IFS – Sensex


These are the notes obtained from Prof. Manjunath. I just spoke to Vidyuth, who scanned and emailed the following information to me. I didn’t attend the IFS class today and thus I’m not really sure about what Prof. Manjunath said. What Vidyuth told me is: We have to answer the 4 questions based on the material given below. He expects a handwritten copy to be submitted to him in class on Saturday (9th August) – today.

All credit to Vidyuth for doing all the work.

Hope this is of use just as the Accounts CIA was…


  1. what is sensex?
  2. what is the methodology in calculating sensex?
  3. history of sensex
  4. what are the advantages of sensex?



SENSEX, first compiled in 1986, was calculated on a Market Capitalization-Weighted” methodology of 30 component stocks representing large, well-established and financially sound companies across key sectors. The base year of SENSEX was taken as 1978-79. SENSEX today is widely reported in both domestic and international markets through print as well as electronic media. It is scientifically designed and is based on globally accepted construction and review methodology. Since September 1, 2003, SENSEX is being calculated on a free-float market capitalization methodology. The “free-float market capitalization-weighted” methodology is a widely followed index construction methodology on which majority of global equity indices are based; all major index providers like MSCI, FTSE, STOXX, S&P and Dow Jones use the free- float methodology.

The growth of the equity market in India has been phenomenal in the present decade. Right from early nineties, the stock market witnessed heightened activity in terms of various bull and bear runs. In the late nineties, the Indian market witnessed a huge frenzy in the ‚ÄėTMT’ sectors. More recently, real estate caught the fancy of the investors. SENSEX has captured all these happenings in the most judicious manner. One can identify the booms and busts of the Indian equity market through SENSEX. As the oldest index in the country, it provides the time series data over a fairly long period of time (from 1979 onwards). Small wonder, the SENSEX has become one of the most prominent brands in the country.

SENSEX Calculation Methodology

SENSEX is calculated using the “Free-float Market Capitalization” methodology, wherein, the level of index at any point of time reflects the free-float market value of 30 component stocks relative to a base period. The market capitalization of a company is determined by multiplying the price of its stock by the number of shares issued by the company. This market capitalization is further multiplied by the free-float factor to determine the free-float market capitalization.

The base period of SENSEX is 1978-79 and the base value is 100 index points. This is often indicated by the notation 1978-79=100. The calculation of SENSEX involves dividing the free- float market capitalization of 30 companies in the Index by a number called the Index Divisor. The Divisor is the only link to the original base period value of the SENSEX. It keeps the Index comparable over time and is the adjustment point for all Index adjustments arising out of corporate actions, replacement of scrips etc. During market hours, prices of the index scrips, at which latest trades are executed, are used by the trading system to calculate SENSEX every 15 seconds. The value of SENSEX is disseminated in real time.


BSE also calculates a dollar-linked version of SENSEX and historical values of this index are available since its inception. (For more details click ‚Äė series of BSE indices’

SENSEX – Scrip Selection Criteria

The general guidelines for selection of constituents in SENSEX are as follows:

1. Listed History: The scrip should have a listing history of at least 3 months at BSE. Exception may be considered if full market capitalization of a newly listed company ranks among top 10 in the list of BSE universe. In case, a company is listed on account of merger! demerger! amalgamation, minimum listing history would not be required.

2. Trading Frequency: The scrip should have been traded on each and every trading day in the last three months at BSE. Exceptions can be made for extreme reasons like scrip suspension etc.

3. Final Rank: The scrip should figure in the top 100 companies listed by final rank. The final rank is arrived at by assigning 75% weightage to the rank on the basis of three- month average full market capitalization and 25% weightage to the liquidity rank based on three-month average daily turnover & three-month average impact cost.

4. Market Capitalization Weightage :The weightage of each scrip in SENSEX based on three-month average free-float market capitalization should be at least 0.5% of the Index.

5. Industry/Sector Representation :Scrip selection would generally take into account a balanced representation of the listed companies in the universe of BSE.

6. Track Record :In the opinion of the BSE Index Committee, the company should have an acceptable track record.

Understanding Free-float Methodology


Free-float methodology refers to an index construction methodology that takes into consideration only the free-float market capitalization of a company for the purpose of index calculation and assigning weight to stocks in the index. Free-float market capitalization takes into consideration only those shares issued by the company that are readily available for trading in the market. It generally excludes promoters’ holding, government holding, strategic holding and other locked-in shares that will not come to the market for trading in the normal course. In other words, the market capitalization of each company in a free-float index is reduced to the extent of its readily available shares in the market.

Subsequently all BSE indices with the exception of BSE-PSU index have adopted the free-float methodology.

Major advantages of Free-float Methodology

  • A Free-float index reflects the market trends more rationally as it takes into consideration only those shares that are available for trading in the market.
  • Free-float Methodology makes the index more broad-based by reducing the concentration of top few companies in Index.
  • A Free-float index aids both active and passive investing styles. It aids active managers by enabling them to benchmark their fund returns vis-A -vis an investible index. This enables an apple-to-apple comparison thereby facilitating better evaluation of performance of active managers. Being a perfectly replicable portfolio of stocks, a Free float adjusted index is best suited for the passive managers as it enables them to track the index with the least tracking error.
  • Free-float Methodology improves index flexibility in terms of including any stock from the universe of listed stocks. This improves market coverage and sector coverage of the index. For example, under a Full-market capitalization methodology, companies with large market capitalization and low free-float cannot generally be included in the Index because they tend to distort the index by having an undue influence on the index movement. However, under the Free-float Methodology, since only the free-float market capitalization of each company is considered for index calculation, it becomes possible to include such closely-held companies in the index while at the same time preventing their undue influence on the index movement.
  • Globally, the Free-float Methodology of index construction is considered to be an industry best practice and all major index providers like MSCI, FTSE, S&P and STO)(X have adopted the same. MSCI, a leading global index provider, shifted all its indices to the Free-float Methodology in 2002. The MSCI India Standard Index, which is followed by Foreign Institutional Investors (FIls) to track Indian equities, is also based on the Free- float Methodology. NASDAQ-100, the underlying index to the famous Exchange Traded Fund (ETF) – QQQ is based on the Free-float Methodology.

Definition of Free-float

Shareholding of investors that would not, in the normal course come into the open market for trading are treated as ‚ÄėControlling! Strategic Holdings’ and hence not included in free-float. Specifically, the following categories of holding are generally excluded from the definition of Free- float:

  • Shares held by founders/directors! acquirers which has control element
  • Shares held by persons! bodies with “Controlling Interest”
  • Shares held by Government as promoter/acquirer
  • Holdings through the FDI Route
  • Strategic stakes by private corporate bodies! individuals
  • Equity held by associate/group companies (cross-holdings)
  • Equity held by Employee Welfare Trusts
  • Locked-in shares and shares which would not be sold in the open market in normal course.

The remaining shareholders fall under the Free-float category.

Determining Free-float Factors of Companies

BSE has designed a Free-float format, which is filled and submitted by all index companies on a quarterly basis. (Format available on http://www.bseindia.com). BSE determines the Free-float factor for each company based on the detailed information submitted by the companies in the prescribed format. Free-float factor is a multiple with which the total market capitalization of a company is adjusted to arrive at the Free-float market capitalization. Once the Free-float of a company is determined, it is rounded-off to the higher multiple of 5 and each company is categorized into one of the 20 bands given below. A Free-float factor of say 0.55 means that only 55% of the market capitalization of the company will be considered for index calculation.

Free-float Bands:

>0 Р5%       0.05   >50 Р55%   0.55

>5-10%       0.10   >55-60%     0.60

>10-15%     0.15   >60-65%     0.65

>15-20%     0.20   >65-70%     0.70

>20 Р25%   0.25   >70 Р75%   0.75

>25 Р30%   0.30   >75 Р80%   0.80

>30 Р35%   0.35   >80 Р85%   0.85

>35 Р40%   0.40   >85 Р90%   0.90

>40 Р45%   0.45   >90 Р95%   0.95

>45-50%     0.50   >95-100%   1.00

Index Closure Algorithm

The closing SENSEX on any trading day is computed taking the weighted average of all the trades on SENSEX constituents in the last 30 minutes of trading session. If a SENSEX constituent has not traded in the last 30 minutes, the last traded price is taken for computation of the Index closure. If a SENSEX constituent has not traded at all in a day, then its last day’s closing price is taken for computation of Index closure. The use of Index Closure Algorithm prevents any intentional manipulation of the closing index value.

Maintenance of SENSEX

One of the important aspects of maintaining continuity with the past is to update the base year average. The base year value adjustment ensures that replacement of stocks in Index, additional issue of capital and other corporate announcements like ‚Äėrights issue’ etc. do not destroy the historical value of the index. The beauty of maintenance lies in the fact that adjustments for corporate actions in the Index should not per se affect the index values.

The BSE Index Cell does the day-to-day maintenance of the index within the broad index policy framework set by the BSE Index Committee. The BSE Index Cell ensures that SENSEX and all the other BSE indices maintain their benchmark properties by striking a delicate balance between frequent replacements in index and maintaining its historical continuity. The BSE Index Committee comprises of capital market expert, fund managers, market participants and members of the BSE Governing Board.

On-Line Computation of the Index

During trading hours, value of the Index is calculated and disseminated every 15 seconds. This is done automatically on the basis of prices at which trades in Index constituents are executed.

Adjustment for Bonus, Rights and Newly Issued Capital

SENSEX calculation needs to be adjusted for issue of Bonus or Rights shares If no adjustments were made, a discontinuity would arise between the current value of the index and its previous value despite the non-occurrence of any economic activity of substance. At the BSE Index Cell the base value is adjusted, which is used to alter market capitalization of the component stocks to arrive at the SENSEX value.

The BSE Index Cell keeps a close watch on the events that might affect the index on a regular basis and carries out daily maintenance of all the 19 Indices.

  • Adjustments for Rights Issues

When a company, included in the compilation of the index, issues right shares, the free- float market capitalization of that company is increased by the number of additional shares issued based on the theoretical (ex-right) price. An offsetting or proportionate adjustment is then made to the Base Market capitalization (see ‚ÄėBase Market capitalization Adjustment’ below).

  • Adjustments for Bonus Issue

When a company, included in the compilation of the index, issues bonus shares, the market capitalization of that company does not undergo any change. Therefore, there is no change in the Base Market capitalization, only the ‚Äėnumber of shares’ in the formula is updated.

  • Other Issues

Base Market capitalization adjustment is required when new shares are issued by way of conversion of debentures, mergers, spin-offs etc. or when equity is reduced by way of buy-back of shares, corporate restructuring etc.

  • Base Market capitalization Adjustment

The formula for adjusting the Base Market capitalization is as follows:

New Base Market Capitalization= Old Base Market Capitalization √ó New Market Capitalization√∑Old MarketCapitalization

To illustrate, suppose a company issues right shares which increases the market capitalization of the shares of that company by say, Rs. 100 crores. The existing Base Market capitalization (Old Base Market capitalization), say, is Rs.2450 crores and the aggregate market capitalization of all the shares included in the index before the right issue is made is, say Rs.4781 crore. The “New Base Market capitalization “will then be:

2450 x (4781+100)√∑4781=Rs.2501.24 crores

This figure of Rs. 2501.24 crore will be used as the Base Market capitalization for calculating the index number from then onwards till the next base change becomes necessary.

Index Review Frequency

The BSE Index Committee meets every quarter to discuss index related issues. In case of a revision in the Index constituents, the announcement of the incoming and outgoing scrips is made six weeks in advance of the actual implementation of the revision of the Index.

Sensex is the most popular and precise barometer of the Indian stock markets. As such it has to keep itself in tune with the constantly changing scenario. It is, after all, a matter of great responsibility to represent a market of more than 6,300 stocks through a 30 composite.

The Bombay Stock Exchange, or BSE, authorities have to, therefore, keep a close watch on its composition, so that the Sensex always represents the maximum market capitalisation and the maximum number of sectors.

However, every once in a while there is a need to revamp the Sensex composition. And this raises numerous queries regarding the implication of any such alteration. Debates rage over whether a particular sector is getting more weightage or otherwise. Then there is talk of Sensex heavyweights that can be used to ‚Äėmanipulat& the Sensex value.

Since billions of rupees are at stake, these are valid questions. However, they require detailed understanding of the mechanics of Sensex calculation. Let us try to understand this aspect.

Basics of Sensex:

1. “Sensex’ is the popular name for the Bombay Stock Exchange Sensitive Index.

2. It is the oldest stock market index currently in use.

3. Sensex is the index of market capitalisation.

4. The base value is 100 on April 1, 1979.

5. Sensex consists of only 30 representative stocks.

6. These 30 are the most active and representative stocks selected from over 6,300 scrips that are listed on the BSE.

7. The total market capitalisation of these 30 stocks accounts for more than 38 per cent of the aggregate market capitalisation of all BSE stocks.

8. The Sensex composition is modified by the BSE authorities at irregular intervals, to keep it in tune with the latest realities of the market.

9. A major reshuffle took place in the Sensex on August 19, 1996, when 15 stocks were replaced.

10. Recently, on April 10, 2000, four stocks were replaced. Satyam Computer, Zee Telefims, Dr. Reddy’s Labs, and Reliance Petroleum have been included in place of Indian Hotels, Tata Power, Tata Chemicals and IDBI.

Basics of Sensex calculation

1. Market capitalisation is the market value of equity shares, (i.e. market price multiplied

by the number of shares). For instance: if ACC has an equity capital of Rs 1.72 billion

with each share having a face value of Rs 10 and its closing price on BSE on April 10,

2000 was Rs 166, then ACC’s market capitalisation on that date is 17.234*166/10 = Rs

28.61 billion.

2. Calculate market capitalisation of all 30 Sensex stocks on a particular date in the same maimer and add this up to get the total market capitalisation of Sensex stocks.

3. Assume that this total market capitalisation is equal to the closing Sensex value on that particular date. The Sensex of any future date can be calculated as a proportion of market capitalisation applied to this Sensex value.

4. An example below shows that the total market capitalisation on April 10, 2000 was Rs

3,731.38 billion, when the Sensex value was 5442.86. If, the total market capitalisation on April 17, 2000 was Rs 3,346.18 billion, then the Sensex for April 17, 2000 is calculated as:

5442.86 * 334617.19 / 373137.82 = 4880.97

If on a panicky day, the Sensex falls by 8 per cent (the maximum permissible fall for each of the constituent stock) from the level of say 4880 points, it would mean a fall of 390- odd points. And this would be calculated as follows:

Now consider the fall in Sensex from 5541.54 on April 11, 2000 to 4657.42 on April 20,

2000. It’s a drop of 884.12 points. During this fall, Infosys came down from Rs 10,626 to

Rs 7,556, i.e. by Rs 3,070. Every Rs 100 of Infosys contributes 9.66 Sensex points.

Therefore, the contribution of Infosys to the Sensex fall can be calculated as:

3070/100*9.66 = 297 Sensex points

Similar calculations will show that the new economy stocks were the major contributors to the fall. Infosys, NuT, Satyam and Zee together contributed about 531 points out of the total Sensex fall of 884 points, which is about 60 per cent by just by these four stocks.

If the Sensex moves wildly, investors can now pin-point the exact reason and take appropriate action.


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