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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 one-day 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 2313-1578), VOL. 2(3), 12-28


1. Review of literature

This paper belongs to a series of studies that examine the relationship between the rates of one-day 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 one-day 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 one-day 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 2010-2014.):

  • 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 one-day 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 2010-2014). 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 Dickey-Fuller 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

  1. Yandiev M. The Damped Fluctuations as a Base of Market Quotations // Economics and Management. 2011. N 16. URL: http://ssrn.com/abstract=1919652
  2. 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
  3. Matveev, Aleksandr (2014) «Proving The Association Between Stock Market And Interbank Lending Market Parameters: The Bahrain Stock Exchange». Journal of Russian Review (ISSN 2313-1578), VOL. (0), 21-32. Available at: http://rusreview.com/journal/vol-0-2014/14-proving-the-association-between-stock-market-and-interbank-lending-market-parameters-the-bahrain-stock-exchange-aleksandr-matveev.html
  4. Verbeek M. A Guide to Modern Econometrics. 2nd ed. Chichester, 2004.


7. Appendices

Appendices 1-6. Input data

Appendix 1

Appendix 2

Appendix 3

Appendix 4

Appendix 5

Appendix 6


Appendices 7-11. 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 12-14. 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 one-day 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 Dickey-Fuller test for u_small_dep
including 18 lags of (1-L)u_small_dep (max was 22)
sample size 1213
unit-root null hypothesis: a = 1

test with constant
model: (1-L)y = b0 + (a-1)*y(-1) + ... + e
1st-order 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 p-value 6.397e-006


13.2 Unit root test for u_small_vol

Augmented Dickey-Fuller test for u_small_vol
including one lag of (1-L)u_small_vol (max was 22)
sample size 1230
unit-root null hypothesis: a = 1

test with constant
model: (1-L)y = b0 + (a-1)*y(-1) + ... + e
1st-order autocorrelation coeff. for e: 0.000
estimated value of (a - 1): -0.886475
test statistic: tau_c(1) = -22.1575
asymptotic p-value 1.601e-050


13.3 Unit root test for I

Augmented Dickey-Fuller test for I
including 17 lags of (1-L)I (max was 22)
sample size 1214
unit-root null hypothesis: a = 1

test with constant
model: (1-L)y = b0 + (a-1)*y(-1) + ... + e
1st-order 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 p-value 2.491e-012

 

13.4 Unit root test for R

Augmented Dickey-Fuller test for R
including 22 lags of (1-L)R (max was 22)
sample size 1209
unit-root null hypothesis: a = 1

test with constant
model: (1-L)y = b0 + (a-1)*y(-1) + ... + e
1st-order 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 p-value 0.004453


13.5 Unit root test for u_big_dep

Augmented Dickey-Fuller test for u_big_dep
sample size 1231
unit-root null hypothesis: a = 1
test with constant
model: (1-L)y = b0 + (a-1)*y(-1) + e
1st-order autocorrelation coeff. for e: 0.000
estimated value of (a - 1): -0.00140949
test statistic: tau_c(1) = -0.778644
p-value 0.8242

Augmented Dickey-Fuller test for d_u_big_dep
sample size 1230
unit-root null hypothesis: a = 1
test with constant
model: (1-L)y = b0 + (a-1)*y(-1) + e
1st-order autocorrelation coeff. for e: -0.000
estimated value of (a - 1): -1.00049
test statistic: tau_c(1) = -35.0601
p-value 9.696e-025


13.6 Unit root test for u_big_vol

Dickey-Fuller test for u_big_vol
sample size 1231
unit-root null hypothesis: a = 1
test with constant
model: (1-L)y = b0 + (a-1)*y(-1) + e
1st-order autocorrelation coeff. for e: -0.000
estimated value of (a - 1): -1.00024
test statistic: tau_c(1) = -35.0651
p-value 9.836e-025


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
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 1-1232
Dependent variable: u_small_dep

  Coefficient Std. Error t-ratio p-value  
const -5.39328e-05 0.000191808 -0.2812 0.77862  
R 1.44129e-013 0 52.9767 <0.00001 ***
u_big_dep 0.0148303 0.00249189 5.9514 <0.00001 ***
u_big_dep -4.66606e-013 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
R-squared 0.721051   Adjusted R-squared 0.720369
F(3, 1228) 1058.078   P-value(F) 0.000000
Log-likelihood 6463.734   Akaike criterion -12919.47
Schwarz criterion -12899.00   Hannan-Quinn -12911.77
rho 0.014530   Durbin-Watson 1.970819

 

ADF test results for residuals:

Augmented Dickey-Fuller test for u_small_dep_residual
including 5 lags of (1-L)u_small_dep_residual (max was 22)
sample size 1226
unit-root null hypothesis: a = 1
test with constant
model: (1-L)y = b0 + (a-1)*y(-1) + ... + e
1st-order 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 p-value 1.053e-022


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 1-1232
Dependent variable: u_small_vol

  Coefficient Std. Error t-ratio p-value  
const -48.3371 188.06 -0.2570 0.79720  
I 6.18352e-09 3.17654e-09 1.9466 0.05181 *
R 1934.66 2636.76 0.7337 0.46325  
u_big_vol -2.8605e-05 2.51251e-05 -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
R-squared 0.003776   Adjusted R-squared  0.001342
F(3, 1228) 1.551350   P-value(F) 0.199535
Log-likelihood -10632.30   Akaike criterion 21272.59
Schwarz criterion 21293.06   Hannan-Quinn 21280.29
rho 0.007715   Durbin-Watson 1.984558

 

ADF test results for residuals

Augmented Dickey-Fuller test for u_small_vol_residual
including one lag of (1-L)u_small_vol_residual (max was 22)
sample size 1230
unit-root null hypothesis: a = 1

test with constant
model: (1-L)y = b0 + (a-1)*y(-1) + ... + e
1st-order autocorrelation coeff. for e: 0.000
estimated value of (a - 1): -0.886062
test statistic: tau_c(1) = -22.1592
asymptotic p-value 1.594e-050

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