Price Weighting
It is an arithmetic average of current prices. Index movements are influenced by the differential prices of the components.
The weight of each security is calculated using this formula:
The index itself is computed by:
Example
The shares of firm A sells for $100, and the shares of firm B sells for $25. The initial price index is (100 + 25) / 2 = 62.5. The divisor is therefore 2.
Price-weighting is simple, but a price-weighted index has a downward bias.
Both Dow Jones Industrial Average (DJIA) and Nikkei-Dow Jones Average use this method to weight an index.
Equal Weighting
All stocks carry equal weight regardless of their price or market value. A $1 stock is as important as a $10 stock, and a firm with $200 million market value is the same as one with $200 billion.
The actual movements in the index are typically based on the arithmetic average of the percent changes in price or value for the stocks in the index: each percent change has equal weight. Such an index can be used by individuals who randomly select stock for their portfolio and invest the same dollar amount in each stock.
The weight of each security is calculated using this formula:
It assumes that equal dollar amounts are invested in each stock in the index at the beginning of the period. It is typically generated by taking the arithmetic or geometric mean of the percentage changes in the value for the stocks in the index.
The primary advantage of equal weighting is its simplicity. However, since the prices of securities keep changing, the index needs to be rebalanced frequently to maintain equal weights.
Market-Capitalization Weighting
It is generated by deriving the initial total market value of all stocks used in the series. The importance of individual stocks in the sample depends on the market value of the stocks. There is an automatic adjustment for stock splits and other capital changes in this series.
The weight of each security is calculated using this formula:
Qi is the number of shares outstanding of security i.
A market-value-weighted series is generated by:
Example
The shares of firm A sells for $100 with 1 million shares, and the shares of firm B sells for $25 with 20 million shares. Their market value is therefore $100 million and $500 million, respectively. If A increases by 10% to $110, and B increases by 20% to $30, their market value will be $110 million and $600 million, respectively. The rate of return would be: (710 - 600) / 600 = 18.3%.
As you can see firms with large market value have greater impact on the index than firms with small market value. Thus, over time the large market value stocks will dominate changes in a market-value-weighted series.
A free float adjustment factor is introduced in the float-adjusted market-capitalization weighting. It represents the proportion of shares that is free floated as a percentage of issued shares. The index therefore does not include restricted stocks.
Fundamental Weighting
Fundamentally based indices are indices in which stocks are weighted by one of many economic fundamental factors, especially accounting figures which are commonly used when performing corporate valuation, or by a composite of several fundamental factors.
Index Management: Rebalancing and Reconstitution
Rebalancing is adjusting the weights of the constituent securities in the index. This is to maintain the weight of each security consistent with the index's weighting method. There is no need to rebalance price-weighted indices.
Companies may disappear through mergers, acquisitions, or they can become insolvent. A company may no longer satisfy the requirements for index inclusion. Changing the composition of an index is called reconstitution. Reconstitution is to ensure the index represents the desired target market.
Rebalancing and reconstitution create turnover in an index. Reconstitution can dramatically affect prices of current and prospective constituents.
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