stock index – indicator of the state and dynamics of the securities market. By comparing the current value of the index with its previous values, it is possible to assess the behavior of the market, his reaction to certain changes in the macroeconomic situation, various corporate events (mergers, takeovers, share split, resignations and appointments of leading managers), speculative processes.
Depending on whether, what securities are sampled, used in calculating the index, it can characterize the market as a whole, market for a certain class of securities (government obligations, corporate bonds, shares, etc.. P.), industry market (securities of companies of the same industry: telecommunications, transport, insurance, Internet sector, etc.. P.).
Comparing the dynamics of different indices can show, which sectors of the economy are developing the fastest. The index may represent a national stock market in general or a specific trading platform in this market (for example, stock exchange index). Stock indices are calculated and published by various organizations, most often by news or rating agencies and stock exchanges.
Methodology for determining stock indices
So that the stock index adequately reflects the processes, occurring on the securities market, and depended as little as possible on subjective factors, such, how to manipulate the prices of individual financial instruments, corporate policy of issuing companies, including new emissions, splitting up or consolidation of shares, issue of warrants, etc., it is necessary to apply correct and reasonable methods of calculating stock indices. Besides, understanding of the methodology for calculating the index is necessary for the correct interpretation of its changes.
When determining the methodology for calculating stock indices, the following issues should be considered:
• formulas for calculating stock indices;
• reliability and completeness of information, used in the calculation of stock indices;
• the procedure for adjusting the calculation formula, the need for which is caused by certain corporate events, changes in market conditions.
Methods for calculating stock indices
There are four main methods for calculating stock indices:
1. Method for calculating unweighted arithmetic mean. This formula is used to calculate the Dow Jones Industrial Average (Dow Jones Industrial Average).
2. A method for calculating a weighted arithmetic mean using various weighing methods:
– weighting by the price of shares in a sample;
– sample cost weighting;
– weighting by equating the weights of stocks of companies;
This technique is used to calculate the average index of the rating agency Standard & Poor’s (S&P 500).
3. Method for calculating the unweighted geometric mean. This formula calculates the oldest UK stock index FT-30 (FT-30 Share Index, Financial Times Industrial Ordinary Index), which began to be published since 1935 G.
4. Method for calculating the weighted geometric mean. This formula is used to calculate the Value Line Composite Average, used in the US stock market.
Information requirements, used in the calculation of stock indices.
Any formula will be useless, if inaccurate or incomplete data is entered into it. For reasonable use in calculations, information must meet the following criteria:
• sample size. It is advisable to use a sufficiently large number of companies when calculating the index., which makes it possible to reduce the likelihood of the impact on the final result of random deviations in the value of securities of individual companies relative to the average market value.
• representativeness of the sample. List of companies, securities of which are part of, for example, sectoral index, must be complete enough to, so that the index adequately reflects the state of a certain segment of the economy. Besides, so that the index changes correctly reflect the changes, occurring on the market, distribution of issuers by capitalization and industry should correspond to the distribution in the market as a whole. The use of computers made it possible to start calculating the index for all shares, traded in a particular market, without resorting to some sample.
• weight. Desirable, so that the value of securities, included in the index, had its weight, proportional to their impact on the stock market as a whole.
• objectivity of financial information. Should be considered, that the stock index is calculated on the basis of publicly disclosed information about changes in prices for financial instruments. Most of the indices are calculated during the trading day., moreover, their updated values appear at short intervals.
Index adjustments
Index calculation methodology may change from time to time., which is mainly associated with various corporate events, experienced companies, securities of which are included in the index. Changes may also apply to the list of securities, participating in the calculation of the index.
The greater history of the stock index, the more valuable it is for predicting the future reaction of the market to certain events based on its past behavior. But the market situation is constantly changing – mergers and acquisitions, bankruptcy of old companies and the emergence of new, rapidly increasing their capitalization. Therefore, from time to time it becomes necessary to make changes to the sample., based on which the index is calculated.
If such adjustments are rarely made, there is a danger, that the index will start to lag behind the development of the market, if adjustments are made too often – the index will start “lose” history and, keeping the previous name, reflect changes in another market sector.
Major stock indices.
USA
Dow Jones Indices. The most famous in this family of indices is the Dow Jones Industrial Average (Dow Jones industrial average). This index was first published in 1884 G. Charles Doe, founder of the company, who was the publisher of a famous financial newspaper “Wall Street Journal”. This index was first calculated for stocks 11 railway companies. IN 1897 G. the list has been increased to 20 railway companies. The first Dow Jones Industrial Average was calculated in 1896. by shares 12 companies. IN 1916 G. the sample size has been increased to 20 companies, and in 1928. – to 30. The last change in the composition of the index was made 1 November 1999, when instead of Union Carbide companies, Goodyear Tire & Rubber, Sears and Chevron are indexed by Home Depot, Intel, Microsoft и SBC Communications.
The index is calculated as the arithmetic average of stock prices 30 largest companies. The divisor is not a number 30 (number of companies in the sample), and the special divisor, allowing for multiple splits (share split), produced by issuing companies since 1928. (from the moment of increasing the sample to 30 companies).
Other Dow Jones indices are also used: Dow Jones weighted stock index, calculated according to 700 shares, listed on the New York Stock Exchange (published since 1988 G.), Dow Jones Indices for Transportation and Utilities (Dow Jones Transportation Average (20), Dow Jones Utilities Average(15)) and by 40 bonds.
AMEX Composite – market capitalization-weighted index of all stocks, traded on the American Stock Exchange (American Stock Exchange).
NASDAQ 100 – index 100 of the largest companies in the non-financial sector on the NASDAQ exchange.
NASDAQ Composite – capitalization-weighted over-the-counter market index, published daily by the National Association of Securities Dealers and covering about 3500 Shares, traded in the Nasdaq market system (Nasdaq Market System).
NYSE Composite – market capitalization-weighted index of all stocks, traded on the New York Stock Exchange (NYSE).
Russell Index Family (calculated by Frank Russell, Frank Russell Company). Among the most famous:
Russell 3000 Index reflects the dynamics of shares 3,000 largest American companies by market capitalization, which account for about 98% the value of the entire American stock market.
Russell 1000 Index reflects the dynamics of shares 1,000 largest companies from Russell 3000 Index, which account for about 92% total capitalization of companies, presented in Russell 3000 Index.
Russell 2000 Index reflects dynamics 2,000 smaller companies, presented in Russell 3000 Index, which account for about 8% the total market capitalization of companies from Russell 3000 Index.
Standard family of indexes & Poor’s
Standard & Poor’s Composite 500 Index. The index includes 400 industrial, 20 transport, 40 communal and 40 financial companies. Weighted by market capitalization. Covers approximately 80% total capitalization of companies, traded on the New York Stock Exchange. The capitalization of the companies in the sample ranges from 73 million to 75 billion dollars.
Standard Index & Poor’s Composite 500
A source – Bloomberg – World Stock Indexes
Standard & Poor’s 400 Index (S&P Midcap) analogous to S&P 500, but covers 400 industrial companies, whose capitalization varies from 85 million to 6.8 billion dollars. Standard & Poor’s 100 analogous to S&P 500, but only covers 100 Shares, for which there are options contracts on the Chicago Board Options Exchange. “OEX” – the name of the option on this index, which is one of the most popular and traded options.
Price-weighted index as opposed to index, capitalization weighted. Somebody think, that this index gives a better idea of investment performance, since individual stocks do not alter in it, and most individual investors do not build their portfolio weighted by market capitalization. (until they buy index funds).
Wilshire 5000. The index covers all companies, headquartered in the USA, for which price information is available. Historically, that pink leaf companies were not included in the index, but with the progress of ways of transmitting information, list of companies, included in the index increased to more than 7000. Index weighted by market capitalization. Since some companies, in the index S&P 500 are headquartered outside the United States, not true to say, what wilshire 5000 includes S&P 500.
France
The main stock indices are CAC-40 and CAC General. SAS 40 calculated according to 40 shares of the largest issuers, traded on the Paris Stock Exchange. Futures contract for this index, maybe, is the most popular and traded futures contract worldwide. CAC General is calculated by shares 250 Issuers.
Germany
The main stock index is DAX 30, encompassing 30 most traded shares (based on trade statistics for 3 last years) on the Frankfurt Stock Exchange. Index weighted by market capitalization. Based on the results of trading in the electronic system, the Xetra DAX index is calculated, it is almost the same as DAX 30. However, the e-session is longer, therefore, closing prices can vary significantly. DAX is also calculated 100 and CDAX composite index by 320 shares.
United Kingdom
FTSE 30 Share Index, The Financial Times Industrial Ordinary Share Index was first published in 1935. and covers shares 30 industrial and trading companies. Calculated as geometric mean, obtained by multiplying the rates 30 shares from the sample and subsequent extraction from the product of the 30th root.
FTSE Index 100
A source – Bloomberg – World Stock Indexes
FTSE 100 – the most common index in the UK, commonly known as' footsie’ (Futsi 100). Represents a weighted arithmetic index, calculated on the basis 100 largest UK companies by market capitalization on a per minute basis. On components “Futsi” accounts for about 70% total capitalization of the UK stock market.
FTSE Mid 250 – Mid-cap stock index, which account for approximately 20% UK market. These are the following 250 companies after hundreds of largest, included in the FT-SE index 100. Calculated from December 1985.
Japan
Main stock index of Japan – “Nikkei” (abbreviated from phrase “nihon keizai” – “nihon” more Japanese Japan, and “keizai” – “finance, economics”). His sample includes 225 Shares, traded on the Tokyo Stock Exchange. This is the arithmetic mean unweighted index., calculated by the same method, what is DJIA. Published since 1950.
Nikkei Index 225
A source – Bloomberg – World Stock Indexes
The second fairly popular index – Topix, calculated since 1968. for all shares, traded on the 1st section of the TFB. The JPN Index is a modified price-weighted index, reflecting dynamics 210 ordinary shares, actively traded on the Tokyo Stock Exchange and representing a broad cross-section of all sectors of the Japanese economy. JPN is closely related, but not identical to the Nikkei index.
Canada
The most famous index of the Toronto Stock Exchange TSE 300, capitalization-weighted and covering 14 sectors of the economy.
Mexico
The Mexican Stock Exchange calculates the IPC index. This is a capitalization-weighted index., encompassing 35 largest Mexican companies. The composition of the sample for calculation is adjusted every 2 months.
Hong Kong
The most famous index – market capitalization-weighted Hang Seng Index, share-based 33 companies, capitalization of which is about 70% total market capitalization. The index includes companies 4 Sectors: trade and industry, finance, utilities, land ownership.
