SENSEX Calculation

What is the beta of SENSEX scrips?

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.


How is SENSEX calculated?

SENSEX is calculated using a "Market Capitalization-Weighted" methodology. As per this methodology, the level of index at any point of time reflects the total 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). An index of a set of a combined variables (such as price and number of shares) is commonly referred as a 'Composite Index' by statisticians. A single indexed number is used to represent the results of this calculation in order to make the value easier to work with and track over time. It is much easier to graph a chart based on indexed values than one based on actual values.

The base period of SENSEX is 1978-79. The actual total market value of the stocks in the Index during the base period has been set equal to an indexed value of 100. This is often indicated by the notation 1978-79=100. The formula used to calculate the Index is fairly straightforward. However, the calculation of the adjustments to the Index (commonly called Index maintenance) is more complex.

The calculation of SENSEX involves dividing the total 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 maintenance adjustments. 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.


How is the closing Index calculated?

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.


How is the routine maintenance of SENSEX carried out?

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.


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

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.


With what frequency is SENSEX calculation done?

During market hours, prices of the index scrips, at which trades are executed, are automatically used by the trading computer to calculate the SENSEX every 15 seconds and continuously updated on all trading workstations connected to the BSE trading computer in real time.

Sensex: An Introduction

The BSE SENSEX is scientifically designed and is based on globally accepted construction and review methodology. First compiled in 1986, SENSEX is a basket of 30 constituent stocks representing a sample of large, liquid and representative companies. The base year of SENSEX is 1978-79 and the base value is 100. 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 over the years become one of the most prominent brands in the country.

What is SENSEX?

The SENSEX, short form of the BSE-Sensitive Index, is a "Market Capitalization-Weighted" index of 30 stocks representing a sample of large, well-established and financially sound companies. It is the oldest index in India and is widely used to measure the performance of the Indian stock markets.

What are the objectives of SENSEX?

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.

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

1. QUANTITATIVE Criteria:

• 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)

• Liquidity:


• 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.


• 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.


• 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.

• 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.

• 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.

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

1. QUALITATIVE Criteria: In the opinion of the Index Committee, the company should have an acceptable track record

CALCULATION OF SENSEX

The Index was initially calculated based on the "Full Market Capitalization" methodology but was shifted to the free-float methodology with effect from September 1, 2003. The "Free-float Market Capitalization" methodology of index construction is regarded as an industry best practice globally. Details of how the SENSEX is calculated will be provided in the next post.

Source: Traders' Guide

Why Trade - The Heckscher-Ohlin Trade Theory

Bertil Ohlin was born in 1899. At the age of five, Bertil was very fond of calculating the cost of the various cakes his mother baked. Because mathematics was his favorite subject in school, he decided to study mathematics, statistics, and economics in college. After graduating from college, Bertil Ohlin enrolled at the Stockholm School of Economics, where he studied under the guidance of the economics historian Eli Heckscher. Together they developed the pathbreaking Heckscher-Ohlin theory in the 1920s. Many years later, in 1977, Bertil Ohlin was awarded the Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel for his contribution to the theory of international trade, based on the work he did with Heckscher. Eli Heckscher, who died in 1952, did not share the prize since it is not awarded posthumously. Instead Ohlin shared the prize with the British economist James E. Meade.

The Heckscher-Ohlin Trade Theory :
The Heckscher-Ohlin theory explains why countries trade goods and services with each other. One condition for trade between two countries is that the countries differ with respect to the availability of the factors of production. They differ if one country, for example, has many machines (capital) but few workers, while another country has a lot of workers but few machines. According to the Heckscher-Ohlin theory, a country specializes in the production of goods that it is particularly suited to produce. Countries in which capital is abundant and workers are few, therefore, specialize in production of goods that, in particular, require capital. Specialization in production and trade between countries generates, according to this theory, a higher standard-of-living for the countries involved.

Gains from Trade
By specializing in production, and by trading with other countries, it is possible for countries to increase their incomes. Even though countries as a whole benefit from specialization and international trade, all groups in society, workers and capitalists, do not gain according to the Heckscher-Ohlin theory. If international trade leads a country to specialize in producing goods that require lots of workers and little capital, such a specialization increases wages (which benefits the workers) but decreases the income of the capital owners. But the country as a whole benefits because the gain of the workers is bigger than the loss of the capital owners

The Heckscher-Ohlin theory says that two countries trade goods with each other (and thereby achieve greater economic welfare), if the following assumptions hold:
a)The major factors of production, namely labor and capital, are not available in the same proportion in both countries.
b)The two goods produced either require relatively more capital or relatively more labor.
Labor and capital do not move between the two countries.
c)There are no costs associated with transporting the goods between countries.
The citizens of the two trading countries have the same needs.

(source: http://nobelprize.org/economics/educational/trade/)