CFA Program Level I

Price-weighted vs market-cap-weighted index: CFA Level I

In a price-weighted index such as the Dow Jones Industrial Average, the stock with the highest share price has the most weight. In a market-cap-weighted index, the company with the largest market capitalisation has the most weight. A total return index adds reinvested income to price changes.

Weighting methods, worked

Price weighting: each stock's weight comes from its price per share. Market-cap weighting: each weight comes from price times shares outstanding, so larger companies count for more. Equal weighting gives every constituent the same weight. Fundamental weighting is a further method.

Example: stock A trades at USD100 with 10 million shares (cap USD1,000 million); stock B at USD20 with 100 million shares (cap USD2,000 million). A price-weighted index with divisor 2 stands at (100 + 20) / 2 = 60.

If A rises 10%, the price-weighted index goes to (110 + 20) / 2 = 65, up 8.33%. If instead B rises 10%, it goes to (100 + 22) / 2 = 61, up 1.67%.

Market-cap weighted: A up 10% takes total cap from 3,000 to 3,100, up 3.33%. B up 10% takes it to 3,200, up 6.67%. The smaller company by value moves the price-weighted index more because its share price is higher.

Price return vs total return

A price return index reflects only constituent prices. A total return index also reflects reinvestment of all income received since inception.

Total return levels chain-link: level(t) = level(t-1) x (1 + total return). Example: an index at 1,000 with a 5% price return and 2% income stands at 1,050 as a price index and 1,000 x 1.07 = 1,070 as a total return index.

Over two years, 2,000 with returns of 9% then 6% gives 2,000 x 1.09 x 1.06 = 2,310.80, not 2,000 x 1.15.

Rebalancing and reconstitution

Rebalancing adjusts weights periodically so the index keeps its intended weighting. Reconstitution changes the list of constituents so the index still represents its target market, for example dropping companies that have outgrown a mid-cap range.

Both create turnover for funds that track the index. Reconstitution can sharply move the prices of stocks being added or removed.

Where the exam catches people

Believing the largest company dominates the Dow Jones Industrial Average: it is price-weighted, so the highest share price carries the most weight.
Believing a total return index adds returns across years: levels are chain-linked by multiplying (1 + return) each period.
Believing rebalancing changes the constituents: rebalancing resets weights; reconstitution changes membership.
Believing a price return index includes dividends: only a total return index includes reinvested income.

Written from CFA Institute's documentation

Try 3 questions on this

Pick an answer to see why each option is right or wrong.

In the Dow Jones Industrial Average, the constituent that carries the largest weight is the one with the highest:
Right. In the game that’s Renown for your Equities building.
Not that one: C is right. In the game your Equities building would lose a little Renown, and this question would come back later.
Your answerA.Market capitalizationMarket capitalization sets weights in a market-cap-weighted index, which many indexes use. The Dow Jones Industrial Average is price-weighted instead, so the highest share price carries the largest weight.Your answerB.Trading volumeTrading volume plays no part in the index's weights. In a price-weighted index such as the Dow Jones Industrial Average, the share price sets each weight.The answerC.Share priceThe Dow Jones Industrial Average is a price-weighted index: each constituent's price per share determines its weight, so the stock with the highest share price counts the most, whatever the company's size.
Written from www.investor.gov/introduction-investing/investing-basics/investment-products/mutual-funds-and-exchange-traded-4
A total return index on a basket of stocks stands at 2,000.00 at the start of Year 1. Constituent prices rise 8.0% in Year 1 and 5.0% in Year 2. In each year the constituents also pay dividends equal to 1.0% of the index value at the start of that year, reinvested at year-end. The total return index level at the end of Year 2 is closest to:
Right. In the game that’s Renown for your Equities building.
Not that one: C is right. In the game your Equities building would lose a little Renown, and this question would come back later.
Your answerA.2,268.002,000.00 x 1.08 x 1.05 = 2,268.00 uses the price returns only. That is the price return index, which ignores the dividends a total return index reinvests.Your answerB.2,300.002,000.00 x (1 + 0.09 + 0.06) = 2,300.00 adds the yearly total returns. Index levels compound: Year 2's 6.0% applies to the Year 1 ending level of 2,180.00, which gives 2,310.80.The answerC.2,310.80A total return index includes price changes and reinvested income, and its level is chain-linked period by period: level(t) = level(t-1) x (1 + total return(t)).
Show the full explanation and doc quotes
Year 1 total return = 8.0% + 1.0% = 9.0%; Year 2 = 5.0% + 1.0% = 6.0%. Level = 2,000.00 x 1.09 x 1.06 = 2,180.00 x 1.06 = 2,310.80.
Written from www.msci.com/eqb/methodology/meth_docs/MSCI_IndexCalcMethodology_Feb2022.pdf
At its annual review, the provider of a mid-cap equity index removes three companies whose market capitalizations have grown beyond the mid-cap range and adds three companies that now fall within it. Like resetting constituent weights, this step generates turnover for funds tracking the index. The step described is best described as:
Right. In the game that’s Renown for your Equities building.
Not that one: B is right. In the game your Equities building would lose a little Renown, and this question would come back later.
Your answerA.Reinvestment of incomeReinvesting income received from constituents is how a total return index differs from a price return index. It leaves the membership of the index unchanged, whereas this review replaced three companies.The answerB.ReconstitutionIndex management has two parts. Rebalancing is done periodically so that the index keeps its intended weightings. Reconstitution changes the list of constituents so that the index continues to represent its target market, here mid-cap companies.Your answerC.RebalancingRebalancing also creates turnover, but it adjusts weights among the existing constituents to bring the index back to its intended weightings. Removing companies that left the mid-cap range and adding new ones changes the membership itself, which is reconstitution.
Show the full explanation and doc quotes
Dropping companies that have outgrown the mid-cap range and adding ones that now qualify is reconstitution. Both create turnover, and reconstitution can move the prices of the stocks added and dropped sharply.
Written from www.cfainstitute.org/insights/professional-learning/refresher-readings/2026/security-market-indexes