CONFIRMATION OF THE RELATIONSHIP BETWEEN STOCK MARKET PARAMETERS AND INTERBANK CREDIT MARKET ON THE EXAMPLE OF THE KAZAKHSTAN STOCK EXCHANGE
MAGOMET YANDIEV
LOMONOSOV MOSCOW STATE UNIVERSITY, FACULTY OF ECONOMICS
ALTANA ANDZHAEVA
LOMONOSOV MOSCOW STATE UNIVERSITY, FACULTY OF ECONOMICS
Abstract: The paper presents calculations confirming practical applicability of the earlier formulated theoretical model that explains the relationship between the rate of oneday loans in the interbank market, volume of speculative investments and total securities under which transactions have been closed. The paper is based on the Kazakhstan stock exchange data.
Keywords: interbank credit market, equity market, stock market, speculations, trading volumes, KASE .
JEL Classification G12, G14, G17, G21
YANDIEV, MAGOMET; ANDZHAEVA, ALTANA (2015) "CONFIRMATION OF THE RELATIONSHIP BETWEEN STOCK MARKET PARAMETERS AND INTERBANK CREDIT MARKET ON THE EXAMPLE OF THE KAZAKHSTAN STOCK EXCHANGE". Journal of Russian Review (ISSN 23131578), VOL. 2(3), 1228
1. Review of literature
This paper belongs to a series of studies that examine the relationship between the rates of oneday loans in the interbank market and a mumber of stock market parameters.
The original formula (Yandiev, 2011) describes the relationsship in the following way:
 u is the mean loss per a deal involving one stock;
 I is the volume of speculative investments (amount of money on accounts in the authorized bank to the stock exchange and intended for speculations);
 R is the rate of oneday loans on the interbank market, in fractions;
 U is the total amount of stocks involved in the deals;
The logic of the formula means that: the rate of oneday loans on the interbank market is inversely proportional to the number of securities traded on the stock exchange. The formula is purely theoretical as for its proof assumptions were used, but, because of its simplicity, it is quite suitable for implementation of practical calculations. According to the logic of the formula, it can be considered workable in practice if the parameter u remains constant during calculations.
Calculations in the paper of Pakhalov and Yandiev (2013) were carried out on the basis of data received from Moscow Stock Exchange. In another paper (Matveev, 2014) calculations were carried out based on the Bahrain Stock Exchange. In both cases, positive results were obtained, indicating that the formula correctly reflects the relationship of the parameters for the studied time intervals.
It should be noted that stock exchange management usually prefer not to disclose some parameters of the formula, such as the amounts of clients’ money and number of securities deposited within the exchange system. This position is understandable as the disclosure of this information under certain circumstances may be a bad marketing move capable of undermining investor confidence in the validity of quotations received at the exchange. On the other hand, general lack of such information in free access only aggravates consequences of quite common situations when the quotation of particular issuer is formed at the exchange in the course of trading of absolutely scanty number of actions stocks.
In the present paper, we test the formula using the data of Kazakhstan stock exchange for the period 2010 – 2014.
2. Input data
In order to test the applicability of the formula, the following data provided by Kazakhstan Stock Exchange were used (on a daily basis, for the period 20102014.):
 total amount of money deposited within the exchange system in m. tenge (analogue of I parameter, refer to Appendix 1);
 number of stocks (blue chips) deposited in the clearing exchange system, in pcs (U parameter, refer to Appendix 2);
We examined data on 10 most liquid stocks traded on KASE rather than on all of them, i.e. blue chips: Bank CenterCredit, Kazkommertsbank, KEGOC, Kazakhtelecom, KazMunaiGas Exploration Production, KazTransOil, KAZ Minerals, Kcell, Halyk Bank, Eurasian Natural Resources Corporation;  fraction of blue chips in the total volume of stock trading, % (this information is needed to be sure that blue chips data are representative and reflect the situation on the stock market, refer to Appendix 3);
 rate of oneday loans on the interbank market, % a year (R parameter, refer to Appendix 4);
 number of securities involved in the stock exchange deals (as the analogue and substitute for the “number of all deposited stocks within the exchange system”, refer to Appendix 5).
Verification of practical applicability of the formula is performed as follows. The parameter u is calculated for every day during the entire analyzed period (1232 trading days for 20102014). Next, we use two different approaches. The formula will be considered correct if the parameter u has the minimum volatility (the first approach). The formula will be considered correct if the constructed regression equation corresponds to the theoretical model (the second approach)
At the same time in both approaches, the parameter U is substituted in two ways; firstly and mainly as the quantity of all deposited stocks within the exchange system and, secondly, as the quantity of securities involved in the stock exchange deals (the second option).
It is noteworthy that substantially more securities are deposited in the exchange system, than it is necessary for daily trading, 5000 times approximately (refer to Appendix 6). This reserve provides the Kazakhstan Stock Exchange with an extremely high degree of stability in case of a surge in demand for the shares.
3. First approach. Formula verification based on standard deviation of the “u” parameter
The purpose of the first approach is to make sure that the standard deviation of parameter u is insignificant. We calculated mean and standard deviation for both options and plotted graphs for visual analysis of parameter u dispersion degree.
On the basis of performed calculations one can draw the following conclusions:
 If we compare the standard deviation of parameter u with the average value of parameter u for the entire period of our analysis, the range of values of the parameter u looks rather wide, but if we compare the standard deviation with the average quotation per share, the volatility of the parameter u seems to be of insignificant value (refer to Appendix 7).
 From a visual assessment of the u parameter dispersion, it is obvious that in general it is insignificant (refer to Appendices 8, 9, where parameter u is shown in historical sequence and to Appendices 10, 11, where parameter u is shown after sorting «from bigger to smaller»).
Thus, it can be argued that parameter u has low volatility and can be considered as a value close to a constant.
4. Second approach. Formula verification based on linear regression
This approach involves the use of regression analysis of time series in order to identify relationships between the model parameters and to check them for compliance with the theoretical model under consideration.
Input set of data consists of 1232 observations for each of six variables (refer to Appendix 12). Calculations were performed in the Gretl econometric package.
Since the regression analysis of time series requires that all variables be stationary, the first stage of econometric analysis involves an augmented DickeyFuller test (ADF) for each of the variables. Lag length in each case was set based on the Schwarz information criterion (SIC). All time series were examined for stationarity excluding trend. Results of tests are given in Appendix 13.
ADF test has shown that all variables except u_big_dep are stationary, therefore the variable has to be tested for cointegration. According to Verbeek M., the existence of cointegration between the variables allows to get super consistent estimates of the model parameters, and the received results will make sense. Residuals of both regressions based on the deposited quantity and trading volume are stationary at 1% level of significance (refer to Appendix 14). It allows us to draw some conclusions:
 The first regression equation is on the whole significant, as well as all its variables. The second equation is insignificant, and only one variable in it has the 10% level of significance, which implies that the option of U calculation as the number of securities involved in the stock exchange deals is unreliable, and the impact of the variables included in the equation on the dependent variable may not even exist.
 Despite this, in both regression equations the I and R variables have positive coefficients, and the variable U has negative coefficient that completely corresponds to the logic of theoretical model.
Thus, the regression analysis confirms the significance of the tested formula.
5. Summary
Results of calculations for both options prove that the tested formula accurately reflects the relationship between parameters of the interbank credit market and the stock market.
Calculation of parameter U as the number of all deposited stocks within the exchange system is more correct, than understanding under it the number of securities involved in the stock exchange deals.
The findings of this work are consistent with the conclusions obtained in the previous similar studies in Moscow (Pakhalov, Yandiev, 2013) and Bahrain stock exchanges (Matveev, 2014).
6. References
 Yandiev M. The Damped Fluctuations as a Base of Market Quotations // Economics and Management. 2011. N 16. URL: http://ssrn.com/abstract=1919652
 Yandiev, Magomet and Pakhalov, Alexander, The Relationship between Stock Market Parameters and Interbank Lending Market: An Empirical Evidence (September 23, 2013). Available at SSRN: http://ssrn.com/abstract=2329871
 Matveev, Aleksandr (2014) «Proving The Association Between Stock Market And Interbank Lending Market Parameters: The Bahrain Stock Exchange». Journal of Russian Review (ISSN 23131578), VOL. (0), 2132. Available at: http://rusreview.com/journal/vol02014/14provingtheassociationbetweenstockmarketandinterbanklendingmarketparametersthebahrainstockexchangealeksandrmatveev.html
 Verbeek M. A Guide to Modern Econometrics. 2nd ed. Chichester, 2004.
7. Appendices
Appendices 16. Input data
Appendix 1
Appendix 2
Appendix 3
Appendix 4
Appendix 5
Appendix 6
Appendices 711. Results of the first approach calculations
Appendix 7. U parameter calcualtions
Calculation, where U parameter is the number of securities involved in the stock exchange deals 
Calculation, where U parameter is the total number of all deposited stocks within the exchange system 

Arithmetic mean, tenge  0,0011  124,90 
Standard deviation, tenge  0,0024  1 357,60 
Appendix 8
Appendix 9
Appendix 10
Appendix 11
Appendices 1214. Results of the second approach calculations
Appendix 12
Variable name in the theoretical model  Variable name in Gretl  Definition 
u  u_small_dep  Mean loss per deal involving one stock (calculated using the amount of deposited stocks) 
u  u_small_vol  Mean loss per deal involving one stock (calculated using the amount of stocks involved in deals) 
I  I  Volume of speculative investment (amount of money in the exchange’s authorized bank) 
R  R  Rate of oneday loans in the interbank market 
U  U_big_dep  Total amount of deposited stocks within the exchange system 
U  U_big_vol  Total amount of stocks involved in the stock exchange deals 
Appendix 13
13. 1 Unit root test for u_small_dep
Augmented DickeyFuller test for u_small_dep
including 18 lags of (1L)u_small_dep (max was 22)
sample size 1213
unitroot null hypothesis: a = 1
test with constant
model: (1L)y = b0 + (a1)*y(1) + ... + e
1storder autocorrelation coeff. for e: 0.001
lagged differences: F(18, 1193) = 6.776 [0.0000]
estimated value of (a  1): 0.363392
test statistic: tau_c(1) = 5.24083
asymptotic pvalue 6.397e006
13.2 Unit root test for u_small_vol
Augmented DickeyFuller test for u_small_vol
including one lag of (1L)u_small_vol (max was 22)
sample size 1230
unitroot null hypothesis: a = 1
test with constant
model: (1L)y = b0 + (a1)*y(1) + ... + e
1storder autocorrelation coeff. for e: 0.000
estimated value of (a  1): 0.886475
test statistic: tau_c(1) = 22.1575
asymptotic pvalue 1.601e050
13.3 Unit root test for I
Augmented DickeyFuller test for I
including 17 lags of (1L)I (max was 22)
sample size 1214
unitroot null hypothesis: a = 1
test with constant
model: (1L)y = b0 + (a1)*y(1) + ... + e
1storder autocorrelation coeff. for e: 0.001
lagged differences: F(17, 1195) = 2.007 [0.0088]
estimated value of (a  1): 0.793051
test statistic: tau_c(1) = 7.75998
asymptotic pvalue 2.491e012
13.4 Unit root test for R
Augmented DickeyFuller test for R
including 22 lags of (1L)R (max was 22)
sample size 1209
unitroot null hypothesis: a = 1
test with constant
model: (1L)y = b0 + (a1)*y(1) + ... + e
1storder autocorrelation coeff. for e: 0.001
lagged differences: F(22, 1185) = 2.461 [0.0002]
estimated value of (a  1): 0.0349829
test statistic: tau_c(1) = 3.67816
asymptotic pvalue 0.004453
13.5 Unit root test for u_big_dep
Augmented DickeyFuller test for u_big_dep
sample size 1231
unitroot null hypothesis: a = 1
test with constant
model: (1L)y = b0 + (a1)*y(1) + e
1storder autocorrelation coeff. for e: 0.000
estimated value of (a  1): 0.00140949
test statistic: tau_c(1) = 0.778644
pvalue 0.8242
Augmented DickeyFuller test for d_u_big_dep
sample size 1230
unitroot null hypothesis: a = 1
test with constant
model: (1L)y = b0 + (a1)*y(1) + e
1storder autocorrelation coeff. for e: 0.000
estimated value of (a  1): 1.00049
test statistic: tau_c(1) = 35.0601
pvalue 9.696e025
13.6 Unit root test for u_big_vol
DickeyFuller test for u_big_vol
sample size 1231
unitroot null hypothesis: a = 1
test with constant
model: (1L)y = b0 + (a1)*y(1) + e
1storder autocorrelation coeff. for e: 0.000
estimated value of (a  1): 1.00024
test statistic: tau_c(1) = 35.0651
pvalue 9.836e025
ADF test results summary:
Variable name in Gretl  ADF test result 
u_small_dep  Variable is stationary at the 1% level of significance 
u_small_vol  Variable is stationary at the 1% level of significance 
I  Variable is stationary at the 1% level of significance 
R  Variable is stationary at the 1% level of significance 
U_big_dep  Variable is stationary in first differences at the 1% level of significance 
U_big_vol  Variable is stationary at the 1% level of significance 
Appendix 14
14.1 Calculation with amount of deposited stocks
Linear regression of u_small_dep using u_big_dep, I, R and constant
Model 1: OLS, using observations 11232
Dependent variable: u_small_dep
Coefficient  Std. Error  tratio  pvalue  
const  5.39328e05  0.000191808  0.2812  0.77862  
R  1.44129e013  0  52.9767  <0.00001  *** 
u_big_dep  0.0148303  0.00249189  5.9514  <0.00001  *** 
u_big_dep  4.66606e013  0  15.0063  <0.00001  *** 
Mean dependent var  0.001137  S.D. dependent var  0.002413  
Sum squared resid  0.002000  S.E. of regression  0.001276  
Rsquared  0.721051  Adjusted Rsquared  0.720369  
F(3, 1228)  1058.078  Pvalue(F)  0.000000  
Loglikelihood  6463.734  Akaike criterion  12919.47  
Schwarz criterion  12899.00  HannanQuinn  12911.77  
rho  0.014530  DurbinWatson  1.970819 
ADF test results for residuals:
Augmented DickeyFuller test for u_small_dep_residual
including 5 lags of (1L)u_small_dep_residual (max was 22)
sample size 1226
unitroot null hypothesis: a = 1
test with constant
model: (1L)y = b0 + (a1)*y(1) + ... + e
1storder autocorrelation coeff. for e: 0.002
lagged differences: F(5, 1219) = 9.465 [0.0000]
estimated value of (a  1): 0.671148
test statistic: tau_c(1) = 11.0798
asymptotic pvalue 1.053e022
14.2 Calculation with volume of trade
Linear regression of u_small_vol using u_big_vol, I, R and constant
Model 2: OLS, using observations 11232
Dependent variable: u_small_vol
Coefficient  Std. Error  tratio  pvalue  
const  48.3371  188.06  0.2570  0.79720  
I  6.18352e09  3.17654e09  1.9466  0.05181  * 
R  1934.66  2636.76  0.7337  0.46325  
u_big_vol  2.8605e05  2.51251e05  1.1385  0.25513 
Mean dependent var  124.9018  S.D. dependent var  1357.595  
Sum squared resid  2.26e+09  S.E. of regression  1356.684  
Rsquared  0.003776  Adjusted Rsquared  0.001342  
F(3, 1228)  1.551350  Pvalue(F)  0.199535  
Loglikelihood  10632.30  Akaike criterion  21272.59  
Schwarz criterion  21293.06  HannanQuinn  21280.29  
rho  0.007715  DurbinWatson  1.984558 
ADF test results for residuals
Augmented DickeyFuller test for u_small_vol_residual
including one lag of (1L)u_small_vol_residual (max was 22)
sample size 1230
unitroot null hypothesis: a = 1
test with constant
model: (1L)y = b0 + (a1)*y(1) + ... + e
1storder autocorrelation coeff. for e: 0.000
estimated value of (a  1): 0.886062
test statistic: tau_c(1) = 22.1592
asymptotic pvalue 1.594e050