{"id":46395,"date":"2023-09-08T16:46:19","date_gmt":"2023-09-08T16:46:19","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=46395"},"modified":"2026-03-18T06:42:16","modified_gmt":"2026-03-18T06:42:16","slug":"relationship-among-a-bonds-holding-period-macaulay-duration-and-investment-horizon","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/fixed-income\/relationship-among-a-bonds-holding-period-macaulay-duration-and-investment-horizon\/","title":{"rendered":"Relationship among a Bond\u2019s Holding Period, Macaulay Duration, and Investment Horizon"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Interest Rate Risk and Return (2025 CFA\u00ae Level I Exam \u2013 Fixed Income \u2013 Learning Module 10)\",\n  \"description\": \"This CFA\u00ae Level I Fixed Income lesson explains Interest Rate Risk and Return with a clear, exam-focused approach. The video covers the sources of bond returns, reinvestment risk versus price (market) risk, and how these risks interact over different investment horizons. You\u2019ll learn Macaulay duration, duration\u2013horizon alignment (immunization), and how to calculate and interpret horizon and holding-period yields, with practical calculator tips and Excel-style intuition designed to mirror CFA Level I exam questions.\",\n  \"uploadDate\": \"2023-11-25\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/NMlnM5vQGh8\/hqdefault.jpg\",\n  \"contentUrl\": \"https:\/\/www.youtube.com\/watch?v=NMlnM5vQGh8\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/NMlnM5vQGh8\",\n  \"duration\": \"PT35M42S\"\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\": \"What is the primary risk for a bond when its Macaulay duration exceeds the investment horizon?\",\n    \"text\": \"Which of the following statements about a bond with a Macaulay duration higher than the investment horizon is the most accurate?\\n\\nA. The bond predominantly faces reinvestment risk.\\nB. The bond is primarily exposed to price risk.\\nC. The bond is nearly hedged against interest rate risk.\",\n    \"answerCount\": 3,\n    \"suggestedAnswer\": [\n      {\n        \"@type\": \"Answer\",\n        \"text\": \"A. The bond predominantly faces reinvestment risk.\"\n      },\n      {\n        \"@type\": \"Answer\",\n        \"text\": \"B. The bond is primarily exposed to price risk.\"\n      },\n      {\n        \"@type\": \"Answer\",\n        \"text\": \"C. The bond is nearly hedged against interest rate risk.\"\n      }\n    ],\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"B. The bond is primarily exposed to price risk.\",\n      \"commentary\": \"When a bond\u2019s Macaulay duration is greater than the investment horizon, the bond is more sensitive to changes in interest rates before the investor exits the position. As a result, price risk dominates, particularly the risk of capital losses if interest rates rise. Reinvestment risk is dominant when the investment horizon exceeds the Macaulay duration, while interest rate risk is minimized only when the horizon equals the duration.\",\n      \"url\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/fixed-income\/relationship-among-a-bonds-holding-period-macaulay-duration-and-investment-horizon\/\"\n    },\n    \"author\": {\n      \"@type\": \"Organization\",\n      \"name\": \"AnalystPrep\"\n    }\n  }\n}\n<\/script>\n\n\n\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/NMlnM5vQGh8?si=aoswqvFQc9UiRw5G\" 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<h2 class=\"wp-block-heading\"><strong>Holding Period Return (Horizon Yield)<\/strong><\/h2>\n\n\n\n<p>This represents the total return an investor anticipates from holding a bond over a specific duration. It&#8217;s influenced by the coupon payments received and any change in the bond&#8217;s price due to interest rate movements.<\/p>\n\n\n\n<p>Formula:<\/p>\n\n\n\n<p>\\[r = \\left( \\frac{FV + F}{PV} \\right)^{\\frac{1}{T}} &#8211; 1\\]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\\(r =\\) Realized rate of return or Horizon Yield.<\/li>\n\n\n\n<li>\\(FV =\\) Future value of the reinvested coupons.<\/li>\n\n\n\n<li>\\(F =\\) Face value of the bond (often considered as 100).<\/li>\n\n\n\n<li>\\(PV =\\) Present value or the bond&#8217;s current price.<\/li>\n\n\n\n<li>\\(T\\) = Investment horizon.<\/li>\n<\/ul>\n\n\n\n<p>The previous learning objective provided an example of calculating the horizon yield.<\/p>\n\n\n\n<div style=\"text-align:center; margin: 25px 0;\">\n  <a href=\"https:\/\/analystprep.com\" target=\"_blank\" style=\"display:inline-flex; align-items:center; justify-content:center; padding:10px 18px; border:2px solid #1a73e8; border-radius:999px; color:#1a73e8; text-decoration:none; font-weight:500; background-color:#f5f9ff; white-space:nowrap;\">\n    Master Macaulay duration with CFA Level I practice\n  <\/a>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Macaulay Duration<\/strong><\/h2>\n\n\n\n<p>Introduced by Frederick Macaulay in 1938, the Macaulay duration provides a measure of the weighted average time until a bond&#8217;s cash flows are received. It serves as an indicator of the bond&#8217;s price sensitivity to interest rate changes. When the investment horizon matches the Macaulay duration of a bond, the bond is nearly hedged against interest rate risk. Any loss from price risk due to rising rates is approximately offset by gains from reinvestment risk and vice versa. We will delve deeper into the Macaulay Duration on the next learning objective.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Investment Horizon<\/strong><\/h2>\n\n\n\n<p>This is the period an investor plans to hold onto a bond. The relationship between the investment horizon and the Macaulay duration determines the bond&#8217;s dominant source of interest rate risk:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Investment Horizon &gt; Macaulay Duration<\/strong>: The bond faces a dominant risk from reinvestment, arising due to the reinvestment of coupons, possibly at a less favorable rate.<\/li>\n\n\n\n<li><strong>Investment Horizon &lt; Macaulay Duration<\/strong>: Price risk is the prevailing concern. The bond&#8217;s price might be adversely affected by rising interest rates.<\/li>\n\n\n\n<li><strong>Investment Horizon = Macaulay Duration<\/strong>: The bond is nearly immune to interest rate risk. Here, price risk and reinvestment risk balance out.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Duration Gap<\/strong><\/h2>\n\n\n\n<p>This represents the difference between a bond&#8217;s Macaulay duration and the investor&#8217;s investment horizon. Duration&nbsp;gap=Macaulay&nbsp;duration\u2212Investment&nbsp;horizon<\/p>\n\n\n\n<p>A negative duration gap indicates that the bond&#8217;s Macaulay duration is lower than the investment horizon of the investor. In this scenario, the primary concern is reinvestment risk, predominantly arising due to falling interest rates. On the other hand, a positive duration gap suggests that the bond&#8217;s Macaulay duration is higher than the investor&#8217;s investment horizon. Here, the main risk stems from potential price fluctuations, mainly driven by increasing interest rates.<\/p>\n\n\n\n<p>Overall, the duration gap helps in identifying the primary source of interest rate risk a bond faces, be it from reinvestment or price changes.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<h3 class=\"wp-block-heading\"><strong>Question<\/strong><\/h3>\n\n\n\n<p>Which of the following statements about a bond with a Macaulay duration higher than the investment horizon is <em>the most<\/em> accurate?<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>The bond predominantly faces reinvestment risk.<\/li>\n\n\n\n<li>The bond is primarily exposed to price risk.<\/li>\n\n\n\n<li>The bond is nearly hedged against interest rate risk.<\/li>\n<\/ol>\n\n\n\n<p><strong>Solution<\/strong><\/p>\n\n\n\n<p>The correct answer is<strong> B<\/strong>.<\/p>\n\n\n\n<p>When the Macaulay duration of a bond is higher than the investment horizon, the bond is primarily exposed to price risk, especially from rising interest rates.<\/p>\n\n\n\n<p><strong>A is incorrect<\/strong>: This would be the case when the investment horizon is higher than the Macaulay duration.<\/p>\n\n\n\n<p><strong>C is incorrect<\/strong>: The bond is nearly hedged against interest rate risk when the investment horizon matches the Macaulay duration<\/p>\n<\/blockquote>\n\n\n\n<div class=\"wp-block-group is-nowrap is-layout-flex wp-container-core-group-is-layout-ad2f72ca wp-block-group-is-layout-flex\"><\/div>\n\n\n\n<div style=\"text-align:center; margin: 40px 0;\">\n  <a href=\"https:\/\/analystprep.com\" target=\"_blank\" style=\"display:inline-flex; align-items:center; justify-content:center; padding:12px 20px; border-radius:999px; background-color:#1a73e8; color:#ffffff; text-decoration:none; font-weight:600;\">\n    Start Free Trial \u2192\n  <\/a>\n  <p style=\"font-size:15px; margin-top:12px; color:#555;\">\n    Practice duration, interest rate risk, and bond sensitivity with exam-style questions and clear explanations.\n  <\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Holding Period Return (Horizon Yield) This represents the total return an investor anticipates from holding a bond over a specific duration. It&#8217;s influenced by the coupon payments received and any change in the bond&#8217;s price due to interest rate movements&#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-46395","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 Holding Period, Duration &amp; Investment Horizon | CFA<\/title>\n<meta name=\"description\" content=\"A bond\u2019s Macaulay duration shorter than an investor&#039;s horizon creates a negative duration gap, affecting interest rate risk and investment strategy.\" \/>\n<meta name=\"robots\" content=\"index, follow, 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