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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.20 No.2 pp.297-303
DOI : https://doi.org/10.7232/iems.2021.20.2.297

# Mathematic Models for Analysis of Financial and Economic Activity of Organizations under Various Condition

Sergushina Elena Sergeevna, Kabanov Oleg Vladimirovich, Valentina Sergeevna Kolesnik, Yakovlev Alexander, Kozhukalova Oxana Yurievna, Gurkin Andrey Borisovich, Garankina Rimma Yuiryevna*
National Research Mordovia State University, Russian Federation
Kuban State Agrarian University, Russia
State University of Management, Diplomatic Academy of the Ministry of Foreign Affairs of the Russian Federation, Moscow, Russia
Moscow Pedagogical State University (MPGU), Moscow, Russia
Saint Petersburg state University "LETI" Department of icgp, History, History, culture and law Cand, Russia
Department of Regulatory Relations on the Circulation of Pharmaceuticals and Medical Products, First Sechenov Moscow State Medical University, Moscow, Russia
*Corresponding Author, E-mail: khayb.aa@mail.ru
March 12, 2021 April 12, 2021 April 29, 2021

## ABSTRACT

The aim of this work is to find suitable solutions for the financial activity with various kind of uncertainty. For this purpose, two methods are proposed based on the security and optimal efficacy. In the first method, the rule base uncertainty is considered and a math model is proposed. In the second one, the random function is employed to find the optimal finance options. The article is devoted to the analysis of financial and economic activities of organizations in modern conditions; its essence, main goal and methods are revealed; recommendations for its use in the activities of organizations. In addition, the rule base mathematical model can determine the finance rate of return. The results of experimental calculations also confirmed that the results obtained are acceptable for shares of various issuers and organizations of various fields of activity.

## 1. INTRODUCTION

Analysis of financial and economic activities is an assessment of the financial condition of the organization and the consequences of management decisions. The main purpose of the analysis of the financial and economic activities of the enterprise is to collect the necessary data for further management decisions. For example, if a firm's sales are falling, it is necessary to clarify the data on the competitive base, investigate the ratio of the price and quality of the product, and more accurately assess the demand among the population for a particular product. Perhaps the time has come to find a new sales market or completely change the type of activity. The financial activity of an organization is a set of methods, strategies aimed at providing financial support to business processes in order to achieve certain results. As a result, the activity of the enterprise provides protection of financial reserves, provides for versatile management of internal cash flows. The economic activities of enterprises are divided into two groups: reproduction and basic (Abdullin and Farrachetdinova, 2015;Kosareva, 2017).

All of the above makes it clear that the market has a complex and very heterogeneous structure. In this regard, we can conclude that the financial market can be considered in the course of the study from several sides. First of all, this is a view of the market from the point of view of fundamental analysis. With this approach, the subject of research is the existing patterns, phenomena and influences that have been observed for a long time and are based on a whole group of macro- and microeconomic indicators. The second approach to the assessment and analysis of the financial market is a view from the point of view of technical analysis. In this case, the market is considered as if “from within”. The subject of research is internal movements, patterns of behavior and market structure.

A fundamental analysis of financial markets assesses the economy state as a whole, studies the fluctuations in supply and demand, which in turn affect the price fluctuations of an individual financial instrument. Technical analysis allows you to analyze the value of financial instruments in the absence of access to data on financial statements. Such an approach assumes that all market information necessary for the analysis is contained in the general access, namely in the current and past value of a financial instrument, and this allows the investor to make the right decision (Sergeevna et al., 2020a).

The basis of technical analysis is the study of repeating patterns and patterns of behavior identified on price charts. Based on the data obtained, we can make an assumption about the expected dynamics of the price movement of a financial instrument over the future period, since patterns and behavior patterns are prone to repetition. As mentioned earlier, technical analysis is directly based on data on transactions completed on the market, in other words, it illustrates the attitude of investors at a given moment in time to the organization.

All market participants are constantly working with charts and analytical tools in order to make assumptions about fluctuations in the demand for securities and their offers. This helps predict prices and shape trading strategies for all financial markets.

Reproduction is associated with the continuous movement and resumption of the release of any product. The reproduction group of the economic activity of the enterprise includes, first of all, the finance of a certain capital value with a predetermined goal, for example, in the form of capital finances. This includes the process of buying and repairing fixed assets, capital construction, and the like. In other words, this group includes all business operations that are aimed at modernizing, replenishing and producing objects. As a rule, the main goal is to increase the invested funds over time, in the process of activity. Finance is the most significant component of the reproductive group (Sergeevna et al., 2020b;Vladimirovna et al., 2019).

The main group includes processes and tools directly related to the production process. The production process is the totality of all the actions of people and instruments of labor required at a given enterprise to manufacture products. As a result of this aggregate, resources and components supplied to production are transformed into finished services or products in the planned quantity, a given property and assortment at a certain time (Williams, 1999; Abdel-Basset, 2020).

Before the formation of this hypothesis, financial markets were considered only from the point of view of the effective market hypothesis (EMN). Prerequisites for the emergence of this hypothesis appeared in the XIX century. In particular, Gibson expressed one of the main postulates of this hypothesis: price is the best source of information about a stock (financial instrument) (Tirkolaee et al., 2020). Bachelterre later proposed a mathematical model of the efficient market hypothesis. The subsequent analysis and justification of the possibility of forecasting the rates of financial instruments within the framework of the effective market hypothesis was formulated and improved in the 1950s by Robers.

Currently, the efficient market hypothesis is based on the following assumptions.

Firstly, it is assumed that the price that has been established in the market at a given time is fair and brings the market into equilibrium.

Secondly, all market participants uniformly interpret information and similarly adjust decisions when receiving new data.

Thirdly, the goals of market participants are always uniform, their actions are of a “collective rational” nature (Tykkyläinen and Ritala, 2021).

Despite the controversial nature of the postulates, the efficient market hypothesis was a major breakthrough in the study of markets and the construction of mathematical models to describe them.

Subsequent study and analysis of the hypothesis, testing its ideas in practice showed that the hypothesis does not completely take into account the main feature of market participants, namely, that they all have heterogeneous expectations. In particular, substantiated criticism of the hypothesis is contained in the works of Abdullin and Farrachetdinova (2015), Williams (1999), Tirkolaee et al. (2020).

## 2. METHOD

It has been proven that linear models are poorly adapted to explain real processes. This was the impetus for the creation of alternative approaches, which are based on non-linear methods of analysis of financial markets. These methods consider financial markets as nonlinear dynamic systems, where all new emerging prices are in connection with their past values, and information entering the market is not always instantly reflected in market prices.

The fractal market hypothesis that came to the place of the effective market hypothesis allows one to take into account the heterogeneity indicated above due to the assumptions underlying it.

First, it is assumed that the market is stable, while investors who work on a large number of finance horizons are included in its structure. This principle is a necessary and sufficient condition for market liquidity.

Secondly, the hypothesis states that the reaction to information among investors with different finance horizons is significantly different. As finance horizons increase, longer-term fundamental information dominates.

Thirdly, it is believed that any event that casts doubt on the relevance of fundamental information leads to the fact that long-term investors either stop participating in the market or start trading based on a short-term information set.

Frankly speaking, the fractal business hypothesis is also criticized, but, according to the authors, it more correctly and accurately describes the processes that occur in the financial markets, and much more realistically reflects the mood and behavior of market participants.

Also, the fractal market hypothesis allows you to correctly combine the ideas of technical and fundamental analysis, use the ideas of fundamental analysis (for example, a finance portfolio) in the plane of technical analysis. This can be achieved by dividing investors by finance horizons within the framework of one financial instrument. Since the fractal market hypothesis implies the existence of investors with different finance horizons, it follows that they will interpret the incoming information in different ways, carry different risks and receive different returns. Therefore, we can hypothesize that the same financial instrument A can be considered as a set of instruments ${ A 1 , A 2 , ... , A n }$, where Ai is the value of a financial instrument on the i-th finance horizon

It should be noted that such an assumption can be formulated only if the nature of the time series, in each horizon, of behavior does not depend on the time series of other finance horizons.

In order to show that the nature of the time series corresponds to that described earlier, we analyze the stocks traded on the Moscow Exchange MICEX-RTS in the first and second tier. In addition to choosing stocks of companies of different echelons, companies were selected that belong to different industries and business lines:

• •Ordinary shares of PJSC Gazprom,

• •Ordinary shares of PJSC LUKOIL Oil Organization,

• •Ordinary shares of OJSC Novolipetsk Metallurgical Plant,

• •Ordinary shares of Magnit JSC.

The values of the correlation coefficient for four periods are shown in Table 1.

### 2.1 Proposed Rule Base Model

The rule base relations are described for optimization of finance under uncertainty in this part of the article. It is worth reminding that the above confidence intervals are obtained using a section of triangular rule base numbers (a1, a2, a3) and based on the following formula:

(1)

To model the selection problem, the optimal portfolio, two objective functions and two constraints are considered as follows:

The expected return on each portfolio is considered by investors as an ideal. Therefore, maximizing the portfolio’s return is an objective for investors, which can be presented, as follows:

(2)

In the mentioned objective function, we have:

• rp = finance portfolio’s return

• ri = i-th share returns

• xi = percentage of investable funds invested in the ith securities of finance.

On the other hand, (rational) investors avoid risks and attempt to minimize them. (However, given the direct relationship between risk and return, a low risk level leads to low return rates, and minimizing risk without attention to return results in high opportunity costs. This is the main reason for simultaneous assessment of risk and return by Markowitz and other experts). As such, risk minimization was modeled as an objective, as follows:

(3)

In the mentioned objective function, we have:

• Var(rp) = Portfolio return variance

• Var(ri) = Variance of returns of the i-th securities

• COV(ri, rj) = Covariance between the returns of the i-th and j-th securities

• xi = Percentage of investable funds invested in the i-th securities

Notably, Formula 4 was used to calculate the covariance:

$C O V ( r i , r j ) m = ∑ k = 1 m ( [ r i k − E ( r i ) ] [ r j k − E ( r j ) ] )$
(4)

where m is the number of fiscal years studied, rik is the return rate of the i-th securities in the k-th period and rjk is the return rate of the j-th securities in the k-th period.

### 2.2 Random Based Model

In order to apply the second model which was a random based model, the calculated values of the correlation coefficient is performed. Therefore, it can be considered as independent assets that can become part of the finance portfolio.

It is quite important to analyze the financial and economic activities of the enterprise, since, thanks to these studies, it is possible to determine both the unfavorable areas of the organization that affect the deterioration of production and the decline in profits, and to identify improvements in the operation of the enterprise. Based on the analysis of financial and economic efficiency, the development of the economic strategy of the enterprise is being built. Based on the data of the analysis of financial and economic activities, recommendations are made for improving the production and management process. The results of calculating the correlation coefficient for assets are shown in Table 2.

The obtained values for the correlation coefficient show that the correlation between the quotes of one stock, considered at different finance horizons, is comparable with the correlation of two independent financial assets, and therefore each set of quotation values can be considered as an independent financial instrument.

The proposed approach is used in the formation and subsequent analysis of the Markowitz’s and Sharp’s finance portfolios (Davnis and Dobrina, 2017). Based on the constructed portfolios, one can come to the following conclusion: using the fractal hypothesis when analyzing financial markets gives finance portfolios with higher profitability and significantly lower risks, in comparison with profitability when investing in one asset.

The effectiveness of financial activities can be judged by two aspects: The results of financial activities; the financial condition of the enterprise. The first is expressed by how effectively the organization can use its existing assets, and most importantly-whether it is able to generate profit and to what extent. The higher the financial result for each ruble of invested resources, the better the result of financial activity. However, profitability and turnover are not the only indicators of a organization's financial performance. The opposite and related category is the level of financial risk. The current financial condition of the enterprise just means how stable the economic system is. If the organization is able to meet its obligations in the short and long term, to ensure the continuity of the production and sales process, as well as to reproduce the resources spent, then it can be assumed that the organization will continue to operate while maintaining current market conditions. In this case, the financial condition can be considered acceptable. If the organization is able to generate high profits in the short and long term, then we can talk about effective financial activities. In the process of analysis of the financial activities of the organization as at the analysis of financial results and the assessment process, you should use such techniques: horizontal analysis – the analysis of the dynamics of financial results and assets and sources of their financing, to determine the General trends of development of the enterprise. As a result, it is possible to understand the medium - and long-term prospects of its work; vertical analysis-an assessment of the formed structure of assets, liabilities and financial results will allow you to identify imbalances or make sure of the stability of the current position of the organization; the comparison method-comparing data with competitors and industry averages will allow you to determine the effectiveness of the organization's financial activities. If the organization demonstrates higher profitability, then we can talk about high-quality work in this direction; the method of coefficients – in the case of the study of the financial activity of the enterprise, this method is important, since its use will allow you to get a set of indicators that characterize both the ability to demonstrate high results and the ability to maintain stability. Factor analysis-allows you to determine the main factors that affected the current financial position and financial performance of the organization (Vladimirovich et al., 2019).

## 3. RESULTS

To optimize the rule base model, the portfolio of a finance organization related to years 2017-2019 was evaluated. The return rate of the finance organization during this period is shown in Table 3.

Now, using the Equation 1, the table 3 is rewritten as follows:

The most important purpose of financial analysis is to analyze the financial results and financial condition of the organization for the past reporting periods, and at the time of the analysis, as well as to analyze the potential of the organization for the future, i.e., economic diagnostics of economic activity. Accounting and financial reporting data are the information base for financial analysis. Their analytical review can restore all the essential aspects of economic activity and operations performed in a generalized form (Davnis and Dobrina, 2017). In an unstable economy, the accounting statements of organizations are becoming the most important means of communication and the main element of information support for financial analysis. It is customary to distinguish the following stages of financial analysis:

• - establishing the purpose of the analysis and the approach to it;

• - analysis of the completeness and quality of the information available for evaluation;

• - defining the analysis methods, conducting the analysis itself, grouping and summarizing the collected data.

At the initial stage, an approach to the analysis is established, which is related to its purpose. Economic scientists distinguish the following main approaches:

- comparison of the organization’s indicators with the industry’s average indicators (reference values);

• - a comparison of the current reporting period with data of previous periods or planned current reporting period;

• - comparison of the organization’s indicators with those of counterparties, i.e. other similar firms: partners or competitors (Davnis and Yurova, 2017;Herman et al., 2020).

The ability to evaluate the results of the analysis of financial and economic activities makes it possible to make competent management decisions to increase the profitability of the financial and economic activities of the enterprise and decisions to reduce risk, to identify indicators and reserves for increasing the efficiency of the enterprise's economic activities (Kosareva, 2019)

## 4. CONCLUSION

The results of a computational experiment show that the authors proposed approach to assessing and analyzing financial markets from the point of view of the fractal hypothesis allows us to build a suitable portfolio under two kind of uncertainty. Also, the results confirm the arguments made earlier that one asset in the financial market can be considered as a combination of assets according to their finance horizons. These assumptions are valid for shares of various echelons and companies whose activities relate to various fields.

On the other hand, it has been cleared that the classic Markowitz portfolio loses significantly in terms of total profitability on the algorithmic portfolio proposed by the authors. Optimization of finance portfolio allows us to see that the profitability shown in the control sample is on average 30% higher than the profitability obtained with the classical approach. Also, the algorithmic construction of the finance portfolio is applicable to the approach proposed by the authors to consider an asset as a group of assets under the conditions of a fractal hypothesis and does not depend on the choice of a financial instrument.

## Figure

Rule base intervals related to language variables.

## Table

The value of the correlation coefficient between the time series of financial instruments

Calculation of the correlation coefficient for asset pairs

Portfolio of a finance organization

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