# Understanding How Stock Indices Are Calculated

Indian stock markets have two large-cap indices, namely S&P BSE Sensex and the S&P CNX Nifty. Both these indices are statistical aggregates of the market performance. The changes in the market can be measured based on the performance of these indices using an online trading app.

## The BSE Sensex calculation

The Sensex is an acronym for Sensitive Index and comprises of 30 large and well established companies. It can be called a cross section of the market, as the companies are chosen from various sectors. The Sensex is calculated using the free float market capitalisation method. Free float refers to the shares that are free for trading. All shares of a company are not free to be traded. Some may be government held, some may be in the hands of promoters and others may be pledged. Thus, the Sensex represents the free float market value of its 30 stocks relative to a base period.

Now, let us understand the concept of market capitalisation. Market capitalisation is the combined worth of all the stocks of the different companies in the stock exchange. A companyâ€™s market capitalisation is arrived at by the product of the price of one stock and the total number of shares issued by the company.

Each company listed on the exchange also has to share free float information with the exchange on a quarterly basis. The market capitalization is thus multiplied by the free float factor to arrive at the free float market capitalization. The free float market capitalization is divided by an index divisor to get the Sensex value, which can be tracked using a stock market app. The value of the Sensex in the base year is used as a divisor.

## Let’s understand this with an example

Suppose the Sensex has two companies A and B. Now, A has 500 shares, 300 of these are free floating. The price of each share of A is Rs80. B has 1,000 shares, 700 are free floating. The price of each share of B is Rs100. Market capitalisation of A = 40,000. Market capitalisation of B = 100,000. Free float of A = 0.60 and free float of B = 0.70. Thus, total free float market capital of the index = 40,000 x 0.60 + 100,000 x 0.70 = 94,000. Let’s assume, the base year index was 5,000, so the value of the index will be 94,000 x 100/5,000 =1,880.

## The Nifty calculation

Nifty is also calculated in the similar manner like that of the Sensex. Like the Sensex, a mathematical formula is used to arrive at the calculation. Here is how it is calculated

Market Capitalisation = Equity Capital x Price

Free float market capitalisation = Equity Capital x Price x IWF (Investible Weight Factor, a factor used to determine the number of shares that are tradeable)

Index Value = Current market value/ Base Market Value x Base Index Value (1000)

## How do the Sensex and Nifty differ?

It is evident from the above explanation that the Sensex and Nifty are calculated similarly. However, it may be pointed out in this context, that the Nifty is slightly more broad based as it comprises of 50 stocks. This is as compared to the Sensex that has 30 stocks.