**The possibility of manipulating stock indices**

*Material posted: -*

*Publication date: 10-02-2009*

The article considers the vulnerability of the stock market, allowing speculators to manipulate their values. Such "tricks" can easily provoke the crises in the financial system of the country.

Estimating possibilities of manipulation of the values of stock indices should be considered a description of the indexes and methodology of their formation (annexes 1,2).

For the future we should define what is meant by the term "manipulation index". It is clear that it is not influence by politicians, the fed management, emergencies, etc. For the problems this policy brief under the manipulation of the index implies purposeful action on the part of participants of the stock market on the value of the index in the interest of more profit, for example, at the expense of derivatives whose underlying asset is the respective stock index.

When the manipulation amount of the manipulator should spend some of the money for the deformation of the stock market in the desired direction. Therefore, it is necessary to distinguish between the potential for manipulation and the manipulation that is implemented in practice (*cost-effective* manipulation). In the latter case, the manipulation index is not only possible, but can bring the manipulator some profit, equal to the difference between the expected income produced and the financial costs associated with the reallocation of a portion of the capital stock between the companies.

This note is devoted to the analysis of the potential manipulation of the values of the other most well-known stock indexes.

Manipulation is possible if at the expense of redistribution of funds inside the stock market is practically without change of its total capitalization may change the value of the stock index.

The analysis showed that the following factors contributing to the manipulation of the value of stock indices:

· limit the list of shares into account in determining the value of the stock index;

· different values of weight coefficients that take into account the capitalization of individual companies (stock prices) in additive form stock index (the arithmetic mean of the "weighted" values, capitalisation or stock price);

· taking into account in the formula index of free float coefficient, which determines the proportion of the free float shares;

· nonlinear (e.g. multiplicative) character of functional dependence, which determines the value of the stock index, depending on the value of capitalization of companies (this case is typical when the index is calculated as geometric mean and not the arithmetic mean of the values of capitalisation or stock price).

Summarizing, we can note the following: if in the formula for calculating the values of the index include factors that discriminate against some actions against the other, this leads to potential manipulation of the values of this index.

In Fig. 1 shows a possible classification of the best known stock indices from the point of view of assessing the possibility of manipulation of their values.

**Fig.1** the First (leftmost) group of indices characterizes the economy as a whole.

If the stock index this type is defined as the arithmetic mean of the capitalization of companies, the possibility of manipulation, its value is minimal. Practically they are limited to moving funds from stocks included in the index structure, the shares of the 2nd and subsequent trains (to reduce the size of the index) or in the opposite direction (to increase the value of the index) — Fig. 2.

**Fig.2**

In other words, it can be argued that almost any stock index is potentially subject to manipulation because it generates a limited list of stocks (the exceptions to this rule are the indexes of the stock exchange the New York Stock Exchange, which take into account *all exchange traded stocks*; on the other hand, and the NYSE Composite index can also manipulirovat, but for a different reason, which is discussed below). Therefore, to manipulate the indices comprising hundreds or thousands of stocks is theoretically possible, although practically very difficult.

If the stock index is defined as the geometric mean of the values of capitalization (stock price), then there is an additional possibility of manipulation of its values. Because the geometric mean is always less than the arithmetic mean (they are equal in the equality of all the averaged values), for increasing values of such indexes (like the American the FTSE-30) is sufficient to approximate the averaged factors to each other (to align their values). On the contrary, to reduce the value of the geometrically averaged index should increase the dispersion of averaged factors in their continued amount.

From (1) shows that the higher the capitalization K_{i} a company, the less "weight" in determining the increment of the index. That is why stocks of large-cap companies (analogs of the Russian "Gazprom") are discriminated against in relation to the shares of companies with low capitalization.

If at some point of time to sell on the exchange part of the shares of the company's high capitalization and transfer the proceeds in equities of small cap, then the I becomes positive, i.e. the value of the stock index will increase. To reduce I the specified operation should be performed in the opposite direction.

Thus, the nonlinear (by capitalization) the nature of the formula for determining the index stock provides the additional capability of manipulating its values.

A further possibility is the use of differences in "scale" with which are formed an additive index of different stocks. Consider the case of the example the well-known DJIA index, arithmetical average of share prices:

I.e. there is the potential for manipulation of the index, DJIA and all indices specified in the 3rd the lower rectangle in Fig. 1.

The same applies to the NASDAQ-100 index (USA), placed in a 4-m bottom rectangle Fig. 1. For proof of this assertion is even not necessary to carry out elementary transformations, because the index structure initially present unequal weights.

Fig. 3 Scheme of manipulating the values of the additive indices for different values of weight coefficients of stock

From the point of view of mathematics in the global MSCI index, the situation is similar to the two previous cases, although the actual cause of the other different values of the coefficients of the free float. But these coefficients play the role of different "weights" of the shares, and makes the possibility of manipulating the index MS in the above scheme.

The situation is even worse for Russian stock indices RTS and MICEX: here is the superposition of two factors — the weights of the different shares and different values of the coefficients of the free float. Moreover, despite the different methods of determining the index RTS and MICEX (Annex 2), the ability to manipulate the values of these indexes are currently about the same.

More for the Ukrainian PFTS index. The value of this index is calculated as follows:

From (3) that the most capitalized Ukrainian companies have the least "weight" in the index PFTS. The situation is the same as on the Russian stock market: OAO Gazprom, Sberbank, LUKOIL have decreased the weight in the RTS and MICEX indexes. But it is compounded almost 3 times smaller number of shares used to calculate the PFTS index than the RTS index (Appendix 1), which presents additional opportunities for manipulation. Therefore, in the case of development of derivatives market in Ukraine is possible the manipulation of the values of the PFTS index.

**Conclusions:**

- Potentially the values of all of the stock indexes can be manipulated, but the sensitivity of the index to manipulation significantly different.
- The least affected by the manipulation of stocks, defined as an arithmetic average (with equal coefficients) values of capitalization of companies; however, the more stocks included in the index calculation base, the less opportunity for manipulation.
- Potentially most vulnerable to the manipulation of indexes that use different "weights" of shares, free float factors and a small list of stocks that form the index. As a rule, these indexes are used in emerging markets with a high degree of monopolization of individual companies.
- Of the stock indexes the greatest susceptibility to manipulation is the Ukrainian index PFTS.
- To determine whether manipulation of stock index it is possible to propose a simple General rule: you should write down the ratio for small changes (variations) of value I of the index depending on the change of variables K
_{i,}the capitalization of companies whose shares comprise the index calculation base. In accordance with the General rules of mathematical analysis, I must be a linear form on K_{i}. If the coefficients of this linear form (multipliers K_{i}) are different, then consider stock index is potentially subject to manipulation by market participants. This rule is useful when analyzing the manipulative properties of the stock indices that may appear in the future.

** **

**Appendix 1. The methodology of calculation of stock indices**

The most common and recognized method of constructing "models" of this index.

1. Select the market. As such are typically used either separate store sites, or a set of securities traded (issued) in any region (country).

2. The selection of securities for inclusion in the listing of the index. Goal of a company is the owner of the index to select the most relevant for this market securities that best reflects its diversity (representativeness). Usually records are kept and other parameters, the most important of which is the liquidity of the selected securities. Indices of stock exchanges or trading systems generally include all securities which circulate on this site.

3. Selected information partners needed to calculate the index options. Usually as such data is used selected trading floors, or data information agencies in actual sales.

4. Is the weighting of securities, to determine the effect of varying the index. Usually, the method of "weighing" applies the principle of proportionality market capitalization, i.e. a security the more so for the market, the higher its total market capitalization.

5. Direct calculation of the index is conducted mainly by 2 methods:

The first is "the method of direct calculation". By this method the index at a time (for each period) is a function from prices at this time (during this period). For example, if you select as the base formula weighted average arithmetical value of the index at each moment of time will be equal to the quotient of the sum of pieces prices of all shares listed on the index on the "weight" coefficients, divided by the sum of "weight" ratios.

When the "degenerate" case (when the weighting factors equal to unity) we obtain the case of indexes such as the Dow-Jones, then an index equal to the quotient of the sum of the prices of all shares listed on the index, divided by the number of shares in the listing. But equal "weight" in the price averaging does not imply their equality by averaging over capitalization.

Almost always after the calculation of the index, multiply/divide by the coefficient of reduction, which serves to create a memorable number at the initial time (rarely), or conditional to the existence of a continuous derivative on the chart of the index (usually), which may be missing either because of the events of the Issuer (e.g. stock split), or because of the events of index (changes in listing).

The second "methodology of index calculation". According to this method each time (for each period) is calculated cumulative value of the virtual portfolio as a function of stock price at this time. The obtained value is divided into the similarly obtained value of the virtual portfolio at the start of the index calculation multiplied by the initial value (or divided by the previous value of the portfolio and multiplied by the previous value of the index). To bring the values of the index in this case use a similar technique.

Methods of calculation of indices and averages are different ways of averaging. The most widely arithmetic averaging, and weight component included in the index, may be different. If you add up the share price with a single weight, get the index the Dow Jones or the index is weighted by price.

The disadvantage of this method of averaging is more a strong sensitivity of the index to changes of quotations of stocks with high absolute price. In the US it is customary to support the stock price in the range of $10-$100 (if the price is higher is crushing, below — consolidation), and the distortion is not too great.

If the "weight" to take the total number of issued shares, in fact, will sum of the market capitalization (price multiplied by shares on total number of issued shares determines the market value or capitalization of the Issuer). In this case, the index change corresponded to a relative change of the average market value of fixed assets. The index is capitalization-weighted, has a macro-economic sense and can be compared with other macroeconomic parameters. This opens up broad opportunities for its use in macroeconomic models and forecasts. So arranged, the S&P 500, the Nasdaq, the FT-SE 100, and the indices of RTS and MICEX. The disadvantage is the large sensitivity of the index to changes in the prices of stocks with high capitalization. Famous example — almost the entire growth in the S&P 500 index in 1998 was due to the growth of all top 50 companies. The indices of RTS and MICEX is also too "overloaded" the shares of oil companies, and changes in this sector almost predetermine the behavior of the index.

To avoid unwanted effects, you can build the index, which is computed as an average of changes in all its components. Unfortunately, indices of this type (with equal weights) of spread. From publish you can specify the Ukrainian PFTS index.

Instead of total number of shares issued can take the number of shares in free circulation (free float), the number of issued shares excluding public package, etc.

When calculating the index virtual investment portfolio as weights convenient to take the number of shares of the Issuer in the portfolio, then the index portfolio will reflect the change in its market value.

In addition to the arithmetic mean can be used the geometric mean (nth root of the product of M M component). So arranged index Value Line U.S. and the UK FT-SE 30. Geometric averaging underestimates the change in the index compared to arithmetic averaging.

**The calculation of the index, averaged by market capitalization.** Typically, the indices are calculated by a recurrent method. Knowing average market capitalization of the index on the date of the previous (n-1), we can calculate the index of the current date (n) by the formula:

I_{n}=I_{n-1} MC_{n}/MC_{n-1},

where MC is the sum of the market capitalizations of issuers.

On the initial date of calculation the value of the index is arbitrary, often 100. When fragmentations and consolidations, amendments do not need to enter: capitalization of the Issuer does not change.

Usually the index is not calculated on all the shares traded on the market, but on a relatively small sample. The number of shares in the sample taken to result in the end of the title index S&P 500, FT-SE 100, Nikkei 225, DAX 30, etc. To change the index correctly reflects the market changes, the distribution of issuers by capitalization and industry sector in the sample should match the distribution in the market as a whole.

The requirement of representativity is often violated — usually to calculate the index are selected by the largest companies and changes in the sector of medium and small companies are not taken into account. Industry ratios are changing, for correct identification of these changes would be required to review a sample too often. *The use of computers made it possible to calculate indexes for all traded shares, making selections. For example, the index of the new York stock exchange (NYSE) is calculated for all ordinary shares, having passed the listing*.

For index calculation is usually used the latest transaction price. If the stock trades for a long time no, the index is "behind life". If many of such shares, then the index becomes too slow and poorly meets the needs of investors. Attempts to circumvent this difficulty by replacing the transaction price the average price between the best proposals for the purchase and sale does not lead to success — low liquidity accompanied by high spreads, the prices of rare trades are near the bid and offer prices can be several times higher than the demand price. Therefore, the revival of liquidity and rising prices of deals of this kind are accompanied by a decrease in its contribution to the index, which is contrary to common sense.

The longer a story has an index, the higher is its value: it is possible to trace how the stock market in the past reacted to certain events in different macroeconomic conditions, which gives grounds to predict future movements of the market. Meanwhile, the situation on the stock market is constantly changing: bankruptcy, mergers, acquisitions.

There are new companies, rapidly increasing capitalization (example: Microsoft). Appropriate changes need to be made in the calculation of the index — some stocks are removed from the sample, others are included. If changes are made too infrequently, the index begins to "keep up", if too often "lose the history": retaining the old name, actually starts to reflect changes in other sector of the market. Formal criteria for changing the sample and accounting for acquisitions does not exist, in practice these issues are decided by the organization, calculates the index with attraction of authoritative experts.

The indexes built for the same market, always strongly correlated, regardless of the samples or averaging methods, the market growth will increase almost any index. However, the rate of change of various indices may differ significantly, for a short period discrepancies may occur. They can be used for prediction. For example, if a new maximum index of "blue chips" is not confirmed by a new high the broader index, on the market will probably fall. Globalization of investment processes has led to the correlation of the indexes in different countries, so that the behavior of indexes of the USA can make a prediction on changes in the indexes such as Germany or Russia, etc.

Futures on the S&P 500 and Nasdaq 100 are traded around the clock, which allows you to continuously consider the impact of changes in the U.S. market.

**The main foreign stock indices**

*USA*

In 1884, Charles Dow and Edward Jones began to consider the arithmetic mean value of the 11 shares. Modern industrial Dow Jones (**Dow Jones Industrial Average, DJIA**) is calculated from 1928 in a similar way for the 30 companies traded on the new York stock exchange. Now its value is about 13 thousand points. But it is wrong to assume that all securities average cost $13 thousand the fact that the total cost of 30 shares now is not divisible by 30, and 0,123. In this regard, the index value is rather high, and in fact, the average cost of the shares now around $54. The factor by which the shares amount of the securities has changed in over 100 years because many issuers have ceased to exist, it required adjustments in the calculations. But the essence of the index from the value of the correction factor remains the same: to understand what moves the stock market in General, you need to look at the chart of the stock index. On the DJIA index and the shares of IBM, and Pfizer, and McDonalds have exactly the same effect. This Dow Jones is often criticized, but most are ages-old traditions, and the methodology does not change.

Indexes the new York stock exchange (New York Stock Exchange, NYSE) common stocks, for which as one of the constant parameters included in the listing is TorqueMaster securities on that exchange.

In the listing of stock index composed of the shares comprised in the listings of the stock exchange and the main index generally includes all stocks traded on a specified site.

The main index is the NYSE composite index exchange — **NYSE Composite**. This index weighs the cost (including adjustments related to fragmentation, mergers, acquisitions) the shares of all corporations that have registered their securities on the new York stock exchange Jorskoj (about 2300 companies). The NYSE Composite index represents the average price of the shares on the stock exchange and in contrast to the indexes of the Dow Jones is measured not in points but in $.

*Futures on indexes traded NYSE on the exchange, options with futures contracts on the new York futures exchange, a division of the NYSE.*

**Nasdaq Composite index **— the composite index that takes into account the behavior 4381 American and foreign corporations ("weighting by market capitalization") listed in the system (a total capitalization of approximately $6000 billion). The history of the site contributed to the fact that most of these companies are representatives of the new economy, the developers and manufacturers of computer hardware, software, telecommunications and biotechnology companies. Another feature is the presence of a significant number of foreign companies, more than on NYSE and AMEX combined.

Feature index **NASDAQ-100** is not just a "weighting by market capitalization", but also the introduction of an additional quarterly update weighting factor for each event (beginning with 1998), which contributes to the behavior of the index for more unpredictability, though, according to developers, the methodology is useful.

The crown of all indexes of the USA today is the **Dow Jones Composite Average**, which includes 65 stocks included in other indices of the family of Dow Jones and traded on the NYSE. It combines industrial Dow Jones (calculated for 30 stocks), the index of transport companies of Dow Jones industrial average (calculated for 20 shares) and the index of the gas and electric companies of Dow Jones industrial average (calculated to 15 shares).

Methodology of indices calculation for all the time remained virtually unchanged, however, included in the listing of the shares has changed. Of all of the equity indices only General Electric has an enviable stability, and the remaining shares were entered, then came out and all was lost from the market. It should be noted that in the Dow Jones long enough was not included stocks of "new economy" and their inclusion brought the value of the index big trouble. The fact of the inclusion increased the representativeness of the indicator and brought his composition to the real balance of forces on the U.S. stock market.

One of the most popular indices in the world are the indicators calculated largest rating Agency Standard&Poors (S&P). The history of the majority of them is from the years 1935-1937 the Initial value of indexes is 10.

**Standard&Poors 100** — "capitalization-weighted" index of the 100 largest companies in the U.S., for which there are options traded on the Chicago Mercantile exchange (Chicago Mercantile Exchange). Consists mainly of industrial corporations.

**Standard&Poors 500** is the main index, composed of 500 of the largest (most capitalized) American companies, using the technology of "weighting by capitalization." Currently integrated sectoral proportion in it is as follows: 400 industrial companies, 20 transportation, 40 utility and 40 financial. In representativeness of the index closes on the NYSE, although there are more than 80% of traded issues (market value), in his listing are also traded on the AMEX and in the over-the-counter turnover. This indicator is one of the most recognized assessment of the U.S. economy in General, and is considered the most respected among traders and managers associated with the real sector.

**Sectoral indices Standard&Poors** is about 90 indexes, indicating that virtually all sectors of the U.S. economy.

*Futures on the Dow Jones, NASDAQ and S&P traded in Chicago exchange-Chicago Mercantile Exchange.*

*UK*

The oldest index of the UK by the Financial Times in 1935 is called the **Financial Times Industrial Ordinary Share Index** or abbreviated as **FT-30 (FTSE-30)**. It includes shares of 30 largest industrial and trading companies; calculated as the geometric mean (root of the 30th degree of the product of the stock prices included in listing).

More popular and common today, is the **FTSE-100 (Footsie)**. It consists in listing the shares of 100 companies, and is not limited to industrial and commercial. The selection of the shares to listing are made by specialists, among whom there are representatives of the newspaper Financial Times. Currently, the capitalization of companies included in the listing of this index reflects 70% of the total capitalization of the stock market in the UK. The calculation is made by weighting stock prices of the companies by market capitalization on January 3, 1984, when the index value was 1000.

**FTSE Mid 250** — the index in the listing which includes the following after the first hundred of the 250 UK companies (by market capitalization). Calculated since December 1985, when its value was $ 100; designed to characterize the market shares of medium-sized companies in the UK make up 20% of the economy.

Calculation and publication of these indexes company FTSE International.

*Germany*

The business activity index Germany **DAX Indexes** are calculated by the Frankfurt stock exchange. Among them:

**DAX30** is the main, most important and most authoritative index in Germany, calculated on 30 of the largest stocks, the quotes "are weighted by capitalization."

**Xetra DAX** index which is almost identical to DAX30, however, is calculated according to the e-session, which is longer than usual.

**DAX100** — analogue DAX30, except for the presence in his listing of a number of stocks.

**CDAX** composite index by 320 the.

*France*

The main indexes are the French **CAC 40 and CAC General**.

Absolutely classical indices, including listing 40 and the 250 largest French corporations, shall be calculated jointly by the Paris stock exchange and the Society of French stock exchanges. On the initial date of calculation is December 31, 1987, the value of the CAC 40 index was 1000 points.

*Japan*

The Japanese index **Nikkei-225 (Nikkei Dow Jones Average)** includes in the listing of the shares of 225 companies who turn into the largest after the U.S. (NYSE) Tokyo stock exchange. The method of calculation of this index coincides with the methodology of the Dow Jones Industrial Average; published with 1950

*Hong Kong*

The leading Asian index **Hang Seng index**, is calculated according to the Hong Kong stock exchange. The index is considered by HSI Services Limited. 33 of the stocks listed in the index comprise about 70% of the capitalization of all traded issues and are primarily 5 market sectors — manufacturing, Commerce, Finance, utilities and ownership. The publication of the index is July 31, 1964, when he was 100 points.

*Canada*

Toronto stock exchange calculates an index, **TSE300**, as "weighting by market capitalization" 300 corporations that are traded on this exchange, representing 14 sectors of the canadian economy. Start of index calculation — 1975, when its value was 1000.

*Mexico*

**IPC Index** is calculated the Mexican stock exchange. Is a value that is "capitalization-weighted" 35 leading Mexican companies. Start of index calculation — October 30, 1978, when the value of 0.78. The listing index is reviewed every 2 months.

*Ukraine*

**Index PFTS** Ukrainian stock index, which is calculated daily based on results of trades in Stock Persei Torgovelno System (PFTS) on the basis of weighted average prices for trades. In the "index basket" consists of the most liquid shares, which occurs on most deals.

Date 1 October 1997 is the base period from which to begin calculation of the index. The essence of the index — *the percentage growth of the weighted average stock prices of "index basket" in relation to the base period*. As of August 2007, the PFTS index had a value of around 1000.

For calculation takes into account only those shares that are freely traded on the stock market. Do not count shares that are owned by the state, the Issuer, strategic investors, management and workforce, as well as in cross holding. This method of calculation increases the impact on the index of securities of companies, whose privatization was completed.

As of June 2007 in the "index basket" included shares of the following companies (table. 1).

*Global indices*

Indexes exist for the vast majority of equity markets. Despite the fact that the local (local) markets, they are recognized as a benchmark, when comparing the situation in different local markets there are difficulties due to the difference in methods of index construction. To resolve these difficulties, there were developed family of global indices that are computed using the same methodology for each sector of the market.

*Table 1*

**The MSCI index**. At present, the global investors the greatest authority is the MSCI (Morgan Stanley Capital International). It oriented funds with capital estimated at $3 trillion. This is one of the few popular indices are not independent organization, and the investment Bank — a market participant (Morgan Stanley Dean Witter). Ability to react quickly to the changing environment here was more valuable than independence.

It includes a number of securities markets in 23 developed countries. The calculation of the index is from December 31, 1969 the Level of the index serves as the indicator of "global" state of the stock market. List of countries: Australia, Austria, Belgium, Canada, Germany, Hong Kong, Greece, Denmark, Ireland, Spain, Italy, Canada, Netherlands, New Zealand, Norway, Portugal, Singapore, USA, Finland, France, Switzerland, Sweden, Japan.

The "weight" of companies in the MSCI index is determined based on the aggregate market value of its shares in free float (free-float). The MSCI index family oriented the majority of global investors in the shares. Many investment funds even form their portfolios in accordance with the structure of the relevant index, and some do not have the right to invest in stocks not included in these indices. Therefore, the placement of some of the securities in the index automatically increases the demand for it, and with it quotes.

In addition to the indexes of individual countries, the family consists of regional indexes, of which the most famous EAFE (Europe, Australia and far East) and **Emerging Markets** (emerging markets).

The index of **Emerging Markets**, in turn, is divided into several subregional families. In one of them, namely, EMEA (Eastern Europe, middle East and Africa), and enters the Russian market. On 30 November 2001, Russia's weight in Emerging Markets was 2.54%, in EMEA is 12.9%. Initially, the index was weighted by capitalization, but may 31, 2002 in weighting from the total number of shares issued will be deducted packets belonging to the state, management and strategic investors. Will only shares held in free float.

**The S&P/IFC**. IFC (international Finance Corporation) is a subsidiary of the world Bank and is considered an independent organization. Using the S&Ps it calculates the S&P/IFCI (investment) S&P/IFCG (global) and S&P/IFCF (frontier), which includes very very underdeveloped markets. The investment index was developed specifically for the needs of international investors — in the calculation of capitalization takes into account the restrictions imposed on non-residents. Therefore, as long as the law restricts the share of non-residents (for example, RAO UES — 25%), in weighting will be used only the percentage available to non-residents (weight RAO UES in the index — 25% of the capitalization). Also, are the stakes belonging to the state, and the packets held in cross ownership.

For the global index limits for non-residents are not taken into account, and all eligibility rules less strict, so there is a larger number of shares. On 31.10.01 Russia's share in the investment index stood at 4,18%, global — 4,43%.

Table 2 presents the main characteristics of these stock indexes.

Note to the scheme of calculation of the index:

K — arithmetic averaging of capitalization;

k — geometric averaging by capitalization;

With the average price of the shares;

with the averaging over the relative change in the stock price.

*Table 2*

**The main Russian stock indices**

Russian RTS and MICEX indices are calculated in more complicated way. The impact of each paper on an index depends primarily on the capitalisation of the Issuer and from the free float shares — the number of freely traded securities. The more expensive the company, the stronger its influence in the index; the fewer turns in the stock market, the lower the impact on the index paper. But in order for the resulting index is not dominated by the giants (the most expensive companies — Gazprom, Sberbank, LUKOIL), their degree of influence is limited to 15%.

The methodology of calculation of RTS Index is given in a previous research note, the method of calculation of the MICEX Index in Annex 2.

**The MICEX index (MICEX)** is calculated from September 22, 1997, the Value at that date is taken as 100 points. The index is weighted by the effective capitalization of the market index of most liquid shares of Russian issuers admitted to circulation on the MICEX.

In determining the effective (market) capitalization of the stock market MICEX is taken by the full amount of the issue shares, adjusted to take into account the liquidity of the stock market, the MICEX and the share of the share capital of each of the Issuer, and are freely tradable in the secondary market, by removing:

· the number of shares owned by the state;

· the number of shares, a proportionate amount of the share capital owned by another Issuer, whose shares are also included in the calculation base of the MICEX index;

· the number of shares owned by shareholders owning more than 5% of the share capital, while shares belonging to such shareholders, may not be excluded when calculating the effective capitalization of the stocks in case the decision of the Index Committee, these shareholders are not considered as strategic holders of shares (for example, settlement depositories of organizers of trading, etc.).

When considering corporate events not to avoid due to the market conditions of a sharp deviation in the direction of increasing or decreasing the value of the MICEX index is used a correction factor, which is the next day after changes in the base for computing the index associated with this event, is set to unity.

A comparative analysis of schemes of construction and application of the RTS and MICEX indexes are presented in table. 3.

It can be seen that, despite the difference methods of calculation of indexes of RTS and MICEX (Annex 2), their principles of calculation (limiting the "weights" of stock — market leaders, accounting of free float, the weighting by market capitalization) leads to go (up to a multiplier close to 1,19) results.

*Table 3*

29 June 2007 started trading futures contracts on the MICEX index. The main parameters of the contract are presented in table 4.

*Table 4*

**The MICEX 10 index** is published on 19 March 2001. Its initial value is taken at 18:00 Moscow time on 30 December 1997. The MICEX 10 is a price non-weighted index, calculated as *the mean of the change of prices* of 10 most liquid stocks admitted to circulation in the stock market Section and regardless of their belonging to the quotation sheets. The index reflects in real time (from 10:59 to 18:00) the growth in the value of portfolio consisting of 10 stocks, the weight of which in the composition of the portfolio at the initial moment of time the same. This indicator is focused primarily on dау traders, and allows you to monitor the slightest fluctuations in prices of underlying financial instruments. The MICEX 10 is the first stock index in Russia, the method which does not provide temporal averaging of prices, and the recalculation of the index values is performed after each transaction concluded with any of the 10 selected stocks in the main trading mode. The composition of the index basket is determined quarterly on the basis of 4 indicators of liquidity.

**Appendix 2. The method of calculation of the MICEX index**

For the discrimination of some of the shares relative to other shares when determining the value of the MICEX index the MICEX is necessary to consider the method of determining this index.

The sequence of ratios of the MICEX index calculation is as follows:

*Determination of effective (market) capitalization of Cap ^{k}_{i} shares*

As of the effective emission volume is taken by the full amount of shares, adjusted for the liquidity of the shares on the MICEX stock exchange and shares of capital stock of each of the Issuer, and are freely tradable in the secondary market, by removing:

· the number of shares owned by the state;

· the number of shares, a proportionate amount of the share capital owned by another Issuer, whose shares are also included in the index calculation base;

· the number of shares owned by shareholders owning more than 5% of the share capital, while shares belonging to such shareholders, may not be excluded when calculating the effective capitalization shares, in the case that the decision of the Index Committee, these shareholders are not considered as strategic holders of shares (for example, settlement depositories of organizers of trading, etc.).

*Corporate events included in the calculation of the MICEX index by using the factor Adj ^{n}_{i}*

If additional emission coefficient Adj^{n}_{i} is calculated by the ratio:

Adj^{n}_{i} = P^{prev}_{i}/P^{j}_{i},

where P^{prev}_{i} — the price of the last transaction with the i-th share prior to the placement of the new issue of i-th stocks (of the same species, category and type);

P^{j}_{i} = { Cap^{k}_{i} + P^{offer}_{i} Q^{offer}_{i}}/(Q^{0}_{i} + Q^{offer}_{i})

P^{offer}_{i} — the offering price of the new issue of i-th stock;

Q^{offer}_{i} — the number of securities in the new issue of i-th stock.

When splitting and consolidation of shares:

Adj^{n}_{i} = Q_{i}/Q^{prev}_{i},

where Q_{i} is the number of securities in all editions (of the same species, category and type) in the i-th shares in circulation after crushing (consolidation);

Q^{prev} is the number of securities in all editions of the i-th stocks (same species, category and type) that were in circulation prior to crushing (consolidation).

*The change in calculation base of MICEX index*

Avoid not due to market conditions, a sharp deviation in the direction of increasing or decreasing the value of the MICEX index in day trading, a correction factor D in the General case other than one:

D = MICEX ^{old base}/ MICEX ^{base new},

where MICEX ^{old base} is the value of the index at the end of the bidding before the change in the index calculation base;

MICEX ^{new base} is the value of the index at the end of the bidding after making changes in the index calculation base;

The analysis of the presented algorithm for calculation of the MICEX index shows that it is the same as in the method of calculation of an index of RTS (and even more), there is discrimination of some stocks relative to other stocks. This is mainly reflected in determining the effective (market) capitalization Capki shares: all these exceptions are, in fact, and there is discrimination of some shares.

In addition, when calculating the MICEX index is used less representative in relation to RTS stock list (tables 5,6).

*Table 5*. **The list of shares for calculation of the MICEX Index (15.10. 2007)**

*Table 6*. **The list of shares for calculation of RTS Index (valid from September 15 to December 14, 2007)**

In the list of 50 companies for calculation of the RTS index includes all companies, the prices of the shares which form the index of the MICEX, in addition to "Bank of Moscow" (table 5). On the other hand, in table 6 on a yellow background denoted by 29 companies that make up the RTS index and is also included in the calculation of the MICEX index.

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