{"id":1826,"date":"2019-09-12T13:33:00","date_gmt":"2019-09-12T13:33:00","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=1826"},"modified":"2026-01-26T06:38:27","modified_gmt":"2026-01-26T06:38:27","slug":"price-return-total-return-index","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/equity\/price-return-total-return-index\/","title":{"rendered":"Price Return and Total 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 Module 2)\",\n  \"description\": \"This lesson covers Security Market Indexes for the 2025 CFA\u00ae Level I Equity Investments curriculum. It explains how security market indexes are constructed, compares different weighting methods, and discusses rebalancing and reconstitution. The video also shows how to calculate and interpret index values, price return, and total return, and examines the use of equity, fixed-income, and alternative indexes as benchmarks in portfolio management.\",\n  \"uploadDate\": \"2024-01-26T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/qBqq7dMkZwY\/default.jpg\",\n  \"contentUrl\": \"https:\/\/youtu.be\/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<h2><strong>Index Value<\/strong><\/h2>\n<p>The formula for calculating the value of a price return index is as follow:<br \/>\n$$ V_{PRI} = \\frac{ \\sum_{i=1}^{N}{n_iP_i} } { D } $$<\/p>\n<p>Where:<\/p>\n<p><em>V<sub>PRI<\/sub><\/em> = the value of the price return index<\/p>\n<p><em>n<sub>i<\/sub><\/em> = the number of units of constituent security \u00a0held in the index portfolio<\/p>\n<p><em>N<\/em> = the number of constituent securities in the index<\/p>\n<p><em>P<sub>i<\/sub><\/em> = the unit price of constituent security<\/p>\n<p><em>D<sub>i<\/sub><\/em> = the value of the divisor<\/p>\n<p>While the formula for calculating the value of an index may seem somewhat complicated at first glance, it is similar to calculating the value of any other normal portfolio of securities as it involves adding up the values of constituent securities. Index value calculation has just one additional step of dividing the sum of constituent securities\u2019 values by a divisor, which is usually chosen at the inception of the index to set a convenient beginning value and then adjusted to offset index value changes unrelated to changes in the prices of constituent securities.<\/p>\n<h4><strong>Example 1: Index Value<\/strong><\/h4>\n<p>An index is made up of two constituent securities, Stock A and Stock B. What beginning divisor must be used to achieve a beginning value of 1,000?<\/p>\n<p>$$<br \/>\n\\begin{array}{l|r|r}<br \/>\n\\textbf{Security} &amp; \\textbf{Units} &amp; \\textbf{Price\/Unit} \\\\<br \/>\n\\hline<br \/>\n\\text{Stock A} &amp; 50 &amp; 10 \\\\<br \/>\n\\text{Stock B} &amp; 30 &amp; 100 \\\\<br \/>\n\\end{array}<br \/>\n$$<\/p>\n<p>Let\u2019s first calculate the sum of the values of both constituent securities.<\/p>\n<p>Stock A value = 50 \u00d7 10 = 500<\/p>\n<p>Stock B value = 30 \u00d7 100 = 3,000<\/p>\n<p>Stock A value + Stock B value = 3,500<\/p>\n<p>The divisor must be set such that this figure is adjusted down to 1,000.<\/p>\n<p>$$ 1,000 = \\frac{ 3,500 } { D } $$<\/p>\n<p>$$ D = \\frac{ 3,500 } { 1,000 } $$<\/p>\n<p>$$ D = 3.5 $$<\/p>\n<h2><strong>Price Return and Total Return<\/strong><\/h2>\n<p>The price return calculation \u2013 the return from the index in percentage terms \u2013 is simply the difference in value between the two periods divided by the beginning value.<\/p>\n<p>$$ PR_I = \\frac{ V_{ PRI1 } &#8211;\u00a0V_{ PRI0 } } { V_{ PRI0 } } $$<\/p>\n<p>The formula for total return is the same, except we need to add the income generated from the securities, usually in the form of dividends:<\/p>\n<p>$$ TR_I = \\frac{ V_{ PRI1 } &#8211;\u00a0V_{ PRI0 } + \\text{Income}_I } { V_{ PRI0 } } $$<\/p>\n<p><em>PR<sub>I<\/sub><\/em> = the price return of the index portfolio<\/p>\n<p><em>V<sub>PRI1<\/sub><\/em> = the value of the price return index at the end of the period<\/p>\n<p><em>V<sub>PRI0<\/sub><\/em> = the value of the price return index at the beginning of the period<\/p>\n<p><em>TR<sub>I<\/sub><\/em> = \u00a0\u00a0 the total return of the index portfolio<\/p>\n<p><em>Income<sub>I<\/sub><\/em> = the total income from all securities in the index over the period<\/p>\n<p>Another way to calculate these returns would be to sum up the weighted returns of each constituent security in the index portfolio.<\/p>\n<p>$$ R_I = w_1R_1 + w_2R_2 + &#8230; + w_NR_N $$<\/p>\n<p><em>R<sub>I<\/sub><\/em> = the return of the index portfolio number (as a decimal number)<\/p>\n<p><em>R<sub>i<\/sub><\/em> = the return of constituent security<em> i<\/em> (as a decimal number)<\/p>\n<p><em>w<sub>i<\/sub><\/em> = the weight of security <em>i<\/em> (the fraction of the index portfolio allocated to security<\/p>\n<p>Note that this formula works for both price and total return calculations.<\/p>\n<h4><strong>Example 2: Price Return and Total Return<\/strong><\/h4>\n<p>Calculate the one-year price return and total return for the Uncommon &amp; Riches 5, a fictional index made up of five constituent securities. The divisor\u2019s value begins and ends the year at 1.<\/p>\n<p>$$<br \/>\n\\begin{array}{l|r|r|r}<br \/>\n\\textbf{Constituent Security} &amp; \\textbf{Units (billions)} &amp; \\textbf{Beginning Value} &amp; \\textbf{Dividend} &amp; \\textbf{Ending Value} \\\\<br \/>\n\\hline<br \/>\n\\text{Orange} &amp; 5 &amp; 107 &amp; 2.15 &amp; 116 \\\\<br \/>\n\\text{Macrotough} &amp; 7.75 &amp; 55 &amp; 1.20 &amp; 62 \\\\<br \/>\n\\text{Enout Stationary Corp} &amp; 4 &amp; 75 &amp; 2.70 &amp; 91 \\\\<br \/>\n\\text{Draintree} &amp; 0.5 &amp; 660 &amp; 0.00 &amp; 750 \\\\<br \/>\n\\text{Smith &amp; Smith} &amp; 2.75 &amp; 100 &amp; 3.00 &amp; 115 \\\\<br \/>\n\\end{array}<br \/>\n$$<\/p>\n<p>Let\u2019s first calculate the beginning index price by multiplying the number of units and price of each constituent security and totaling the values.<\/p>\n<p><em>V<sub>PRI0\u00a0<\/sub><\/em>= (5 \u00d7 107) + (7.75 \u00d7 55) + (4 \u00d7 75) + (5 \u00d7 660) + (2.75 \u00d7 100)<\/p>\n<p><em>V<sub>PRI0\u00a0<\/sub><\/em>= 535 + 426.25 + 300 + 330 + 275 = 1,866.25<\/p>\n<p>We\u2019ll do the same calculation again, except replace the beginning values with ending values.<\/p>\n<p><em>V<sub>PRI1\u00a0<\/sub><\/em>= (5 \u00d7 116) + (7.75 \u00d7 62) + (4 \u00d7 91) + (5 \u00d7 750) + (2.75 \u00d7 115)<\/p>\n<p><em>V<sub>PRI1\u00a0<\/sub><\/em>= 580 + 480 + 364 + 375 + 316.25 = 2,115.75<\/p>\n<p>And one more time to calculate portfolio income.<\/p>\n<p>Income<em><sub>I\u00a0<\/sub><\/em>= (5 \u00d7 2.15) + (7.75 \u00d7 1.20) + (4 \u00d7 2.70) + (5 \u00d7 0) + (2.75 \u00d7 3)<\/p>\n<p>Income<em><sub>I\u00a0<\/sub><\/em>= 10.75 + 9.30 + 10.80 + 8.25 = 39.10<\/p>\n<p>The one-year price return for the Uncommon &amp; Riches 5 comes out to: (2,115.75 \u2013 1,866.25)\/1,866.25 = <strong>13.37%<\/strong><\/p>\n<p>To calculate the total return, we\u2019ll add in the portfolio income: (2,115.75 + 39.10 \u2013 1,866.25)\/1,866.25 = <strong>15.46%<\/strong><\/p>","protected":false},"excerpt":{"rendered":"<p>Index Value The formula for calculating the value of a price return index is as follow: $$ V_{PRI} = \\frac{ \\sum_{i=1}^{N}{n_iP_i} } { D } $$ Where: VPRI = the value of the price return index ni = the number&#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-1826","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>Price Return vs. Total Return | CFA Level 1<\/title>\n<meta name=\"description\" content=\"Learn the differences between price return and total return indexes, their formulas, and 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