# Capitalization-weighted index

A capitalization-weighted index is an index whose components are weighted according to the total market value of their outstanding shares. Also called a market-value-weighted index. The impact of a component's price change is proportional to the issue's overall market value, which is the share price times the number of shares outstanding.

For example, the AMEX Composite Index (XAX) has more than 800 component stocks. The weighting of each stock constantly shifts with changes in the stock's price and the number of shares outstanding. The index fluctuates in line with the price move of the stocks.[1]

## Mathematical formula

$\frac{ index_{\rm_{new}}}{ index_{\rm_{old}}} = \frac{ \sum {\# shares} \cdot price_{\rm_{new}}}{ \sum {\# shares} \cdot price_{\rm{old}}}$

## Other types of indices

An index may also be classified according to the method used to determine its price. In a price-weighted index such as the Dow Jones Industrial Average, the price of each component stock is the only consideration when determining the value of the index. Thus, price movement of even a single security will heavily influence the value of the index even though the dollar shift is less significant in a relatively high-value name. In a market-share weighted index, price is weighted relative to the number of shares, rather than their total value. In a fundamentally weighted index, stocks are weighted by fundamental factors like sales or book value.

Traditionally, capitalization-weighted indices in the United States tended to have a full weighting, i.e., all outstanding shares were included; overseas, because partial government ownership of large companies was more common, so-called float-weighted indexing has been the norm for many non-U.S. indices. Recently, many of the U.S. indices, such as the S&P 500, have been changed to a float-adjusted weighting which makes their calculation more consistent with non-U.S. indices.

A free float adjustment factor is introduced in calculations for the index. This represents the proportion of shares that is free floated as a percentage of issued shares and then is rounded to the nearest multiple of 5% for calculation purposes. To find the free-float capitalization of a company, first find its market cap (number of outstanding shares x share price) then multiply its free-float factor. The free-float method, therefore, does not include restricted stocks, such as those held by company insiders.[2]

## Notes

1. ^ John Downes & Jordan Elliot Goodman, Finance and Investment Terms, Barrons Financial Guides, 2003
2. ^ Market Cap calculations via Wikinvest

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