{"id":36413,"date":"2021-10-22T00:57:33","date_gmt":"2021-10-22T00:57:33","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=36413"},"modified":"2025-12-30T11:34:11","modified_gmt":"2025-12-30T11:34:11","slug":"analytical-duration-and-empirical-duration","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/fixed-income\/analytical-duration-and-empirical-duration\/","title":{"rendered":"Analytical Duration and Empirical Duration"},"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 (2022 Level I CFA\u00ae Exam \u2013 Reading 43)\",\n  \"description\": \"This study session covers fixed income risk and return, focusing on bond pricing, duration, convexity, and the impact of interest rates. Key concepts include sources of return from bonds (coupon payments, reinvestment, and capital gains\/losses), interest rate risk, and how duration helps measure sensitivity to yield changes. It also introduces convexity as a second-order adjustment to price changes and explains the effects of credit spreads and liquidity on bond yields.\",\n  \"uploadDate\": \"2019-02-03T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/rRcQKHgC16c\/maxresdefault.jpg\",\n  \"contentUrl\": \"https:\/\/youtu.be\/rRcQKHgC16c\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/rRcQKHgC16c\",\n  \"duration\": \"PT33M20S\"\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\": \"Which of the following is the most appropriate portfolio where empirical duration is applicable?\",\n    \"text\": \"Question\\nEmpirical duration utilizes statistical and historical data to explain the price-yield relationship for particular bond or bond portfolios, especially in stressed market conditions. Which of the following is the most appropriate portfolio where empirical duration is applicable?\\n\\nA. A portfolio of highly rated corporate bonds all from the same issuer.\\nB. A portfolio of highly rated sovereign bonds, all from the same issuer.\\nC. A portfolio of 30% highly rated sovereign bonds, 40% highly rated corporate bonds, and 30% speculative-grade corporate bonds, all from different issuers.\",\n    \"answerCount\": 1,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is C. Empirical duration is best suited for portfolios that include different bonds from multiple issuers, as it accounts for the effects of yield changes in diverse bonds under stressed market conditions.\"\n    }\n  }\n}\n<\/script>\n\n\n\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/rRcQKHgC16c?si=hxN0Uro49dQOvLNg\" 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<h2><strong>Differences between Analytical Duration and Empirical Duration<\/strong><\/h2>\n<p><strong>Analytical duration<\/strong> refers to estimating duration and convexity using mathematical formulas (as done in the previous learning objectives). Analytical duration approximates the effect of changes in benchmark yields on bond prices by assuming that the government bond yields and spreads are independent and uncorrelated variables.<\/p>\n<p>On the other hand, <strong>empirical duration<\/strong> refers to constructing statistical models using historical data to estimate duration. The statistical data includes diverse factors impacting bonds prices. Since empirical duration gives estimates over a period of time, it is normally used in the decision-making process.<\/p>\n<h2><strong>Choice between Analytical Duration and Empirical Duration<\/strong><\/h2>\n<p>The decision to either use analytical or empirical duration approaches depends on the correlation between benchmark yields and the credit spreads. For instance, when the correlation between benchmark yields and the credit spreads is negative, the empirical duration estimates will be lower since wider credit spreads will partly or fully offset the decrease in government benchmark yields.<\/p>\n<p>As such, for a bond portfolio consisting of only government bonds (from the same issuer), the benchmark yields are the primary determinant of the bond yields. Thus, the outcomes of analytical duration and empirical duration are majorly the same. However, for a bond portfolio consisting of corporate bonds from different issuers, the interaction between benchmark yield changes and credit and liquidity spreads offset each other (especially when the market is stressed), leading to lower empirical duration estimates than analytical duration.<\/p>\n<blockquote>\n<h2><strong>Question<\/strong><\/h2>\n<p>Empirical duration utilizes statistical and historical data to explain the price-yield relationship for particular bond or bond portfolios, especially in stressed market conditions. Which of the following is the <em>most appropriate <\/em>portfolio where empirical duration is applicable?<\/p>\n<p>A portfolio of:<\/p>\n<ol style=\"list-style-type: upper-alpha;\">\n<li>highly rated corporate bonds all from the same issuer.<\/li>\n<li>highly rated sovereign bonds, all from the same issuer.<\/li>\n<li>30% highly rated sovereign bonds, 40% highly rated corporate bonds, and 30% speculative-grade corporate bonds, all from different issuers.<\/li>\n<\/ol>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is <strong>C.<\/strong><\/p>\n<p>Empirical duration is appropriate compared to analytical duration in measuring the effect of yield changes to portfolio value, particularly under stressed market conditions and a bond portfolio consisting of different bonds from different issuers. Given the combination in option C, credit spreads on the high yield bond may be offset by yield changes on the highly-rated corporate and sovereign bonds.<\/p>\n<p><strong>Option A and B are incorrect.\u00a0 <\/strong>The bond portfolios described are of the same type and from the same issuers. Therefore, empirical and analytical duration estimates should be broadly the same.<\/p>\n<\/blockquote>","protected":false},"excerpt":{"rendered":"<p>Differences between Analytical Duration and Empirical Duration Analytical duration refers to estimating duration and convexity using mathematical formulas (as done in the previous learning objectives). Analytical duration approximates the effect of changes in benchmark yields on bond prices by assuming&#8230;<\/p>\n","protected":false},"author":15,"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-36413","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>Analytical &amp; Empirical Duration | CFA Level 1 - AnalystPrep<\/title>\n<meta name=\"description\" content=\"Compare analytical and empirical duration in bond analysis, exploring their calculations, applications, and significance in fixed-income valuation.\" \/>\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\/analytical-duration-and-empirical-duration\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Analytical &amp; Empirical Duration | CFA Level 1 - 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