Ask Mint | Understanding how the value of the Sensex is calculated

Ask Mint | Understanding how the value of the Sensex is calculated
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First Published: Sun, Jun 22 2008. 11 58 PM IST

Updated: Sun, Jun 22 2008. 11 58 PM IST
Tasting tomato ketchup does not require much effort. Simply dip your finger and put it in your mouth and you will know the taste. But understanding how ketchup is made requires some mental exercise. Our friend Johnny is also busy doing some mental exercise. But he is not interested in knowing how ketchup is made. He wants to understand how the value of the Sensex is calculated.
Johnny: Hi, Jinny! For the last one week, I have been doing all sorts of mathematical calculations. I hope I am now fully ready to resume our discussion.
Jinny: Okay, let’s start from where we had left last week. I had told you that in the beginning the Sensex was calculated using the market capitalization
weighted methodology but from September 2003, it shifted to the free-float market capitalization weighted methodology. You may be wondering what the difference between the two is. Well, the full market capitalization of a company is determined by multiplying the current market price of the shares with the total number of shares issued by the company. But, all shares of the company may not be available for trading. Some of them remain locked with promoters, institutional investors, government, etc. The total number of shares actually available for day-to-day trading is known as free float. So, we can calculate the free-float market capitalization by multiplying the number of shares actually available for trading with the market price. In other words, free-float market capitalization tells us how much money will be required for buying all the shares of a company that are available for trading.
Johnny: What role does market capitalization or free-float market capitalization play in calculating the value of the Sensex?
Jinny: You can use either market capitalization or free-float market capitalization for calculating the value of an index. The Sensex now uses free-float market capitalization so let’s talk only about that. To start with, you need to calculate the free-float market capitalization of stocks in the base year of all the companies included in the index. Suppose in the base year the free-float market cap of company A is Rs100, B is Rs200, C is Rs300, and so on. Suppose the value of the total free-float market capitalization of all the 30 companies in the index is Rs1,000. After this, you need to establish a proportional relationship between the base value of your index and the free-float market cap of all the 30 companies. How would you do that? You can do that by using some elementary mathematics. Do you see a proportional relationship between the base value of 100 of your index and Rs1,000 of free-float market capitalization?
Illustration: Malay Karmakar / Mint
Johnny: Yes! Each Rs10 of market capitalization seems worth a single point of our base value of the index. So, if the market cap rises by Rs100, our index should rise by 10 points.
Jinny: That’s right! But this whole relationship can be put in a scientific formula. The proportional link between the base value of the index and the free-float market cap is provided by what is called the index divisor. If you divide the free-float market cap of Rs1,000 by the index divisor 10, you get 100, which is your base value. The next day, suppose the free-float market cap increases by 20% to Rs1,200. You again divide it by your index divisor 10, which gives you 120 as the value of the index, which is exactly 20% higher than the previous day’s index. So, to calculate the value of the index on any day, you just need to divide the free-float market cap of all the shares with the index divisor. The index divisor acts as a link between the past and present value of the index. It also helps in ensuring that corporate actions, such as stock splits, bonus and rights issue, mergers, etc., do not distort the value of our index.
Johnny: How is the index divisor able to do that?
Jinny: Well, the index divisor plays a great role in what is known as “maintenance of index” in technical terms. Maintenance of index requires making the necessary changes in the value of the index divisor to counterbalance the effects of corporate actions. Suppose there is no increase in the market price of shares but some company has come out with a bonus issue of shares. In that case also, your free-float market cap will show an increase. But in reality, the prices have not moved at all. If your index shows a rise or fall due to corporate actions such as bonus issue, rights issue, stock split, etc., then that will not be a true representation of the market trend. To take care of such situations, the necessary adjustments are made in the index divisor so that the continuity of the index is not affected. So, choosing the right index divisor is always important.
Johnny: That’s true, Jinny. Choosing the right knife for cutting your ingredients is the first step for making good ketchup.
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First Published: Sun, Jun 22 2008. 11 58 PM IST