{"id":3478,"date":"2019-09-06T12:00:00","date_gmt":"2019-09-06T12:00:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=3478"},"modified":"2026-02-02T10:04:55","modified_gmt":"2026-02-02T10:04:55","slug":"bond-hpr-duration-investment-horizon","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/fixed-income\/bond-hpr-duration-investment-horizon\/","title":{"rendered":"Bond\u2019s Holding Period Return, Duration, and Investment Horizon"},"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\": \"CFA\u00ae Level I Fixed Income video lesson from AnalystPrep covering Understanding Fixed-Income Risk and Return (Module 5). This lecture explains the sources of return for fixed-rate bonds, Macaulay, modified, and effective duration, key rate duration, and how maturity, coupon, and yield level affect interest rate risk. It also covers portfolio duration, money duration and PVBP, convexity (approximate vs effective), estimating price changes using duration and convexity, yield volatility, holding period return and horizon effects, credit spread and liquidity impacts, and empirical vs analytical duration.\",\n  \"uploadDate\": \"2022-06-01\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/ys7hMfL_EIs\/hqdefault.jpg\",\n  \"contentUrl\": \"https:\/\/www.youtube.com\/watch?v=ys7hMfL_EIs\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/ys7hMfL_EIs\",\n  \"duration\": \"PT1H1M0S\"\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"@id\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/fixed-income\/bond-hpr-duration-investment-horizon\/#qapage-question-1\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"@id\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/fixed-income\/bond-hpr-duration-investment-horizon\/#question-1\",\n    \"name\": \"What is the duration gap when the investment horizon exceeds the Macaulay duration?\",\n    \"text\": \"Assume that an investor plans to retire in 10 years. The investor buys a newly issued, 10-year, 8% annual coupon payment bond. The bond\u2019s Macaulay duration is 8.6 years. What is the duration gap at the time of purchase?\\nA. \u22121.525\\nB. \u22121.425\\nC. \u22121.400\",\n    \"answerCount\": 1,\n    \"author\": {\n      \"@type\": \"Organization\",\n      \"name\": \"AnalystPrep\"\n    },\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"@id\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/fixed-income\/bond-hpr-duration-investment-horizon\/#answer-1\",\n      \"text\": \"C. \u22121.400. The duration gap equals Macaulay duration minus the investment horizon: 8.6 \u2212 10 = \u22121.400.\",\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\/ys7hMfL_EIs?rel=0&#038;modestbranding=1&#038;playsinline=1&#038;vq=hd1080\"\n  title=\"YouTube video player\"\n  frameborder=\"0\"\n  allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\"\n  allowfullscreen>\n<\/iframe>\n\n\n<p>\u00a0<\/p>\n<p>Although short-term interest rate risk is a concern to some investors, other investors have a long-term horizon. Day-to-day changes in bond prices cause unrealized capital gains and losses. A long-term investor is concerned mostly with the total return over the investment horizon. The investor considers both coupon reinvestment risk and market price risk in case the bond needs to be sold before maturity.<\/p>\n<p>The buy-and-hold investor has a higher total return if interest rates rise and a lower total return if rates fall. When interest rates rise, duration measures the immediate drop in value or price. Thereafter, as time goes by, the bond price is \u201cpulled to par.\u201d At some point in the bond&#8217;s lifetime, those two effects offset each other, and the gain on reinvested coupons is equal to the loss on the sale of the bond. That point is the Macaulay duration statistic.<\/p>\n<h2><strong>Duration Gap<\/strong><\/h2>\n<p>The duration gap is the difference between the Macaulay duration and the investment horizon. Mathematically:<\/p>\n<p>$$\\text{Duration gap = MacDur \u2013 Investment quad horizon}$$<\/p>\n<ul>\n<li>when the investment horizon is greater than the Macaulay duration of a bond, coupon reinvestment risk dominates market price risk. The investor\u2019s risk is to lower interest rates. The duration gap is negative;<\/li>\n<li>when the investment horizon is equal to the Macaulay duration of a bond, coupon reinvestment risk offsets market price risk. As such, the investor is hedged against interest rate risk, and the duration gap is zero;<\/li>\n<li>when the investment horizon is less than the Macaulay duration of the bond, market price risk dominates coupon reinvestment risk. The investor\u2019s risk is to higher interest rates, and the duration gap is positive.<\/li>\n<\/ul>\n<blockquote>\n<h2><strong>Question<\/strong><\/h2>\n<p>Assume that an investor plans to retire in 10 years. The investor buys a newly issued, 10-year, 8% annual coupon payment bond. Macaulay duration is 8.6 years. What is the duration gap at the time of purchase?<\/p>\n<ol style=\"list-style-type: upper-alpha;\">\n<li data-tadv-p=\"keep\">-1.525<\/li>\n<li data-tadv-p=\"keep\">-1.425<\/li>\n<li data-tadv-p=\"keep\">-1.400<\/li>\n<\/ol>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is <strong>C<\/strong>.<\/p>\n<p>Duration gap = MacDur \u2013 Investment horizon<\/p>\n<p>= 8.6 \u2013 10 = -1.400<\/p>\n<\/blockquote>","protected":false},"excerpt":{"rendered":"<p>\u00a0 Although short-term interest rate risk is a concern to some investors, other investors have a long-term horizon. Day-to-day changes in bond prices cause unrealized capital gains and losses. A long-term investor is concerned mostly with the total return over&#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-3478","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>Bond HPR and Duration | CFA Level 1 - AnalystPrep<\/title>\n<meta name=\"description\" content=\"Understand how bond holding period return (HPR), duration, and investment horizon impact reinvestment and market price risk.\" \/>\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\/bond-hpr-duration-investment-horizon\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Bond HPR and Duration | CFA Level 1 - 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