Beta measures the sensitivity of a scrip movement relative to movement in the benchmark index i.e. SENSEX. A Beta of one means that for every change of 1% in index, the scrip moves by 1%. Statistically Beta is defined as: Covariance (SENSEX, Stock )/ Variance(SENSEX)

(Note: Covariance and variance are calculated from the Daily Returns data of the SENSEX and SENSEX scrips.)

The SENSEX is the benchmark index of the Indian Capital Markets with wide acceptance among individual investors, institutional investors, foreign investors and fund managers. The objectives of the index are:

■ To measure market movements Given its long history and its wide acceptance, no other index matches the SENSEX in reflecting market movements and sentiments. SENSEX is widely used to describe the mood in the Indian Stock markets.

■ Benchmark for funds performance The inclusion of blue chip companies and the wide and balanced industry representation in the SENSEX makes it the ideal benchmark for fund managers to compare the performance of their funds.

■ For index based derivative products Institutional investors, money managers and small investors all refer to the SENSEX for their specific purposes The SENSEX is in effect the proxy for the Indian stock markets. The country’s first derivative product i.e. Index-Futures was launched on SENSEX.

A. Quantitative Criteria:
1. Market Capitalization: The scrip should figure in the top 100 companies listed by market capitalization. Also market capitalization of each scrip should be more than 0.5 % of the total market capitalization of the Index i.e. the minimum weight should be 0.5 %. Since the SENSEX is a market capitalization weighted index, this is one of the primary criteria for scrip selection. (Market Capitalization would be averaged for last six months)

2. Liquidity: (i) Trading Frequency: The scrip should have been traded on each and every trading day for the last one year. Exceptions can be made for extreme reasons like scrip suspension etc. (ii) Number of Trades: Number of Trades: The scrip should be among the top 150 companies listed by average number of trades per day for the last one year. (iii) Value of Shares Traded: Value of Shares Traded: The scrip should be among the top 150 companies listed by average value of shares traded per day for the last one year.

3. Continuity: Whenever the composition of the index is changed, the continuity of historical series of index values is re-established by correlating the value of the revised index to the old index (index before revision). The back calculation over the last one-year period is carried out and correlation of the revised index to the old index should not be less than 0.98. This ensures that the historical continuity of the index is maintained.

4. Industry Representation: Scrip selection would take into account a balanced representation of the listed companies in the universe of BSE. The index companies should be leaders in their industry group.

5. Listed History: The scrip should have a listing history of at least one year on BSE.

B. Qualitative Criteria:
Track Record: In the opinion of the Index Committee, the company should have an acceptable track record.

The closing SENSEX is computed taking the weighted average of all the trades on SENSEX constituents in the last 15 minutes of trading session. If a SENSEX constituent has not traded in the last 15 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.

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 additional issue of capital and other corporate announcements like bonus etc. do not destroy the 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 Index Cell of the Exchange does the day-to-day maintenance of the index within the broad index policy framework set by the Index Committee. The Index Cell takes special care to ensure that SENSEX and all the other BSE indices maintain their benchmark properties by striking a delicate balance between high turnover in Index scrips and its representative character. The Index Committee of the Exchange has experts from different field of finance related to the capital markets. They include Academicians, Fund-managers from leading Mutual Funds, Finance – Journalists, Market Participants, Independent Governing Board members, and Exchange administration.

The arithmetic calculation involved in calculating SENSEX is simple, but problem arises when one of the component stocks pays a bonus or issues rights shares. If no adjustments were made, a discontinuity would arise between the current value of the index and its previous value. The Index Cell of the Exchange periodically adjusts the base value to take care of such corporate announcements.

■ Adjustments for Rights Issues: When a company, included in the compilation of the index, issues right shares, the market capitalisation 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 Capitalisation (see ‘ Base Market Capitalisation Adjustment’ below).

■ Adjustments for Bonus Issue: When a company, included in the compilation of the index, issues bonus shares, the market capitalisation of that company does not undergo any change. Therefore, there is no change in the Base Market Capitalisation, only the ‘number of shares’ in the formula is updated.

Other Issues: Base Market Capitalisation 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 Capitalisation Adjustment: The formula for adjusting the Base Market Capitalisation is as follows: New Base Market Capitalisation = Old Base Market Capitalisation X (New Market Capitalisation /Old Market Capitalisation) To illustrate, suppose a company issues right shares which increases the market capitalisation of the shares of that company by say, Rs.100 crores. The existing Base Market Capitalisation (Old Base Market Capitalisation), say, is Rs.2450 crores and the aggregate market capitalisation of all the shares included in the index before the right issue is made is, say Rs.4781 crores. The “New Base Market Capitalisation ” will then be: Rs.2501.24 crores = 2450 X (4781+100)/4781 This figure of 2501.24 will be used as the Base Market Capitalisation for calculating the index number from then onwards till the next base change becomes necessary.

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 and disseminated in real time.

Dollex-30
BSE also calculates a dollar-linked version of Sensex and historical values of this index are available since its inception.

Understanding Free-float Methodology
Free-float Methodology refers to an index construction methodology that takes into consideration only the free-float market capitalisation of a company for the purpose of index calculation and assigning weight to stocks in Index. Free-float market capitalization is defined as that proportion of total 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.

In India, BSE pioneered the concept of Free-float by launching BSE TECk in July 2001 and Bankex in June 2003. While BSE TECk Index is a TMT benchmark, Bankex is positioned as a benchmark for the banking sector stocks. Sensex becomes the third index in India to be based on the globally accepted Free-float Methodology.

Explanation with example
Suppose the Index consists of only 2 stocks: Stock A and Stock B.

Suppose company A has 1,000 shares in total, of which 200 are held by the promoters, so that only 800 shares are available for trading to the general public. These 800 shares are the so-called ‘free-floating’ shares.

Similarly, company B has 2,000 shares in total, of which 1,000 are held by the promoters and the rest 1,000 are free-floating.

Now suppose the current market price of stock A is Rs 120. Thus, the ‘total’ market capitalisation of company A is Rs 120,000 (1,000 x 120), but its free-float market capitalisation is Rs 96,000 (800 x 120).

Similarly, suppose the current market price of stock B is Rs 200. The total market capitalisation of company B will thus be Rs 400,000 (2,000 x 200), but its free-float market cap is only Rs 200,000 (1,000 x 200).

So as of today the market capitalisation of the index (i.e. stocks A and B) is Rs 520,000 (Rs 120,000 + Rs 400,000); while the free-float market capitalisation of the index is Rs 296,000. (Rs 96,000 + Rs 200,000).

The year 1978-79 is considered the base year of the index with a value set to 100. What this means is that suppose at that time the market capitalisation of the stocks that comprised the index then was, say, 60,000 (remember at that time there may have been some other stocks in the index, not A and B, but that does not matter), then we assume that an index market cap of 60,000 is equal to an index-value of 100.

Thus the value of the index today is = 296,000 x 100/60,000 = 493.33

This is how the Sensex is calculated.

The factor 100/60000 is called index divisor.

BSE Sensex or Bombay Stock Exchange Sensitive Index is a value-weighted index composed of 30 stocks started in 01 of jan, 1986. It consists of the 30 largest and most actively traded stocks, representative of various sectors, on the Bombay Stock Exchange. These companies account for around one-fifth of the market capitalization of the BSE. The base value of the Sensex is 100 on April 1, 1979, and the base year of BSE-SENSEX is 1978-79.

At irregular intervals, the Bombay Stock Exchange (BSE) authorities review and modify its composition to make sure it reflects current market conditions. The index is calculated based on a free-float capitalization method; a variation of the market cap method. Instead of using a company’s outstanding shares it uses its float, or shares that are readily available for trading. The free-float method, therefore, does not include restricted stocks, such as those held by promoters, government and institutional investors.

The index has increased by over ten times from June 1990 to the present. Using information from April 1979 onwards, the long-run rate of return on the BSE Sensex works out to be 18.6% per annum, which translates to roughly 9% per annum after compensating for inflation.

See also:

How is SENSEX calculated?

With what frequency is SENSEX calculation done?

How are adjustments for Bonus, Rights and newly issued Capital carried out in SENSEX?

How is the routine maintenance of SENSEX carried out?

How is the closing index calculated?

What are the criteria for selection and review of scrips for the SENSEX?

What are the objectives of SENSEX?

What is the beta of SENSEX scrips?