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WORKING OUT OF A METHODS OF CONSTRUCTION OF A RATING OF LIQUIDITY OF FUNCTIONING OF COMMERCIAL BANKS OF UZBEKISTAN
УДК 339.13
Altinbek Ya. Abdullaev,
PhD in Economics, the Department of Menejment, Jizzakh Polytechnic institute, Uzbekistan Tel.: (+ 99893) 306-85-85 E-mail: oltinbek60@gmail.com
Article is devoted to a technique of construction of a rating of liquidity of functioning of commercial banks. In article are analyzed probability of event which consists that commercial bank during a certain interval of time will be liquid to function taking into account influence of random factors, i.e. regularly and in due time to carry out all functions. The special attention is given to questions of a problem of working out and introduction of a method of a rating of liquidity of commercial banks in Uzbekistan. By working out and research of the given problem methods and receptions of probability theory, the mathematical statistics and econometric modeling are used. The author comes to conclusion, that in article the technique of forecasting of a financial condition of commercial bank according to which liquidity of commercial bank is defined by probability of the event, consisting is proved what to be during a certain interval of time in the near future will be liquid to function taking into account influence of casual parameters. By imitation of parameters of the equations there is a possibility of monitoring, the control and the forecast of a rating of liquidity of commercial bank in the near future. By results of research are prepared corresponding prognosis recommendations and offers for the persons making of the decision.
Keywords: probability, liquidity, the forecast, factor, a rating, imitation, experiment, the decision, operated system, event, fortuitous, the factor, parameter, a method, reception, monitoring, the control.
Алтинбек Янгибаевич Абдуллаев,
к.э.н., доцент кафедры Менежмента Джизакского политехнического института Тел. (+99893) 306-85-85 Эл.почта: oltinbek60@gmail.com
РАЗРАБОТКА МЕТОДИКИ ПОСТРОЕНИЯ РЕЙТИНГА ЛИКВИДНОСТИ ФУНКЦИОНИРОВАНИЯ КОММЕРЧЕСКИХ БАНКОВ УЗБЕКИСТАНА
Статья посвящена методике построения рейтинга ликвидности функционирования коммерческих банков Узбекистана. В статье анализируются вероятность события, которое заключается в том, что коммерческий банк в течение определенного отрезка времени будет ликвидно функционировать с учетом воздействия случайных факторов, т.е. исправно и своевременно выполнять все свои функции. Особое внимание уделяется вопросам проблемы разработки и внедрения методики рейтинга ликвидности коммерческих банков в Узбекистане. При разработке и исследовании данной проблемы используются методы и приемы теории вероятностей, математической статистики и эконометрического моделирования. Автор приходит к выводу, что в статье обоснована методика прогнозирования финансового состояния коммерческого банка, в соответствии с которой ликвидность коммерческого банка определяется вероятностью события, заключающегося в том, что быть в течение определенного отрезка времени в ближайшем будущем будет ликвидно функционировать с учетом воздействия случайных параметров. Путем имитации параметров уравнений появляется возможность мониторинга, контроля и прогноза рейтинга ликвидности коммерческого банка в ближайшем будущем. По результатам исследования подготовлены соответствующие прогнозные рекомендации и предложения для лиц, принимающих решения.
Ключевые слова: вероятность, ликвидность, прогноз, фактор, оценка, имитация, эксперимент, решение, управляла системой, случае, случайным, фактор, параметр, метод, прием, контроль, контроль.
For last ten years positive tendencies were outlined in economy of Uzbekistan. Dynamics of recession of volume of manufacture and insolvency crisis are overcome, the financial condition of commercial banks has considerably improved. Stable growth of economy promoted, both to growth of incomes of the population, and improvement of an investment climate. Extra financing at the expense of large credits became the basic source of financing of new projects in the circumstances.
For this period risks not return of bank resources and investments have essentially increased. Badly developed system of an estimation of liquidity of commercial banks can become causal occurrence of defaults, and as consequence lead to loss of potential investors and commercial banks for economy.
In the western practice the role of independent appraisers of liquidity of commercial banks is carried out by rating agencies. Most known of them Standard and Poor's, Moody's. These agencies also actively conduct the activity and in our country, but the circle of their clients for the present is not great. Rating agencies are at present only at the initial stage of the development and their ratings yet have not received wide application among financial and investment institutes.
Mostly such low activity explained by bad base of a financial condition of commercial banks and absence of history on defaults owing to what statistical methods of research which use rating agencies, in practice are difficultly applicable to the market. At the same time constantly growing economy demands more and more financial and bank resources on development of new investment projects. The weak level of scrutiny financial and not the financial factors influencing liquidity of commercial banks, increases risk not return of bank resources and investments.
The liquidity - rating is the standardised value judgment of probability of full and timely performance by the debtor of obligations on payment of percent and repayment of the basic sum of a debt. It are a reference point not only for commercial banks and investors, but, and act as the tool of regulation of liquidity and stability of the market of promissory notes. By means of comparison of values of ratings for various commercial banks it is possible to make lists of ratings of liquidity of commercial banks. (Our) purpose of definition of liquidity of bank much bigger value has probability of that commercial bank will be liquid to function and in the future.
In this connection pressing questions are working out of a technique of a rating of liquidity of commercial banks. A problem of working out and introduction of a technique of construction of a rating of liquidity of commercial banks one of actual directions of research of commercial banks of the country. Working out of a technique of construction of a rating of liquidity of commercial banks and effective administrative decisions it is impossible without application of the corresponding economic-mathematical toolkit, allowing to make the
system analysis and to prove perspective developments of commercial bank.
At construction of ratings the author starts with the special importance for liquidity of commercial bank of observance of distribution of a random variable. This problem should be solved constantly to managers of bank. Therefore in the given work liquidity of commercial bank is defined by probability of event which consists that commercial bank during a certain interval of time will be liquid to function taking into account influence of random factors, i.e. regularly and in due time to carry out all functions [1-8].
The specified features of construction of a rating of liquidity of functioning of commercial banks allow to carry out mathematical formalisation of its indicators [9-10]. It is thus used three groups of parameters. Symbols of these parameters the following. Indexes:
i - number of month of the accounting period;
p - number of month of the look-ahead period;
Exogenous parameters: Pi - value of rating sizes; ai and ai - value of factors in the equation for approximation of size P;
n - quantity of values of size of rating
ti - Time moments, corresponding values P;
tp - Time moments (forecast date), corresponding values P; a - The bottom limit; b - The top limit; Pk - Some critical rating size; Endogenous parameters: ffp - A dispersion of random variable P;
8 - Value mean square deviation; 8S - Value mean square deviation, prolonged on an interval of time At of size P;
Factor of plural correlation; s - Value of argument of function of integral of probability;
m - Probability of liquid functioning of bank;
Pp - Predicted value of size R for three months;
8p - Predicted value of size mean square deviation for three months.
Let's define probability of liquid functioning of commercial bank as
probability of that value of size of rating P at the moment of time t will be more than some critical size Pk.
Size Pk is the bottom boundary value of a rating and characterises a condition of the bank which completely has lost liquidity and solvency, i.e. settled own capital as a result of the suffered losses at a rate of own capital. Values of parameters of balance of the bank, corresponding to such condition, are calculated by means of model of bank for twelve months and then with use of numerical values of these parameters of balance under the formula (1) sizes of ratings for each month are calculated.
As size P is the sum of size Qi, and those in turn also are the sum enough the big number composed (the sum of the rests under various accounts of balance) with the sufficient basis it is possible to speak about normal distribution of random variable P.
Normal distribution, as is known, is defined by two parameters, These parameters are the moments of the first and second order, or population mean HP and dispersion ffp of random variable P.
In our case random variable P depends on time, i.e. P = P(t). Function of time P(t), accepting at everyone fixed casual values, is called as casual process. For example, if to settle an invoice size of rating P on the basis of monthly balances of bank size P will accept casual values during the fixed moments of time ti, proper to last numbers of each month. For the decision of a problem of definition of probability of liquid functioning of bank during some time (from a present situation till the moment of time tp), it is necessary to predict value of random variable P at the moment of time tp (for reception of value P(tp)).
Function P(t) is defined under the available information on values P for the last period of time as set of points (Pi, ti), (P2, t2), ..., (Pn, tn). The received function can be prolonged for certain time forward, i.e. to predict a random variable population mean in the future with a certain error.
With the help of a method of the least squares it is possible to solve a problem of carrying out of the best straight line through set of points (Pi, ti), (P2, t2), ..., (Pn, tn). If selective distribution is normal the estimation of
a method of the least squares coincides with an estimation of a method of the maximum credibility [ii].
Really for sample (Pi, ti), (P2, t2), ., (Pn, tn)Pi has normal distribution with a population mean:
HP = ai + a2t (i)
and dispersion ffp.
Theorem of Gauss-Markov says, that the estimation of a method of the least squares has the minimum dispersion in a class of all linear not displaced estimations of parameters ai and a2.
For a finding of parameters ai and a2 from the equation (i) the following matrix expression is used:
£ ^ I"' ^
Z ti ZJ £ ъ
(2)
Solving the equation (2), we will define values of parameters ai and a2:
I P I ti-I Pt I ti
"I t-2-(I t, )2 "I Pt-I PI ti = "I t-(I ti )2
(3)
(4)
The dispersion of random variable P is defined under the formula:
H, = ^KHP -P)2 (5)
Size of mean square deviation of random variable P from its mathematical expectation HP is defined as:
o = 4TP (6)
The error of prolongation of function HP will be equal to a square root from a dispersion of random variable. Thus the prediction error will be that more than more period of a prediction. The mean square deviation, prolonged on an interval of time At of size P is defined under the formula:
es =V Д + ДР («А )2
(7)
For definition of factor of plural correlation it is necessary to use the following dependences:
Z( a + a2li )2
(8)
m X P
Now, knowing a population mean of size P and its dispersion at the moment
a
2
a, =
2
Table 1
Calculation of probability of liquid functioning of commercial banks
a1 a2 q rm Pp q s О
Bank № 1 0,6499 -0,0063 0,1389 0,033 0,5491 0,1389 1,2892 0,9013
Bank № 2 0,6826 -0,0233 0,1520 0,280 0,3098 0,1524 -0,3951 0,3464
Bank № 3 0,6832 0,0046 0,1145 0,026 0,7568 0,1146 3,3778 0,9996
Bank № 4 0,7401 -0,0216 0,0555 0,714 0,3945 0,0556 0,4405 0,6702
Bank № 5 0,4388 -0,0037 0,0422 0,111 0,3796 0,0422 0,2274 0,5899
Bank № 6 0,5376 0,0077 0,1790 0,030 0,06608 0,1791 1,6241 0,9478
of time tp (Forecast date), i.e. the sizes completely defining normal distribution H(P, HP, ffp), it is possible to define probability (m) that random variable P, distributed under the normal law, will be for the settlement moment of time in a certain interval of values:
m\a
( a < P < b ) =
f J a
-(P-HP) Ив2
dP
(9)
e 2ds
(10)
For definition of values of this integral of probabilities there are detailed tables (*) on which values of probability are defined. If in expression for definition of probability (9) to make the following substitution:
P - HP
a - HP
в
или s =
в
Probability of a finding of random variable P in the range from (a) indefinitely (®) it is possible to express that through tabular function Q(t) as follows:
со
(a<P< oo) =
= Ф
oo- HP в
-Ф
-HP
or
a(a < P <<») =
n < Ja - HP = 0,5 - Ф
в
I да-HP , where ФI-I = 0,5.
(11)
Thus, value of probability necessary for us is defined on a parity (11) with use of the table for definition of values
„ j&-hps
of function 0
The forecasting interval gets out of conditions of full loss by liquidity and solvency bank, i.e. a full exhaustion of its own capital.
Thus, the bottom limit of integration a = Pk, and top b - infinity.
Probability (o>) it is possible to express through integral of probabilities:
0
The received value of probability also will be that value which defines probability of preservation by bank of the solvency and liquidity, i.e. probability of liquid functioning.
Probability (m) that till the moment of time tp the bank will be solvent, i.e. will not suffer bankruptcy, it is defined by substitution of tabular value of integral of probabilities in the formula (11).
In table 1 the application example described techniques for probability definition is resulted is liquid functioning of six commercial banks and results of calculations of sizes:
In table 2 is given the list of commercial banks in process of decrease of size of probability of their liquid functioning within three months following after December, 31st, 2013.
From table 2 it is visible, that liquidity of functioning of the banks which have taken places in a rating of liquidity with 1 on 3, does not raise the doubts; liquidity of the banks which have taken places in a rating with 4 on 5, can cause fears. The banks taking in a rating of liquidity of a place 6, are in critical, From the point of view of liquidity, position.
Change of value of parameters in the equation (1) influences value of function HP. When parameters a1 and a2 in this equation (1) grows on certain quantity, quantity HP grows
accordingly. By means of imitation of parameters a1 and a2 during one time, change the data given to function will change at a time. If this process repeats some times the flexible (elastic) factor is formed.
For definition of flexible (elastic) factor of the equations relative growth of one of factors is defined by the relation of relative growth of liquidity of bank. We will assume, if parameter a1 has grown on 10% function HP grows on relative quantity. However many was parameters participating in the equation, each of them and in the place is used in due time. As a result, on each parameter of the equations there is a flexible (elastic) factor.
Means, when the quantity of parameters participating in the equations grows and liquidity of commercial bank leads to high flexible (elastic) factor m. If volume of liquidity of bank below growth of factors, then m < 1. By check flexible (elastic) factor at once several parameters, it is possible to define the sum flexible (elastic) factors. If m > 1, on a number with the size of parameters, the size of liquidity of banks grows also.
By means of the equations (1) there is a possibility of the short-term, intermediate term and long-term forecast of liquidity of commercial bank. Here operating system HP by the analysis and synthesis of a supply with information of object, accepts the decision on liquidity of bank in the near future, operated system a1 and a2 directly car-
Table 2
Rating of liquidity of commercial banks according to size of probability of their liquid functioning
Rating place 1 2 3 4 5 6
Bank № Bank № 3 Bank № 6 Bank № 1 Bank № 4 Bank № 5 Bank № 2
Probability o(a < P < œ) 0,9999 0,9878 0,9113 0,6702 0,5899 0,3464
1
e
s =
ries out execution of decisions accepted by operated system. By imitation of the equations (1), there is a possibility of the control and the forecast of liquidity of bank in the near future [12, 13].
In the given work the technique of forecasting of a financial condition of commercial bank according to which liquidity of commercial bank is defined by probability of the event, consisting is proved what to be during a certain interval of time in the near future will be liquid to function taking into account influence of casual parameters.
Thus, the complex approach to consideration of commercial bank as the difficult dynamic system functioning in changing conditions of the market environment, has allowed to make the developed definition of liquidity of commercial bank, to open the maintenance of its liquidity and to apply the methods of research widely used in the theory of management by difficult systems. The complex approach has defined also to main principles of construction of a rating of liquidity which gives to its users not only a
comparative estimation of a current condition of banks, but also allows to judge liquidity of their financial position in the future.
References
1. Baltensperger Emst. Alternative Approaches to the Theory of the Banking Firm. //Journal of Monetary Economics (January), i97i.
2. Kane Edward J. and Malkiel Burton G. Bank Portfolio Allocation. Deposit Variability, and the Availability Doctrine. //Quorterly Journal of Economics (February), i965.
3. Klein Michael A. A Theory of the Banking Firm. //Journal of Money, Credit and Banking (May), i97i.
4. Pale David H. On the Theory of Financial Intermediation. //Journal of Finance (June), i97i.
5. Sealy C.W. and Lindlcy J.T. Inputs, Outputs, and Theory of Production and Cost at Depository Financial Institutions. //Journal of Finance (September), i977.
6. Sealy C. W. Deposit Rate Setting, Risk Aversion, and the Theory of
Depository Financial Intermediates. // Journal of Financc (Dcccmbcr), 1980.
7. Sheshukova T.G., Katz E.B. Rating an estimation of a financial condition of commercial banks. - Perm, 2001.
8. Karimskij A.M., etc. Ratings in economy: methodology and practice. - M: the Finance and statistics, 2005. pp. 240.
9. Dr. Gerhard Tintner. Handbuch der Ökonometrie. - Springer-Verlag. Berlin: Göttingen, Heidelberg. 1960. pp.381.
10. Kremer N.S. Ekonometrika. -M: JUNITI-DIANA, 2002. pp. 311.
11. The directory on the applied statistics/under the editorship of E.Llojda, U.Ledermana, a translation from English/under the editorship of S.A.Ajvazjana and J.N.Tjurina. - M: the Finance and statistics, 1990.
12. Neylor T, 1975. Machine imitating experiments with models of economic systems. M.: the World. pp.500.
13. Afanasev M. J, Bagrinovskij K.A., MairomoK V.M. Prikladnye of the research problem of operations. - M: : INFRA-M, 2006. Pp. 352.
