11k or 12k, Sensex and Dow are different

MUMBAI: “A little knowledge is a dangerous thing,” said Alexander Pope, more than 130 years back. And how right he was.

The Bombay Stock Exchange Sensitive Index, popularly known as the Sensex, overtook the Dow Jones Industrial Average (DJIA) for the first time in 10 years. 

But the fact is one cannot compare the DJIA to the Sensex. In fact the only thing common to both the indices is that both have 30 stocks. The way both these indices are constructed are very different. The DJIA is a price weighted index vis-a-vis the Sensex, which is a free-float market  capitalisation weighted index.

To calculate DJIA, all one needs to do is add up the prices of the 30 stocks that constitute the index and divide it by a number known as index divisor. In fact, when DJIA was first published on May 26, 1896, the methodology used to compute it was even more simple. It was just the sum of the price of the 12 stocks that constituted the index.

Over the years, this has been modified and the index divisor has been brought in. The divisor was brought in primarily to smoothen out the effects of stock splits and other corporate actions.

Currently, the value of the index divisor is 0.12493117. On March 31, 2006, the sum of the closing value of the 30 stocks that constitute the index was 1,393.07. On dividing this by the index divisor (0.12493117) we get the closing value of the index, which was 11150.7. 

Sensex, on the other hand, was initially calculated on the basis of the “full market capitalisation” methodology, but was shifted to the free-float methodology with effect from September 1, 2003.

To calculate the index, the market capitalisation of a company is first determined by multiplying the price of its stock by the number of shares issued. This is then multiplied by the free float factor to arrive at the market capitalisation.

Free-float market capitalisation is essentially the proportion of total shares of the company that are readily available for trading in the stock market. This was introduced to take care of companies like Wipro, NTPC, ONGC etc, which are mostly owned by their promoters, and hence, their liquidity has to be taken into account while calculating the index value.

As the BSE website explains, the free-float market cap excludes promoters’ holdings, government holdings, strategic holdings and other locked-in shares that will not come to the market for trading in the normal course. The companies need to inform this to the exchange every quarter.

Let’s take the case of Wipro. If, at a given moment, the market cap of Wipro is Rs 79,632.42 crore (at a market price of Rs 560.5 and 1420739099 shares outstanding), then a market cap of Rs 15,926.49 crore will be considered while calculating the index.

This is the free-float market cap, which is arrived at by multiplying the market capitalisation of the company, with the free float factor, which for Wipro is .2. Wipro has a free float factor of .2, because 81.73% of its stock is held by promoters and hence is unavailable in the market for trading.

This free float market capitalisation is then calculated for the all the thirty stocks that constitute the index and then added up. The sum is then divided by the index divisor to arrive at the Sensex figure.
 
The movement of the DJIA is affected only by changes in the price of stocks, the Sensex by  the price change of the stock, the change in number of stocks outstanding and the change in the free-float factor.

Clarification: The article “Why are pop corn, coffee so expensive in multiplexes?” carried on March 30, 2006, was based on the book, The Undercover Economist by Tim Harford. Unfortunately, a reference to the book was missing in the piece. DNA Money apologises for the error.