{"id":140,"date":"2019-08-17T13:28:00","date_gmt":"2019-08-17T13:28:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=140"},"modified":"2026-02-10T06:28:26","modified_gmt":"2026-02-10T06:28:26","slug":"time-weighted-rate-return","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/time-weighted-rate-return\/","title":{"rendered":"Time-Weighted Rate of Return"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Discounted Cash Flow Applications (2019 Level I CFA\u00ae Exam \u2013 Reading 7)\",\n  \"description\": \"This video lesson covers discounted cash flow applications in quantitative methods. It includes capital budgeting techniques like NPV and IRR, holding period returns, money and time-weighted returns, and short-term financial metrics such as bank discount yield, effective annual yield, and bond equivalent yield, with practical examples for deeper understanding.\",\n  \"uploadDate\": \"2019-06-06T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/lYpi92G13U4\/maxresdefault.jpg\",\n  \"contentUrl\": \"https:\/\/youtu.be\/lYpi92G13U4\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/lYpi92G13U4\",\n  \"duration\": \"PT27M31S\"\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\": \"How do you calculate the annual time-weighted rate of return (TWRR) when there are multiple cash flows?\",\n    \"text\": \"A chartered analyst buys a share of stock at time t = 0 for $50. At t = 1, he purchases an extra share of the same stock for $53. The share gives a dividend of $0.50 per share for the first year and $0.60 per share for the second year. He sells the shares at the end of the second year for $55 per share. Calculate the annual time-weighted rate of return.\",\n    \"answerCount\": 1,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct annual time-weighted rate of return is 5.9%. The calculation involves splitting the investment into two holding periods, computing each period\u2019s holding period return, compounding them to get the total time-weighted return, and then annualizing the result over two years.\",\n      \"dateCreated\": \"2025-12-22\",\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\/lYpi92G13U4\"\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 time-weighted rate of return (TWRR) measures the compound growth rate of an investment portfolio. &nbsp;Unlike the <a href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/using-money-weighted-rate-return-evaluate-performance-investment\/\">money-weighted rate of return<\/a>, TWRR is not sensitive to withdrawals or contributions. Essentially, the time-weighted rate of return is the geometric mean of the <a href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/holding-period-return-example-question\/\">holding period returns <\/a>of the respective sub-periods involved.<\/p>\n\n\n\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Time-weighted Rate of Return Formula<\/strong><\/h2>\n\n\n\n<p>When working out time-weighted measurements, we break down the total investment period into many sub-periods. Each sub-period ends at the point where we have a significant withdrawal or contribution. It could also end after a month, quarterly or even semiannually. We encourage candidates to follow the procedure below when computing TWRR:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Establish the holding period return (HPR) for each sub-period<\/li>\n\n\n\n<li>Add 1 to each HPR<\/li>\n\n\n\n<li>Multiply all the (1 + HPR) terms<\/li>\n\n\n\n<li>Subtract 1 from the final product to get the compounded TWRR<\/li>\n<\/ol>\n\n\n\n<p>Summarily, compounded TWRR = {(1 + HPR<sub>1<\/sub>)*(1 + HPR<sub>2<\/sub>)*(1 + HPR<sub>3<\/sub>)\u2026*(1 + HPR<sub>n-1<\/sub>)*(1 + HPR<sub>n<\/sub>)} &#8211; 1<\/p>\n\n\n\n<p>Finally, annual time-weighted rate of return = (1 + compounded TWRR)<sup> 1\/n<\/sup> &#8211; 1<\/p>\n\n\n\n<p>Where n is the number of years<\/p>\n\n\n\n<!-- TOP CTA \u2013 Full Width Outline Button -->\n<div style=\"margin:24px 0;\">\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\"\n     target=\"_blank\"\n     rel=\"noopener noreferrer\"\n     style=\"\n       display:block;\n       width:100%;\n       padding:14px 0;\n       border:2px solid #3b6fd8;\n       border-radius:50px;\n       font-size:18px;\n       font-weight:500;\n       text-align:center;\n       text-decoration:none;\n       color:#3b6fd8;\n       background-color:#f4f6f9;\n       box-sizing:border-box;\n     \">\n     Practice time weighted return questions with free trial access.\n  <\/a>\n<\/div>\n\n\n\n<h2><strong>Example <\/strong><\/h2>\n<p>An investor purchases a share of stock at t = 0 for $200. At the end of the year (at t = 1) the investor purchases an additional share of the same stock, this time for $220. She then sells both shares at the end of the second year for $230 each. She also received annual dividends of $3 per share at the end of each year. Calculate the annual time-weighted rate of return on her investment.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>First, we break down the 2-year period into two 1-year periods:<\/p>\n<p><em>Holding period 1:<\/em><\/p>\n<p>Beginning value\u00a0\u00a0= 200<\/p>\n<p>Dividends paid\u00a0= 3<\/p>\n<p>Ending value = 220<\/p>\n<p><em>Holding period 2:<\/em><\/p>\n<p>Beginning value = 440 (2 shares * 220)<\/p>\n<p>Dividends paid\u00a0= 6 (2 shares * 3)<\/p>\n<p>Ending value\u00a0\u00a0= 460 (2 shares * 230)<\/p>\n<p><em>Secondly, we calculate the HPR for each period:<\/em><\/p>\n<p>$$ \\text{HPR}_1 =\\cfrac {(220 \u2013 200 + 3)}{200} = 11.5\\% $$<\/p>\n<p>$$ \\text{HPR}_2 =\\cfrac {(460 \u2013 440 + 6)}{440} = 5.9\\% $$<\/p>\n<p>Lastly,<\/p>\n<p>$$ (1 + \\text{annual TWRR})^2 = 1.115 * 1.059 $$<\/p>\n<p>Therefore,<\/p>\n<p>$$ \\text {annual TWRR} = (1.115 * 1.059)^{0.5} \u2013 1 = 8.7\\% $$<\/p>\n<h2><strong>Money-weighted Rate of Return Vs Time-weighted Rate of Return<\/strong><\/h2>\n<p>The money-weighted rate of return is sensitive to the amount and timing of cash flows and could lead to an unfair rating of the fund manager \u2013 They have no control over the amount or timing of cash flows. This effect is eliminated by the time-weighted rate of return. The money-weighted rate of return would only be superior to the TWRR if and only if the fund manager had complete control over cash flows and their timings.<\/p>\n<blockquote>\n<h2><strong>Question<\/strong><\/h2>\n<p>A chartered analyst buys a share of stock at time t = 0 for $50. At t = 1, he purchases an extra share of the same stock for $53. The share gives a dividend of $0.50 per share for the first year and $0.60 per share for the second year. He sells the shares at the end of the second year for $55 per share. Calculate the annual time-weighted rate of return.<\/p>\n<p>A. 5.9%<\/p>\n<p>B. 12.24%<\/p>\n<p>C. 7%<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is A.<\/p>\n<p>We have two 1-year holding periods:<\/p>\n<p><em>HP<sub>1<\/sub>:<\/em><\/p>\n<p>P<sub>0<\/sub> = 50<\/p>\n<p>D= 0.5<\/p>\n<p>P<sub>1<\/sub> = 53<\/p>\n<p><em>HP<sub>2<\/sub>:<\/em><\/p>\n<p>P<sub>0<\/sub>= 106<\/p>\n<p>D = 1.2<\/p>\n<p>P<sub>1<\/sub> = 110<\/p>\n<p><em>We now calculate the holding period returns:<\/em><\/p>\n<p>$$ \\begin{align*}<br \/>\\text{HPR}_1 &amp; =\\cfrac {(53 &#8211; 50 + 0.5)}{50} = 7\\% \\\\<br \/>\\text{HPR}_2 &amp; =\\cfrac {(110 &#8211; 106 + 1.2)}{106} = 4.9\\% \\\\<br \/>\\text{Compounded TWRR} &amp; = 1.07 * 1.049 = 12.24\\%<br \/>\\end{align*} $$<\/p>\n<p>Therefore,<\/p>\n<p>$$ \\text {Annual TWRR} = (1 + 0.1224)^{0.5} &#8211; 1 = 5.9\\% $$<\/p>\n<\/blockquote>\n<p><em>Reading 7 LOS 7d<\/em><\/p>\n<p><em>Calculate and compare the money-weighted and time-weighted rates of return of a portfolio and evaluate the performance of portfolios based on these measures. (Part two)<\/em><\/p>\n<div class=\"notes_inv\"><hr \/>\n<p><a href=\"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/learning-sessions-curriculum\/\"><em>Quantitative Methods \u2013 Learning Sessions<\/em><\/a><\/p>\n<\/div>\n\n\n<!-- BOTTOM CTA \u2013 Refined Version -->\n<div style=\"text-align:center; background-color:#f4f6f9; padding:35px 20px; border-radius:12px; margin-top:40px;\">\n\n  <a href=\"https:\/\/analystprep.com\/free-trial\/\"\n     target=\"_blank\"\n     rel=\"noopener noreferrer\"\n     style=\"\n       display:inline-block;\n       padding:14px 34px;\n       background-color:#3b6fd8;\n       color:#ffffff;\n       border-radius:50px;\n       font-size:16px;\n       font-weight:600;\n       text-decoration:none;\n       margin-bottom:18px;\n     \">\n     Start Free Trial\n  <\/a>\n\n  <p style=\"max-width:700px; margin:0 auto; font-size:16px; line-height:1.6; color:#333;\">\n    Improve your CFA Level I performance measurement skills with exam-style time weighted rate of return problems, step by step solutions, and timed quizzes inside AnalystPrep\u2019s free trial.\n  <\/p>\n\n<\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>The time-weighted rate of return (TWRR) measures the compound growth rate of an investment portfolio. &nbsp;Unlike the money-weighted rate of return, TWRR is not sensitive to withdrawals or contributions. Essentially, the time-weighted rate of return is the geometric mean of&#8230;<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[2],"tags":[],"class_list":["post-140","post","type-post","status-publish","format-standard","hentry","category-quantitative-methods","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>Time-Weighted Rate of Return | CFA Level 1<\/title>\n<meta name=\"description\" content=\"The time-weighted rate of return measures investment performance by calculating the compound growth rate per dollar invested. 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