{"id":46751,"date":"2023-09-22T16:34:19","date_gmt":"2023-09-22T16:34:19","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=46751"},"modified":"2026-08-10T21:17:51","modified_gmt":"2026-08-10T21:17:51","slug":"properties-of-duration","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/fixed-income\/properties-of-duration\/","title":{"rendered":"Properties of Duration"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following bonds is most likely to have the highest duration?\",\n    \"text\": \"Which of the following bonds is most likely to have the highest duration? 1. A bond with a high coupon rate and short time to maturity. 2. A bond with a low coupon rate and long time to maturity. 3. A bond with a high coupon rate and long time to maturity.\",\n    \"answerCount\": 1,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is B. Bonds with lower coupon rates and longer times to maturity typically have higher durations, which indicates greater interest rate risk for such bonds. Option A is incorrect because a high coupon rate leads to a lower duration. Option C is incorrect because, although a long time to maturity increases duration, a high coupon rate decreases it.\"\n    }\n  }\n}\n<\/script>\n\n\n\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/0FIG6azO9Do?si=RDAeXwxpI65WafUq\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n\n\n\n<p class=\"wp-block-paragraph\">The sensitivity of a bond&#8217;s price to changes in interest rates can be captured using Macaulay duration, modified duration, money duration, and the price value of a basis point (PVBP).<\/p>\n\n\n\n<div style=\"margin: 18px 0;\">\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\"\n     target=\"_blank\"\n     rel=\"noopener noreferrer\"\n     style=\"display: block; text-align: center; padding: 14px 18px; border: 2px solid #2F5BFF; border-radius: 18px; color: #ffffff; font-weight: 600; font-size: 16px; text-decoration: none; background-color: #1a73e8;\">\n    Master duration concepts with AnalystPrep\u2019s Free Trial.\n  <\/a>\n<\/div>\n\n\n<h2><!-- [if lt IE 9]>\n    <script src=\"\/\/cdnjs.cloudflare.com\/ajax\/libs\/html5shiv\/3.7.3\/html5shiv-printshiv.min.js\"><\/script>\n  <![endif]--><strong>Relationships Between Bond Features and Duration<\/strong><\/h2>\n<h4><strong>Coupon rate (c))<\/strong><\/h4>\n<p>An increase in the coupon rate leads to a decrease in duration (inverse relationship). Bonds with lower coupon rates have higher durations. This implies more interest rate risk for lower-coupon bonds.<\/p>\n<h4><strong>Yield to Maturity (r)<\/strong><\/h4>\n<p>An increase in the yield to maturity results in a decrease in duration (inverse relationship). A bond with a lower yield-to-maturity will have a higher duration. This is because lower yields emphasize the weight of the bond&#8217;s later cash flows, especially the maturity value.<\/p>\n<h4><strong>Time-to-Maturity<\/strong><\/h4>\n<p>An increase in the time to maturity leads to an increase in duration (direct relationship). Bonds with longer times to maturity will generally have higher durations, suggesting greater interest rate risk. However, a peculiarity arises with long-dated discount bonds: their Macaulay duration can decrease after reaching a certain time-to-maturity.<\/p>\n<h4><strong>Fraction of current coupon period elapsed (t\/T)<\/strong><\/h4>\n<p>An increase in <span class=\"math inline\">\\(\\frac{t}{T}\\)<\/span> leads to a decrease in duration (inverse relationship). As more time passes within a coupon period, the Macaulay duration decreases. However, once a coupon is paid, the duration jumps slightly, creating a &#8220;saw-tooth&#8221; pattern.<\/p>\n<blockquote>\n<h3><strong>Question<\/strong><\/h3>\n<p>Which of the following bonds is most likely to have the highest duration?<\/p>\n<ol style=\"list-style-type: upper-alpha; text-align: left;\">\n<li>A bond with a high coupon rate and short time to maturity.<\/li>\n<li>A bond with a low coupon rate and long time to maturity.<\/li>\n<li>A bond with a high coupon rate and long time to maturity.<\/li>\n<\/ol>\n<p><strong style=\"font-size: revert; color: initial; font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen-Sans, Ubuntu, Cantarell, 'Helvetica Neue', sans-serif;\">Solution<\/strong><\/p>\n<p>The correct answer is<strong> B.<\/strong><\/p>\n<p>Bonds with lower coupon rates and longer times to maturity typically have higher durations. This indicates greater interest rate risk for such bonds.<\/p>\n<p><strong>A is incorrect:<\/strong> A high coupon rate would lead to a lower duration.<\/p>\n<p><strong>C is incorrect:<\/strong> While a long time to maturity increases duration, a high coupon rate decreases it.<\/p>\n<\/blockquote>\n\n\n<div style=\"text-align: center; margin: 30px 0;\">\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\"\n     target=\"_blank\"\n     rel=\"noopener noreferrer\"\n     style=\"display: inline-flex; align-items: center; justify-content: center; padding: 12px 26px; border-radius: 9999px; background: #1e5bd8; color: #ffffff; font-weight: bold; text-decoration: none;\">\n    Start Free Trial \u2192\n  <\/a>\n  <p style=\"margin-top: 12px; font-size: 16px; line-height: 1.5;\">\n    Strengthen your understanding of duration, its properties, bond price sensitivity, interest-rate risk, and fixed-income analysis with CFA Level I study notes, practice questions, and mock exams.\n  <\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>The sensitivity of a bond&#8217;s price to changes in interest rates can be captured using Macaulay duration, modified duration, money duration, and the price value of a basis point (PVBP). Master duration concepts with AnalystPrep\u2019s Free Trial. Relationships Between Bond&#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-46751","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 v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Properties of Duration | CFA Level 1 - AnalystPrep<\/title>\n<meta name=\"description\" content=\"Explore how duration measures bond price sensitivity to interest rates and its relationship with maturity and yield.\" \/>\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\/cfa-level-1-exam\/fixed-income\/properties-of-duration\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Properties of Duration | CFA Level 1 - 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