{"id":3428,"date":"2019-09-06T12:00:00","date_gmt":"2019-09-06T12:00:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=3428"},"modified":"2026-04-02T14:37:22","modified_gmt":"2026-04-02T14:37:22","slug":"portfolio-duration-limitations","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/fixed-income\/portfolio-duration-limitations\/","title":{"rendered":"Portfolio Duration and its Limitations"},"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\": \"When using the weighted average of time to receipt of the aggregate cash flows method, which values are used to calculate the weights?\",\n    \"text\": \"When using the weighted average of time to receipt of the aggregate cash flows method (method 1), which values are used to calculate the weights?\",\n    \"answerCount\": 1,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The weights are calculated using the par values of the bonds. Under method 1, par values are used to compute the weights for the aggregate cash flow yield before calculating Macaulay duration and modified duration.\",\n      \"dateCreated\": \"2025-12-19\",\n      \"upvoteCount\": 0\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>Like equities, bonds are typically held in a portfolio. Therefore, bond portfolio managers need to measure the whole portfolio duration.<\/p>\n\n\n\n<p>There are two methods for calculating the duration of a bond portfolio:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>the weighted average of time to receipt of the aggregate cash flows; and<\/li>\n\n\n\n<li>the weighted average of the individual bond durations comprising the portfolio.<\/li>\n<\/ul>\n\n\n\n<p>The first method is the theoretically correct approach which is, nevertheless, practically hard to implement. The second method is commonly used by fixed-income portfolio managers but has its own limitations.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Portfolio Duration<\/strong><\/h2>\n\n\n\n<p>Assume that an investor holds the following portfolio of two zero-coupon bonds.<\/p>\n\n\n\n<p>$$<br>\\begin{array}{c|c|c|c|c|c|c|c|c}<br>\\textbf{Bond} &amp; \\textbf{Maturity} &amp; \\textbf{Price} &amp; \\textbf{Yield} &amp; \\textbf{Mac. Dur} &amp; \\textbf{Mod. Dur} &amp; \\textbf{Par Value} &amp; \\textbf{Market Value} &amp; \\textbf{Weight} \\\\ \\hline<br>\\text{X} &amp; \\text{1 year} &amp; \\text{98.00} &amp; \\text{2.0408%} &amp; \\text{1.000} &amp; \\text{0.980} &amp; \\text{\\$1,000,000} &amp; \\text{\\$980,000} &amp; \\text{16.81%} \\\\<br>\\text{Y} &amp; \\text{2 years} &amp; \\text{97.00} &amp; \\text{1.5346%} &amp; \\text{2.000} &amp; \\text{0.984} &amp; \\text{\\$5,000,000} &amp; \\text{\\$4,850,000} &amp; \\text{83.19%} \\\\<br>\\end{array}<br>$$<\/p>\n\n\n\n<div style=\"margin: 30px 0;\">\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"\n     style=\"display:block;\n            width:100%;\n            padding:16px 20px;\n            border:2px solid #2f6fed;\n            border-radius:999px;\n            background:#f2f4f8;\n            color:#2f6fed;\n            font-size:16px;\n            font-weight:500;\n            text-decoration:none;\n            text-align:center;\n            line-height:1.2;\">\n    Access our CFA free trial for duration and interest rate risk practice\n  <\/a>\n<\/div>\n\n\n<h4><strong>Portfolio Duration Using Method 1: The Weighted Average of Time to Receipt of the Aggregate Cash Flows<\/strong><\/h4>\n<p>The prices are per 100 of par value. The yields-to-maturity are effective annual rates. The total market value for the portfolio is 5,830,000. The portfolio is unevenly weighted in terms of market value between the 2 bonds (with weights of 16.81% and 83.19% for X and Y, respectively). Assume the yield per period to be 12.366%.<\/p>\n<p>The first approach views the portfolio as a series of aggregated cash flows, in which case the aggregate cash flow yield is 1.5811% (the solution to the following equation).<\/p>\n<p>$$5,830,000=\\frac{1,000,000}{(1+r)^1} +\\frac{5,000,000}{(1+r)^2}; \\quad r = 1.5811\\%$$<\/p>\n<p>There are just 2 future cash flows in the portfolio, which are the redemption of the principal of the 2 zero-coupon bonds. However, in more complex portfolios, a series of coupon and principal payments may occur on various dates.<\/p>\n<p>Using a discount rate of 1.5811%, we can, therefore, find the portfolio\u2019s Macaulay duration as the weighted average of time to receipt of aggregated cash flow.<\/p>\n<p>$$MacDur=\\frac{\\frac{1\u00d71,000,000}{1.015811^1} +\\frac{2\u00d75,000,000}{1.015811^2}}{\\frac{1,000,000}{1.015811^1}+\\frac{5,000,000}{1.015811^2 }}=\\frac{8,810,040}{4,850,000}=1.8311$$<\/p>\n<p>The modified duration for the portfolio is 1.8026<\/p>\n<p>$$ModDur=\\frac{1.8165}{1+0.12366}=1.8026$$<\/p>\n<p>The modified duration indicates the percentage change in the market value given a change in the cash flow yield. For example, if the cash flow yield increases or decreases by 100 bps, the portfolio&#8217;s market value is expected to increase or decrease by about 1.8026%.<\/p>\n<p>Although this approach is theoretically correct, it is difficult to use in practice. To begin with, the cash flow yield is not commonly calculated for bond portfolios. Aside from this, the amount and timing of future cash payments are uncertain. Lastly, interest rate risk is not usually expressed as a change in benchmark interest rates. In practice, the second approach to portfolio duration is commonly used, and there is a stronger likelihood you will have to use the second formula in your CFA level 1 exam.<\/p>\n<h4><strong>Portfolio Duration Using Method 2: The Weighted Average of the Durations of Individual Bonds That Make Up the Portfolio<\/strong><\/h4>\n<p>Using this approach:<\/p>\n<p>$$\\text{Portfolio duration} =w_1 D_1+w_2 D_2+\u22ef+w_n D_n$$<\/p>\n<p>Where:<\/p>\n<p><em>w<sub>i<\/sub><\/em>\u00a0 = market value of bond <em>i<\/em> \/ market value of portfolio<\/p>\n<p><em>D<sub>i<\/sub><\/em>\u00a0 = duration of bond <em>i<\/em><\/p>\n<p><em>n<\/em> = number of bonds in portfolio<\/p>\n<p>Using the above data, we can calculate portfolio duration as follows:<\/p>\n<p>$$\\text{Portfolio Macaulay duration} =0.1681\u00d71+0.8319\u00d72=1.8319$$<\/p>\n<p>$$\\text{Modified duration} =\\frac{1.8319}{1+0.12366}=1.6303$$<\/p>\n<p>One of the advantages of this approach is that it can be an effective measure of interest rate risk. For instance, if the yields-to-maturity on the bonds in the portfolio increase by 100 bps, the estimated drop in the portfolio value is 1.6303%. However, its main disadvantage is that it assumes a parallel shift in the yield curve where all rates change by the same amount in the same direction. As is usually observed, interest rates change in an irregular manner, resulting in a steeper or flatter yield curve.<\/p>\n<blockquote>\n<h3><strong>Question 1<\/strong><\/h3>\n<p>When using the weighted average of time to receipt of the aggregate cash flows method (method 1), you would <em>most likely<\/em> use:<\/p>\n<ol style=\"list-style-type: upper-alpha;\">\n<li data-tadv-p=\"keep\">The price of the bonds calculate the weights.<\/li>\n<li data-tadv-p=\"keep\">The par value of the bonds calculate the weights.<\/li>\n<li data-tadv-p=\"keep\">The market value of the bonds calculate the weights.<\/li>\n<\/ol>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is <strong>B<\/strong>.<\/p>\n<p>According to method 1, you would use the par values of the bonds to come up with the weights used to calculate the aggregated cash flow yield. After that, you would compute the Macaulay duration and finally, the modified duration.<\/p>\n<h3><strong>Question 2<\/strong><\/h3>\n<p>A bond portfolio consists of the following three fixed-rate bonds. Assume annual coupon payments and no accrued interest on the bonds. Prices are per 100 of par value.<\/p>\n<p>$$<br \/>\\begin{array}{c|c|c|c|c|c|c}<br \/>\\textbf{Bond} &amp; \\textbf{Maturity} &amp; \\textbf{Price} &amp; \\textbf{Yield} &amp; \\textbf{Coupon} &amp; \\textbf{Modified Duration} &amp; \\textbf{Market Value} \\\\<br \/>\\hline<br \/>\\text{1} &amp; \\text{6 years} &amp; \\text{85.00} &amp; \\text{4.95%} &amp; \\text{2.00%} &amp; \\text{5.42} &amp; \\text{170,000} \\\\<br \/>\\text{2} &amp; \\text{10 years} &amp; \\text{80.00} &amp; \\text{4.99%} &amp; \\text{2.40%} &amp; \\text{8.44} &amp; \\text{850,000} \\\\<br \/>\\text{3} &amp; \\text{9 years} &amp; \\text{85.78} &amp; \\text{5.00%} &amp; \\text{3.00%} &amp; \\text{7.54} &amp; \\text{180,000} \\\\<br \/>\\end{array}<br \/>$$<\/p>\n<p>The bond portfolio\u2019s modified duration is <em>closest<\/em> to:<\/p>\n<ol style=\"list-style-type: upper-alpha;\">\n<li data-tadv-p=\"keep\">6.55<\/li>\n<li data-tadv-p=\"keep\">7.54<\/li>\n<li data-tadv-p=\"keep\">7.88<\/li>\n<\/ol>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is <strong>C<\/strong>.<\/p>\n<p>The portfolio\u2019s modified duration is closest to 7.62. Portfolio duration is commonly estimated as the market-value-weighted average of the yield durations of the individual bonds in the portfolio.<\/p>\n<p>The total market value of the bond portfolio is 170,000 + 850,000 + 180,000 = 1,200,000.<\/p>\n<p>The portfolio duration is 5.42 \u00d7 (170,000\/1,200,000) + 8.44 \u00d7 (850,000\/1,200,000) + 7.54 \u00d7 (180,000\/1,200,000) = 7.88<\/p>\n<\/blockquote>\n\n\n<div style=\"background:#f2f4f8; border-radius:16px; padding:32px 20px; text-align:center; margin:40px 0;\">\n  \n  <a href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"\n     style=\"display:inline-block;\n            background:#4a74c9;\n            color:#ffffff;\n            font-size:16px;\n            font-weight:600;\n            text-decoration:none;\n            padding:14px 34px;\n            border-radius:999px;\n            margin-bottom:16px;\">\n    Start Free Trial\n  <\/a>\n\n  <p style=\"margin:0 auto; max-width:520px; font-size:16px; line-height:1.6; color:#1f2937;\">\n    Strengthen your understanding of duration limitations, yield curve shifts, and fixed income risk with structured CFA Level I practice.\n  <\/p>\n\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Like equities, bonds are typically held in a portfolio. Therefore, bond portfolio managers need to measure the whole portfolio duration. There are two methods for calculating the duration of a bond portfolio: The first method is the theoretically correct approach&#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-3428","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>Portfolio Duration Limitations | CFA Level 1<\/title>\n<meta name=\"description\" content=\"Discover how to measure portfolio duration, its limitations, and the challenges bond portfolio managers face. 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