The ways market indices are determined.

In any particular time period several stocks appreciate in value and several others depreciate. It is easy to miss the big picture when we look at the individual stock prices. On the National Stock exchange (NSE) alone shares of more than 1900 companies are available for trading. So, except for the periods when the markets move decisively pushing up almost all the stocks or hammering down almost all the stocks, it is pretty hard to gauge the performance of the “overall” market looking at the performance of the individual stocks in the time period considered. This is where market indices come to our rescue. Market indices may be structured to mirror a section of the market or the market as a whole. For instance the Bombay Stock Exchange’s (BSE) Sensex (Sensex is derived from the words Sensitive and Index) tracks stocks of 30 biggest and the most actively traded companies listed on the BSE and serves as a good proxy to measure the performance of stocks of large companies. National Stock Exchange’s (NSE) Nifty tracks 50 biggest and most actively traded stocks on the NSE. There are several other indices developed and maintained by the NSE and the BSE. These indices are either designed on the basis of market cap (size) of the companies or are based on specific sectors. CNX MIDCAP is an example of an index designed on the former basis and BANK NIFTY is an index based on the later basis.
A full list of all the NSE Indices and BSE Indices is available at the following links:

http://www.nse-india.com/
http://www.bseindia.com/

Mutual Funds often follow either the market cap strategy or the sectoral strategy i.e. a particular mutual fund may invest in mid-cap stocks or in the technology stocks only. A mutual fund follows a sectoral strategy will most likely choose the appropriate sectoral index as its benchmark and aims to outperform the chosen benchmark. Likewise large-cap, mid-cap, small-cap, micro-cap oriented mutual funds will measure their performance against large-cap, mid-cap, small-cap, micro-cap indices respectively. Also a few mutual funds use the index strategy to invest i.e. these funds invest in the same stocks as those comprise the index and in the same proportions as the index so that the returns they produce closely match index returns. We will dedicate a separate post to mutual funds sometime later.
For, now let us see how the values of these indices calculated. There are two steps in which the index values are calculated .The first step of course is the selection of stocks that make up the index, the stocks selected must be representative of the sector on which the index is based or in case of size based indices must have appropriate the market capitalisation. After the first step is over, the weights to be ascribed to the index constituents are determined. Based on how the weights are determined the indices may be divided into three categories:

1) Price weighted Indices
2) Value Weighted Indices
3) Un-weighted Indices

Price Weighted indices- These are based on the arithmetic average of the “prices” of the stocks constituting the index. The steps involved are
1) Select a date as the base date. Take the arithmetic average of the prices on the base date. Further divide this by a number (called “the index divisor”) so that the arithmetic average becomes a standard base value (say 100 or 1000).
2) For index calculation on any date after the base date, take the arithmetic average of the prices on that day and again divide by the index divisor determined in the step 1.

Price weighted indices are inherently flawed. This is simply because a bigger company with a lower share price has less impact on the index than a smaller company with a greater share price. Sample this, Bajaj Auto (Current Market Price Rs 2200 approx) is much smaller a company than Reliance Industries Limited (CMP Rs 1000 approx) in terms of profits and market capitalisation. While Bajaj autos earned a profit of Rs 570 crores in the quarter ending March 2010, RIL earned a profit of whopping Rs 4800 crores in the same period. Still such an index would place a higher weight on Bajaj Auto than RIL. Bahut naa-insaafi hai !!.

Before we discuss the next big defect with the price weighted indices let us discuss what stock splits are .When the share price of a company’s stock rises to such a great value that it becomes costly to acquire even a single share of the company, the company may decide to split a share into several shares. There is another reason for stock splits i.e. when share a reaches a high value an ordinary investor may get psychologically wary of entering the stock (the “pehle se hi itna badha hua hai, ab aur kya badega” psychology). Suppose you own 10000 shares of Reliance Industries Limited (CMP Rs 1000 approx), so that your holdings in RIL are worth 1 crore rupees approx (a very welcome scenario indeed!!) and the company decides to split its shares 10-1(10 for 1).Post split you will end up owning 1lac shares and the price of each share would approximate Rs 100 so that the worth of your holdings remains unchanged. However, a few companies do not seem to believe the above two arguments for stock splits given above, for ex, the price of single share of Berkshire Hathaway (Warren Buffet’s company) is around-hold your breath ladies and gentlemen- 1.1 lac USD. Closer home the price of a single share of MMTC is Rs 30000 approx.

The figure below shows the one year price chart of telecom major Bharti Airtel.Notice the vertical fall in the price of the stock indicates the split.

Now, consider a hypothetical index with a value 600 comprised of almost two equal sized companies, A and B, each having their shares priced at Rs 1000. Since (1000+1000)/2=1000, the divisor must be 1.67 so as to translate the simple arithmetic average to the index value (1000/1.67=600). At this point of time the two shares have an equal weight in the index, i.e. a 1% increase in either stock will affect the index equally. Now suppose the management of company A decides to split the stock 10-1, so that its price of share changes to Rs100. The value of the index using 1.67 as the index divisor comes out to be ((1000+100)/2)/1.67 =329. To ensure that a price weighted index does not reduce in value post a stock split the value of the divisor needs to be adjusted. Since in the present example the index needs to have a value of 600 post split the new divisor value is 0.916 , so that ((1000+100)/2)/0.916 (=600) equals the pre split index value. Having seen the mechanics of index divisor adjustment in the event of a stock split we come to the second major defect of price weighed indices. You must have noticed that post split the weight of the splitting stock has reduced relative to the other stock. That is 1% percent increase in the value of stock A will affect the index much less than 1% percent increase in stock B. In general faster growing companies split more often than slower growing ones. For example, try finding out the number of times the stocks of Infosys Tech. or Unitech have split since they got listed. I can bet(without googling and verifying) that the number of splits experienced by the above mentioned companies is much higher than by slower growing companies like HUL or Cipla. Since, there is a constant reduction in the index weight of the rapidly growing companies (and stock splitting companies), this type of index understates (underreports) the market performance. If all this leads you to believe that no stock exchanges in countries with well developed capital markets would be following the price weighing methodology to measure the index value here’s the real shocker, Dow Jones uses the price weighting technique to measure its flagship Dow Jones Industrial Average Index(DJIA) in spite of the clear cut warts of the technique.

3) Market Cap Weighted Index- A company’s market cap is a measure of the size of a company and is measured as Price of Each Share*No of Shares outstanding. Here outstanding shares refer to the number of shares issued – no of shares bought back (and extinguished) by the company. We shall postpone the discussion of share buybacks for a later post. Every time the company splits its shares the number of shares outstanding increase and the share price decreases by the same percentage, so that the product (i.e. the market cap) remains constant. Every time the share price of a company changes its market capitalisation changes. The value of index at any point of time is “directly proportional” to the arithmetic average market cap of the stocks comprising the index adjusted of course by a divisor to get to the base value (such as 100) at the base date. There are two distinct advantages of these types of indices over the previously discussed price weighted indices i.e. these indices rightfully give more weights to companies with larger market caps and increase in value of these types of indices is truly reflective of increase in the wealth of the holders of the script. Likewise for decrease in the index values .The second advantage being that the divisor need not be adjusted for splits and the weight of the stock does reduce post splits. Another refinement of the market capitalisation index weighting methodology is the free float market capitalisation methodology. Freely floating shares of a company are the shares available for trading, as opposed to the non tradable shares held by the promoters. Companies differ vastly in terms of the percentages of stake held by the promoters, for ex Infosys the promoter stake is around 16% (well distributed among the promoter families) and rest 84% is available to the public. Contrast this to the more than 70% of Wipro’s stake being held by Mr Azim Premji alone, which is one of the reasons why Mr. Premji was once upon a time the 2rd richest person in the world and Mr Narayanamurthy with his less than 0.5% stake in Infosys will probably never feature even in the list of 500 richest in the world. The free float market cap is calculated by multiplying the price of the share with the number of freely floating shares. An index based on this strategy is better than the index based on the pure market cap strategy as changes in it represent the true increase in value of market investors. Sensex used to be a market cap weighted index but later switched to the free float market capitalisation methodology.

Unweighted Indices: An unweighted index assumes equal Rupee/Dollar worth investments in each stock representing the index on the base date. For ex if on the base date an unweighted index is to be constructed using two component stocks X & Y with share prices Rs 10 and Rs100, the index can be constructed by taking arithmetic average of the values of 10 stocks of X and a single stock of Y, and then selecting the divisor that the value becomes the desired base value. The advantage of this again is that this type of index need not be adjusted for splits. The disadvantage of these types of indexes is obvious i.e. they give equal weightage to all the stocks representing the index irrespective of their size i.e. a 1% increase in value of Bajaj Autos or a 1% increase in the value of RIL will affect the index equally, which is not of course fair, since RIL is likely to be held by much larger number of market investors than Bajaj Autos.

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