PROVING THE RELATIONSHIP BETWEEN THE PARAMETERS OF THE STOCK MARKET AND INTERBANK LENDING MARKET: THE KYRGYZ STOCK EXCHANGE
EKATERINA ROMANOVA,
LOMONOSOV MOSCOW STATE UNIVERSITY, ECONOMICS FACULTY
ROMANOVA.EKO@GMAIL.COM
MARIA ELCHANINOVA,
LOMONOSOV MOSCOW STATE UNIVERSITY, ECONOMICS FACULTY
YULIA LOS,
LOMONOSOV MOSCOW STATE UNIVERSITY, ECONOMICS FACULTY
Abstract. This paper presents calculations reaffirming practical application of an earlier posed theoretical model explaining relationship between the rate of one-day credits in the interbank market, volume of speculative investments and total securities under which transactions have been closed. This article is written based on the Kyrgyz stock exchange data.
Keywords: interbank credit market, equity market, stock market, speculations, trading volumes, KSE
JEL Classification: G12, G14, G17, G21
ROMANOVA, EKATERINA. ELCHANINOVA, MARIA. LOS, YULIA (2016) "PROVING THE RELATIONSHIP BETWEEN THE PARAMETERS OF THE STOCK MARKET AND INTERBANK LENDING MARKET: THE KYRGYZ STOCK EXCHANGE". Journal of Russian Review (ISSN 2313-1578), VOL. 1(4), 13-23.
1. Introduction
This paper continues the research into the relationships between stock market and interbank lending market, using the database of Stock Exchange of Kyrgyzstan.
The purpose of the study is to check the correctness of the formula [1], according to which the day-rate of loans in the interbank market is inversely proportional to the number of securities traded on the stock exchange:
Where the formula describes the relationship between the parameters:
The key point of the formula is the fact that the parameter u remains constant for the duration of the period under review. In this regard, verification of the formula’s compliance with real practice boils down, to showing that the parameter u is indeed constant. In practice, this may indicate a low value of the standard deviation of the parameter. In addition, the use of regression analysis can confirm or disprove the theory about the nature of the relationship between the parameters
2. Literature review
Three articles were published in the period 2013-2016, which tested the applicability of the formula to practice. The first paper [2] uses the data provided by the Moscow Stock Exchange. The authors conclude that the formula as a whole, correctly reflects the relationship between the interbank market parameters and those at Moscow Stock Exchange in 2012.
Another study [3] was carried out on the basis of the Bahrain Stock Exchange data. It has also been noted that the overall formula correctly reflects the real situation, since the parameter u has a low value volatility. In addition, the econometric model confirmed the existence of correlations between variables.
The third work [4] was made on the basis of the Kazakhstan Stock Exchange data. The results are broadly similar to those presented in the other two papers.
Next, the search was carried out for publications, which also address the issue of the relationship between interbank market parameters and the stock market.
The search for Russian language sources was carried out on the site of the Scientific Electronic Library RISC (elibrary.ru), English - the search engine Google Scholar (scholar.google.com) and Online Social Science Research Network International Libraries (ssrn.com).
The search in RSCI was conducted using the keywords stock market, interbank credit market, stock index, overnight rate. As a result, the system showed 47 articles, out of which 2 were chosen after reading the abstracts. However, after the full reading they were dismissed as not relevant to the subject. That is why there are no Russian-language part sources in the literature review.
After looking through SSRN with the keywords: stock market, interbank credit market, rate of one-day credits, lending market, overnight rate, stock index and their different combinations, the websites’ search engine came up with 20 articles, out of which 3 were chosen after analysis of their titles and abstracts for future reading. However, only 1 paper [5] proved to be relevant. It describes the role of the stock market and the market of interbank credits in the measurement of bank performance in Malaysia and Thailand. The author argues that the price of shares in individual banks may reflect the risk in the interbank market.
To search on Google Scholar website the following key words were used: stock market, the market of interbank loans, the rate of one-day loans, stock market index, the overnight rate, the industrial index Dow Jones. As a result 134 works were found, of which after reading the abstracts 12 were selected for the study of the full text. As it turned out, only one of them [6] was relatively close to the subject of the study. This is a fairly popular work, with 72 citations. The authors trace the dynamics of stock prices of Japanese banks during the banking crisis in the mid-1990s. Their research shows that the bank’s shareholders may use financial indicators to quickly differentiate between the activities of banks.
3. Description of the data and methodology
To test the practicability of the formula two approaches were used. The first is to determine whether the standard deviation of the parameter u is of constant or negligible value. As the available data were not detailed or structured they were approached in two steps: first, the analysis of all the available sample and, second, the analysis of the data for December 2015 (for this month the data were full and regular).
The meaning of the second approach is the use of regression analysis to determine the nature of the relationship between the parameters and compare it with the nature of the relationships in the formula itself.
To verify the applicability of the formula the data were used for the research during the period 2010-2015 years provided by the Kyrgyz Stock Exchange:
4. The first approach
The calculations show that the standard variations are below one hundredth of the mean price of a single stock. It allows to recognize u parameter as a generally constant value (refer to Appendix 4 and 5). In addition, visual examination of the daily u parameter value shows that it is slightly volatile (refer to Appendices 6-9). Because of the small amounts of data, the first approach consists of two parts: one is dealing with all data that we have and the other dealing with the data for December 2015.
From a visual assessment of the u parameter dispersion it is obvious that in general it is insignificant. Thus, it can be argued that the u parameter has low volatility and can be considered as a value close to a constant.
5. The second approach
The second approach includes the use of regression analysis of time series in order to verify the relationships between the variables of the model again.
The time series input consists of 76 observations for each of the 5 variables (refer to Appendix 10). All calculations are made in the Gretl econometrics package.
The first stage of the econometric analysis is checking the stationarity of all the variables according to the regression analysis of time series. For this reason an augmented Dickey–Fuller test (ADF) is used. At present it is one of the most popular tests for a unit root in a time series sample. All variables are examined for stationarity with constant. The results of the testing procedure are given in Appendices 11-14.
ADF test has shown all variables except R to be stationary. Due to the similarity of the R indicators during the last periods there is no point in testing its stationarity in this particular period. However, the first 10 observations are different. Therefore the ADF test is held separately for the first 10 observations of parameter R. This test shows non-stationarity of the variable. (refer to Appendix 15) The use of non-stationary variables in linear regressions may lead to invalid estimators. For this reason, an additional test of the R first differences (d_R) is arranged and finally the stationarity of the variable is revealed at 1% level of significance (refer to Appendix 16).
Taking everything into consideration it is possible to formulate several conclusions from analyses of these regressions. Both equations are completely significant, and the relationships between parameter u and other variables correspond to logic of the theoretical formula. The R and I variables have positive coefficients (it means the direct relationship with the dependent parameter), and the U variable has a negative coefficient (it means the inverse relationship with the dependent parameter) (refer to Appendices 17, 18). This kind of analysis also proves the significance of the observed formula.
6. Conclusion
The results of calculations made in both cases prove constant relative stability and general correctness of the tested formula. The relationships between parameters correspond to reality. Therefore, it can be argued that the formula can adequately describe the situation at the Kyrgyz Stock Exchange during the period 2010-2015 years and can be useful for financial market regulation.
7. References
8. Appendices
Appendix 1
Appendix 2
Appendix 3
Appendix 4
"u" parameter, KSE, Dec. 2015 | With U as volume of stocks traded | With U as total amount of deposited stocks |
Average, KSE | 0,0000061900 | 0,0022593348 |
Volatility, KSE | 0,0000004862 | 0,0001755129 |
Appendix 5
"u" parameter, KSE, 2010 - 2015 | With U as volume of stocks traded | With U as total amount of deposited stocks |
Average, KSE | 0,0000053277 | 0,0019446140 |
Volatility, KSE | 0,0000052658 | 0,0019220080 |
Appendix 6
The whole period (2010-2015)
Appendix 7
The whole period (2010-2015)
Appendix 8
01.12.15-31.12.15
Appendix 9
01.12.15-31.12.15
Appendix 10
Variable name in the theoretical model | Variable model in Gretl | Definition |
u | u_small_vol | Mean loss per deal (calculated using the volume of trade) |
u | u_small_dep | Mean loss per deal (calculated using the amount of deposited stocks) |
I | I | Volume of speculative investment (amount of money in the bank autorised by the Exchange) |
R | R | One-day loan interest rates |
R | d_R | First difference of R |
Appendix 11
Unit root test for u_small_vol
Results of the ADF test
Augmented Dickey-Fuller test for u_small_vol
including 0 lags of (1-L)u_small_vol
(max was 11, criterion AIC)
sample size 76
unit-root null hypothesis: a = 1
test with constant
model: (1-L)y = b0 + (a-1)*y(-1) + e
estimated value of (a - 1): -0.589324
test statistic: tau_c(1) = -5.58178
p-value 9.829e-06
1st-order autocorrelation coeff. for e: -0.005
The variable is stationary at the 1% level of significance.
Appendix 12
Unit root test for u_small_dep
Results of the ADF test
Augmented Dickey-Fuller test for u_small_dep
including 0 lags of (1-L)u_small_dep
(max was 11, criterion AIC)
sample size 76
unit-root null hypothesis: a = 1
test with constant
model: (1-L)y = b0 + (a-1)*y(-1) + e
estimated value of (a - 1): -0.589324
test statistic: tau_c(1) = -5.58178
p-value 9.829e-06
1st-order autocorrelation coeff. for e: -0.005
The variable is stationary at the 1% level of significance.
Appendix 13
Unit root test for I
Results of the ADF test
Augmented Dickey-Fuller test for I
including 0 lags of (1-L)I
(max was 11, criterion AIC)
sample size 74
unit-root null hypothesis: a = 1
test with constant
model: (1-L)y = b0 + (a-1)*y(-1) + e
estimated value of (a - 1): -0.542084
test statistic: tau_c(1) = -5.17475
p-value 4.32e-05
1st-order autocorrelation coeff. for e: -0.019
The variable is stationary at the 1% level of significance
Appendix 14
Unit root test for R
The ADF test (R, d_R) cannot be held because most dependent variables are constant.
Appendix 15
Unit root test for R (first 10 observations)
Results of the ADF test
Augmented Dickey-Fuller test for R
including one lag of (1-L)R
(max was 2, criterion AIC)
sample size 10
unit-root null hypothesis: a = 1
test with constant
model: (1-L)y = b0 + (a-1)*y(-1) + ... + e
estimated value of (a - 1): -0.414669
test statistic: tau_c(1) = -1.12293
asymptotic p-value 0.7091
1st-order autocorrelation coeff. for e: 0.425
Appendix 16
Unit root test for d_R
Results of the ADF test
Augmented Dickey-Fuller test for d_R
including 2 lags of (1-L)d_R
(max was 2, criterion AIC)
sample size 8
unit-root null hypothesis: a = 1
test with constant
model: (1-L)y = b0 + (a-1)*y(-1) + ... + e
estimated value of (a - 1): -1.90414
test statistic: tau_c(1) = -4.27636
asymptotic p-value 0.0004832
1st-order autocorrelation coeff. for e: -0.288
lagged differences: F(2, 4) = 2.359 [0.2105]
Appendix 17
Calculation with volume of trade
Linear regression of u_small_vol using I and R
Model 2: OLS, using observations 1-75
Dependent variable: u_small_vol
Coefficient | Std. Error | t-ratio | p-value | ||
const | -4.4881e-06 | 9.46334e-07 | -4.7426 | <0.0001 | *** |
I | 7.48608e-11 | 1.51878e-12 | 49.2899 | <0.0001 | *** |
R | 4.36902e-07 | 7.87213e-08 | 5.5500 | <0.0001 | *** |
Mean dependent var | 5.33e-06 | S.D. dependent var | 6.80e-06 | |
Sum squared resid | 9.66e-11 | S.E. of regression | 1.16e-06 | |
R-squared | 0.971755 | Adjusted R-squared | 0.970970 | |
F(2, 72) | 1238.561 | P-value(F) | 1.71e-56 | |
Log-likelihood | 920.2480 | Akaike criterion | -1834.496 | |
Schwarz criterion | -1827.544 | Hannan-Quinn | -1831.720 | |
rho | 0.862350 | Durbin-Watson | 0.274967 |
Appendix 18
Calculation with amount of deposited funds
Linear regression of u_small_dep using I and R
Model 3: OLS, using observations 1-75
Dependent variable: u_small_dep
Coefficient | Std. Error | t-ratio | p-value | ||
const | 0.00163816 | 0.000345412 | -4.7426 | <0.0001 | *** |
I | 2.73242e-08 | 5.54356e-10 | 49.2899 | <0.0001 | *** |
R | 0.000159469 | 2.87333e-05 | 5.5500 | <0.0001 | *** |
Mean dependent var | 0.001945 | S.D. dependent var | 0.002482 | |
Sum squared resid | 0.000013 | S.E. of regression | 0.000423 | |
R-squared | 0.971755 | Adjusted R-squared | 0.970970 | |
F(2, 72) | 1238.561 | P-value(F) | 1.71e-56 | |
Log-likelihood | 477.7557 | Akaike criterion | -949.5115 | |
Schwarz criterion | -942.5590 | Hannan-Quinn | -946.7354 | |
rho | 0.862350 | Durbin-Watson | 0.274967 |