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DOI: 10.18454/IRJ.2016.49.078 Иремадзе Э.О.1, Антонова Н.А.2
1 Кандидат химических наук, доцент; 2кандидат педагогических наук, доцент, Стерлитамакский филиал Башкирского государственного университета ОПТИМИЗАЦИОННАЯ МОДЕЛЬ ПОРТФЕЛЯ ПОТРЕБИТЕЛЬСКИХ КРЕДИТОВ КОММЕРЧЕСКОГО БАНКА С УЧЕТОМ СОВРЕМЕННЫХ ПРОБЛЕМ НА ПРИМЕРЕ ЗАО «РУССКИЙ СТАНДАРТ»
Аннотация
Целью работы является разработка практических рекомендаций для формирования банковских пассивов, оптимизация их структуры и использования кредитных ресурсов коммерческого банка «Русский стандарт».
Решается задача оптимизации при составлении кредитного портфеля с целью получения максимальной прибыли. Практические рекомендации по оптимизации формирования и использования кредитных ресурсов коммерческого банка «Русский стандарт» могут быть применимы другими банковскими структурами.
Ключевые слова: оптимизационная задача, математическая модель, денежные средства, кредитный портфель, прибыль.
Iremadze E.O.1, Antonova N.A.2
1PhD in Chemistry, assosiate professor, 2PhD in Pedagogy, associate professor, Sterlitamak branch of Bashkir State University OPTIMIZATION MODEL OF CONSUMER LOANS PORTFOLIO IN COMMERCIAL BANKS ACCORDING TO CURRENT PROBLEMS ON THE EXAMPLE OF JSC "RUSSIAN STANDARD" BANK
Abstract
The purpose of the study is to work out practical recommendations for the formation of bank liabilities, optimization of their structure and the use of credit resources in the commercial bank "Russian Standard".
The objective of the study is to find ways for optimization of the loan portfolio to get maximum profit. Practical recommendations, given for optimizing the formation and the use of credit resources in the commercial bank "Russian Standard" can be used in different bank organizations.
Keywords: optimization problem, a mathematical model, cash, loan portfolio, profit.
The formation of loan portfolio in a commercial bank is the major step in implementing its credit policy. The introduction of mathematical methods and models in the management of banking, in particular credit processes, is a factor of effectiveness for the bank's decisions and the formation of the bank's strategy [1].
The analysis of the activity of JSC "Russian Standard" Bank has shown that in general it works well and has a large profit [2]. Having analyzed the loan portfolio by types of borrowers it became clear that a large part of the portfolio consists of loans
given to individuals due to the consumer credit boom of recent years in our country. To achieve the highest profitability it is necessary for the bank to optimize the structure of the loan portfolio for consumer loans, as they bring the most profit [3].
This paper considers how to continue further optimization of the bank's product portfolio, consisting of 15 retail bank loans with different maturities and how to construct a mathematical model of loan portfolio of JSC "Russian Standard" [4]. The presented loan portfolio was studied as a set of assets, loans, being a composite asset with parameters of risk and profit, changing under the influence of a combination of two factors: changes in risk and profit of assets components, due to the changes in the assets and the other conditions and changes in portfolio composition [5]. In the model we used the following key economic indicators characterizing the financial activities of the bank: the amount of money allocated to consumer loan "Blown interest», quality category I (Xj) (million rubles); allocated to consumer loan "Million in pocket», quality category I (X2) (million rubles); for consumer loan "Personal offer», quality category I (X3) (million rubles); for consumer loan "Gold standard" (X4) (million rubles); on consumer loan "All good" (X5) (million rubles); for consumer loan "Standard Plus" (X6) (million rubles); for consumer loan "Consumer" (X7) (million rubles); the credit card "Russian Standard Classic Online» (X8) (million rubles); the amount of funds allocated for the credit card "Russian Standard Classic», quality category I (X 9) (million rubles); the credit card "Russian Standard Gold" (Xi0) (million rubles); the amount of funds allocated for the credit card "Russian Standard Discover», quality category I (Xn) (million rubles); the amount of funds allocated for the credit card "Russian Standard Visa® FIFA Gold », quality category I (Xj2) (million rubles); the amount of funds allocated for the credit card "Russian Standard UNICS», quality category II (Xj3) (million rubles); the amount of funds allocated for the credit card «Imperia Platinum», quality category II (XM) (million rubles); the amount of funds allocated for the credit card "Russian Standard -Student's card», quality category II (X15) (million rubles) .
So, the problem of optimization for compiling the loan portfolio at maximum profit has been solved. The following appropriate requirements that this procedure must comply with, have been worked out: the bank's management has decided that the total amount of retail loans, planned for placement next year should reach 310 billion rubles. Taking into account risk assessment of the planning period and the structure of the liabilities of the credit organization, this amount of money should be divided the following way: not more than 35% should fall on the consumer loans of quality category, not more than 50% - for the credit cards of quality category I, at least 10% - for consumer loans of quality category II, at least 5% - on the credit cards of category II . In addition, the proportion of delay across the portfolio should not exceed 12.5% of all granted loans, and the average loan term should not exceed 365 days, due to the time structure of bank liabilities. On the basis of these restrictions, the optimization purpose is to maximize profits, i.e., to increase the annual interest income from the loans granted to individuals. In this case the procedure of portfolio optimization by linear programming method involves the transformation of all the above-stated limitations and the bank targets into the appropriate mathematical formulas.
The solution of the optimization problem allowed to obtain recommendations for optimizing the retail loan portfolio of the bank [6]: if you forcibly include credit products № 3, 4, estimated 1 billion rubles, the new structure of the loan portfoli o will bring profits to 0,15 billion rubles less for each included loan product than the previous optimal structure; if you include credit product 8, 10 or №12, estimated 1 billion rubles in the structure of the loan portfolio, the new structure of the consumer l oan portfolio will bring profit to 0.07 billion rubles less than the previous optimal structure; if you include credit product № 2 estimated 1 billion rubles in the structure of the loan portfolio, the new structure of the portfolio of consumer credit will bring profit to 0.24 billion rubles less than the previous optimal structure; if you include credit product № 5 estimated 1 billion rubles in the structure of the loan portfolio, the new structure of consumer loan portfolio will bring profits to 0.08 billion rubles less than the previous optimal structure; if you include credit product № 6 estimated 1 billion rubles in the structure of the loan portfolio, the new structure of consumer loan portfolio will bring profits to 0.04 billion rubles less than the previous optimal structure; if you include credit product № 14 estimated 1 billion rubles in the structure of the loan portfolio, the new structure of the consumer loan portfolio will make a profit to 0.1 billion rubles less than the previous optimal structure; if the interest rate varies (36; 1E + 30), the optimal solution will be unchanged at the optimum point.
First of all, we can recommend "Russian Standard" Bank to increase the funds for the provision of credit cards of quality category I. The optimized retail portfolio with regard to the limits should include the following items: loan product № 1 issued in the amount of 35 billion rubles, product № 7 - in the amount of 40 billion rubles, product № 11 - in the amount of 15 billion rubles and product №15 - in the amount of 10 billion rubles. As a result, the total amount of interest income earned for the year, will be estimated as 36.35 billion rubles, or 36.35% per annum.
Thus, to obtain the greatest profitability, we can recommend top managers of the bank to optimize the structure of the loan portfolio for consumer loans, because these loans are the most profitable ones; at the same time, they should choose such criteria for optimization of the loan portfolio, which ensure the relatively high sustainability of its total return, irrespective the implementation of any scenario for the market development.
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