
How Stock Indices Work 
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This article is a part of Wikinvest's Personal Finance section and Guide to Investing. Please contribute or edit to improve it. 
A stock index is generally a portfolio of stocks, bonds or other kinds of investments which are used to represent either segments of an exchange or the whole exchange. One of the most common ways to understand a stock index is to have a look at the composition of the stocks it represents. Generally, the set of rules require the stocks to satisfy certain criteria, such that^{[1]}:
The benchmark indices of various exchanges not only represent the stocks, but the scenario of the market as a whole. Hence, they are used to depict the overall health of the economy as well. Understanding how the index works, is a good way to begin analysis on various stocks and their importance to the economy. A good way to analyze and index is to understand the composition of the stocks it represents.
A broad based index or composite index is the one which covers almost all stocks on the exchange (or a certain majority percentage of the market capitalization on the exchange). The main purpose of the broad based index is to act as a proxy for the performance of the economic conditions of the entire market, or reveal investor sentiment towards the market.
Based on the definition of a stock index, a global index could include indices which span across exchanges and possibly countries. The Dow Jones Wilshire 5000 Total Stock Market Index spans all publicly traded index in America, excluding foreign stocks and ADRs. The Euronext 100 includes stocks from all over the European Union and the Russell Investment group have something called the Global Index.
These indices are also called market capitalization weighted indices or the valueweighted indices. They involve the total market capitalization of the companies weighted by their effect on the index, so the larger stocks would make more of a difference to the index as compared to a smaller market cap company. This is also called the free float method. The basic formula for any index is (be it capitalization weighted or any other stock index)^{[2]}:
The Free float Adjustment factor represents the proportion of shares that is freefloated as a percentage of issued shares and then its rounded up to the nearest mulitple of 5% for calculation purposes. To find the freefloat capitalization of a company, first find its market cap (number of outstanding shares x share price) then multiply its freefloat factor. The freefloat method, therefore, does not include restricted stocks, such as those held by company insiders.
While one might track this portfolio’s value in dollar terms, it would probably be an unwieldy number – for example, the S&P 500 market value is roughly $11.8 trillion. Rather than deal with ten or more digits, the figure is scaled to a more easily handled number, currently around 1250. Dividing the portfolio market value by a factor, usually called the Index divisor, does the scaling.
Continuity in index values is maintained by adjusting the divisor for all changes in the constituents’ share capital after the base date. This includes additions and deletions to the index, rights issues, share buybacks and issuances, and spinoffs. The divisor’s time series is, in effect, a chronological summary of all changes affecting the base capital of the index. The divisor is adjusted such that the index value at an instant just prior to a change in base capital equals the index value at an instant immediately following that change^{[3]}.
The Standard and Poor's indices are the best examples of this method. The S&P 500 (.SPXE) was the original index for which this formula was created for. Other examples include the S&P/ASX 200 Index (XJOAU) index and the S&P/TSX Composite Index (.TTTT). The FTSE and Russell indices also follow this weighted method.
Another version of this method is called the LasPeyres Index or the Baseweighted aggregative method^{[4]}. They are weighted by shares instead of the index divisor. The formula now would be:
The DAX indices on the Frankfurt Stock Exchange use this method to calculate the index value.
A modified market cap weighted index is a hybrid between equal weighting and capitalization weighting. It is similar to a general market cap with one main difference: the largest stocks are capped to a percent of the weight of the total stock index and the excess weight will be redistributed equally amongst the stocks under that cap (similar to the calculations above).
Where the Adjusting Weight Factor for each index component would be calculated as^{[5]}:
The NASDAQ 100 and the OMX Nordic 40 (OMXN40SK) are great examples of modified capitalizationweighted indices, that are designed to track the performance of their respective markets.
A price weighted stock or a equal weighted stock index is one which places equal importance to each stock and such that changes in stock values will not have an adverse effect on the index. The stocks are included in terms of their quoted price, such that a 20$ stock will have twice the proportion of a 10$ stock. In comparison, the capitalization weighted method places importance on the total equity of the stock in the market.
The Dow Jones Industrial Average (.DJIA) is the most famous example of a price weighted index.
To calculate an equal weighted index, the quoted price for each stock used in the calculation of the index is redefined so that each index constituent has an appropriate weight in the index at each rebalancing date. In addition to being the product of the stock price, the stock’s shares outstanding, and the stock’s float factor – and the exchange rate when applicable; a new adjustment factor is also introduced in the market capitalization calculation to establish equal weighting.
The Adjustment factor of a stock is assigned to the stock at each rebalancing date, allows for price weighting. For index component, the value would be:
The main criticism with this index is that a $5 priced share would have less weighting as the $200 priced share, which might be a smaller company than the former, which gives the smaller shares more weight than their due. Moreover, the stocks keep changing and so does the equality, so the stock has to be rebalanced from time to time^{[7]} as compared to a cap weighted index.
Another way of classification of indices and subsequent calculations involves basing the index value on the fundamental data rather than having the market capitalization as the basis. These resemble Style indices or Attribute Weighted indices, usually value style indices. The main fundamentals used for such an index generally include accounting terms such as^{[8]}:
The difference in this approach is that one is not tracking the market, hence can use the index to exploit the anamolies in order to gain profits. However, this is not strictly passive investing. Moreover, its still a relatively new method of investing, hence the jury is still out on its effectiveness.
At the dawn of the new century, new approaches to weighting stocks have emerged as alternatives to market cap and price value weighting methods. In 2005, Standard & Poor's introduced the S&P Pure Growth Style Index and S&P Pure Value Style Index which was attribute weighted. That is, a stock's weight in the index is decided by the score it gets relative to the value attributes that define the criteria of a specific index, the same measure used to select the stocks in the first place. For these two stocks, a score is calculated for every stock, be it their growth score or the value score (a stock cant be both) and accordingly they are weighted for the index^{[9]}
In order to rebalance, the relative score must be proportional to the relative weights of the stock on the index. The weight itself is a function of the total market value of the stock.The structure of the index ascertains the number of each stock to be represented in the index and the market decides the price.
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