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The system of strategic planning "JOKER"
Material posted: -Publication date: 12-01-2009

Your attention is invited to the tool means of system of strategic planning "Joker". It is intended for the optimization of the structure and quantitative composition of the portfolio of securities and can be considered as an integral element of the special expert-analytical system of planning of activity of firm.

A meaningful statement of a task of forming a rational portfolio of securities (shares) is as follows.

The investor (aka - the MOP user "Joker", the expert) has a securities portfolio. Periodically, once at the end of the planning period (the length of the period is not specifically set, because for each firm it can be owned) comes to the stock market and updates its portfolio, buying the most promising stocks and selling less promising. However, he understands that the future price is a random variable. So he focuses all his attention only on a small number of shares, even the most attractive and diversifying portfolio, complementing its other promotions. In the event of adverse market conditions, they will help the user to reduce financial losses.

In the implementation of purchase and sale of shares the investor pays taxes, which in General can be different for each type of shares (a special case where taxes are not available, can be easily taken into account without changing the design scheme).

Buying shares, the investor acknowledges the limitations on the sizes of the sets (lots) of shares sold.

The main problem facing the investor is to form such a rational (optimal) portfolio of securities (i.e. the portfolio composition and its content of different shares), which at the end of the plan period had the greatest marketable value.

The complexity of the solution due to the following three circumstances:

  • the need to predict future values of external factors that affect stock prices; factors can be considered the rate of $, EURO, world prices for exported goods, the excise duties, customs duties, etc., i.e. those parameters that the user is unable to change;
  • the need to establish the dependency of prices of shares of the relevant factors (the formation of price patterns). Generally speaking, an investor cannot know exactly how it will affect stock price change factor; but it may be on this account certain assumptions;
  • the need for complex optimization procedure of the portfolio when taking into account the many ties and restrictions.

Especially it is necessary to emphasize the following circumstance.

Currently the analytical group in many organizations that deal in buying and selling securities, offer software products, allowing to predict the expected value of the most significant factors affecting future share prices. But for the formation of rational portfolio fundamental importance to evaluate not only expected values but also values of dispersion factors around these expected values. And such data in these software products are usually not submitted (and if submitted, they are obviously not enough). Therefore, the task of forming a rational securities portfolio mathematically can be solved even in the presence of these prognostic procedures.

Expert MOP "Joker" intended to generate recommendations on the structure and content of the securities portfolio.

The solution of the task includes the following steps.

a) Establishing a comprehensive set of factors, from the values of which depend on the share price.

The basic requirements for the factors:

  1. MEASURABILITY - the ability to quantify;
  2. SIGNIFICANCE - the effect on stock prices;
  3. The eventuality is partial predictability of the future value;
  4. INDEPENDENCE (quasistability) - change factors due to their mutual influence should be small compared with the variance of each random factor;
  5. The completeness of the SET - the set of factors from the point of view of determining the prices of all shares must be exhaustive.

b) formation of the laws of distribution of factor values at the end of the planning period.

To solve this part of problem use of mathematical techniques of pairwise comparisons. Their main peculiarity consists in the large number of examinations - the problem is considered from different points of view. In the end, due to the high information REDUNDANCY is possible to obtain a SUFFICIENTLY EXACT solution of the problem of forecasting.

In the MTSP, the "Joker" user-expert offers three possibilities for the formation of matrices of pairwise comparisons. He can choose any of them or use a convenient combination. The main objective of these tools is to facilitate the user-expert with expertise, allow him to concentrate on the substantive part of the analysis, not particularly caring about its shape.

The results of examinations are processed by formal methods and presented in the form of visual diagrams allowing to control the quality of the solution.

b) Forming models of prices of various shares - dependency of the price from the significant factors. This also applies methods of pairwise comparisons. Information REDUNDANCY and in this case provides a reasonably accurate solution. The results of examinations are processed in near real-time and presented in tables and charts.

g) the Most intensive step is the solution of the optimization problems of formation of rational securities portfolio, the source of information, which are lined in the previous stages the laws of probability for values of factors and models in stock prices.

An optimization problem belongs to the class of mathematical problems of stochastic integer programming of high dimension with a well-developed system of restrictions.

With strict solution of the problem, in addition to the indexes of future prices of shares, account is taken of the dispersion of their prices (so called "variance portfolio"), the maximum size of the sets of the purchased shares (lot sizes) as well as the initial structure and content of the portfolio.

In the General case the solution of the problem cannot be obtained by analytical methods; therefore, it is on the PC is solved numerically by the statistical Monte Carlo method. The solution process, which takes about 10-60 minutes on a PC with a Pentium-II,III, is visually displayed on the graph.

In other words, the MTP in "Joker" is proposed to divide the decision problems of formation of rational securities portfolio into several stages, each of which is proposed to use expert and (or) formal methods. It is proposed that the combination of these fundamentally different methods, which does not oppose, but rather combines their advantages. This is the "Golden mean", which allows you to combine the predictive abilities of experts with high capability PC speed and accuracy of information processing in solving complex optimization problems of formation of rational portfolio securities.

The question naturally arises: why use the MTP "Joker" will improve the quality of decisions, what are the features of its functioning increase accuracy and reliability?

The principle of operation SSP "Joker" is based on the following five assumptions.

1. Not obvious (but confirmed in numerous psychophysical experiments) - expert feels the situation (in this case, is the situation on the securities market) much better than he thinks. But the high dimensionality (complexity) of the task prevents him from fully exploiting its potential for optimal decision making.

The use of the methods of pairwise comparisons will allow you to "extract" from the expert all information, even that which he considers to be important, to fully use to construct a rational portfolio.

2. The obvious - when carrying out structuring (drilling, decomposition) of any complex problems, including problems of forming a rational stock portfolio, it is possible to divide the problem between several experts and use their advanced intellectual potential to develop more competent decision.

Structuring will allow the user (the expert) do not dwell alone in your problem, and connect to its solution experts on various issues.

3. Controversial, but, as a rule, the right - the collective opinion of the expert group potentially precise opinion of only one expert, at least - with a large number of examinations.

4. Obvious - processing of the expert information most accurately and quickly carried out with the PC.

5. The obvious - the task of optimizing the stock portfolio associated with enumeration and analysis of a very large number of variants, is solved faster and more accurately by numerical methods formal on the PC than expert evaluation of even the most skilled and trained user.

We present a tool MOP "Joker" is an independent software product with a very simple control system, a reference section and a clear presentation of intermediate and final results. It can be applied in analytical departments of different firms or banks with quick configuration on the relevant problem area (as in different companies, its shares, its resource capabilities, etc.).

A preliminary assessment of the effectiveness of show that the application of MTSP "Joker" can increase Your revenue by not less than (5...15)% in each scheduled period of sale and purchase of securities. Even with a 5 percent increase in efficiency after 15 periods planned Your capital by applying MTSP "Joker" will be DOUBLED, if You will use the additional funds to expand their businesses.

Thus, the use of MTP "Joker" will enhance Your expertise, creating a more rational decision on the content of the securities portfolio and increase Your income. But, working amplifier, is not a qualified user of the MTP will become almost useless - if "increase" is initially nothing, then the application system will not provide significant additional benefit. Here there is an analogy with the card game of poker: with a good set of cards Joker can significantly enhance the original card combination to lead to win but with a weak card, it is almost worthless.

MOP the developers hope that the application of this system will more efficiently and reliably plan Your future work and increase Your income. We offer You not a substitute for expert analysts, and an assistant.

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