How Index is constructed ? (From Quora)

The construction technique of index is quite easy to understand if we assume that there is only one stock in the market. In that case, the base value is set to 100 and let’s assume that the stock is currently trading at 200. Tomorrow the price hits 260 (30% increase in price) so, the index will move from 100 to 130 to indicate that 30% growth. Now let’s assume that on day 3, the stock finishes at 208. That’s a 20% fall from 260. So, to indicate that fall, the Sensex will be corrected from 130 to 104(20%fall).

As our second step to understand the index calculation, let us try to extend the same logic to two stocks – A and B. A is trading at 200 and let’s assume that the second stock ‘B’ is trading at 150. Since the Sensex follows the market capitalization weighted method, we have to find the market capitalization (or size of the company- in terms of price) of the two companies and proportionate weightage will have to be given in the calculation.
How do we compute size of the company- in terms of price?That’s simple. Just multiply the total number of shares of the company by the market price. This figure is technically called ‘market capitalization’.Back to our example-

We assume that company A has 100,000 shares outstanding and B has 200,000 shares outstanding. Hence, the total market capitalization is (200 x 100000 + 150 x 200000) Rs 500 lakhs. This will be equivalent to 100 points.

Lets assume that tomorrow, the price of A hits 260 (30% increase in price) and the price of B hits 135. (10% drop in price).  The market capitalization will have to be reworked. It would be – 260 x 100,000 + 135 x 200,000 = 530 lakhs. That means, due to the changes in price, the market capitalization has moved from 500 lakhs to 530 indicating a 6% increase. Hence, the index would move from 100 to 106 to indicate the net effect.
This logic is extended to many selected stocks and this calculation process is done every minute and that’s how the index moves! 
CALCULATION OF SENSEX. 
What we said was the general method to construct indices. Since, the Sensex consists of 30 large companies and since it’s shares may be held by the government or promoters etc, for the purpose of calculating market capitalization only the free float market value is considered, instead of the total number of shares.
What is free float?That’s the total number of shares available for the public to trade in the market. It excludes shares held by promoters, governments or trusts, FDIs etc..To find the free float market value, the total value of the company (total shares x market price) is further multiplied by a free float market value factor, which is nothing but the percentage of free float shares of a particular company.So logically, the company which has more public holding will have the highest free float factor in the Sensex. This equalizes everything.Example- let’s assume that the market value of a company is Rs 100,000 Crore and  it has 100 Crore shares having a value of Rs 1,000 each but only 20% of it are available to the public for trade. The free float factor would be 20/100 or 0.20 and the free float market value would be .20 x 100,000 = 20,000 Crores.You need not calculate the free float market capitalization since its available straight on the BSE website – Click this link to get it.
NOW, LET’S SE HOW THE SENSEX MOVES.Sensex value = Current free-float market value of constituents stocks/Index Divisor
So, the numerator is available straight from the BSE site. It’s the total of free float factors of 30 stocks x market capitalization.
NOW, THE DENOMINATOR.
The index divisor nothing but the present level of index.
So, now, we have all the figures.
Lets assume that the  free-float market capitalisation is Rs 10,00,000 Crore. At that point, the Sensex is at 12500. What would be the value of Sensex if the free-float market capitalization is Rs 11,50,000 Crore? 
(Those who can’t find the answer may go back to the ratios and proportions chapter elsewhere in school text book)

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About Ashutosh Tilak

Tracking Indian Capital Market since 2010. Finance Student, On this blog I am writing about finance and Investing. You can contact me analystashu@gmail.com or @androidashu & @InsideFinanc on twitter