nikita@galkin.in.ua

ABSTRACT ON THE THEME:

Author: Galkin Nikita

«Optimizing an economic system on the basis of “Profitability over risk” criterion»

At present, any type of economic activity is carried out under conditions of uncertainty. Here the analyst faces the problem of bigger income vs lesser risk. This is a bicriterial task, in which the significance of the criteria will be different for every analyst. Usually criteria are evaluated subjectively, and the same researcher may consider the same criteria to be of a different importance at different points of time.

            The economic system selected as a research subject is the Mechanical Trading System (MTS) for the Forex market. This is caused by following reasons:

• Wide availability of the statistical data;
• Topicality and plurality of Forex research;
• Existence of the designated software for analysis and optimization.

There are many criteria for the evaluation of MTS. Most of then are based either on the risk (measure of uncertainty, most often expressed in root-mean square error), or the economic efficiency (revenue or income per period).

It is completely natural to use several criteria for evaluation. However, it is possible that some criteria will duplicate each other, providing no extra informativity. This increases the odds of making the wrong decision, since several criteria with the same essence are more convincing than one. To avoid this situation, before evaluating obtained results it is necessary to carry out the correlation analysis and discard the criteria, which have correlated figures on the source data.

Once the criteria have been selected and calculated, one needs to make a management decision. It is very simple if there are 2 or 3 criteria and 5 to 10 possible alternatives. But in the case where there are a dozen of criteria and thousands of alternatives, one cannot do without the linear folding of partial criteria into one general criterion.

,

where and correspond to the minimum and maximum value of the criteria for a set of economic systems under consideration.

            It is obvious that. Linear folding is carried out by the following formula:

,

where is a subjectively determined weight ratio for a criteria i. It is customary to determine weights by the formula:

,

since has to be equal 1, because.

To eliminate this subjectivism while evaluating an economic system according to «Profitability over risk» criterion, it is recommended to determine the weights according to root-mean square error of the criteria.

For that, the criteria were calculated repeatedly for the same systems based on the statistical data for different time periods. For this economic system, (criterion i for a time period j) was calculated. On this basis, and (expectation of a criterion of every economic system) were calculated.

The samples  belong to one universal set, since the economic systems under consideration differ only by optimization parameters. Therefore, we can use:

“Total variance of the whole sample, comprised of partial samples, is equal to average weighted variance: s 02 = (1 / f ) ·(n j s j2). Here, the weights of partial variances are f_j  — numbers of degrees of freedom that correspond to every partial sample j of the volume n. f_j = n_j -- 1;  f  = еf_j.” [2]

On this basis we get, where is root-mean square error of the criterion i for all economic systems. After normalizing by formulas (2) and (3) we get a linear folding of partial criteria, with weights determined mathematically rather then subjectively.

This method is based on the fact that if a criterion has bigger root-mean deviation, its weight must be less, since it bears less information.

Sources:

1.                  Смирнов А.В., Павлова Е.А. Инвестиционный риск в биржевой торговле. Экономика: проблемы теории и практики. Сборник научных трудов. Выпуск 201, том IV. – Днепропетровск, ДНУ, 2005, с 863-871

2.                  Трифонов Е.В. Психофизиология человека. Толковый русско-английский словарь

3.                  Швангер Д. Технический анализ. Полный курс: Пер. с англ. – М.:Альпина, 2001. – 768 с.

4.                  Шапкин А.С. Экономические и финансовые риски. Оценка, управление, портфель инвестиция. – М.: Издательско-торговая корпорация «Дашов и К» 2003. – 544с.

5.                  Боди З., Кейн А., Маркус Алан Дж. Принципы инвестиций. – 4-е изд.: Пер. с англ. – М.: Изд. дом «Вильямс», 2002. – 984 с.

nikita@galkin.in.ua