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Contrast indexes weighted by price with those weighted by market capitalisation

CFA® Level I · Equities · 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. Most capitalisation-weighted indexes are float-adjusted: they count only the float, the shares actually available to public investors, and leave out shares locked up by governments, founders or other companies. 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.

A price-weighted index adds up the share prices and divides by a fixed number called the divisor. Formula: Index = (sum of share prices) / divisor. So each share's weight is Weight = its price / total of all prices. A 10% move in a $500 share changes the index ten times as much as a 10% move in a $50 share. A small firm with a high share price can outweigh a much bigger firm with a low one, because size is ignored.

A harder one

A market-capitalisation-weighted index is often criticised for:

  1. overweighting the smallest companiesWhy not: Small companies get the smallest weights here. It is equal weighting that gives them more than their size warrants.
  2. requiring frequent rebalancing tradesWhy not: Capitalisation weights follow prices automatically, so this scheme needs the least trading of all. Equal weighting is the one that drifts.
  3. overweighting stocks that have risen - correct

Market capitalisation is the total value of a company's shares, found as price x number of shares. Each weight is Weight = company's market cap / total market cap. When a share price rises, its market cap and weight rise automatically, so the index holds more of what has already gone up and less of what has fallen. Critics say this builds in a bias towards shares that may now be overpriced. The index does not ignore size, and it needs the least trading to maintain.

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 indices hold the same shares but weight them differently. A price-weighted index gives most influence to shares with a high price per share (Weight = price / sum of prices). A capitalisation-weighted index gives most influence to big companies (Weight = market cap / total market cap). They can move in opposite directions when a share with a high price but a small company value did well while the largest companies did badly. The rest do not fit the facts, since both cover the same shares.

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