Last week, we attempted to demystify a stock index for you ( Index Basics - I ) . Hope it was useful to some of you who previously had very little to do with stock markets. This week, we will try and explain how a stock index is actually constructed. Rest assured that it would not be a lesson in BSc level statistics. Instead, as is our wont, we will use simple mathematics to tell the story. So here it goes…

An ideal index must serve two purposes. First, it should represent the changes taking place in the scrips. Secondly, it must be able to reflect movements in price of some typical shares in order to represent the market better. Starting from this premise, let us see how an index is constructed. The process can be divided into three areas - coverage, base year selection and method of compilation.

As explained above, an index should ideally consist of scrips, which represent a wide cross-section of the industry, have good liquidity and a high market cap. The BSE Sensex today lists shares of 30 companies from the so-called 'specified' group. The table below lists the shares along with their market caps.

Source: Quantum Information Services

The scrips in the BSE index do not remain a permanent feature. The index has been revamped a total of three times since its formation. The revamp was necessitated to remove scrips which have fallen out of favor with investors for whatever reasons and to bring in those scrips which have enthused marketmen and represent industries which have been the flavor for some time. Take the recent revamp of the Sensex, which took place in March 2000. Indian Hotels (hospitality), Industrial Development Bank of India (finance), Tata Chemicals (chemicals) and Tata Power (electricity) made their way out and in their place came Satyam Computers (software), Zee Telefilms (media), Dr. Reddy's (pharma) and Reliance Petroleum (refining). If you are not a complete ignoramus, this development should seem hardly surprising. Old economy stocks gave way to the new economy ones.

The base of an index is chosen so as to have a suitable starting point. In case of the BSE, the year was taken as 1979-80. Considerations for the choice were the price stability during the year and proximity to the year in which the index was introduced.

The two important methods for computation of an index are:

1. Price weighted arithmetic mean method, and
2. Capitalization weighted arithmetic mean method.

An example would illustrate the methodology and the differences between the two methods.

Suppose the index comprises the following four securities on the base date:

Prices of the same scrips today:

Under the price weighted arithmetic mean method, the index as at the base date and today would be:

Index = 1.0000 x 1000 = 1000

Index = 1.0596 x 1000 = 1,059.60

Under the capitalization weighted arithmetic mean method, the index as at the base date and today would be:

Index = 1.0000 x 1000 = 1000

Index = 1.0000 x 1.041 = 1,041

As mentioned some time before, the capitalization-weighted method is preferable to the price weighted method. This is especially true in the Indian context where a number of firms have a low number of outstanding shares.

Fund / Portfolio managers:

• Derivatives trading – Fund managers can use indices to hedge their exposures in equities
• Passive investment management – Index funds replicate the indices to earn the market returns
• Benchmarking performance – Open and close-ended funds’ performances can be effectively benchmarked against the indices and this forms the basis for evaluation of performance of the various funds.

Traders / Market intermediaries:

• Evaluating market sentiment – The indices help traders and the various market intermediaries to gauge the performance and sentiment for the market as a whole.

Corporates:

• Comparison across market – Corporates can compare their performance with competitor’s performance, business group performance or market performance as a whole with the help of indices.

Individuals:

• Individual investors can benchmark their own portfolio’s performance against the performance of the market as well as to gauge the performance of the market as a whole.