }\\) = the bond price after a 1% decrease in yield<\/p>\n<p>\\({ PV }_{ + }\\) = the bond price after a 1% increase in yield<\/p>\n<p>\\({ PV }_{ 0 }\\) = the original bond price<\/p>\n<div style=\"background-color: #f5f7fa; padding: 20px; text-align: center; margin: 30px 0; border-radius: 8px;\">\n<div style=\"max-width: 620px; margin: 0 auto;\"><a style=\"display: flex; align-items: center; justify-content: center; width: 100%; padding: 10px 20px; border: 2px solid #1a73e8; border-radius: 999px; text-decoration: none; color: #1a73e8; font-size: 15px; font-weight: 600; line-height: 1.4;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"> Practice key rate duration with our Free Trial <\/a><\/div>\n<\/div>\n<h4><strong>Example: Key Rate Duration<\/strong><\/h4>\n<p>A bond is originally priced at $1,000. With a 1% increase in yield for a certain maturity on the yield curve, the bond\u2019s price would decrease to $980. A 1% decrease in the same yield, would occasion a rise of the price to $1,030. Based on the formula above, the key rate duration of the bond would be:<\/p>\n<p>$$ KRD =\\frac { { 1,030 }-{ 980 }}{ 2\\times 0.01 \\times { 1,000 } } =2.5$$<\/p>\n<h2><strong>Why Use Key Rate Duration?<\/strong><\/h2>\n<p class=\"Text001\">A financial analyst may want to know how the price of the callable bond is expected to change if benchmark rates at short maturities shift by a specific number of basis points, but longer maturity benchmark rates remain constant. This case would represent a flattening of the yield curve, given that the yield curve is upward sloping. <span class=\"Style2AltBaslikChar\"><span lang=\"EN-US\">For parallel shifts in the benchmark yield curve, key rate durations could indicate the same interest rate sensitivity as effective duration.\u00a0<\/span><\/span><\/p>\n<h2><strong>Interpretation of Key Rate Duration<\/strong><\/h2>\n<p>Interpreting each key rate duration in isolation can be quite difficult. That is because, in practice, it\u2019s highly unlikely that a single point on the yield curve will exhibit an upwards or downwards shift while all other points remain constant. For this reason, analysts tend to compare key rate durations across the curve.<\/p>\n<blockquote>\n<h3><strong>Question<\/strong><\/h3>\n<p>The key rate duration formula is similar to which of the following formulas?<\/p>\n<ol style=\"list-style-type: upper-alpha;\">\n<li data-tadv-p=\"keep\">Effective duration.<\/li>\n<li data-tadv-p=\"keep\">Modified duration.<\/li>\n<li data-tadv-p=\"keep\">Macaulay duration.<\/li>\n<\/ol>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is <strong>A<\/strong>.<\/p>\n<p>The key rate formula is similar to the effective duration formula, except that it uses 0.01 in the denominator to reflect a 1% change in the yield at a specific point on the yield curve:<\/p>\n<\/blockquote>\n<div style=\"background-color: #f5f7fa; padding: 32px 20px; text-align: center; margin: 40px 0; border-radius: 8px;\"><a style=\"display: inline-block; background-color: #1a73e8; color: #ffffff; text-decoration: none; font-size: 16px; font-weight: 600; padding: 12px 28px; border-radius: 999px; line-height: 1.4;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"> Start Free Trial \u2192 <\/a>\n<p style=\"margin: 14px auto 0; max-width: 620px; font-size: 15px; line-height: 1.6; color: #444444;\">Build CFA Level I readiness with structured study materials, guided learning, and focused practice across fixed income and duration-based risk measures.<\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>The effective duration calculates expected changes in price for a bond or portfolio of bonds given a basis point change in yield. This, however, is only valid for parallel shifts in the yield curve. The key rate duration presents an&#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-3418","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>Key Rate Duration Explained | CFA Level 1<\/title>\n<meta name=\"description\" content=\"Key rate duration measures a bond&#039;s sensitivity to changes in the benchmark yield curve at specific maturity segments, aiding in interest rate risk analysis.\" \/>\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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