{"id":3439,"date":"2019-09-06T12:00:00","date_gmt":"2019-09-06T12:00:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=3439"},"modified":"2026-03-27T13:35:02","modified_gmt":"2026-03-27T13:35:02","slug":"money-duration-pvbp","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/fixed-income\/money-duration-pvbp\/","title":{"rendered":"Money Duration and Price Value of a Basis Point"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Understanding Fixed-Income Risk and Return (2025 Level I CFA\u00ae Exam \u2013 Fixed Income \u2013 Module 5)\",\n  \"description\": \"Explore key concepts in data analysis with this session on measures of central tendency, dispersion, skewness, kurtosis, and correlation. Learn to calculate, interpret, and visualize data effectively for investment and analysis problems. Perfect for mastering quantitative techniques!\",\n  \"uploadDate\": \"2022-06-01T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/ys7hMfL_EIs\/default.jpg\",\n  \"contentUrl\": \"https:\/\/youtu.be\/ys7hMfL_EIs\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/ys7hMfL_EIs\",\n  \"duration\": \"PT1H1S\"\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\": \"A bond has a money duration of 4. By how much will the full price of this bond change after a 0.25% change in yield-to-maturity?\",\n    \"text\": \"A bond has a money duration of 4. By how much will the full price of this bond change after a 0.25% change in yield-to-maturity?\",\n    \"answerCount\": 3,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is A. The approximate change in the bond\u2019s full price is calculated using the money duration formula: \u0394PV \u2248 \u2212(Money Duration \u00d7 \u0394Yield). Substituting the values gives \u22124 \u00d7 0.25% = \u22120.01, indicating an approximate price change of $0.01.\"\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\n<p>The modified duration is a measure of the percentage price change of a bond given a change in its yield-to-maturity. On the other hand, the money duration of a bond is a measure of the price change in units of the currency a bond is denominated. In the United States, the money duration is commonly called \u201cdollar duration.\u201d<\/p>\n\n\n\n<p><strong>Calculating Money Duration<\/strong><\/p>\n\n\n\n<p>The money duration (MoneyDur) is calculated as the annual modified duration times the bond&#8217;s full price (PV<sup>Full<\/sup>), including accrued interest.<\/p>\n\n\n\n<p>$$ MoneyDur = \\text{Annual ModDur} \u00d7 PV^{Full}$$<\/p>\n\n\n\n<p>and<\/p>\n\n\n\n<p>$$ \u0394PV^{Full} \u2248 \\text{-MoneyDur} \u00d7 \u0394Yield$$<\/p>\n\n\n\n<div style=\"text-align:center; background:#f3f5f9; padding:20px 16px; margin:24px 0;\">\n  <div style=\"max-width:760px; margin:0 auto;\">\n    <a href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"\n       style=\"display:inline-flex; align-items:center; justify-content:center; width:100%; padding:12px 32px; border:2px solid #2f6fdd; border-radius:999px; color:#2f6fdd; text-decoration:none; font-size:15.5px; font-weight:500; line-height:1;\">\n      Practice money duration and PVBP concepts with a Free Trial.\n    <\/a>\n  <\/div>\n<\/div>\n\n\n<h4><strong>Example: <\/strong><strong>Money Duration<\/strong><\/h4>\n<p>Assume that an investor holds a $5 million (par value) in a 4.5% bond maturing on March 31, 2015. The bond is priced at 97.250 per 100 of par value to yield 5.250% on a semi-annual basis for settlement on 30 June 2014. The total market value including accrued interest is $4,980,000 or 4.980 per 100 par value. The bond\u2019s annual Macaulay duration is 2.500.<\/p>\n<p>The money duration is equal to the annual modified duration times the full price per 100 of par value:<\/p>\n<p>$$ \\text{MoneyDur} = \\text{Annual ModDur} \u00d7 PV^{Full}$$<\/p>\n<p>$$=\\frac{MacDur}{(1+y)}\u00a0\u00d7 PV^{Full}=\\frac{2.5}{1+\\frac{0.0525}{2}}\u00d7$97.25=$236.90$$<\/p>\n<p>Note: periodicity = 2; hence the reason for the\u00a0\\(1+\\frac{0.0525}{2}\\).<\/p>\n<p>This means that for a 1% in yield, the bond price will lose $239.90.<\/p>\n<h2><strong>Price Value of a Basis Point<\/strong><\/h2>\n<p>Another version of the money duration is the price value of a basis point (PVBP) for the bond. The PVBP estimates the change in full price given a 1 bp change in the yield-to-maturity.<\/p>\n<p>$$PVBP=\\frac{(PV_- )-(PV_+)}{2}$$<\/p>\n<p class=\"Text001\"><span lang=\"EN-US\">PV<sub>&#8211; <\/sub>and PV<sub>+<\/sub>\u00a0represent the bond prices calculated after decreasing and increasing the yield-to-maturity by 1 bp. The PVBP is also called the \u201c<span class=\"Style2AltBaslikChar\">PV01<\/span>\u201d, standing for the \u201c<span class=\"Style2AltBaslikChar\">price<\/span> or <span class=\"Style2AltBaslikChar\">present value<\/span> of 01\u201d, where \u201c01\u201d means 1bp. In the United States, it is commonly called the \u201cDV01\u201d (Dollar value).<\/span><\/p>\n<h4><strong>Example: PVPB<\/strong><\/h4>\n<p>A bond with exactly five years remaining until maturity offers a 4% coupon rate with annual coupons. The bond, with a yield-to-maturity of 6%, is priced at 91.575272 per 100 of par value. Estimate the price value of a basis point for the bond.<\/p>\n<p>Lowering the yield-to-maturity by one basis point to 5.99% results in a bond price of 91.615115:<\/p>\n<p>$$PV_-=\\frac{4}{1.0599^1} +\\frac{4}{1.0599^2} +\\frac{4}{1.0599^3} +\\frac{4}{1.0599^4} +\\frac{100+4}{1.0599^5} =91.615115$$<\/p>\n<p>Increasing the yield-to-maturity by one basis point to 6.01% results in a bond price of 91.535451:<\/p>\n<p>$$PV_+=\\frac{4}{1.0601^1} +\\frac{4}{1.0601^2} +\\frac{4}{1.0601^3} +\\frac{4}{1.0601^4} +\\frac{100+4}{1.0601^5} =91.535451$$<\/p>\n<p>$$PVBP=\\frac{(PV_- )-(PV_+)}{2}=\\frac{91.615115-91.535451}{2}=0.039832$$<\/p>\n<h3><strong>PVPB Using Modified Duration<\/strong><\/h3>\n<p>Alternatively, the PVBP can be derived using modified duration:<\/p>\n<p>$$Approx. \\quad modified \\quad duration = \\frac{PV_&#8211;PV_+}{2\u00d7\u0394yield\u00d7PV_0 }$$<\/p>\n<p>$$=\\frac{91.615115-91.535451}{2\u00d70.0001\u00d791.575272}=4.349646$$<\/p>\n<p>$$PVBP = 4.349646 \u00d7 91.575272 \u00d7 0.0001=0.039832$$<\/p>\n<blockquote>\n<h3><strong>Question<\/strong><\/h3>\n<p>A bond has a money duration of 4. By how much will the full price of this bond change after a 0.25% change in yield-to-maturity?<\/p>\n<ol style=\"list-style-type: upper-alpha;\">\n<li data-tadv-p=\"keep\">$0.01<\/li>\n<li data-tadv-p=\"keep\">$1<\/li>\n<li data-tadv-p=\"keep\">$4<\/li>\n<\/ol>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is <strong>A<\/strong>.<\/p>\n<p>\\(\u0394PV^{Full} \u2248\u00a0\\quad -MoneyDur \u00d7 \u0394Yield\\)<\/p>\n<p>\\(\u2248 \\quad -4 \u00d7 0.25\\% = -0.01\\)<\/p>\n<\/blockquote>\n<div style=\"text-align: center; margin: 30px 0;\"><a style=\"display: inline-block; padding: 12px 24px; border-radius: 9999px; background: #1e5bd8; color: #ffffff; font-weight: bold; text-decoration: none;\" href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"> Start Free Trial \u2192 <\/a>\n<p style=\"margin-top: 12px; font-size: 16px; line-height: 1.5;\">Strengthen your fixed-income skills with CFA exam-style practice on duration, PVBP, and interest-rate risk measurement.<\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>The modified duration is a measure of the percentage price change of a bond given a change in its yield-to-maturity. On the other hand, the money duration of a bond is a measure of the price change in units of&#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-3439","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>Money Duration and PVBP | CFA Level 1 - AnalystPrep<\/title>\n<meta name=\"description\" content=\"The modified duration is a measure of the percentage price change of a bond given a change in its yield to maturity. - CFA Level 1\" \/>\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\/money-duration-pvbp\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Money Duration and PVBP | CFA Level 1 - 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