## How BSE index is calculated?

This is a few mathematical formula, that everyone should know.

Suppose the Index consists of only 2 stocks: Stock A and Stock B. (BSE has allocated x no. of stocks for index calculation).

Suppose company A has 1,000 shares in total, of which 200 are held by the promoters, so that only 800 shares are available for trading to the general public. These 800 shares are the so-called ‘free-floating’ shares.

Similarly, company B has 2,000 shares in total, of which 1,000 are held by the promoters and the rest 1,000 are free-floating.

Now suppose the current market price of stock A is Rs 120. Thus, the ‘total’ market capitalisation of company A is Rs 120,000 (1,000 x 120), but its free-float market capitalisation is Rs 96,000 (800 x 120).

Similarly, suppose the current market price of stock B is Rs 200. The total market capitalisation of company B will thus be Rs 400,000 (2,000 x 200), but its free-float market cap is only Rs 200,000 (1,000 x 200).

So as of today the market capitalisation of the index (i.e. stocks A and B) is Rs 520,000 (Rs 120,000 + Rs 400,000); while the free-float market capitalisation of the index is Rs 296,000. (Rs 96,000 + Rs 200,000).

The year 1978-79 is considered the base year of the index with a value set to 100. What this means is that suppose at that time the market capitalisation of the stocks that comprised the index then was, say, 60,000 (remember at that time there may have been some other stocks in the index, not A and B, but that does not matter), then we assume that an index market cap of 60,000 is equal to an index-value of 100.

Thus the value of the index today is = 296,000 x 100/60,000 = 493.33

This is how the Sensex is calculated.

The factor 100/60000 is called index divisor.

-Yuva

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