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

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

Many of us deal with the stock markets on a daily basis — as investors, brokers, dealers or financial analysts. And, to gauge the performance of the market, we typically seek information on a stock index number. What is an index number? It is a summary measure of the performance of the stock market as a whole.

Changes in its value serve as a barometer of happenings that have a bearing on the performance of financial securities. Why do we need an index number?

As of July 2012, about 1,650 companies were listed on the National Stock Exchange (NSE). If someone were to give you information on the price changes or returns for these companies from one day till the next, in the form of 1,650 values, can a rational mind deduce meaningful conclusions about the performance of the market? Clearly, it would be impossible and we would seek a summary statistic.

There is more than one method for computing a stock index number. The common approaches are: the price-weighted technique, the value-weighted technique and the equally weighted method. Irrespective of the computational method, the first step in constructing a stock market index is to decide how many companies ought to be represented, and which ones in particular.

Although the number of companies represented by an index is usually constant, the composition of the indices will typically change over time as the global economy evolves. For instance, the Dow Jones Industrial Average (Dow), which is by far the best known stock index in the world, is based on the prices of 30 companies, and was computed for the first time in 1896. Over the years, as the industrial and information revolutions have unfolded, the structure of the world economy has changed.

Information technology companies now command a lot of attention, both in the West and in India. Quite obviously, 30 years ago, this would not have been the case. An index ought to be broad-based and represent a significant cross-section of the market that it is trying to mirror.

The Dow is based on 30 stocks and is price-weighted. A price-weighted index is computed by adding up the latest prices of all the component stocks and dividing the price aggregate by a number known as the ‘divisor’.

On the ‘base date’, which is the day on which the index is being computed for the first time, the divisor can be 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.

In addition to the Dow, the Nikkei 225 index based on the Japanese stock market is also a well-known price weighted index. However, other global indices, such as the S&P 500 and the Nasdaq 100, are value weighted. In India, both the Sensex and the Nifty are value weighted.

An equally weighted index is very simple to compute in practice. We need to calculate one plus the arithmetic average return of all the constituent stocks from one day till the next. The number is multiplied by the previous day’s index value to compute the latest index value. Once again, the index value on the base date can be any arbitrary number.

The writer has authored ‘Fundamentals of Financial Instruments’, published by Wiley, India

In a nutshell

* A stock index number is a summary measure of the performance of the stock market as a whole

* The methods to compute a stock index number include: the price-weighted technique, the value-weighted technique and the equally weighted method.

* Irrespective of the computational method, the first step in constructing a stock market index is to decide how many companies ought to be represented, and which ones in particular.

* A price-weighted index is computed by adding up the latest prices of all the component stocks and dividing the price aggregate by a number known as the ‘divisor’

* In the value-weighted technique, 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

* In equally weighted method, one needs to calculate one plus the arithmetic average return of all the constituent stocks from one day till the next. The number is multiplied by the previous day’s index value to compute the latest index value. Once again, the index value on the base date can be any arbitrary number

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