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Contrast indexes weighted by price with those weighted by market capitalisation

CFA® Level I · Equity Investments · Equity Issuance and Trading · EQ.3.a

The idea

An index is defined by its weighting scheme, and the scheme decides what the number means. A price-weighted index adds share prices and divides by a divisor, so a high-priced share sways it regardless of the company's size — and every split forces the divisor to be reset. A market-capitalisation-weighted index weights by value, which matches what an investor holding the whole market would own, but tilts toward whatever has already risen. An equal-weighted index gives every constituent the same say, which tilts toward smaller companies and needs constant rebalancing to stay equal. None is neutral: choosing an index is choosing a view about what should count.

Formulas

Price-weighted index

index = Σ Pᵢ ÷ d

Pᵢ
the price of one share of each member
d
the divisor, reset on splits and on changes of membership

One share of each, so a high-priced company moves the index more than a large one. The divisor exists only to stop a split changing the level, and it drifts away from the number of members over time.

Weight in a market-capitalisation-weighted index

wᵢ = MVᵢ ÷ Σ MV

MVᵢ
the market value of a member — its price × its shares outstanding
Σ MV
the market values of every member added together

Weights move with prices, so the index rebalances itself and a risen company takes a larger share. Float-adjusted versions count only the shares actually available to buy.

A practice question

From the question bank, with the reason each wrong option is wrong.

A price-weighted index gives the greatest influence to the constituent with the highest:

  1. share price — correct
  2. market capitalisationWhy not: That is the capitalisation-weighted scheme. A price-weighted index never looks at shares outstanding, so a small company with an expensive share can dominate it.
  3. revenueWhy not: No common index weights by revenue. Fundamental schemes use measures such as sales or book value, but a price-weighted index sums prices and nothing else.

It sums prices, so a share priced at 500 moves the index ten times as much as one priced at 50.

A harder one

Three shares are priced at $10, $20 and $60. In a price-weighted index their weights are closest to:

  1. 33% eachWhy not: That is the equal-weighted answer. A price-weighted index divides each price by the total of 90, which is nowhere near equal.
  2. 11%, 22% and 67% — correct
  3. equal to their market valuesWhy not: Market values need shares outstanding, which the question never gives. Price weighting ignores them by construction.

The prices total 90, so the weights are 10/90, 20/90 and 60/90 regardless of how big the companies are.

The hardest tier

A price-weighted index rises 2% while a capitalisation-weighted index of the same shares falls 1%. The most likely explanation is that:

  1. one index has more constituentsWhy not: The question states that both cover the same shares, so membership cannot be the difference.
  2. dividends were excluded from oneWhy not: A dividend difference would be a small, one-directional gap, not a reversal of sign over the same shares.
  3. high-priced but smaller companies outperformed — correct

The two schemes disagree exactly when price and size point in different directions.

In the app: 21 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.

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