{"id":1834,"date":"2019-09-12T13:33:00","date_gmt":"2019-09-12T13:33:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=1834"},"modified":"2026-02-02T09:23:10","modified_gmt":"2026-02-02T09:23:10","slug":"value-return-index-given-weighting-method","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/equity\/value-return-index-given-weighting-method\/","title":{"rendered":"The Value and Return of an Index"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Security Market Indexes (2025 Level I CFA\u00ae Exam \u2013 Equity \u2013 Learning Module 2)\",\n  \"description\": \"CFA\u00ae Level I Equity Investments video lesson from AnalystPrep covering Security Market Indexes (Learning Module 2). This lecture explains how security market indexes are constructed, including price-weighted, market-cap-weighted, and equal-weighted methods. It also covers index rebalancing and reconstitution, calculation of index values, price return and total return, and the use of equity, fixed-income, and alternative indexes as benchmarks in portfolio management, with exam-focused examples.\",\n  \"uploadDate\": \"2024-01-26\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/qBqq7dMkZwY\/hqdefault.jpg\",\n  \"contentUrl\": \"https:\/\/www.youtube.com\/watch?v=qBqq7dMkZwY\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/qBqq7dMkZwY\",\n  \"duration\": \"PT41M19S\"\n}\n<\/script>\n\n\n\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/qBqq7dMkZwY\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Every index weighting method has a formula that calculates the weighting of a given constituent security within an index. For the following examples, the same portfolio of three securities will be used to help illustrate the weighting methods. Note that while income from constituent securities could hypothetically be reinvested in the index, the index level adjusts only for price changes.<\/p>\n<p>$$<br \/>\n\\begin{array}{l|r|r|r}<br \/>\n\\textbf{Security} &amp; \\textbf{Beg. Price\/Share} &amp; \\textbf{Income} &amp; \\textbf{End Price\/Share} \\\\<br \/>\n\\hline<br \/>\n\\text{Security A} &amp; 500 &amp; 0 &amp; 750 \\\\<br \/>\n\\text{Security B} &amp; 20 &amp; 1 &amp; 21 \\\\<br \/>\n\\text{Security C} &amp; 45 &amp; 1 &amp; 25 \\\\<br \/>\n\\hline<br \/>\n\\textbf{Total} &amp; &amp; \\mathbf{2} &amp; \\\\<br \/>\n\\end{array}<br \/>\n$$<\/p>\n<h2><strong>Price Weighting<\/strong><\/h2>\n<p>Here, the weight of each security <em>i<\/em> is given by:<\/p>\n<p>$$ w_{i}^P = \\frac{ P_i } { \\sum_{i=1}^{N}{P_i} } $$<\/p>\n<p>Where:<\/p>\n<p><em>w<sub>i<\/sub><\/em> = fraction of the portfolio that is allocated to the security or weight of the security<\/p>\n<p><em>N<\/em> = number of securities in the index<\/p>\n<p><em>P<sub>i<\/sub><\/em> = price of the security<\/p>\n<h4><strong>Example <\/strong><strong>of a price-weighted index<\/strong><\/h4>\n<p>$$<br \/>\n\\begin{array}{l|rrrrrrr}<br \/>\n\\textbf{Security} &amp; \\textbf{Beg. Value} &amp; \\textbf{Income} &amp; \\textbf{End Value} &amp; \\textbf{Shares} &amp; \\textbf{Beg. Weight} &amp; \\textbf{End Weight} \\\\<br \/>\n\\hline<br \/>\n\\text{Security A} &amp; 500 &amp; 0 &amp; 750 &amp; 1 &amp; 88.5\\% &amp; 94.2\\% \\\\<br \/>\n\\text{Security B} &amp; 20 &amp; 1 &amp; 21 &amp; 1 &amp; 3.5\\% &amp; 2.6\\% \\\\<br \/>\n\\text{Security C} &amp; 45 &amp; 1 &amp; 25 &amp; 1 &amp; 8.0\\% &amp; 3.1\\% \\\\<br \/>\n\\hline<br \/>\n\\textbf{Total} &amp; \\mathbf{188.33} &amp; &amp; \\mathbf{265.33} &amp; \\mathbf{3} &amp; \\mathbf{1} &amp;\\mathbf{1} \\\\<br \/>\n\\textbf{Price Return} &amp; \\mathbf{40.9\\%} \\\\<br \/>\n\\textbf{Total Return} &amp; \\mathbf{41.2\\%} \\\\<br \/>\n\\end{array}<br \/>\n$$<\/p>\n<p>One share of each security is held in the index, and the divisor is set to 3 \u2013 the total number of shares. The high weighting of Security A in both periods is perhaps the most interesting part of this index. While this is an extremely concentrated index, price\/share is nevertheless very important in how securities are weighted in price indices, even though it remains a mostly arbitrary figure.<\/p>\n<h2><strong>Equal Weighting<\/strong><\/h2>\n<p>Here, the weight of each security <em>i<\/em> is given by:<\/p>\n<p>$$ w_{i}^E = \\frac{ 1 } { N } $$<\/p>\n<p>Where:<\/p>\n<p><em>N<\/em>&nbsp;= number of securities in the index<\/p>\n<h4><strong>Example <\/strong><strong>of an equal-weighted index<\/strong><\/h4>\n<p>$$<br \/>\n\\begin{array}{l|rrrrrr}<br \/>\n\\textbf{Security} &amp; \\textbf{Beg. Value} &amp; \\textbf{Income} &amp; \\textbf{End Value} &amp; \\textbf{Shares} &amp; \\textbf{Beg. Weight} &amp; \\textbf{End Weight} \\\\<br \/>\n\\hline<br \/>\n\\text{Security A} &amp; 500 &amp; 0 &amp; 750 &amp; 1 &amp; 33.3\\% &amp; 48.3\\% \\\\<br \/>\n\\text{Security B} &amp; 500 &amp; 25 &amp; 525 &amp; 25 &amp; 33.3\\% &amp; 33.8\\% \\\\<br \/>\n\\text{Security C} &amp; 500 &amp; 11 &amp; 278 &amp; 11.11 &amp; 33.3\\% &amp; 17.9\\% \\\\<br \/>\n\\text{Total} &amp; 1,500.00 &amp; 36.11 &amp; 1,552.78 &amp; 37.11 &amp; 100\\% &amp; 100\\% \\\\<br \/>\n\\hline<br \/>\n\\textbf{Price Return} &amp; \\mathbf{3.5\\%} \\\\<br \/>\n\\textbf{Total Return} &amp; \\mathbf{5.9\\%} \\\\<br \/>\n\\end{array}<br \/>\n$$<\/p>\n<p>As shown in the table, each of the three securities is equally weighted within the index at the beginning of the period but largely strayed from the initial weights. While the price index posted returns above 40%, returns of the three-security portfolio were much more modest when beginning with the same values.<\/p>\n<h2><strong>Market-capitalization<\/strong><\/h2>\n<p>Here, the weight of each security <em>i<\/em> is given by:<\/p>\n<p>$$ w_{i}^M = \\frac{ Q_i P_i } { \\sum_{i=1}^{N}{Q_i P_i } } $$<\/p>\n<p>Where:<\/p>\n<p><em>Q<sub>i<\/sub><\/em> = number of shares outstanding of security<\/p>\n<h4><strong>Example <\/strong><strong>of a market-capitalization index<\/strong><\/h4>\n<p>$$<br \/>\n\\begin{array}{l|rrrrrrr}<br \/>\n\\textbf{Security} &amp; \\textbf{Beg. Value} &amp; \\textbf{Income} &amp; \\textbf{End Value} &amp; \\textbf{Out. Shares(mm)} &amp; \\textbf{Beg. Weight} &amp; \\textbf{End Weight} \\\\<br \/>\n\\hline<br \/>\n\\text{Security A} &amp; 1,500 &amp; 0 &amp; 2,250 &amp; 3 &amp; 25.6\\% &amp; 46.7\\% \\\\<br \/>\n\\text{Security B} &amp; 300 &amp; 15 &amp; 315 &amp; 15 &amp; 5.1\\% &amp; 6.5\\% \\\\<br \/>\n\\text{Security C} &amp; 4,050 &amp; 90 &amp; 2,250 &amp; 90 &amp; 69.2\\% &amp; 46.7\\% \\\\<br \/>\n\\text{Total} &amp; 5,850.00 &amp; 105.00 &amp; 4,815.00 &amp; 108.00 &amp; 100\\% &amp; 100\\% \\\\<br \/>\n\\hline<br \/>\n\\textbf{Price Return} &amp; \\mathbf{-17.7\\%} \\\\<br \/>\n\\textbf{Total Return} &amp; \\mathbf{-15.9\\%} \\\\<br \/>\n\\end{array}<br \/>\n$$<\/p>\n<p>Note that the column that recorded constituent shares as part of the index portfolio is now equal to millions of outstanding shares. The beginning and ending values now reflect the market capitalizations of the companies in the index portfolio. Since Security C has by far the largest amount of shares outstanding, it accounts for more than two-thirds of market capitalization when multiplied out with the share price at the beginning of the period. As a result of Security C\u2019s heavy weighting, the market-capitalization index performed very poorly during the period.<\/p>\n<h2><strong>Float-adjusted Market-capitalization Weighting<\/strong><\/h2>\n<p>Here, the weight of each security <em>i<\/em> is given by:<\/p>\n<p>$$ w_{i}^{fM} = \\frac{ f_i Q_i P_i } { \\sum_{i=1}^{N}{f_iQ_i P_i } } $$<\/p>\n<p>Where:<\/p>\n<p><em>f<sub>i<\/sub><\/em> = fraction of shares outstanding in the market float<\/p>\n<h4><strong>Example <\/strong><strong>of a float-adjusted market-capitalization index<\/strong><\/h4>\n<p>$$<br \/>\n\\begin{array}{l|rrrrrrr}<br \/>\n\\textbf{Security} &amp; \\textbf{Beg. Value} &amp; \\textbf{Income} &amp; \\textbf{End Value} &amp; \\textbf{Out. Shares(mm)} &amp; \\textbf{Beg. Weight} &amp; \\textbf{End Weight} &amp;\\textbf{Market Float %} \\\\<br \/>\n\\hline<br \/>\n\\text{Security A} &amp; 750 &amp; 0 &amp; 1,125 &amp; 3 &amp; 15.4\\% &amp; 31.7\\% &amp; 50.0\\% \\\\<br \/>\n\\text{Security B} &amp; 270 &amp; 14 &amp; 284 &amp; 15 &amp; 5.5\\% &amp; 8.0\\% &amp; 90.0\\% \\\\<br \/>\n\\text{Security C} &amp; 3,848 &amp; 86 &amp; 2,138 &amp; 90 &amp; 79.0\\% &amp; 60.3\\% &amp; 95.0\\% \\\\<br \/>\n\\text{Total} &amp; 4,867 &amp; 99.00 &amp; 3,546.00 &amp; 108.00 &amp; 100\\% &amp; 100\\% \\\\<br \/>\n\\hline<br \/>\n\\textbf{Price Return} &amp; \\mathbf{-27.1\\%} \\\\<br \/>\n\\textbf{Total Return} &amp; \\mathbf{-25.1\\%} \\\\<br \/>\n\\end{array}<br \/>\n$$<\/p>\n<p>To calculate float-adjusted market capitalization, we multiply each market capitalization by its respective fraction of outstanding shares in the market float. Since Security A is more closely held with just 50% market float, its weight is significantly reduced in the float-adjusted index compared to the unadjusted market capitalization index. In this scenario, the index&#8217;s performance becomes highly skewed by Security C\u2019s losses during the period.<\/p>","protected":false},"excerpt":{"rendered":"<p>Every index weighting method has a formula that calculates the weighting of a given constituent security within an index. For the following examples, the same portfolio of three securities will be used to help illustrate the weighting methods. Note that&#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":[8],"tags":[],"class_list":["post-1834","post","type-post","status-publish","format-standard","hentry","category-equity","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>Value &amp; Return of an Index | CFA Level 1 - AnalystPrep<\/title>\n<meta name=\"description\" content=\"Explore index weighting methods and learn how to calculate the value and return of an index using different weighting approaches.\" \/>\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\/equity\/value-return-index-given-weighting-method\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Value &amp; Return of an Index | CFA Level 1 - 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