# Computation of stock index - Security Analysis and Investment Management

There are three different types of stock indexes.

• Market capitalization weighted index
• Price weighted index
• Equally weighted index

Market capitalization based index is the famous one among the above and is used by most of the exchanges worldwide. BSE Sensex and NSE NIFTY are calculated based on the method of market capitalization weight.

The market value weighted method computes a stock index in which each stock affects the index in proportion to its market value. This is also called the capitalization-weighted index. The price weighted method gives weights to each security forming the index according to the price per share prevailing in the market. Weights can also be given equally to all the shares. This method of computing the index is known as equal weight method.

Example- Assume that stocks A1, A2 and A3 constitute the sample companies for the computation of an index. The base index is 100 and the base date price and current market prices are given below. Compute the current stock index when no change in share representation takes place, dividends or stock splits have not occurred, and no additional shares have been issued. Use the market value weighted method; price weighted method, and equal weight method.

1. Market value weighted method
2. Market price weighted index = 910000000/246000000 × 100 = 370

3. Price weighted method
4. Market price weighted index = 1250/380 × 100 = 329

5. Equal weight method
6. Equal weighted index = 100 + 201.01 = 301.01

The stock exchanges in India compute and publish indices representing different sets of portfolios using the market capitalization weighted average method. In this method, the number of equity shares outstanding is multiplied by the price to arrive at market capitalization. This will ensure that each security will influence the index in proportion to its respective market importance. The current market capitalization is compared with the base market capitalization (base value) in order to get the index value at any point of time.

Index = (Total market capitalization of constituent scrips/base value × base index

The advantage of this method of compilation is that it has the flexibility to adjust for price changes caused by various corporate actions. The methodology of calculation is the same as the one employed in many of the popular indices such as the S & P 500, NASDAQ. Hang Seng Index, and FTSE 100 Index.

All stock exchanges constitute an index committee to identify the representative shares for the index. The Index Committee meets frequently to review the indices. In case of a revision in the constituent scrips of the index, the announcement of the incoming and outgoing scrips will be made ahead of the actual revision of the index.

The selection of securities for the BSE index will be made on the basis of certain quantitative and qualitative criteria such as market capitalization, liquidity, depth, trading frequency, and industry representation.

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:
1. 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.
2. 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.
3. 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.

Qualitative Criteria:

Track Record:

In the opinion of the Index Committee, the company should have an acceptable track record.

Adjustment for bonus, rights, and newly issued capital

Index calculation needs to be adjusted for issue of bonus and rights issue. 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 index value.

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

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.

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 'number 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.

The market value weighted method incorporates the adjustment effectively into the index while the other index computation methods do not show the effect of a bonus issue.

Example. Compute the index using the market value weighted method and price weighted method for the following market information. The base index is 100.

Company A2 issued bonus shares in the ratio of 1 : 2. the current price reflects the share price after the bonus share has become effective in the market. There is no other change in other companies.

1. Market value weighted method
2. *Outstanding shares for A2 after the issue of bonus will be 1,500,000
Market value weighted index = 184000000 / 78000000 × 100 = 236

3. Market price weighted method
4. When a company, included in the computation of the index, issues rights shares, the number of additional shares issued increases the weighting factor for that share. An offsetting or proportionate adjustment is then made to the base year average. Weight factors get revised when new shares are issued by way of conversion of debentures, of loans into equity by financial institutions, mergers, and so on. The base year average is also suitably adjusted to offset the change in the market value thus added. Similarly, when convertible/non-convertible bonds /debentures, preference shares, and so on are issued as rights to equity shareholders, the base year average is adjusted on the basis of the ex-right price of the equity shares.

For the computation of the index, the base value is adjusted and used as a denominator for arriving at the 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 the rights issue and the new capital of the index scrips do not destroy the value of the index.

The changes are, in effect, proportional adjustments in the base year to offset the price changes in the market values upon which the index is based. The formula for changing the base year average is as follows:

New Base Year Average = Old Base Year Average ×

Example. A company included in the computation of the index issues rights shares which increases the market value of its shares by Rs. 500 crores. If the existing base year average value is Rs. 7,590 crores and the aggregate market value of all the shares included in the index before the right issue is Rs. 9,586 crores, the revised base year average will then be computed as follows:

= Rs. 7,985.89 crores

This calculated amount (Rs. 7,985.89) will be used as the base year average for calculating the index number from then onwards till the next base change becomes necessary.

Dividend payment by the constituting company also needs to be adjusted against the ex-dividend price. The dividend declared per share is deducted from the cum-dividend price per share. The ex-dividend price quoted in the market is taken as the price of the constituent security, which will be less than the price of the security Earlier.

Example. The following securities constitute the computation of an index. Security A2 declared a dividend of Rs. 2 per share. The base price and the ex-dividend current price quoted in the market are given below. Compute the value-weighted index and price weighted index. Base index-100.

1. Market value weighted method
2. Market value weighted index = 128000000/116500000 × 100 = 109.87

3. Market price weighted method
4. Market price weighted index = 219/200 × 100 = 109.5