{"id":399,"date":"2019-08-17T13:28:00","date_gmt":"2019-08-17T13:28:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=399"},"modified":"2026-03-25T17:15:40","modified_gmt":"2026-03-25T17:15:40","slug":"arithmetic-return-vs-geometric-return","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/arithmetic-return-vs-geometric-return\/","title":{"rendered":"Arithmetic Mean Return Vs Geometric Mean Return"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Statistical Concepts and Market Returns (2021 Level I CFA\u00ae Exam \u2013 Reading 7)\",\n  \"description\": \"This video on Quantitative Methods: Statistical Concepts and Market Returns introduces key statistical concepts relevant to financial analysis. It covers descriptive vs. inferential statistics, population vs. sample, measurement scales, frequency distributions, measures of central tendency (mean, median, mode), variability (range, variance, standard deviation), skewness, and kurtosis. Emphasis is placed on practical applications in investment decision-making.\",\n  \"uploadDate\": \"2020-07-09T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/alD9eAT2lQU\/default.jpg\",\n  \"contentUrl\": \"https:\/\/youtu.be\/alD9eAT2lQU\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/alD9eAT2lQU\",\n  \"duration\": \"PT31M21S\"\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 is the arithmetic mean return calculated for a series of investment returns?\",\n    \"text\": \"Assume that we have a 6-year sequence of investment returns as follows: {40%, \u221230%, 40%, \u221230%, 40%, \u221230%}. How is the arithmetic mean return calculated?\",\n    \"answerCount\": 1,\n    \"upvoteCount\": 0,\n    \"dateCreated\": \"2025-12-16T00:00:00+00:00\",\n    \"author\": {\n      \"@type\": \"Organization\",\n      \"name\": \"AnalystPrep\"\n    },\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The arithmetic mean return is calculated by summing all periodic returns and dividing by the number of observations. In this example, (0.40 \u2212 0.30 + 0.40 \u2212 0.30 + 0.40 \u2212 0.30) \u00f7 6 = 0.05, or 5%.\",\n      \"dateCreated\": \"2025-12-16T00:00:00+00:00\",\n      \"upvoteCount\": 0,\n      \"url\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/arithmetic-return-vs-geometric-return\/\",\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\/alD9eAT2lQU\" \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>Both arithmetic return and geometric return are methods commonly used to calculate the yield on a given investment. However, the return that really matters is the geometric return, not the arithmetic return. A good understanding of the difference between the two methods of calculating returns helps analysts to invest wisely. A wise investment takes the volatility or, rather, the risk attached to an investment into account. For instance, is the return from year to year fixed or purely volatile?<\/p>\n\n\n\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Arithmetic Mean Return<\/strong><\/h2>\n\n\n\n<p>Most companies report returns in the form of an arithmetic average because it is usually the highest average that can be announced. However, the arithmetic return is actually misleading unless the return earned is fixed for the entire investment period. Two factors cause the inaccuracy:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>the compounding of returns; and<\/li>\n\n\n\n<li>the fluctuation in the percentage return earned from year to year.<\/li>\n<\/ol>\n\n\n\n<div style=\"text-align:center; background:#f3f5f9; padding:26px 16px; margin:24px 0;\">\n  <div style=\"max-width:720px; margin:0 auto;\">\n    <a href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"\n       style=\"display:block; width:100%; padding:14px 20px; border:2px solid #2f6fdd; border-radius:999px; color:#2f6fdd; text-decoration:none; font-size:16px; font-weight:500; line-height:1.2; text-align:center;\">\n      Practice return calculations for CFA Level I with a Free Trial.\n    <\/a>\n  <\/div>\n<\/div>\n\n\n<\/p>\n<h4><strong>Example:\u00a0Arithmetic Mean<\/strong><\/h4>\n<p>Assume that we have a 6-year sequence of investment returns as follows:<\/p>\n<p>{40%\u00a0\u00a0 -30%\u00a0\u00a0 40%\u00a0\u00a0 -30%\u00a0\u00a0 40%\u00a0\u00a0 -30%}<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>The arithmetic mean return is simply the sum of all the returns divided by the number of returns, \u2018n\u2019 (6 in this case):<\/p>\n<p>$$ \\text{Arithmetic mean return} =\\cfrac {(0.4 \u2013 0.3 + 0.4 \u2013 0.3 + 0.4 \u2013 0.3 + 0.4 \u2013 0.3)}{6} = 0.05 \\text{ or } 5\\% $$<\/p>\n<h2><strong>Geometric Mean Return<\/strong><\/h2>\n<p>To calculate the geometric mean return, we follow the steps outlined below:<\/p>\n<ol>\n<li>first, add 1 to each return. The trick is to avoid problems posed by negative values;<\/li>\n<li>multiply all the returns in the sequence;<\/li>\n<li>raise the product to the power of 1 divided by the number of returns \u2018n\u2019; and<\/li>\n<li>finally, subtract 1 from the final result.<\/li>\n<\/ol>\n<h4><strong>Example: Geometric Mean<\/strong><\/h4>\n<p>Again, assume that we have a 6-year sequence of investment returns as follows:<\/p>\n<p>{40%\u00a0\u00a0 -30%\u00a0\u00a0 40%\u00a0\u00a0 -30%\u00a0\u00a0 40%\u00a0\u00a0 -30%}<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>$$ \\text{Geometric mean return} =(1.4 \u00d7 0.7 \u00d7 1.4 \u00d7 0.7 \u00d7 1.4 \u00d7 0.7)^{\\frac {1}{6}} \u2013 1 = -0.01 \\text{ or } -1\\% $$<\/p>\n<h3><strong>Arithmetic vs. Geometric Mean Returns<\/strong><\/h3>\n<p>The media and investment institutions can mislead an investor if they incorrectly use the arithmetic return.<\/p>\n<p>Considering the above example, a fund manager will most likely quote the 5% return. Unfortunately, this is not the real return! The actual return is -1% (a loss).<\/p>\n<p>Perhaps you will understand the idea better if we work with actual figures.<\/p>\n<p>For example, suppose you invested in an emerging mutual fund and earned 100% in the first year, followed by a 50% loss in the second year. The arithmetic mean return will be 25%, i.e., (100 \u2013 50)\/2.<\/p>\n<p>Applying the geometric mean return formula in the case outlined above will give you a mean return of zero! For example, if you start with $1,000, you will have $2,000 at the end of year 1, which will be reduced to $1,000 by the end of year 2. Thus, you earn a return of zero over the 2-year period.<\/p>\n<p>In conclusion, the geometric return is always a better measure of investment performance compared to the arithmetic return, <strong>unless there is no volatility of returns<\/strong>. Then, the\u00a0difference between the arithmetic mean return and the geometric mean return increases as the volatility increases.<\/p>\n<div class=\"notes_inv\">\u00a0<\/div>\n\n\n\n\n<div style=\"text-align:center; background:#f3f5f9; padding:48px 20px 28px; margin:40px 0;\">\n  \n  <a href=\"https:\/\/analystprep.com\/free-trial\/\" target=\"_blank\" rel=\"noopener noreferrer\"\n     style=\"display:inline-block; background:#4274d8; color:#ffffff; text-decoration:none; padding:18px 42px; border-radius:999px; font-size:17px; font-weight:700; line-height:1;\">\n    Start Free Trial\n  <\/a>\n\n  <p style=\"max-width:640px; margin:18px auto 0; font-size:16px; line-height:1.5; color:#1f2937;\">\n    Build confidence in arithmetic and geometric returns with structured practice and\n    exam-focused CFA Level I questions.\n  <\/p>\n\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Both arithmetic return and geometric return are methods commonly used to calculate the yield on a given investment. However, the return that really matters is the geometric return, not the arithmetic return. A good understanding of the difference between the&#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-399","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>Geometric vs Arithmetic Return | CFA Level 1<\/title>\n<meta name=\"description\" content=\"Geometric returns account for compounding and volatility, making them a better measure than arithmetic returns. 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