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Elena Lapsina, Khachik Ambarian, Roman Melnikov I. INTRODUCTION The Russian investment market is a hardly complicated form nowadays. Herewith the volume and intensity of information flaw streams, which service it, sharply increase with every passed year. By any yardsticks Western Theories of the for Investment Portfolio presents an immense challenges for the managing risks in Russian financial Markets. In Russian turbulence economic terms , a simple Hurry M. Markowitz models would amount to a pooling foreign conservative investors interests on a grand scale. In psychological terms the foreign investors would have one's witness the changing of Russian's reform policy risks in favor of a new perspectives economical efficiency for their portfolios. In such cases, the mission to elaborate the mathematics models of adopting the optimal investment decisions becomes much more actual. However, an alternative way of using formal strategies for investor program trading will always exists - You could passively accept markets average income by making wide diversification of investment, or open active positions, based on Your own clear mind. Being on the stage of forming, Russian fund market for a long period of time provided anomaly high income on practically risks -free instruments, that's why the question about the quality of systems, which adopt the investment decisions, wasn't so important. Besides, an ability of some players to access confidential information and full control of single or cooperative operators under the market's segments, which belongs to single or few number of great operators, made the value of analytical decisions practically useless.
But there is no ground to confirm,
that the situation on Russian fund market wouldn't seriously change
in a nearby future. The market itself is developing very quickly,
increasing and complicating permanently. That's why we should
seriously think about the possibility of using the traditional
formal algorithms for the managing risks and controlling the
investment portfolio in Russian conditions. In order to estimate of the Western Investment's theories capabilities, we will first examine Portfolio theory putting Hurry M. Markowitz optimization model to work in modern economic environment of Russian Stocks Exchange Market. The general question for this: should the investor consider itself a portfolio and attempt to accept Western models that reduce the risk ( or standard deviation ) of the portfolio returns to Russian financial market's situation?
Let's define the optimal investment
portfolio as a portfolio, which has maximum expecting profit in
assigned level of risk. As a measure of risk we'll take standard
deviation of investment's profitability( expected returns
on a portfolio ) . In this case, the goal to optimize the structure
of the investment portfolio we'll formulate by that way:
Here rp - portfolio
expected return (profitability (an accidental value), M(rp)-
mathematical expected value of portfolio or Expected Return,
By the characteristic's capabilities
of mathematical expectation
We could write out the dispersion
( standard deviation ) of portfolio Expected Return
So, the goal to finding out the optimal
structure of the investment portfolio could be formulated in such
a way:
Lets call portfolios, which structure
satisfies these criterion's with different meanings
The structure of the worst portfolios
on that risk level (lets call it lower portfolio) determines analogous.
Principal risk level
Because of
Consequently,
Let investor has an ability to attract
and accommodate means without any risk at rate rf.
In this case, his Return on Equity is
Lets express M(ROE)through
Remembered, that
In so far as the function RVARp doesn't
depend on with more free- risk's rate, we'll call " tangential "( or " concerning" ) portfolio. In the capacity of mathematical anticipating 's appeasement, standard deviation and covariance of financial instruments profitability, we could use historical meanings. In that case, we could formulate an algorithm of finding Feasible Sets of out variety of upper and lower portfolios:
1. Constructing matrix of corrected
risk's instruments prices
Here t - number of observation (the
case of price fixation), - period's duration, for which would
be hold the calculations of the profitability, T+ - quantity of
the observations, i - number of the financial instrument,
n - total quantity of observed financial instruments. The corrected
price P(t,i) is a 1/S value of the investor's
investments market cost, who has in the moment of time T+ S stock
number i, in stock i in the moment of time t. That investor
doesn't make any bargains with stocks i for the whole analyzed
period of time, solely reinvesting of the i income (per cents,
dividends) in the same stocks i. Such a procedure should
provide comparenesses of the price levels and strike off the anomaly
return's meanings from the observation, which depends on, for
example, such issuer's actions as split and share's consolidation,
paying out dividends by shares, increasing ownership capital and
accommodating additional shares after summary revaluation of the
capital funds. In case of informational absence about such facts,
the correction could be not provided.
The calculation of the Means or Expected
meanings
An estimating of expected return
of the stock i could be average historical meaning
An estimating of covariance of the
Expected Return on a market portfolio stocks j and k
- should be selection covariance
Finding out the structure of the
Optimal portfolios and Tangential (Concerns )Portfolios by using
the upper shown algorithms.
This algorithm was realized for the case with portfolio from the 12 financial instruments. Among them there are Blue chips- the stocks mostly active trading in Russian trade system single shares of the biggest Russian companies. For them, on the base of quotations of middle-weighted prices per week (the sources- Russian -weekly journal 'Expert 1997 ), were built corrected rows of prices for the period from the August 14, 1996 till August the 13, 1997 (totally 52 levels) and weekly returns were also calculated. On the Tab.1 High monthly correlation among
Russian Blue chips - EESRP (RAO
EES), ESIR (IRKUTSK ENERGO, LUKOIL,
RTKM
(ROSTELECOM ) and other followers
over the last
2 years should offer great confidence
in the opportunity
for all traders to profit with
above average gains.
 Graph 1. Russian Securities Market Line x-axis: Standard Deviation ; y-axis average weekly return for the 52 weekly's holding period Aug.1996- Aug .1997 .
That graph shows, that linen dependence
between the profitability and risk is really exists on the russian
corporation stocks market. Herewith, blue chips (" LUKOIL
"«MOSENERGO», "RAO " «SURGUTNEFTEGAZ»,
«IRKUTSKENERGO») characterizes, practically, by equal
meanings of the middle returns on the investments and standard
deviation of the expected returns. Actually, among them there
are more profitable shares of " RAO EES". The stocks
of the "second echelon", for example
YFPG ( YUGANSKNEFTEGAZ ), could provide much higher return, but with a greater keel of
risk.
First eight stocks are characterized by a strong mutual correlation. They form a group of the financial instruments, which have equal dynamics. Due this ,as a result, it equal react on outer space signals. All of them are the representatives of the russian secondary market's "first echelon of corporation's stocks or " Blue chips" . Dynamics of the stocks " KAMAZ 's and " SPTL"(S-Petersburg Telephone NET" shares, which characterize really high correlation or standard deviation of Returns , deeply differ from the blue chip's dynamics, it could be shown by the positive or negative covariance. From the point of view of reducing the risks of the portfolio, very attractive seems to be the way of inserting a pare of "Megionneftegaz- "KAMAZ". These stocks have negative covariance of returns during average meanings of the standard deviation. Very interesting to observe the investment quality of the « PURNEFTEGAZ"( PFGZ ) shares. On the Figure 1 . they are shown as a dot, which is located upper than the regression line - it testifies about their high profitability. Besides, the correlation coefficient of the profitability of the« PFGS ( PURNEFTEGAZ) shares and stocks, which are in the first eight, rather low, and that shows about the opportunity to accomplish an effective diversification. However, You shouldn't make any long range plans. There is no quarantine for the crisis PFGS ( PURNEFTEGAZ)s stocks market.
The YFPG
( YUGANSKNEFTEGAZ )'s shares
are standing alone. Because of an algorithm of the cluster analyze
in the statistical program packet «STATISTICA»while
dividing 12 stocks on 2 equal groups shows , that the «
YFPG ( YUGANSKNEFTEGAZ's shares
are standing opposite to others( - we should classify them in
the another group). In fact, standard deviation and average
profitability of these stocks are "anomaly" high.
These results confirm our western theoretical observation of the Russian Secondary market portfolio from Table 1 : there are more total middle risks associated with RAO EES, "Rosttelekom " Among these twelve stocks of Russian Blue chips only LUKOH( LUKOIL NK) - 6,35%and MSNG ( MOSENERGO) - 6,35% have minimal standard deviation of Returns. So , diversification of the portfolio assets provides the high reduction of the investment risk. In that case, minimum possible standard deviation of the Expected Returns is 2,49. The Tangential portfolio provides profitability of 3,52% on the level of standard deviation - 5,34%. Comparing the structures of the Tangential and some of the most free-risk's portfolio, we could underline the similar features : there are an essential presence in both of them « PFGS ( PURNEFTEGAZ)' s shares »and KAMAZ's shares. These stocks possess the combination of investment qualities, which are very attractive for the portfolio investor: the independence of the behavior against the market's conditions, the limited risk and acceptable profitability.
From the point of vies of the radical
differences between Portfolio's Models we could
underline differences :risks-free
rate Optimal Model Portfolio has been selected from the most
stocks -"Lukoil"s and "Rostelekom"s shares
's stable stocks»from the most
free-risk's portfolio in the structure of the concerning portfolio
are only on the second place after more profitable «RAO
EES Russia" as shares. The Tangential portfolio is less
diversificated , than the most free-risk portfolio. Concentration
of the Hirfendele - Hishner index -, which could be counted by
the formula  Figure 2. Feasible Set of Portfolio's When the standard deviation is little, the optimal porfolios mainly consist's of PFGS ( PURNEFTEGAZ), RAO EES 's, « SPTL (S- Petersburg TELEPHON-NET) shares. While passing through the point of touch, - LUKOH ( LUKOIL )'s and SNGS ( SURGUTNEFTEGAZ )'s stocks, which entered the optimal portfolio, yield their places to « YFPG -"YUGANSKNEFTEGAZ's shares.
The most inefficient financial instrument
during the analyzed period were" MOSEN- ERGO" shares.
They did play a leading role in the structure of the most inefficient
portfolios. Special interest appears when You see simultaneously
presense KAMAZ's stocks in the composition of the most riskable
and free-riskable portfolios. That strange situation could be
explained very easily: the influence of the financial instrument
on the summary result determines not only by it's individual investment
qualities, but also by the characteristics of the connection it's
profitability with the profitability's of another stocks in that
portfolio. The same stock, inserted in the composition of the
different investment portfolios, could increase and decreases
their risk, and also influence on the summary optimal criterion.
The special role in the modern theory of the investment portfolio plays Wiliam Sharpe's Market Portfolio model. His theory carried these of this ideas further by mouthing thst individuals also have the ability to invest in a risk-free asset ( e.g. Treasure bills, GKO in Russian case ...) It is based on the proposition, that stock's Return has a linear relationship connected with the addition temp of the market index. In that case:
Method of the lowest quads gives us next parameter's meanings of the regression equation:
Condition of the equality of the
0 private derivative functions the sum of the quads of the accidental
deviations provides
Modern theory of the investment portfolio's
management use that equality as a decomposition of the total risk
on systematic and nonsystematic. Herewith, total dispersion
But for some stocks, that market
model wouldn't fit in a real life. The hypothesis about adequacy
of the market model needs checking. Let's think, that the model
is adequate if the regression coefficient After defining the characteristics of the market model for the stocks, we could easily define the characteristics of the investment portfolio. In that case,
Portfolio's risk could be decomposed on systematic and nonsystematic, the same as with a stock's risk. During that operation, we could write nonsystematic portfolio's risk as:
W. Sharp confirms, that profitability's
deviations from the regression line are not correlated In order to estimate the Investment risks in Russian Market we could suppose, that the hypothesis about correlation's absence of the unexplained by the Market model deviations of the stock's returns is very doubtful. Really, it explains, that it couldn't be any groups of stocks, which prices and profitability ( (expected returns) react in the same way on the same changing of the out-environment factors. If W.Sharp was right, than, for example, abolishing an embargo on oil's export from Iraq will reflect differ on the market prices of the oil company's shares (or they wouldn't reflect anyway), and the increasing of the world consumption of copper, while decreasing of the reserves on London's stock of non-ferrous, won't lead to the rise in the exchange rate of the metal enterprise's shares. For the 12 shares of Russian companies was held an assessment of the parameters of the market model, relatively to the two different market indexes. First one was based as average basis temp of growth of the corrected prices of all analyzed financial instruments.
Second index determined by calculating
a weighted average rate of basic growth temp of the corrected
prices. As a criteria of optimal market model, we used maximum
of the determination coefficients sum. As a result of the calculations,
which based on the mathematical model of the optimal index on
the left side, we obtained the structure of the standard portfolio
(on the right side):
If we'll use the first market index, the parameters for the Optimal Market models for the researchable stocks would be:
Tabel 4. Parameter`s optimal portfolio
First of all, let's check hypothesis about the role of the -coeficient. By the traditional used in economic researches role level =0,05, critical meaning of the t-criterion is 2,0096. So, the regression coefficient in the cases with " PURNEFTEGAZ » and «Yuganskneftegaz »couldn't play statistical role, and market model - really truthful. The characteristics of the regression dependence for other 10 stocks are rather interesting. The most aggressive are S-Petersburgs Telnet " shares - their -coefficient is 2,0462, moreover even after subtraction of the standard mistake, is still rather big: 1,5488. As summary, for the portfolio's manager it is very reasonable to increase the portion of SPTL ( S-Petersburg Telnet')shares in his portfolio while awaiting for the growth of the fund market. If there are forming any prerequisites (remises) for the round turn from the " BULL trend " due these stocks would be sell immediately. Among the Russian Blew Ships one of the aggressive stocks are - NKEL( Norilsky Nikel ))'s shares . Conservative financial instruments, which are less dependent on the influence of the market situation's changes and political conjunctures , are " Mosenergo", "LUKOIL " and«Rostelekom's shares. What about the others stocks, it is rather difficult to explain the situation about them because the deviation of the beta-coefficient from the 1, 0 - for them is no more than the standard mistake. This Market Portfolio model better explains the Return's changing of the RAO , Mosenergo, LUKOIL's, ROSTELECOM's, , SURGUTNEFTEGAZ 's shares. Never the less, the forecast for movement of Returns of these stocks, have been based on the regression model, which is extremely unexactitude: prognosis's standard mistake is more than twice bigger than middle profitability's meaning. Determination coefficient is very low in SPTL ( S-Petersburg Telnet )'s and, especially, KAMAZ's stocks.
The most attractive in correlation between profitability and systematic risk (it's exponent is -coefficient) are « RAO EES"'s shares, and the less attractive - 's stocks. Theoretically, lineal character of the dependence between -coefficient and profitability is improved, but the deviations from the regression line are rather essential. The Correlation residues
matrix, which are not explained by the regression equation, could
be shown in such a way:
It's obvious, that William Sharp's proposition doesn't working and fulfill: the deviations of the stock's profitability, which weren't explained by the regression model. For the most stocks, coefficient of the remainder's correlation is positive. Here, it's useful to look at the KAMAZ's and SPTL's shares. It seems to be, that the special factors are influencing on these stock's market. It mean's, that including its ( into the portfolio could decrease total risk.
The Second Market Portfolio
Model based on the increasing 's temps of the second index,
have been characterizing by the following parameters :
In this case the relationship between the temp s of movement of Market' Index and the and asset's returns of portfolio is not such significant for the two shares , excepting the stocks of «PURNEFTEGAZ» and «YUGANSKNEFTEGAZ» , there are only stocks of « KAMAZ» and «SPTL ( S-Petersburg's Telnet ). Generally the mining of the parameters of regression equations have been too much increased due to : increasing of t - of statistics, decreasing of the meaning of the standard mistakes. That's interesting, that meaning of - coefficient of stocks «S-Petersburg
Telephone Net» and «Yuganskneftegaz
» assets are significantly
different for the two different Market Models of Portfolios
: of SPTL ( S-Peterburgs
Telephone net ), which equal
to 2,046 in the First Portfolio
Model ; in the Tangential (Concerns ) Potfolio - of SPTL -
is negative and equal to (-0,2783);
of «Yuganskneftegaz»
has been changed from( -0,5400)
to 3,9546. This
paradox we can easily explain :
the coefficient of the determination is a minute in the first
and second cases. So,
it shows , that even
small Index 's modification
should actuate ( lead) to adjustment
of the parameters of Portfolio Models.
For the regression Models which have some significant statistical meaning , the eta directly depends of the selections Market's Index The important point of W .Sharp of Portfolios Theories - about Market Portfolio is that for individuals holding diversified portfolios of assets , the appropriate measure of risks eta is how the return on an individual asset moves relative to the returns for the market portfolio . According to Western Theories the eta coefficients the measure of asset's volatility in relation to the risking of the market portfolio as a whole. Coefficient eta could play role of -the best measure of investment quality of assets only in the case if the different selection variants of Market Portfolio's Models which could have the similar collections of financial instruments. In this case we could exactly suppose, that the RAO "ÅES» stocks are very aggressive with the high level of systematic risks (1- 1,16 ; -1,23 ) , comparing the LUKOIL stocks- are more stability financial instruments and very attractive for the conservative investors.
Submitted by Elton, Gruberg and
Padberg simple algorithm of determination of the structure
of Tangential Portfolio have been based on the using of parameters
Market Portfolio Model. Due this alghoritms the collections
of Input's parameters have include the coefficients
This methodological approach we can implement only for the assets which , coefficient have been recognized such as important statistic element. In the cases with Russian stocks there is the necessity the exception from the selection process the stocks of PURNEFTRGAZ and YGANSKNEFTEGAZ for the First Market Portfolio Model. and exception of the stocks of KAMAZ and SPTL -« S Petersburg Telephone Net " for the Second Market Portfolio Model » . Given algorithm have been used for the finding of the two assessments of structure of tangential portfolio on the base of the First and Second Indexes . The difference between of indexes was very significant. While the using of optimization index have been permitted to give the best assessment of real structure of Tangential portfolio . As a result it was determinate buy generally , the occurrence's domination of «Purneftegaz» and «RAO EES» 's shares.
The comparing of the differences
of parameter of Tangential Portfolio and it's two assessments
is more convenience to lead
buy using the next table system :
The using a E.Elton- M.Gruber-Padbergs's method have been allow to leave on the level of returns at the real Tangential portfolio (with greater or smaller degree of accuracy depending on used index). However Standard deviation of optimum portfolio in this case obviously unattainable. This is because the market portfolio's model excludes a possibility of account of un-homogeneous reactions of the prices of different financial instruments on one and same entering from the external environment's signals. At the same time the serious way to optimization, which have been used at the in-put the covariance's matrix . Also, this way allows to construct the portfolios , which are the most protected from the influence of disadvantage changing of the most different factors of external environment. If W. Sharps hypothesis on the absence of correlation of the remainders has been corresponded in reality, simplified optimization algorithm will have acted much more effectively. But as far as this may not so, for the following reason we could have satisfaction only the smaller price's risk . This is in contrast with really optimum price of taking risk (0,4602 and 0,4623 against 0,6596), or use much more labor-consuming and demanding to technical parameters PC, but greatly more exact optimization algorithm. The analysis has shown that the Russian Financial Market represents a classical example of " Fresh Market" which has developed and grew up to maturity during Even while academia is debating the relevance of beta , Optimal Portfolios Models, and CAPM in pricing securities in Western markets, we have taken up the briefly research here, and the results are a bit surprising. But first, the usual disclaimers. It is widely known that to make the Markowitz's Portfolios Theories a number of critical assumptions must be made about the characteristics of the Western optimal capital market, including efficiency, convergent investor expectations and goals, adequate and accurate flows of information, etc. Obviously, one need not be a veteran of Russian capital markets to recognize that these assumptions amount to little more than wishful thinking here. Even in Western capital markets, these homogenous assumptions strain the ability of the model to reflect economic reality. Bearing that in mind, we went ahead anyway and calculated betas for the most liquid Russian stocks, which have an Russian Trading System (RTS )trading history for at least one year. The methodology used monthly returns and volatility figures, and the market was defined as the RTS Index. Generally, a longer period, at least three years, should be used, but we opted to limit the data to the more recent Russian Stocks Market history, because of the better transparency and firm pricing rules in the system. Analysis of the most liquid portfolio's instruments of the Russian stocks market has been shown that the portfolio's managing risks via Western Model Portfolio's mechanism is inefficient. It does not reflect the most basic underlying market elements, capturing characteristics. Due to the differences between Western and Russian Market capital of Russian Market Portfolio's Theories could not be implemented for the investors by generally. The portfolios Models could be implemented only on the short term period stability of the russian policy system . The developing of Russian trade system and other market's financial segments now have been formed and still did not reach a stage which adequate to Sharp's Portfolio models. In fact ,that is the crux of the problem - management of investor's risks on the free-riks segments of Russian financial market. Now is more problematical a finding new approaches to mechanisms of portfolio management on the GKO market.
The new intentions of the Russian policy-makers to
revert of the financial market on the new stage. It dictates
the necessity of the developing an introduction a formal managerial
systems of estimating and identifying of investment potential
on the different segments of Russian financial market.
The Neural network - is an uncial instrument of the non -lineal interpolation . Using the Neural Programs market we should investigate and construct the strong relations of market variables elements. The evolution process of different strong and resistant systems which includes the different quantity of the similar micro-objects, has been coordinated by the universal economic rules , should be investigated by Neural Net technologies. In fact , that the most serious complex with specific functional dependencies for the neural investigations represents the Russian GKO -OFZ Market . GKO-OFZ market which is a further crux of the problems evidenced at the begining 2000-2001 years. But managing GKO portfolio's via Neural Network Technologies we should estimate the market volatile and if it will possible to build neural structure for the investor's portfolios. Due this , we could try to formulate some common methodical approaches for the neural test and forecast of the dynamics of object's properties and the movement of rate GKO-OFZ Market yields . The government debt market - GKO-OFZ is the most suitable for the investigation such properties . Each GKO issues is a system's object , described by the range of properties , in which - the " price " and the " yield to maturity" have represent more important portfolio's elements. By changing each other , GKO issues repeat at the same life cycle- from the distribution on the auction until terms to maturity. Dynamic of the prices have subordinate some of the common regularities. Due this , it possible to maintain that the smooth function approximated the relationship between of the call price and the term of conversion, the first of conversion -time derivative of prices - is positive , second - negative. Besides of this , there exist the specific relationships between of the current prices- call and futures prices-call. The most significant role in GKO-portfolio management have play a weekly - seasonal cycle of government GKO-Bond's Market: Monday, Tuesday , Thursday , Friday , in which the deference between the absolute growth rates of call-prices is statistical important. The neural network test help to strong starting and store al relationships by development all historical observations. While the specific regularities of the dynamic raw in one of the same GKO issues, the other kind of relationships there are exist .This relationships have determinate the parity of correlation between the meaning of properties of the different similar objects. At the GKO-OFZ market it appear in smooth of the Yield curve ,that is impossibilities of the existence significant deviations of the yield's and précis's parameters of the neighboring GKO -issues . Besides , there exist some regulators , that determinate the reactions of the system and their incoming subjects on the outside impacts . Most of the outside impacts are difficult formalizes for the GKO-OFZ market cases . This situation has blocks the forecast of the changing of parameters of objects. However some of them should possible take into account , in particular, it is a volume of financial means reserved in trade system , internal cash flaw streams , forgoing cash dividend streams and volatile of financial market . Regrettably , the information about internal market's turbulence was not transparentive and accessible for the our investigation. Due the aforesaid methodological approaches to the common investigations of dynamics and the forecast of the movement 's complexes systems ,such as a specific GKO-OFZ market we should try formulate some key general principals for the Neural Test for the GKO-OFZ Portfolio. The network's performance is measured using GKO-OFZ market's different data sets. Serving as input elements of neuron's pattern for the designing Neural network have been taken the following variables:
3 Gain of GKO closing - price in contrast with preceding tenders and for a trade week. Practicability of use the gestation lags -1 and -4 is confirmed not only by general considerations (these gains are the best, that reflect a marked tendency in a recently tender's situation . Also ,it is confirmed , as well as presence of corresponding maximums of the private automatic correlation function of closing price .
As an output pattern was accepted a value of absolute gain of GKO closing - price at the following sale. Using a first difference of range of closing -prices it is required for the eliminating a significant auto correlation, that obstructing as a process of tutoring and interpreting the output values. Training of the Neural - GKO-Portfolio's Model have been developed on the base of PC- Pentium-200 Brain Maker 3.10 of the California Scientific Software Co. Training and testing sets have been formed on the base of dynamic ranges of closing -prices on à period of March 3 , 1998 ã. of GKO-issues from June 26 1997 ã. till March3,1998 ã. Besides this, the information about these issues , which maturity have been between of these. This approach has been stipulated by two factors: aspiration to build the best representative training set and scarcity of information. > As A Result significant part of observing which were presented in the course of training have described a behavior of issues with a large term before maturity. Intermediate term before maturity of used data testing to facts was rendered equal 208 days, but behavior of short-term GKO ( terms to maturity was less than 90 days) have described only 10,5% observations. Also , it is necessary to note that significant part of t training facts was come for a period of financial convulsions, when market was characterized by low meaning of absolute gains of closing prices and their high volatile. Optimum condition of trained network was achieved in 1,5 hours after the beginning of neural- net learning. The following further learning under the variation of educating parameters have lead only to worsening a quality models : mistake on the educated set was shortened, extremely small, but a number of the «bad» forecasts for the test set have been increased. At the same time the tax have been not taken into account . Built model was used for forecasting of the absolute growth GKO closing -prices on the result of trade session from March 6 till 26 march 1998 - given for these days when educating training were not presented. On the base of received test-forecasts has been tested of hypothetical methodology of neural -portfolio strategy . All GKO transactions have been led by taken into account of the closing -price , it's commission and tax , have not been used. Neural Model Portfolio's instruments have been re- selected due to the results of each trade session. Every time the new Portfolio's selection has included the three of the most attractive GKO instruments in accordance with the received forecasts of the growths of GKO - prices rate follows trade session .In case , when in accordance of neural forecasts have been anticipated decreasing the closing prices of the whole GKO instruments , financial means have been eliminated from the Portfolio ( given portfolio has included 100% pure money ). The used Neural network - methodology has provided the effective GKO gain- 124.27% per year ( a comparative simple GKO market's yield - 82.68%/per year). Market Index , accounted as a multiplication of average -arithmetic rate of growth on the all accessible dynamic rows , during the period of the portfolio's management has been provided only 35.04% effective yield /per year or 30.30%/ per year by the equation of the simple rate of bond's evaluation. For the estimation of quality of Neural Portfolio Model it possible to use of the aggregate of double-measuring f statistical regression analyze . In given case , by considering the forecast as a functional factor and the actual growth of the GKO closing- prices as a result. The criteria of the quality of the prediction it possible account the level of importunes of regressions with the condition of positive correlation coefficient. In essence , if these conditions fulfilled , thus neural net predicts the GKO-closing prices with exactness to homogeneous lineal interpolation. That meant , it should adequately determinate of the relative potential of the growth Portfolio's instruments. Let's assume, that quality of the prediction is" good" under 1% level of meaning of regression coefficient and normal under 10% -level of the regression coefficient meaning. Due these , for the term of the 3 trade session have been received a good predictions, for the 5 - normal predictions and for the 3 - bed , it confirms the good quality of the Prediction's Model . That interesting that , all three series of the bed forecasts has been given by Neural net for the falling down Market . In this case , Neural net was very sensitive . It so effective and truly has determinate the trend of the movement of price index.
One of the error was easy described by the turbulence of weekly
trading cycle
due to the disorder of Russian market calendar by the March
8- t.he Celebration of the International Women Day in Russia. TEST-1. MGU ESIT // Neural Test of the portfolio for the GKO -OFZ YIELD In six cases from the eight an normal series prognoses was
has been assumed the systematic error. The mean of error is
well defined for the underestimation of rates of the
growth of volume market operations. This fact underlined by
the positive dimension of the
liberty segment ( term). This cased by specific of the training
set formed on the
information base data's falling down market and last Russian
crisis  Figure 4. The Test of the GKO OFZ Market There is no doubt that , in practice , market management should be a little different.
Some part of the extra- profit should has been lost due to the
objective different reasons :
Practicable reserves of improvement of reliability of the forecasts have been included in the follows : 
MGU ESIT // Neural Test of the portfolio for the GKO -OFZ YIELD In six cases from the eight an normal series prognoses was has been assumed the systematic error . The mean of error is well defined for the underestimation of rates of the growth of volume market operations . This fact underlined by the positive dimension of the liberty segment ( term). This cased by specific of the training set formed on the information base data's falling down market and crisis wrap. Another specific of using observation under training of neural Portfolio's model is high volatility of the market . It has been reflected in the less mean of regression coefficient è -amplitude of the forecasts has been more exceed the actual changes. While this volatile of the regression line of proportion with the unit tangent of corner of incline , could be caused. Also , it's could not be considered as a bed pattern of Neural net Portfolio's Model.
Moreover , the correction 's algorithms of systematic mistakes
could be estimated by a-priory.
Underlining the analysis of management
risks of the investors Portfolios at the Russian Secondary
Market we could notify follows :
In an effort to prevent investor's interests for the future managing of Portfolio's risks we in briefly , described the key elements of Western Portfolio's Theories which have been implemented for the Russian Secondary Market. The Modern Russian Stock market first of all its secondary markets in Moscow and St Petersburg have not fully matured to be able to be compared to classical model and techniques. Several conclusions are clear: First. Models of the prices forecasting of financial instruments needs to be more fully developed. Second, a model of checking the investment risks must be refined. Third, better approaches to develop of more complete data must be investigated via neural computing techniques . Fourth , other financial mathematical techniques such as " fuzzy logic " must be further explored. Arguing to the benefit of the practical implementation of the Neural Net Portfolio's Models we could outline the futures complexes of methodological investigations which should includes the follows Research Modules: 1. Module of price forecasting of financial instruments 2. Module of checking the investment risks
Module to generations of controlling vectors ( revision
and decryption recommended by Target transactions deals ) in conditions
"financial friction". In the course of modern financial instrument development must be used the most efficient modern methods of "data mining " from accumulated information arrays . The most perspective of the Neural Net Investment Decision Portfolio Net is based on advanced neural network technology that allows highly accurate predictions based on past experience. overcomes limitations common to conventional neural technologies with innovations that improve generalization, accuracy and reduce system training time. This ability to generalize is fundamental to successful data mining, particularly for the case of wide vector and sparse data problems common in database applications. Whereas other technologies will "over-train" to specific examples. Decision Net will discount examples at the possible expense of local accuracy for a better global solution. The result is a model with excellent predictive behavior and accuracy across the entire target data set.
Neural nets are best used for predicting a future outcome based
on prior learned experience Neural Model of risks -testing is based on advanced neural network technology that allows highly accurate predictions based on past risk's -experience. Neural Module overcomes limitations common to conventional neural technologies with innovations that improve generalization, accuracy and reproducibility, and reduce system training time. This ability to generalize is fundamental to successful data mining, particularly for the case of wide vector and sparse data problems common in database applications. Whereas other technologies will "over-train" to specific examples, Neural Test of Portfolio risks will discount examples at the possible expense of local accuracy for a better global solution. The result is a model with excellent predictive behavior and accuracy across the entire target data set.
Neural nets are best used for predicting a future outcome based
on prior learned experience. Potential neural net model applications
are: Risk analysis - which prospective customers are a good credit risk?
Retail analysis - what product is this customer likely
to purchase? Clustering systems are best used for finding groups of items that are similar. The groups can be fixed in advanced (supervised clustering) or determined by the system (unsupervised clustering). Most traditional clustering systems use simple measures of difference such as Manhattan or Euclidean distance. Decision CL allows more sophisticated functions, including using Neural- Risks Model to predict whether two items are the same. Potential clustering applications are: Direct mailing - find groups that exhibit a similar pattern of response Risk analysis - find groups that exhibit a similar pattern of payment history.
Also it necessary to be oriented on the most of the effective
methodologies of risks management which developed by Russian
financial analysts - of Russian Central Bank, Alfa bank . In
particularly , the methodology of the Alpha Bank of percentages
( % ) risks GKO managing.
The Generation Module of the managing vectors should be estimate the financial friction due to the strong fiscal loses, such as ( fiscal transactions with the changing of Tax legislation and changing mechanism of regulation market. The Generation of the Module should have been oriented on the specific of the Russian financial Market and Russian still semi- regulated structure of financial market. Most of important methodological approach to Generation Module - is mathematical support of the flexible parameters of financial and fiscal instruments ,which will help to realize different financial schemes such as offshore portfolios management with different legislation's conditions and different dialers. On the other hand , this Module help to adopted to different changes of institutional structure of Russian financial market which have general impacts on the transactions investors. Such formal portfolio management system does not pretend on the hypothetical Model of financial "perpetual mobile". Actually it have some theoretical and practical restrictions too. Modern Russian Financial Market have been extremely evaluated and have been reach the economical maturity .These has been permitted to use the formal Western theoretical algorithm for themanaging of portfolio risks and to proceed the future fundamental research new systems of managing of the portfolio risks in Russian and Global financial Markets.
REFERENCES
Harry M.Markowitz "Portfolio Selection", Journal of Finance, 7 , no.1 (March 1952), pp.77-91 Hurry M. Markowitz" The Optimization of the Qadratic FunctionSubject to Linear Constraints" Naval Research Logistic Quarterly, 3 , nos.1-2 (March-June 1956 ), pp.111-3. 3 Gordon J. Alexander and Jackk Clark Francis , Portfolio Analysis (Englewood Cliffs., NJ: Prentice Hall , 1986 ,1986 ) Chapter 8. Edwin J.Elton and Martin J Gruber, Modern Portfolio Theory and Investment Analysis Analysis , New York : John Wiley , 1991 . William F Sharpe, " Capital Asset Prices : A Theory of Market Equilibrium Under Conditions of Risk " , Journal of Finance ,19 n03 ( September 1964 ) pp.425-442 William F.Sharpe , Gordon J.Alexander , Jeffery V. Bailey -Investments , Fifth Edition, Prentice Hall International , Inc . , 1995 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
- standard deviation of portfolios
Expected Returns , 
- principal risk's
level. Besides 
, where i - number
of the portfolio stocks, n - the number of possible stocks in
the portfolio, ri- the probability of the
occurrence of the i-th stock ,
xi- share of invests in stock number i.
.
. Here COV (rj, rk)-
is a covariance of the profitability of the stocks numbers j and
k. In so far as 
, 
,
and 
, we'll have
,
upper portfolios.
could be determined
on the any level, which belongs to the multitude admitted meanings
of portfolio risk 
. The lowest meaning
could be determined from the condition
,
where 
- twin correlation coefficient,
which characterize narrowness of the connection between Expected
Return of the financial instruments with numbers j and k, 
.
.
,
where xf- opened by investors position on
the money market (in shares of capital), 1-xf -
volume of investments in risk's securities (in speculative shares
of capital), rp- Expected Return on the
portfolio risk's instruments. With the property of mathematical
awaiting and dispersion we'll have
:
,
we'll see, that in so far as 
, 
,
while 
, where RVARp-
portfolio risk price.
, an optimal combination of
risk's actives is invariant to the risk, which investor was ready
to have. Risk's instruments portfolio, for which 
and which determines an optimal structure of risk's investments
for any investor, who has an ability to attract and accommodate
financial resources
, is 0,30 for the Tangential
portfolio, and is 0,23 - for the most free-riskable one.
, where
ri - stock's i profitability, 
-
addition temp of the market index, 
,
- parameters of the linear regression equation, 
-
occurrence deviation.
, where
- selected covariance of the stock's i
profitability and addition temp of the market index, 
-
selected dispersion of the addition index's profitability, 
-
average meaning of the stock's i profitability, 
-
average addition temp of the market index.
. From the last equality
and dispersion's properties there is 
is a characteristic of the total stock's risk, factor dispersion,
stipulated by changing of the independent recession (it is addition
temp of the market index)
- level of systematic
risk, and remainder dispersion 
- measure
of the nonsystematic risk.
could have statistical meaning.
.
, and risk's
decomposition on systematic and nonsystematic ones becomes 
.
, the remain
dispersion
,
the standard deviation of the Market Index - 
,
and risk free rate - 
,
and also Expected of Returns of financial instruments
and their
correlation.
