Constructing and managing a security market index is similar to constructing and managing a portfolio of securities. Index providers must decide the following:
- Which target market should the index represent?
- Which securities should be selected from that target market?
- How much weight should be allocated to each security in the index?
- When should the index be rebalanced?
- When should the security selection and weighting decision be re-examined?
Target Market and Security Selection
The first decision in index construction is identifying the target market, market segment, or asset class that the index is intended to represent. The target market may be defined very broadly or narrowly. It may be based on asset class (e.g., equities, fixed income, real estate, commodities, hedge funds); geographic region (e.g., Japan, South Africa, Latin America, Europe); the exchange on which the securities are traded (e.g., Shanghai, Toronto, Tokyo), and/or other characteristics (e.g., economic sector, company size, investment style, duration, or credit quality).
Index Weighting
The weighting decision determines how much of each security to include in the index and has a substantial impact on an index’s value. Index providers use a number of methods to weight the constituent securities in an index. Indexes can be price weighted, equal weighted, market-capitalisation weighted, or fundamentally weighted. Each weighting method has its advantages and disadvantages.
Price Weighting
The simplest method to weight an index and the one used by Charles Dow to construct the Dow Jones Industrial Average is price weighting.
The weight is calculated using the following formula:
Equal Weighting
Equal Weighting assigns an equal weight to each constituent security at inception.
The weights are calculated as:
where
- wi = fraction of the portfolio that is allocated to security i or weight of security i
- N = number of securities in the index
Market-Capitalisation Weighting
In market-capitalisation weighting, or value weighting, the weight on each constituent security is determined by dividing its market capitalisation by the total market capitalisation (the sum of the market capitalisation) of all the securities in the index. Market capitalisation or value is calculated by multiplying the number of shares outstanding by the market price per share.
The market-capitalisation weight of security i is:
where
- wi = fraction of the portfolio that is allocated to security i or weight of security i
- Qi = number of shares outstanding of security i
- Pi = share price of security i
- N = number of securities in the index
Float-Adjusted Market-Capitalisation Weighting
In float-adjusted market-capitalisation weighting, the weight on each constituent security is determined by adjusting its market capitalisation for its market float.
Float-adjusted market-capitalisation-weighted indexes reflect the shares available for public trading by multiplying the market price per share by the number of shares available to the investing public (i.e., the float-adjusted market capitalisation) rather than the total number of shares outstanding (total market capitalisation).
The float-adjusted market-capitalisation weight of security i is calculated as:
where
- fi = fraction of shares outstanding in the market float
- wi = fraction of the portfolio that is allocated to security i or weight of security i
- Qi = number of shares outstanding of security i
- Pi = share price of security i
- N = number of securities in the index
Fundamental Weighting
Fundamental weighting attempts to address the disadvantages of market-capitalisation weighting by using measures of a company’s size that are independent of its security price to determine the weight on each constituent security. These measures include book value, cash flow, revenues, earning, dividends, and number of employees.
Letting Fi denote a given fundamental size measure of company i, the fundamental weight on security i is:
