# What’s a stock index number and how to compute it

Dec 11 2012, 10:12 IST
SummaryMany of us deal with the stock markets on a daily basis — as investors, brokers, dealers or financial analysts.

any arbitrary value. A logical value would be the number of companies being included in the index.

Subsequently, the divisor may have to be amended for any of the following reasons. The first is that there could be a corporate action such as, a stock split or a reverse split, a stock dividend or a bonus issue, or a rights issue at a discount to the prevailing market price. Second, there may be a change in the composition of the index in the sense that one constituent company may be replaced with another.

The impact of such changes could be either an increase or a decrease in the divisor. In the case of the Dow, the divisor has been changed so many times over the past 100 plus years, such that it is now less than 1.0 and, hence, should be more appropriately termed as a ‘multiplier’.

One of the shortcomings of a price-weighted index is that the relative importance of a company depends on its market price and not on its market capitalisation. Thus, a 20% change in a R200 stock will have a significantly less impact on the index than a similar percentage change in a R1,200 stock, although the first company may have a higher market capitalisation.

Finance theory postulates that the importance attached to a company should be based on its market capitalisation, which is the product of its share price and the number of shares outstanding, and this is the approach taken by the second category of stock indices termed as value-weighted indices.

In the case of such indices, the aggregate market capitalisation on the day of computation is divided by the aggregate market capitalisation on the base date, and the ratio is multiplied by the base date index value, which is an arbitrary number. Any changes to any of the constituent companies is captured by either modifying the divisor, which in the case of such indices is always assigned a value of 1.0 on the base date, or by changing the base period market capitalisation subsequently.

The beauty of such indices is that, in theory, the market capitalisation of a company is invariant to stock splits and reverse splits, and bonus issues. Consequently, the only actions that mandate a change in the divisor (or the base period market capitalisation) are rights issues, at a discount or otherwise, and changes in index composition.

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