Currency and Stock Exchanges: on the Efficiency Shoals

The purpose of this article is to define the preliminary results of investigation of decision-making management in currency and stock exchanges. The object of the research is decision-making management in currency and capital markets. A particular aim of the research has been creation and practical utilization of a currency and stock trading system which relies upon historical data and provides for trading strategies with a guarantee ensuring positive trading results. The conceptual aim of the paper is to show (according to specially elaborated simple portfolio trading strategies) that today's currency exchange rate and capital markets offer real possibilities to get a bigger than average trading profit, i.e. to show that in these markets there are some "shoals" of effectiveness, which can be realized as inefficiency features of these markets.

The purpose of the paper. In the paper, tentative results of research in decision-making in exchange and capital markets are described. The object of the research was decision-making management in exchange and capital markets (DMMECM). Here management of decisionmaking is recognized as formulation of particular goals, generation, selection and accumulation of information for reaching these goals, creation of measures for attaining them, selection of aim-reaching criteria, preparation and realization of aim-reaching strategies. A particular aim of the research was creation and utilization of a system of trading in currency exchange rates and stocks, which relies only 104 on historical trading data and allows creating the trading strategies that assure positive trading results with a desirable level of guarantee. A particular object was historical trading data in the global market of exchange rates (FOREX) and several capital markets, among them New York Stock Exchange (NYSE), Milan Exchange, etc. Pragmatical aim of the research. On the basis of analytical conclusions it is shown that the proposed DMMECM system is efficient in those markets and has a theoretical background and practical approval. Altogether, it is necessary to bear in mind that the advantages of the proposed system offer opportunities for effectively using the naive stra-tegies, called maximas here. For digital system solution the so-called imitation technologies are used, which allow to solve analytically quite complex systems of mathematical models with stochastical variables, limitations and criteria. Also, it should be mentioned that the proposed variant of the system of strategies is only initial and has a high potential of development.
Historical data, which are the object of practical research, are obtained from official information sources and are used directJywithout correction or adaptation.
Scientific intention of the paper. The conceptual aim of the paper is to show (according to specially created simple portfolio trading strategies) that in today's currency exchange rate and capital markets there are real possibilities to get a higher than average trading profit, i.e. to show that in these markets some "shoals" of effectiveness exist, which can be understood as inefficiency markers of these markets.
Key words and expressions: market efficiency, guarantee of possibility, portfolio adequate for investment profit stochasticity assessment, isoguarantee as a portfolio decision-making instrument, decision-making management in currency exchange and capital markets (DMMECM).
The logical stlUcture of the paper. The integral decision managing effect is usually attained by forming and managing investment or trading portfolios in capital or exchange markets. The final goal of the proposed decision managing system is portfolio decisions made in exchange and capital markets. The preparation and use of the managing system can be assumed to consist of three stages: determination of the system's main parameters for portfolio decisions in exchange rate and stock markets; portfolio decision system information supply; portfolio decision finding. We also want to note that the advantages of the proposed currency system of forecasting exchange rates and stock prices offer opportunities for an effective use of naIve strategies, named maximas here.

Introduction
As is mentioned above, the aim of the paper is to present the management system of decisions made in currency and capital markets. The layout scheme is as follows (Pic. 1): forecasting principles and models of exchange rates and stock prices will be presented, with a discussion of the advantages, disadvantages and real possibilities of technical analysis for implementation of the forecast. Particular forecasts created according to our methods will be presented, their utilization and realization for the formation of naIve trading strategies will be illustrated; analysis of portfolio decision possibilities in exchange rates and capital markets will be carried out, discussing the necessity of developing traditional standard deviation -average or VARprinciples and suggesting an adequate portfolio stochastical nature. Particular possibilities of an adequate portfolio utilization in decision-making in exchange rates and capital market will be presented; the possibilities of portfolio utilization in global exchange and various capital markets will be examined; utilization of imitational technologies in searching for portfolio solutions and the conception of DMMECM monitoring will be presented.
Main dependencies and portfolio decisions (trading strategies) in exchange and stock market systems' parameters detennination stage

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Preparation of adequate forecasting system of Adaptation of the prepared forecasting system exchange rates and stock Although the DMMECM system is intended for the management of portfolio decisions, the non-portfolio decision making management subsystem and the suggested forecasting system for exchange rates and stock prices have a self-sufficient value.
2. General scheme of the research and the subsystem of simple decision making management in exchange rates and capital markets 2.1 Conditional denomination of partial historical data with forecasting information.
As is mentioned before, the particular object of our research is historical data on exchanges rates and stock prices. Picture 1 shows a fragment of the analyzed data. For the purpose of 106 research, historical data were differentiated into "truly" historical and "seemingly" perspective. We will explain the reasons for such differentiation below. At the time of research, part of data (l-t data of days) were accepted as historical; the corresponding assessments were made and information for decision making was selected. t-200-day data were treated as future data; decisions made with their help were tested. As our strategies were oriented to one step, the solution made on the background of t-day data was tested by data of t + 1 days, and the real data of this day for the next step were accepted as historical. The process would continue until the 200 lh day.
It should be noted that the research decisions were differentiated into simple decisions and portfolio decisions. The purpose of such differentiation will be revealed in the further text of the paper. However, we also will note I I <:; -.J that the role of future data for portfolio decisions fell only on data of days 190-200. Before starting the analysis of the forecasting and decision making systems, we will short-1y study analysis methods for exchange rate and capital markets. Because in this paper we will study the decision (trading strategies) search system in exchange rates and capital markets based only on historical data, attention will be focused on the realization and development of methods for technical analysis and forecasting. Therefore, first of all let us study the stage of analysis in the hierarchy of management actions as a necessary presumption for adequate forecasting.

Adequate forecasting system of exchange rates and stock prices
Knowing the abundance and versatility of the set of technical analysis forecasting models, it would be negligent to generalize these properties of this set. Therefore, even though most forecasting methods in technical analysis theoretically are suitable for forecasting exchange rates and stock prices and have a long-time experience not only in this area, we have to admit that they do not satisfy the main attributes indispensable for forecasting methods: the method of forecasting exchange rates and stock prices must be adaptive, i.e. helpful in considering the fact that in each point of variation of exchange rates or stock prices, changes also the sum total of factors, their role, the functional dependence of exchange rates and stock prices on the factors that determine them, as well as the interrelation among these factors themselves; methods of forecasting currency rates and stock prices must be flexible, i.e. their utilization should be possible in every forecasting system, be it a complex system of mathematical models or subjective expert decisions; the forecasting method should be consistent, i.e. factors and their consequences should be strictly differentiated. This is very important when determining and using analytical interrelations between a factor and its consequence and interrelations among the factors; utilization of one or another method should allow a quantitative assessment of the reliability of the obtained results; methods of forecasting must be constructive, i.e. allowing a selection of the most probable values of the variables or processes. Main principles of adequate forecasting .system. Below we will illustrate the main one-step exchange rate and stock price utilization principles of the forecasting system. The core of the forecasting system is the regressive dependence of the value of the forecast index at the (t+ 1) moment on the values of this analyzed index at the t-th and previous moments: yl+l =f(;:,;~, ... ,;~;9(0,t») (1) where yl+1 is the probability distribution of the exchange rate or stock prices at the (t+l) moment; ~I is the I-th factor probability distribution at the t-th moment; 9(0, t) is the resultant of the influence of other factors on the index of the (t+ 1)-th moment; f is regression.
Of course, forecasting in real time, i.e. at the moment when historical data develop and are announced, would not differ from the pre-sented situation, except that a 160-day forecast would take a period of 160 days. For the sake of briefness, Picture 2 contains only five diagrams. These diagrams show a coincidence of historical and forecasting indices of the exchange rates and stock prices presented in Tables 2 and 3.
These forecasting data were used for preparation of simple trading strategies, named maximas in the text. The maxima's content is the elementary truth: buy a stock for its closing price if its price rises next day, and sell it if its price falls next day. For exchange rates, this provision could be expressed like this: capital should be considered as the first currency if its rate grows with respect to the second currency and, vice versa, as the second currency if this rate is falling.
While realizing maxim as, it is very important to guess, the trend of change of exchange rate and stock prices i.e. whether they will rise or fall. That is why in each column of Table 2, in an extra line, the number of coincidences is shown when the forecast and real indices were changing in the same direction.
Picture 4 shows the results of utilization of naIve trading strategies -maximas -in diagrams. Each diagram is formed by the following principle: the value of the initial capital is 100 units; the I't line shows change of the initial capital in case it becomes a deposit giving 8% of annual interest; the 2 nd line shows the real change of the initial capital in the market; the 3rd line shows the possible growth of the initial capital, in case a simple strategymaxima -is used.

Evaluation of maximas' possibilities in DMMECM system
Pictures 4 and 5 show real utilization possibilities of maximas, because the diagram (line 3) is formed considering possible trade expenses. Using the possibilities of maximas, it is possible to increase the initial capital to a greater extent than using passive accumulation, i.e. deposit in bank. In many cases maximas allow to obtain a bigger capital than using the passive "buy and hold" trading strategy, i.e. to trust the situation directly generated by the market.
The possibilities of maximas directly depend on the accuracy and reliability of the forecast of exchange rates and stock prices. If while choosing maximas it is important to guess only the growth directions of currency exchange rates and stock prices, while forming the DMMECM subsystem of portfolio decisions forecast accuracy and reliability in a full sense of these categories are also important. Therefore, let us analyze the adequacy of our forecasting system to the above mentioned adequacy requirements of the forecasting model, first of all while describing the reliability and constructiveness of the forecasts.
Before describing the possibilities of the applied forecasting method, let's have a look at fig. 6 (Picture 3), because it will be the base for empirical conclusions. This picture presents a comparison of the geometrical view of the empirical historical data and the forecast EUR/ CHF rate change probability scatter of 95% reliable intervals. In section a, the upper and bottom lines of reliability zones are identified with the forecast probability distribution mean ± standard deviation with the corresponding values. In section b these lines are idenLified as a mode ± standard deviation from the corresponding values of the mode. In section c, maximums of the lines analyzed in sections a and b are taken for the bottom line and minimums for the upper line.

Creating a portfolio adequate for profit stochasticity
The classic scheme of analysis, management or other use of portfolio is rather clear and convenient for practical application, but the way towards this simplicity is quite sophisticated. The functional expression of effectiveness and envelope (convex) curves, which is necessary in the practical portfolio use, is not obvious in the common case. But if we want to choose and manage a portfolio, it is necessary to present (imagine) different states of that portfolio, to describe the interactions of those states or to study other properties of the portfolio. The portfolio, when it is presented only by its profit average and standard deviation, in a sense is no more stochastic and gives no possibility to evaluate the reliability of many events connected with the portfolio. Moreover, the scheme of modern portfolio selection is not yet adequate for some urgent needs of portfolio owners: • many of risk recipients could hardly present their own impartiality curve, while the function of utility is quite understandable; • profit expectation, which in modern portfolio theory is identified with the mean profit, is not the most probable profitability value, as the mean profit can turn to be very low; • to ensure the desirable level of profit reliability, it is necessary to be able to select portfolios not only on the basis of two targeted indices as in the modern portfolio scheme (mean and standard deviation), but on any level of quintile -standard deviation; • for defining the efficiency zone, i.e. the zone which shows all profit possibilities at any risk (standard deviation) level. For a better understanding of an adequate scheme (Risk metrics group, 1999;Rutkauskas A. V., 2000;Rutkauskas A. V., 2003;Rutkauskas A. V., Miecinskine A., 2002;Rutkauskas A. v., StankeviCiene J., 2003) of investments portfolio risk analysis (see Picture 7), let us compare the scheme of classic portfolio study and the adequate scheme. As already mentioned, according to the modern portfolio theory the investor should be interested only in the portfolios that are located on the efficiency line. The efficiency line is understood as a set of maximum possible values of profits (averages) calculated for a concrete standard deviation magnitude of a portfolio set. Joining the existing investments into a portfolio in all possible proportions creates a set of possible portfolios; then the total portfolio's profit averages and the standard deviations are evaluated.
However, in reality investments are monitored and realised not by their profit averages, but by the possible values that depend on the investment market and purchasing price. Thus, it is important for the investor to see the profit possibilities of the whole set of portfolios, but not only of the portfolios that are on the efficiency line. Therefore the investor is interested in the whole efficiency zone, which is understood as a set of efficiency lines for all possible quintiles. So, studying the efficiency line on which we have the portfolios' maximum averages, for each value of a possible portfolio standard deviation turns into studying the efficiency zone. The investor's indifference curves in their turn should be changed (expanded) by the usefulness functions. Summarizing this stage, it is important to note once again the basic differences that arise when applying the classic portfolio theory (it is often called 'modem' in the literature) and the adequate portfolio theory proposed here. They are presented in (Table 4).

Subsystem of portfolio decision management in currency and capital markets
The described system of forecasting currency rates and stock prices is a component of information support for porfolio decisions in currency and capital markets. If using the elementary strategies -maximas -in forecasting systems the task was to show as often as possible the trends of changes of currency rate or stock prices, as regards portfolio decisions also the reliability and accuracy of the forecast is important.
Portfolio decisions whose origin was the investment market by their content were directed to the possibilities of combining the profitability of optimal investments and the riskiness. This purpose of portfolio decisions remains in the currency as well as in the capital markets -to optimally balance the desirable capital growth and risk (Benth, 2001;Browne, 1999;Dieter, 1999;Dupacova, 1999;Heyeng-Keun Koo, 1999;Hiroshi, Wijayanayake, 2001).
Neverthless, the concept of riskiness whose quantitative measure is usually the instability of the process (here -profitability growth) regarding the medium level is not the feature used by the risk recipient to measure his benefit or loss. We may hardly doubt that the individual designs his behaviour with due regard for its most probable consequences, whereas most commonly used means of risk assessment, such as standard deviation and the value of risk, do not allow evaluating such features of the possibilities as the guarranty to have certain profit, etc. Therefore, risk management requires the new possibilities of portfolio formation and management. In this case, no alternatives are left for choosing adequate investment or trade in the capital and currency markets.
Portfolio decision making management in exchange and capital markets. In this article, as is mentioned before, decisions made in the exchange rate and capital markets will be divided into simple and portfolio decisions. In the previous section we analyzed the possibilities of simple decision making management by participating (trading) in exchange rate and/or capital markets, using the forecasting system suggested there. The main provision of this forecasting system requires a practical regard to all main relationships between separate exchange rates and stock prices, which emerges in those markets and which can be identified and analyzed using only historical market data. Taking portfolio decisions we will use the same forecasting system of exchange rates and stock prices. However, if using the primitive, naive strategies (maxim as) we used only the forecast information about the trend of changes of rates and prices, in portfolio decisions we will make a full use of information about exchange rates and stock prices as the possibilities for stochastical value variations. While choosing the strategy of participating (trading) in the market, we will use the possibilities offered by the adequate portfolio, thus seeking for the solutions that would satisfy both their riskiness and reliability (guaranty) requirements.
Thus, now the results of forecast, as we see in Table 5, are presented as the variation of exchange rates and prices of distribution N (at; S.) with the forecast average at and standard deviation S" the form of the distribution N in various situations is different, but in this particular situation N was identified as a normal distribution. This means that the forecast couple of the parameters fully describes the variation possibilities of exchange rates and stock prices. The 190-200-day forecast presented in Table 5 was received using only earlier historical data. In Table 5, part a shows exchange rate forecast and part b only five forecasts of the NYSE stock prices, although naturally in the portfolio formation all nine selected stocks took part. The real historical data of 190-200 days presented next allow us to evaluate the accuracy and reliability of the forecast.
Since the obtained forecasts were used for choosing portfolio decisions in exchange rates and stock markets, the accuracy and reliability of forecast are evaluated only/not only according to formal methods but and/or from the view of portfolio decision effectiveness. After using an adequate portfolio model in each of 191-200 steps, stock and exchange portfolios were made. In the stock market, it was admitted that some initial capital, named in one monetary unit, was invested at the end of the step t into the named stocks, seeking that in the next (t+1)-e step we seek the optimal capital increase, considering the risk which is measured by standard deviations of stock price variation possibilities. Analogously in exchange rate markets we admitted that a certain, named in units, amount at the end of the period t was invested into USD, GBp, CHF, lPY and CAD, seeking that at the end of the t+ 1 period we have the optimal, regarding the risks of exchange rates, increase of capital measured in euros. portfolio, with an increase that could be obtained according to a model based on the index principle, which further will be called standard portfolio. Its essence in the market will be described so that each index of the portfolio w;' structure is received by dividing the i-th stock turnover value in the t-th interval by the sum turnover of all stocks in the t-th period. In Table 6 (5) part a on the left side, exchange rates for each of the chosen ten days and on the right side the conditional portfolio generating capital increase both in each step and in sum for the whole ten-day period are presented. Part b (left side) presents the structure of the proposed, i.e. managed portfolio, and on the right side we show the capital increase given by the managed portfolio increase. Part c presents the so-called virtual model: its essence is that to the five currency rate positions of the managed portfolio a sixth position -investment to stock market, called activeis attached.
Analogously (see section c in Table 6) results of investing in capital market are presented, but here not capital increase but capital growth rates are compared.    rate and stock price monitoring as well as to the primary selection and systemising of data.

Decision-making management versus search of optimal decisions
If we understand the market as an exchange mechanism which brings together buyers and sellers of commodities (products, services, production elements, financial means) in order to set their prices, the question arises whether and how price change forecasts based on historical data can influence the dynamics of prices.
If we assume that every commodity at a particular moment has its intrinsic value, which by its nature is a stochastic quantity, the concrete (current) price can be perceived as one of the possibilities of stochastic realization of the stochastic quantity. In this case the DMMECM system, which allows an accurate and reliable forecast of a possible scatter of the intrinsic value, reduces the distribution interval of current prices. In turn, the reduction of the scatter or confidence interval allows to reduce the buyers' and sellers' common loss caused by the discrepancy between the current and the most likely expected prices. Factually, whatever the method of price forecast, it influences the behaviour of sellers and buyers. This influence can be negative if the forecast information implies an increase in the reliability intervals. These circumstances show the importance of price forecast reliability and accuracy. Arguments presented in this paragraph show that the DMMECM system is something more than a system of search for optimal decisions, because its application can rationalize the behaviour of market participants in the process of price selection.
Analytical calculations have shown that portfolio decision possibilities, if analyzed in the common market of currency exchange rates and stocks, greatly increase as compared to the possibilities in the currency or the capital markets alone. Adding one component of the other market to the portfolio increases the profitability possibilities of this portfolio no less than 1.3 times (see, for example, Table 5 parts b and c). This component is called active for the currency portfolio and deposit for the capital market.
DMMECM monitoring and mathematical information methods. As is shown in Pic. 9, the monitoring basis of currency and capital markets consists of: • identification of of change regularities and interaction of currency rates and stock prices; • formation of quantitative models of change and interaction of currency rates and stock prices; • creation and utilization of the forecasting system. However, considering the formation of the above mentioned virtual portfolio, in many different markets (currency and stock exchange, real estate, etc.) new, especially important functions of monitoring appear. First of all it is the monitoring of the interaction among different markets, their analysis, modelling and forecast. In many cases these problems are not given a quantitive analysis at all.
As regards the mathematical informational methods of DMMECM, it seems reasonable to note three groups of tasks that required imitation technologies to be created and used for solving them: large systems of complex stochastic equations and stochastic programming problems; • implicit stochastic equations; • assessment of the influence of process interrelations.

Conclusions
The current study allows several conceptual, pragmatic and technical conclusions.
• Conceptual conclusions: • investigations of the possible changes in currency exchange rates and stock prices are usually constricted by the illogical and nonadequate presumption that the intrinsic value of currency rate or stock and the price expressing it are strictly predetermined, i.e. accepted as point-estimated. Here we have to agree to the universal wisdom that future, if it were possible to point-estimate it, would never come. The future price of a stock can be understood and thus analyzed only as a certain range of possibilities, which can be often treated as a cognizable stochastical magnitude; • although analysis of the behaviour of the currency and capital markets, i.e. of the mechanism that uses all the available information to investigate price generation, is based on a rather perfect and throughly verified idea of market effectiveness, at the level of the main categories no adequate agreement has been reached so far.
First, the effectiveness of a market in the field of prices could be realized as its ability to generate the prices that wouldn't allow constructing the trade strategies better than those naive ("buy and hold"). In this case, checking the hypothesis of market effectiveness would mean checking whether having any kind of information the market does it. Further, as regards the range of the possibilities, the meaning of the frequently used category "expected" should be concretized as the most probable (mode), especially in many cases when it is wrongly assumed to be the average value; • practical models describing price dynamics do not account for the circumstance that the behaviour of price as a stochastical pro-cess strongly depends on the state of its possibilities, and that depending on the change of this state both the content and form of the model and the factors influencing price change should also change.
• Pragmatic conclusions: • concrete calculations have shown that even in the most globalized markets such as FOREX, NYSE and others there exist visible shoals of market effectiveness, i.e. situations when using only historical information and the "buy and hold or sell" strategy it is possible to obtain a significant advantage over the "buy and hold" attitude; • analysis of the possibilities of portfolio decision management has shown that in currency and in stock markets, using only the dynamics of historical prices and their interrelations, it is possible to obtain a significant advantage over the "buy and hold" strategy according to the market portfolio structure; • in practice, decisions of investment portfolio become considerably more profitable if a common currency rate and stock portfolio is formed. Practical calculations have shown that the guaranty of the gain higher than the market average of a thus constructed portfolio is close to unity.
• Technical conclusion: • for the search and management of solutions in currency rate and capital markets, mathematical and informational methods are needed to solve large-scale systems of stochastic programming, in which the variables have to meet the restrictions of complex interrelation changes and are interrelated with the help of implicit functions. Besides, the solutions must be obtained within a real time, i.e. almost at the time the tasks are formed. In such cases no alternative is left for imitation technologies allowing to obtain, though usually approximate, solutions of a needed accuracy.