Interest Rate Sensitivity of Banking Sector Stock Returns
Neetu Chadha
Assistant Professor, Delhi Institute of Advanced Studies, Guru Gobind Singh Indraprastha University, Delhi, India
ABSTRACT:
Thecurrent study scrutinizes the influence of interest rate changes on the unpredictability of stock returns and type of association between interest rate movements and stock returns of banking sector in India by applying the methodology of GARCH (1, 1) model, Correlation test and Johansen's Cointegration Test. The study considers the period from April 2000 toMarch, 2018. 11 banks that are listed in the S and P BSE 500 index is taken as sample for the study. Returns of banking sector stocks in India are found to highly sensitive and volatile to interest rate changes. Results of the present study have a great importance for policy regulators and investment community at large.
KEYWORDS: Volatility, Treasury bill, Stock Returns, S and P BSE 500.
INTRODUCTION:
In general, from borrower's point of view, Interest rate can be defined as the amount charged by a lender to a borrower for the use of assets which is expressed as a percentage of principal and known as Annual Percentage return (APR). But in case of banking sector, the meaning of interest rate is quite different from the point of view of people who deposit their hard earned money in savings account or invest them in banking instruments which yield high returns like most popular ones are Fixed deposits, Government bonds, Certificate of Deposits or Treasury bills issued by RBI. Here, interest rate means the returns that depositors earn on depositing money in bank accounts as in reality they are lending money to banks, which is further used by banks to earn interest by lending some part of the deposited money to the needy borrowers. And this type of return is called Annual Percentage Yield (APY).
Post liberalisation, the stock market faced a high level of volatility as liberalisation led to various financial reforms like deregulation of interest rates, operational autonomy to public sector banks, market determined pricing of government securities and also high volatility is due to a much increase in foreign equity inflows. These reforms were initiated with the motive to improve the financial soundness and credibility of banks.
The volatility in the stock market is not due to any one factor, there are many macroeconomic variables which led to volatility. Some of the macroeconomic variables that has an impact on stock market are change in GDP, Inflation, CPI, WPI etc. But interest rate is one of the most important macroeconomic variable that effects stock market. As if interest rate falls, then the investment in stocks will rise leading to rise in stock prices due to investors would switch over to capital market from banks. So, we can say that stock returns are sensitive to the changes in interest rates over a time period. As a result, it has become extremely important for the policy formulators and investment companies to carefully analyze the changes that are happening in interest rates over a period of time.
To earn good returns on money invested in market, one have to be aware about every changes going on in the market as every change has some effect on the returns earned by investors. So, one have to be alert about all information available in market and smartly invest our funds in market to gain high returns.
There are several studies conducted to find the impact of interest rate on textile industry, construction sector industry and also on banking sector. But this study aims at examining the effect of interest rates on individual banks' stock returns listed on S and P BSE 500, S and P BSE 500 index as a whole and to examine volatility in banks' stock returns due to interest rate changes from initial years of introduction of S and P BSE 500 in 1999 till now i.e. March,2018
Figure above shows the yield of 91 days Treasury bill in India over the period of 8 years. It can be clearly seen from the graph that initially after year 2008 the interest rate was rising and rose upto 9.2% just before the year 2009 and then after that reached to its lowest point of the time period i.e. around 3.1% in year 2009. Then it began rising in following years and risen to maximum interest rates being offered on Treasury bills i.e. around 11%. By seeing the graph we can conclude that interest rate keeps on fluctuating and highly volatile in nature.
LITERATURE REVIEW:
Konstantinos Drakos (2001) explored the impact of changes in the interest rate in long run on the common stock returns of banks that are listed in the Athens Stock Exchange by employing a dataset that consisted of the daily closing of nine bank common stock prices by using two econometric strategies single equation framework and system theoretic approach. The findings of all the methods provided unswervingindication for substantial sensitivity of bank stock returns to interest rate changes.
John Beirne, Guglielmo Maria Caporale and Nicola Spagnolo (2008) mainly focused and analyzed the impact of market, interest rate, and exchange rate risk in Banking, Financial Services and Insurance sectors on stock returns in 16 countries, including various European economies, the US and Japan and they also used GARCHinmean model for testing causalityinmean and volatility spillovers. They found that different types of risk play a role in a minority of cases, with mixed signs. Finally, most cases of volatility spillovers are from market return to returns in the banking and insurance sector in European economies, though there are also some instances of interest rate and exchange rate spillovers, both in Europe and the US.
Kasman, S., Vardar, G., and Gokce, T. (2011) investigated the influence of interest rate and exchange rate changes over the period 1999–2009 on Turkish banks' stock returns by using estimation models like OLS and GARCH. He found that conditional bank stock return are greatly influenced by interest rate and exchange rate changes. This implies that market return plays an imperative role in shaping the subtleties of conditional return of bank stocks
Dewan MuktadirAlMukit (2013) inspected the consequence of the exchange rates and interest rates changes on stock market returns in Bangladesh considering the monthly time series data over the period of 1997 to 2010. Study by applying the Cointegration and Error Correction Model and analysis of Variance Decomposition and Granger causality test found that there exists a longterm relationship between the variables. Exchange rate has a positive and interest rate has a negative long run relationship with stock prices. Results of Granger causality testrevealed that there exists a unidirectional causality from market index to exchange rate and from interest rate to market index
Hieu Trung Tran (2013) adopted Two Factor Arbitrage Pricing Theory to explore the impact of changes in longterm interest rates on Financial Sector Index that includes top 10 US banks before and after financial crisis. And he found that there are strong and consistent evidences that volatility of bank common stock returns is very sensitive to the longterm interest rate movement and also changes in long term interest rates exhibited noteworthy impact on banks’ index returns in after crisis period than that before the financial crisis.
Xiangnan Meng and Xin Deng (2015) employed GARCH Model to examine the outcome of interest rate and foreign exchange rate changes on Chinese banks’ stock returns. The results suggested that changes in market and foreign exchange rates brings changes in banks’ stock returns, despite different reactions from different bank portfolios in regard to risks.
K. Latha, Sunita Gupta, RenuGhosh (2016) studied the association between interest rate movements and stock returns of textile sector in India.Results of GARCH (1, 1) model proved that there is a substantial impact of interest rate changes on stock returns of individual textile companies. Compared to interest rate changes, market returns have more power in influencing the returns of textile sector. Thisclearly indicates that a large portion of textile company’s stock returns is explained by the market risk alone.
Priti Verma (2016) using the multivariate version of Exponential Generalized Autoregressive Conditionally Heteroscedastic (EGARCH) model studied the mean, volatility spillovers and response asymmetries between shortterm and longterm interest rates, exchange rates and portfolios of banks in the U.S. Study proved the presence of volatility spillovers from short run to long run interest rates and exchange rates to banks.
OBJECTIVES:
· To examine the sensitivity of individual banks stock returns to interest rate changes
· To examine the sensitivity of S and P BSE 500 to interest rate changes.
· To examine the impact of interest rate volatility on stock returns of banking sector.
HYPOTHESIS:
The study seeks to achieve the abovementioned objectives by testing the following hypotheses:
H_{01}: There is no significant relationship between banking sector stock returns and interest rate changes.
H_{02}: There is no significant relationship between banking S and P BSE 500 returns and changes in interest rate.
H_{03}: There is no significant effect of interest rate volatility on stock returns volatility of banking sector in India.
DATA AND METHODOLOGY:
The interest rate sensitivity of banking sector stock returns is analyzed over a period starting from April 2000 to March 2018. This period is characterized by the deregulation of interest rate in India. Administrative restrictions on interest rates have been steadily eased since 1993.Sample for the study consists of 11 different banks listed on S and P BSE 500 index namely Bank of Baroda, State Bank of India, Corporation Bank, HDFC Bank, ICICI Bank, IDBI Bank, Bank of India, Federal Bank, Oriental Bank of India, Kotak Mahindra Bank, IndusInd Bank. Present study analyzed both the individual stock returns as well as index stock returns. The proxy used for market returns is return on S and P BSE 500 index. The interest rate variable used in the study is monthly implicit yield at cutoff price on 91 days Tbills, as it is the deregulated interest rate which is determined by the forces of demand and supply and collected from respective website of Reserve bank of India. Data for the stock prices and index values is collected from BSE official website.
Correlation test is used to test whether there is interdependencies between interest rates and banks stock returns. Then to test stationarity of individual time series Augmented DickeyFuller (ADF) test is used. And then Granger's causality test is done, followed by Johansen’s cointegration test to test whether tbill interest rates and bank stocks and index returns are cointegrated i.e. having long term association or not and then VAR Model. The volatility in banking stock returns and interest rate movements is examined by using GARCH (1, 1) model.
Johansen’s Cointegration Test:
The Johansen testis a procedure for testing cointegration of several, say k,I(1)time series. This test allows more than one cointegrating equation so is more generally applicable than the Engle–Granger test which is based on the Dickey–Fuller (or the augmented) test for unit roots n the residuals from a single (estimated) cointegrating relationship.
There are two types of Johansen test, either with trace or with eigenvalue, and the inferences might be a little bit different. The null hypothesis for the trace test is that the number of cointegration vectors is r=r*<k, vs. the alternative that r=k. Testing proceeds sequentially for r*=1, 2, etc. and the first nonrejection of the null is taken as an estimate of r. The null hypothesis for the "maximum eigenvalue" test is as for the trace test but the alternative is r=r*+1 and, again, testing proceeds sequentially for r*=1, 2, etc., with the first nonrejection used as an estimator for r.
The Johansen's cointegration test (Johansen and Juselius, 1990) has been applied to check whether the long run equilibrium relationship exists between the variables. The Johansen approach to cointegration test is based on two test statistics, viz., trace statistic, and maximum eigenvalue statistic
GARCH (1, 1) Model:
The Generalized Autoregressive Conditional Heteroscedasticity (GARCH) process, first introduced by Bollerslev (1986), is estimated. In Bollerslev GARCH model the conditional variance is a linear function of past squared innovations and previous own lags. The GARCH (1, 1) process is specified as follows:
_{ (2)}
(3)
Where R_{t} is the return of stock at time t; α is the intercept term; R_{m} is the return on the market index; ∆I_{t} is the changes in interest rate; σ_{t}^{2} is the conditional variance since it is oneperiod ahead estimate for the variance calculated based on any past information about volatility; α_{0}is the average volatility; α_{1} is the previous period’s residual variance the ARCH term and α_{2} is the previous period’s forecast variance the GARCH term. The GARCH specification requires that in the conditional variance equation, parameters α_{0, }α_{1 }and α_{2 }should be positive or nonnegative. The sum of (α_{1 }+ α_{2 }) is a measure of volatility persistence, closer to one the higher the persistence in volatility. Therefore, in a conditional variance equation the sum of α_{1 }and α_{2 }should be less than one to secure the covariance stationarity of the conditional variance. In case the sum is equal to one then the process is nonstationary and the Integrated GARCH model (IGARCH) describes its behaviour.
Lastly, again the following GARCH (1, 1) model is used to examine the effect of interest rate volatility on individual firm stock returns volatility.
(4)
(5)
Where all other coefficients are same as explained in above mentioned GARCH equations (2 and 3) and θ_{1} is the coefficient of interest rate volatility.
Granger Causality Test:
Granger (1969) and Sim (1972) were the ones who first developed Granger causality test to examine the application of causality in economics. Granger causality test is a technique for determining whether one variable is significant in predictingother variable. The standard Granger causality test seeks to determine whether past values of a variable helps to predict changes in another variable. Granger causality technique measures the information given by one variable in explaining the latest value of another variable. In addition, it also says that variable Y is Granger caused by variable X if variable X assists in predicting the value of variable Y. If this is the case, it means that the lagged values of variable X are statistically significant in explaining variable Y. The null hypothesis (H0) that we test in this case is that the X variable does not Granger cause variable Y and variable Y does not Granger cause variable X. In summary, one variable (X_{t}) is said to granger cause another variable (Y_{t}) if the lagged values of X_{t} can predict Y_{t} and viceversa.
ANALYSIS AND RESULTS:
Augmented Dickey Fuller Test (Or Unit Root Test):
It is a recognized fact that the financial time series contains a unit root. The data may be random walk or nonstationary. Test of unit root is necessary for S and P BSE 500 index, 91 day Treasury bill interest rates and individual banks' stock returns listed on this index, as the presence of unit root may give invalid inferences in the analysis. In other words, before testing the impact of the 91 days Indian Treasury bill interest rates on the S and P BSE 500 index and banking sector stock returns, it is necessary to test the presence of a unit root in the series. Augmented DickeyFuller (ADF) Test is the popular test for unit root testing of time series.
Unit Root Test (ADF):
The null and alternative hypotheses are as follows:
Null Hypothesis: ρ > 5% Unit root [Variable is not stationary]
Alternate Hypothesis: ρ < 5% No unit root [Variable is stationary]
Table 1: Augmented Dickey Fuller Test for stationarity
Variables 
t statistics 
pvalue 
BANK_OF_BARODA 
14.66132 
0.0000 
BANK_OF_INDIA 
15.05860 
0.0000 
CORPORATION_BANK 
14.52102 
0.0000 
FEDERAL_BANK 
14.57318 
0.0000 
HDFC_BANK 
14.43508 
0.0000 
ICICI_BANK 
12.40688 
0.0000 
IDBI_BANK 
13.92849 
0.0000 
INDUSIND_ BANK 
11.51054 
0.0000 
KOTAK_MAHINDRA_BANK 
12.10759 
0.0000 
ORIENTAL BANK OF COMMERC 
13.23310 
0.0000 
STATE_BANK_OF_INDIA 
14.57071 
0.0000 
S_P_BSE 500 
13.02666 
0.0000 
D(T_BILL_INTEREST_RATE) 
10.94545 
0.0000 
By looking at the results of ADF test in Table 1, it appears that all the variables i.e. BANK_OF_BARODA, BANK_OF_INDIA, CORPORATION_BANK, FEDERAL_BANK, HDFC_BANK, ICICI_BANK, IDBI_BANK, INDUSIND_BANK, KOTAK_MAHINDRA_BANK, ORIENTAL BANK OF COMMERC, STATE_BANK_OF_INDIA and S_P_BSE 500 at level as the pvalue for all stock returns is lesser than the critical value (5%) i.e. 0.00000<0.05. So we can reject the null hypothesis and we must therefore conclude that returns from these banks are stationary. Although, T_BILL_INTEREST_RATE is nonstationary at 5% level of significance, its first difference is found to be stationary.
Correlation Test:
Table 1: Correlation Test between Tbill interest rates and banks' returns

T Bill Interest Rate 
Bank of Baroda 
Bank of India 
T Bill Interest Rate 
1 
0,1358311 
0.1319003 
Bank of Baroda 
0.1358311 
1 
0.62554873 
Bank of India 
0.1319003 
0.62554873 
1 

T Bill Interest Rate 
Corporation Bank 
Federal Bank 
T Bill Interest Rate 
1 
0.1759728 
0.1393252 
Corporation Bank 
0.1759728 
1 
0.39223539 
Federal Bank 
0.1393252 
0.39223539 
1 

T Bill Interest Rate 
HDFC Bank 
ICICI Bank 
T Bill Interest Rate 
1 
0.0489763 
0.0554099 
HDFC Bank 
0.0489763 
1 
0.57886947 
ICICI Bank 
0.0554099 
0.57886947 
1 

T Bill Interest Rate 
IDBI Bank 
IndusInd Bank 
T Bill Interest Rate 
1 
0.1579071 
0.1435997 
IDBI Bank 
0.1579071 
1 
0.51765301 
IndusInd Bank 
0.1435997 
0.51765301 
1 

T Bill Interest Rate 
Kotak Mahindra Bank 
Oriental Bank of Commerce 
T Bill Interest Rate 
1 
0.00103913 
0.1531220 
Kotak Mahindra Bank 
0.00103913 
1 
0.39744320 
Oriental Bank of Commerce 
0.1531220 
0.39744320 
1 

T Bill Interest Rate 
S and P BSE 500 
State Bank of India 
T Bill Interest Rate 
1 
0,1833490 
0.1394255 
S and P BSE 500 
0.1833490 
1 
0.48957683 
State Bank of India 
0.1394255 
0.48957683 
1 
Correlation test was conducted between 11 banks stock returns listed on S and P BSE 500, SandP BSE 500 and 91days Indian Treasury bill interest rates. Correlation test can be seen as first indication of the existence of interdependency among time series.
From the derived statistics, we observe that coefficient of correlation between almost all banks' stocks returns and interest rate is negative i.e. there is a negative relationship between stocks and index returns and interest rates but there is a positive and weak relationship between Kotak Mahindra Bank returns and T bill interest rates as correlation coefficient is +0.00103913 i.e. if interest rate rises, then returns from this stock also rises. And also all the other variables have weak relationship with interest rates as there value of correlation coefficient lies near the value 0 like correlation coefficient of SandP BSE 500 and IndusInd bank are 0.1833490 and 0.1435997 respectively with tbill interest rates which shows weak relationship between them.
Granger’s Causality Test:
Table 2: Granger's causality test:
Dependent Variable: Interest rate 

Independent Variables 
F Value 
P Value 
S and P BSE 500 
0.89133 
0.4117 
State Bank of India 
2.10579 
0.1243 
Oriental Bank of Commerce 
1.99086 
0.1392 
Kotak Mahindra Bank 
0.10978 
0.8961 
IDBI Bank 
0.44915 
0.6388 
IndusInd Bank 
2.15355 
0.1186 
ICICI Bank 
1.11985 
0.3283 
HDFC Bank 
1.17151 
0.3119 
Federal Bank 
2.10579 
0.1243 
Corporation Bank 
1.17058 
0.3122 
Bank of India 
1.29222 
0.2768 
Bank of Baroda 
0.36647 
0.6936 
Independent Variable: Interest Rate 

Dependent Variables 
F Value 
P Value 
S and P BSE 500 
2.99675 
0.0521 
State Bank of India 
1.55302 
0.2140 
Oriental Bank of Commerce 
1.10326 
0.3337 
Kotak Mahindra Bank 
0.49505 
0.6103 
IDBI Bank 
2.33040 
0.0998 
IndusInd Bank 
2.20459 
0.1129 
ICICI Bank 
0.12159 
0.8856 
HDFC Bank 
0.49683 
0.6092 
Federal Bank 
1.55206 
0.2142 
Corporation Bank 
1.79889 
0.1680 
Bank of India 
0.85946 
0.4249 
Bank of Baroda 
2.08805 
0.1265 
In our empirical research, the Granger Causality test is conducted to study the causal relationship between the banking sector stocks and S and P BSE 500 returns and interest rates. By applying the ADF test is applied at level and first difference for different variables to obtain stationary variables before using them on Granger causality test.
Table above shows the Granger causality test results with a lag of 2 as the lag selection. We can conclude that there is no relationship between S and P BSE 500 returns and tbill interest rates so we cannot reject the null hypothesis i.e. S and P BSE 500 does not Granger Cause Tbill Interest rates or vice versa; as the pvalue is greater than the critical value (5%). Similarly, there is no relation between other 11 banks returns (i.e. Bank of Baroda, Bank of India, Corporation bank, Federal bank, HDFC Bank, IDBI Bank, State Bank of India, Kotak Mahindra Bank, IndusInd Bank, ICICI Bank and Oriental Bank of Commerce) and t bill interest rates.
Johansen's Cointegration Test:
Bank of Baroda:
Table 3: Unrestricted Cointegration Rank Test (Trace)
Hypothesized No. of CE(s) 
Trace Statistic 
0.05 Critical Value 
Prob** 
None* 
79.06125 
15.49471 
0.0000 
At most 1* 
29.13495 
3.841466 
0.0000 
Table 4: Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized No. of CE(s) 
Max Eigen Statistic 
0.05 Critical Value 
Prob** 
None* 
49.92630 
14.26460 
0.0000 
At most 1* 
29.13495 
3.841466 
0.0000 
By analyzing the Trace test above in Table 3 on Bank of Baroda, we found out that the trace statistics is greater than 0.05 Critical value and also pvalue is 0.0000 at both the null hypothesis i.e. there is no cointegrating equation between Bank of Baroda stock returns and T bill interest rates and there is at most one cointegrating equation between the two variables. So, as a result we can reject both the null hypothesis and conclude that there are more than 1 cointegrating equation i.e. there are 2 cointegrating equations at 5% significance level from the results we obtained from Eviews.
These cointegrating equations means interest rates and banks stock returns have long term association or relationship and the tested series will not drift apart in the longterm, and will revert to equilibrium levels following any shortterm drift that may take place.
In order to confirm the results of the Johansen’s Trace test, we also display the results of the Maximum Eigenvalue Test. In Maximum Eigenvalue Test also we found out that MaxEigen statistics is greater than 0.05 Critical value and also pvalue is 0.0000 at both the null hypothesis. This means that there is more than 1 cointegrating equations and as per the results obtained through Maximum Eigenvalue test, there are 2 cointegrating equations at 5% significance level confirming Trace Test. Therefore, these two tests confirm a cointegrating relationship between the two variables.
Bank of India
Table 5: Unrestricted Cointegration Rank Test (Trace)
Hypothesized No. of CE(s) 
Trace Statistic 
0.05 Critical Value 
Prob** 
None* 
82.38723 
15.49471 
0.0000 
At most 1* 
38.28112 
3.841466 
0.0000 
Table 6: Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized No. of CE(s) 
MaxEigen Statistic 
0.05 Critical Value 
Prob** 
None* 
44.10611 
14.26460 
0.0000 
At most 1* 
38.28112 
3.841466 
0.0000 
By looking at the results of the Trace test in Table 5 between Bank of India and T bill interest rates, we first confirmed whether the trace statistics is greater than 0.05 Critical value and also pvalue is less than 0.05, as these two criteria serves as a basis to reject the both null hypothesis given above i.e. there is no cointegrating equation between Bank of India stock returns and T bill interest rates and there is at most one cointegrating equation between the two variables. And the results fulfilled both the criteria to reject null hypothesis and to conclude that there are more than 1 cointegrating equation i.e. there are 2 cointegrating equations at 5% significance level as per the results obtained from Eviews.
These cointegrating equations means interest rates and bank's stock returns have long term association or relationship and the tested series will not drift apart in the longterm, and will revert to equilibrium levels following any shortterm drift that may take place.
In order to confirm the results of the Johansen’s Trace test, we also displayed the results of the Maximum Eigenvalue Test. In Maximum Eigenvalue Test also we found out that MaxEigen statistics is greater than 0.05 Critical value and also pvalue is 0.0000 at both the null hypothesis. This means that there is more than 1 cointegrating equations and as per the results obtained through Maximum Eigenvalue test, there are 2 cointegrating equations at 5% significance level confirming Trace Test. Therefore, these two tests confirm a cointegrating relationship between the two variables.
ICICI Bank:
Table 7: Unrestricted Cointegration Rank Test (Trace)
Hypothesized No. of CE(s) 
Trace Statistic 
0.05 Critical Value 
Prob** 
None* 
79.69772 
15.49471 
0.0000 
At most 1* 
37.67059 
3.841466 
0.0000 
Table 8: Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized No. of CE(s) 
MaxEigen Statistic 
0.05 Critical Value 
Prob** 
None* 
42.02713 
14.26460 
0.0000 
At most 1* 
37.67059 
3.841466 
0.0000 
On analyzing the results obtained from Trace test conducted above in Table 7 on ICICI Bank stock returns and T bill interest rate, we found out that the trace statistics is greater than 0.05 Critical value and also pvalue is 0.0000 at both the null hypothesis i.e. there is no cointegrating equation between ICICI Bank stock returns and T bill interest rates and there is at most one cointegrating equation between the two variables. So, as a result we can reject both the null hypothesis and conclude that there are more than 1 cointegrating equation i.e. there are 2 cointegrating equations at 5% significance level from the results obtained from Eviews.
In order to confirm the results of the Johansen’s Trace test, we also analyzed the results of the Maximum Eigenvalue Test. In Maximum Eigenvalue Test also we found out that MaxEigen statistics is greater than 0.05 Critical value and also pvalue is 0.0000 at both the null hypothesis. This means that there is more than 1 cointegrating equations and as per the results obtained through Maximum Eigenvalue test, there are 2 cointegrating equations at 5% significance level confirming Trace Test. Therefore, these two tests confirm a cointegrating relationship between the two variables.
So, at last we can conclude that ICICI Bank stock returns and T bill interest rates have a long term association or relationship with each other as they are 2 cointegrating equations found out between these two variables.
Corporation Bank:
Table 9: Unrestricted Cointegration Rank Test (Trace)
Hypothesized No. of CE(s) 
Trace Statistic 
0.05 Critical Value 
Prob** 
None* 
83.55963 
15.49471 
0.0000 
At most 1* 
32.89852 
3.841466 
0.0000 
Table 10: Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized No. of CE(s) 
MaxEigen Statistic 
0.05 Critical Value 
Prob** 
None* 
50.66111 
14.26460 
0.0000 
At most 1* 
32.89852 
3.841466 
0.0000 
In order to find out that whether there is cointegration between Corporation Bank returns and T bill interest rates, Johansen's cointegration test is conducted. Johansen's cointegration test consists of two tests within it i.e. Trace Test and Maximum Eigenvalue Test. If both the tests confirm of cointegration relationship, then only we can say two variables used in the study are cointegrated.
By analyzing the Trace test in Table 9, we found out that the trace statistics is greater than 0.05 Critical value and also pvalue is 0.0000 at both the null hypothesis i.e. there is no cointegrating equation between Corporation Bank stock returns and T bill interest rates and there is at most one cointegrating equation between the two variables. So, as a result we can reject both the null hypothesis and conclude that there are more than 1 cointegrating equation i.e. there are 2 cointegrating equations at 5% significance level from the results we obtained from Eviews.
These cointegrating equations means interest rates and bank stock returns have long term association or relationship and the tested series will not drift apart in the longterm, and will revert to equilibrium levels following any shortterm drift that may take place.
To confirm the results of the Johansen’s Trace test, we also displayed the results of the Maximum Eigenvalue Test. In Maximum Eigenvalue Test also we found out that MaxEigen statistics is greater than 0.05 Critical value and also pvalue is 0.0000 at both the null hypothesis. This means that there is more than 1 cointegrating equations and as per the results obtained through Maximum Eigenvalue test, there are 2 cointegrating equations at 5% significance level confirming Trace Test. Therefore, these two tests confirm a cointegrating relationship between the two variables.
And, we can say that Corporation Bank stock returns and T bill interest rates are cointegrated.
Federal Bank
Table 11: Unrestricted Cointegration Rank Test (Trace)
Hypothesized No. of CE(s) 
Trace Statistic 
0.05 Critical Value 
Prob** 
None* 
72.78780 
15.49471 
0.0000 
At most 1* 
30.87323 
3.841466 
0.0000 
Table12: Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized No. of CE(s) 
MaxEigen Statistic 
0.05 Critical Value 
Prob** 
None* 
41.91457 
14.26460 
0.0000 
At most 1* 
30.87323 
3.841466 
0.0000 
By analyzing the Trace test under Johansen's cointegration test in Table 11, we found out that the trace statistics is greater than 0.05 Critical value and also pvalue is 0.0000 at both the null hypothesis i.e. there is no cointegrating equation between Federal Bank stock returns and T bill interest rates and there is at most one cointegrating equation between the two variables. So, we can reject both the null hypothesis and conclude that there are more than 1 cointegrating equation i.e. there are 2 cointegrating equations at 5% significance level from the results we obtained from Eviews.
These cointegrating equations means interest rates and bank stock returns have long term association or relationship and the tested series will not drift apart in the longterm, and will revert to equilibrium levels following any shortterm drift that may take place.
In order to confirm the results of the Johansen’s Trace test, we also display the results of the Maximum Eigenvalue Test. In Maximum Eigenvalue Test also we found out that MaxEigen statistics is greater than 0.05 Critical value and also pvalue is 0.0000 at both the null hypothesis. This means that there is more than 1 cointegrating equations and as per the results obtained through Maximum Eigenvalue test, there are 2 cointegrating equations at 5% significance level confirming Trace Test. Therefore, these two tests confirm a cointegrating relationship between the two variables.
That means that Federal Bank stock returns and interest rates have a long term relationship whether positive or negative but the change in one of them will have an impact on other in long term.
HDFC Bank:
Table 13: Unrestricted Cointegration Rank Test (Trace)
Hypothesized No. of CE(s) 
Trace Statistic 
0.05 Critical Value 
Prob** 
None* 
78.57591 
15.49471 
0.0000 
At most 1* 
33.17764 
3.841466 
0.0000 
Table 14: Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized No. of CE(s) 
MaxEigen Statistic 
0.05 Critical Value 
Prob** 
None* 
45.39827 
14.26460 
0.0000 
At most 1* 
33.17764 
3.841466 
0.0000 
As per the results obtained from Johansen's cointegration Trace test between HDFC Bank stock returns and interest rates, we found out that the trace statistics is greater than 0.05 Critical value and also pvalue is 0.0000 at both the null hypothesis i.e. there is no cointegrating equation between HDFC Bank stock returns and T bill interest rates and there is at most one cointegrating equation between the two variables. So, as a result we can reject both the null hypothesis and conclude that there are more than 1 cointegrating equation i.e. there are 2 cointegrating equations at 5% significance level from the results obtained from Eviews.
These cointegrating equations means interest rates and HDFC Bank stock returns have long term association or relationship and the tested series will not drift apart in the longterm, and will revert to equilibrium levels following any shortterm drift that may take place.
In order to confirm the results of the Johansen’s Trace test, we also display the results of the Maximum Eigenvalue Test. In Maximum Eigenvalue Test also we found out that MaxEigen statistics is greater than 0.05 Critical value and also pvalue is 0.0000 at both the null hypothesis. This means that there is more than 1 cointegrating equations and as per the results obtained through Maximum Eigenvalue test, there are 2 cointegrating equations at 5% significance level confirming Trace Test. Therefore, these two tests confirm a cointegrating relationship between the two variables.
IDBI Bank:
Table 15: Unrestricted Cointegration Rank Test (Trace)
Hypothesized No. of CE(s) 
Trace Statistic 
0.05 Critical Value 
Prob** 
None* 
77.92084 
15.49471 
0.0000 
At most 1* 
32.92994 
3.841466 
0.0000 
Table 16: Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized No. of CE(s) 
MaxEigen Statistic 
0.05 Critical Value 
Prob** 
None* 
44.99090 
14.26460 
0.0000 
At most 1* 
32.92994 
3.841466 
0.0000 
By looking at the results of the Trace test in Table 15 between IDBI Bank stock returns and T bill interest rates, we first checked whether the trace statistics is greater than 0.05 Critical value and also pvalue is less than 0.05, as these two criteria serves as a basis to reject the both null hypothesis given above i.e. there is no cointegrating equation between IDBI Bank stock returns and T bill interest rates and there is at most one cointegrating equation between the two variables. And the results fulfilled both the criteria to reject null hypothesis and to conclude that there are more than 1 cointegrating equation i.e. there are 2 cointegrating equations at 5% significance level as per the results obtained from Eviews.
These cointegrating equations means interest rates and banks stock returns have long term association or relationship and the tested series will not drift apart in the longterm, and will revert to equilibrium levels following any shortterm drift that may take place.
In order to confirm the results of the Johansen’s Trace test, we also display the results of the Maximum Eigenvalue Test. In Maximum Eigenvalue Test also we found out that MaxEigen statistics is greater than 0.05 Critical value and also pvalue is 0.0000 at both the null hypothesis. This means that there is more than 1 cointegrating equations and as per the results obtained through Maximum Eigenvalue test, there are 2 cointegrating equations at 5% significance level confirming Trace Test. Therefore, these two tests confirm a cointegrating relationship between the two variables.
And finally we can say that IDBI Bank stock returns and interest rates have a long term relationship between them.
IndusInd Bank:
Table 17: Unrestricted Cointegration Rank Test (Trace)
Hypothesized No. of CE(s) 
Trace Statistic 
0.05 Critical Value 
Prob** 
None* 
78.60990 
15.49471 
0.0000 
At most 1* 
29.65193 
3.841466 
0.0000 
Table 18: Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized No. of CE(s) 
MaxEigen Statistic 
0.05 Critical Value 
Prob** 
None* 
48.95797 
14.26460 
0.0000 
At most 1* 
29.65193 
3.841466 
0.0000 
To know about the long term relationship between IndusInd Bank stock returns and interest rates, we conducted the Johansen's cointegration Trace test and results are shown above in Table 16, on the basis of which we can say that the trace statistics is greater than 0.05 Critical value and also pvalue is 0.0000 at both the null hypothesis i.e. there is no cointegrating equation between IndusInd Bank stock returns and T bill interest rates and there is at most one cointegrating equation between the two variables. So, now we can reject both the null hypothesis and conclude that there are more than 1 cointegrating equation i.e. there are 2 cointegrating equations at 5% significance level from the results we obtained from Eviews.
These cointegrating equations means interest rates and bank stock returns have long term association or relationship and the tested series will not drift apart in the longterm, and will revert to equilibrium levels following any shortterm drift that may take place.
In order to confirm the results of the Johansen’s Trace test, we also displayed the results of the Maximum Eigenvalue Test in Table 17. In Maximum Eigenvalue Test also we found out that MaxEigen statistics is greater than 0.05 Critical value and also pvalue is 0.0000 at both the null hypothesis. This means that there is more than 1 cointegrating equations and as per the results obtained through Maximum Eigenvalue test, there are 2 cointegrating equations at 5% significance level confirming Trace Test. Therefore, these two tests confirm a cointegrating relationship between the two variables.
Kotak Mahindra Bank:
Table 19: Unrestricted Cointegration Rank Test (Trace)
Hypothesized No. of CE(s) 
Trace Statistic 
0.05 Critical Value 
Prob** 
None* 
73.24902 
15.49471 
0.0000 
At most 1* 
25.85908 
3.841466 
0.0000 
Table 20: Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized No. of CE(s) 
MaxEigen Statistic 
0.05 Critical Value 
Prob** 
None* 
47.38994 
14.26460 
0.0000 
At most 1* 
25.85908 
3.841466 
0.0000 
By looking at the results of Johansen's cointegration Trace test between Kotak Mahindra Bank stock returns and 91 days tbill interest rates above in Table 19, we found out that the trace statistics is greater than 0.05 Critical value and also pvalue is 0.0000 at both the null hypothesis i.e. there is no cointegrating equation between Kotak Mahindra Bank stock returns and T bill interest rates and there is at most one cointegrating equation between the two variables. As a result we can reject both the null hypothesis and conclude that there are more than 1 cointegrating equation i.e. there are 2 cointegrating equations at 5% significance level from the results obtained from Eviews. So, we can definitely say that these two have a long term association between them but to confirm the result of the following, analysis of Johansen's cointegration Maximum Eigenvalue test is also important which is shown in Table 19.
These cointegrating equations means interest rates and banks stock returns have long term association or relationship and the tested series will not drift apart in the longterm, and will revert to equilibrium levels following any shortterm drift that may take place.
In Maximum Eigenvalue Test also we found out that MaxEigen statistics is greater than 0.05 Critical value and also pvalue is 0.0000 at both the null hypothesis. This means that there is more than 1 cointegrating equations and as per the results obtained through Maximum Eigenvalue test, there are 2 cointegrating equations at 5% significance level confirming Trace Test. Therefore, these two tests confirm a cointegrating relationship between the two variables.
Oriental Bank of Commerce:
Table 21: Unrestricted Cointegration Rank Test (Trace)
Hypothesized No. of CE(s) 
Trace Statistic 
0.05 Critical Value 
Prob** 
None* 
69.11267 
15.49471 
0.0000 
At most 1* 
27.73966 
3.841466 
0.0000 
Table 22: Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized No. of CE(s) 
MaxEigen Statistic 
0.05 Critical Value 
Prob** 
None* 
41.37301 
14.26460 
0.0000 
At most 1* 
27.73966 
3.841466 
0.0000 
In order to examine whether there is long term association between Oriental Bank of Commerce stock returns and t bill interest rates, we perform Johansen's Cointegration test which consists of two testsTrace test and Maximum Eigenvalue test. Now, we will first analyze the Trace test above in Table 21, and we found out that the trace statistics is greater than 0.05 Critical value and also pvalue is 0.0000 at both the null hypothesis i.e. there is no cointegrating equation between Oriental Bank of Commerce stock returns and T bill interest rates and there is at most one cointegrating equation between the two variables. So, as a result we can reject both the null hypothesis and conclude that there are more than 1 cointegrating equation i.e. there are 2 cointegrating equations at 5% significance level from the results we obtained from Eviews.
In order to confirm the results of the Johansen’s Trace test, secondly we will perform Maximum Eigenvalue shown in Table 22. And in Maximum Eigenvalue Test also we found out that MaxEigen statistics is greater than 0.05 Critical value and also pvalue is 0.0000 at both the null hypothesis. This means that there is more than 1 cointegrating equations and as per the results obtained through Maximum Eigenvalue test, there are 2 cointegrating equations at 5% significance level confirming Trace Test. Therefore, these two tests confirm a cointegrating relationship between the two variables.
Lastly, we can conclude that Oriental Bank of Commerce stock returns and 91 days tbill interest rates are cointegrated.
S and P BSE 500:
Table 23: Unrestricted Cointegration Rank Test (Trace)
Hypothesized No. of CE(s) 
Trace Statistic 
0.05 Critical Value 
Prob** 
None* 
78.79032 
15.49471 
0.0000 
At most 1* 
30.95508 
3.841466 
0.0000 
Table 24: Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized No. of CE(s) 
MaxEigen Statistic 
0.05 Critical Value 
Prob** 
None* 
47.83524 
14.26460 
0.0000 
At most 1* 
30.95508 
3.841466 
0.0000 
By analyzing the Trace test between S and P BSE 500 and interest rates above in Table 23 under Johansen's Cointegration test, we found out that the trace statistics is greater than 0.05 Critical value and also pvalue is 0.0000 at both the null hypothesis i.e. there is no cointegrating equation between S and P BSE 500 index returns and T bill interest rates and there is at most one cointegrating equation between the two variables. So, as a result we can reject both the null hypothesis and conclude that there are more than 1 cointegrating equation i.e. there are 2 cointegrating equations at 5% significance levelfrom the results we obtained from Eviews.
These cointegrating equations means interest rates and index returns have long term association or relationship and the tested series will not drift apart in the longterm, and will revert to equilibrium levels following any shortterm drift that may take place.
In order to confirm the results of the Johansen’s Trace test, we also display the results of the Maximum Eigenvalue Test. In Maximum Eigenvalue Test also we found out that MaxEigen statistics is greater than 0.05 Critical value and also pvalue is 0.0000 at both the null hypothesis. This means that there is more than 1 cointegrating equations and as per the results obtained through Maximum Eigenvalue test, there are 2 cointegrating equations at 5% significance level confirming Trace Test. Therefore, these two tests confirm a cointegrating relationship between the two variables.
Thus, we can conclude that S and P BSE 500 index and interest rates also has a long term association with each other.
State Bank of India
Table 25: Unrestricted Cointegration Rank Test (Trace)
Hypothesized No. of CE(s) 
Trace Statistic 
0.05 Critical Value 
Prob** 
None* 
72.78037 
15.49471 
0.0000 
At most 1* 
30.86236 
3.841466 
0.0000 
Table 26: Unrestricted Cointegration Rank Test (Maximum Eigenvalue)
Hypothesized No. of CE(s) 
MaxEigen Statistic 
0.05 Critical Value 
Prob** 
None* 
41.91801 
14.26460 
0.0000 
At most 1* 
30.86236 
3.841466 
0.0000 
By analyzing the Trace test between State Bank of India stock returns and 91 days T bill interest rates above in Table 25 under Johansen’s cointegration test, we found out that the trace statistics is greater than 0.05 Critical value and also pvalue is 0.0000 at both the null hypothesis i.e. there is no cointegrating equation between State Bank of India stock returns and T bill interest rates and there is at most one cointegrating equation between the two variables. So, as a result we can reject both the null hypothesis and conclude that there are more than 1 cointegrating equation i.e. there are 2 cointegrating equations at 5% significance level from the results we obtained from Eviews.
In order to confirm the results of the Johansen’s Trace test, we also display the results of the Maximum Eigenvalue Test. In Maximum Eigenvalue Test also we found out that MaxEigen statistics is greater than 0.05 Critical value and also pvalue is 0.0000 at both the null hypothesis. This means that there is more than 1 cointegrating equations and as per the results obtained through Maximum Eigenvalue test, there are 2 cointegrating equations at 5% significance level confirming Trace Test. Therefore, these two tests confirm a cointegrating relationship between the two variables.
Thus, State Bank of India stock returns and interest rates are cointegrated representing there association for long period of time
GARCH (1, 1) Model
Table 27: Estimation of individual Banks conditional stock returns with GARCH (1, 1) model
Banks 
ϲ 
α 
Β 
α + β 
Adjusted R^{2} 
Bank of Baroda 
53.18296 (0.1723) 
0.028012 (0.1908) 
0.746924 (0.0001) 
0.718912 
0.012341 
Bank of India 
25.07990 (0.3397) 
0.077052 (0.2023) 
0.796026 (0.0000) 
0.873078 
0.012241 
Corporation Bank 
19.66457 (0.0218) 
0.021476 (0.0190) 
0.903195 (0.0000) 
0.881719 
0.024690 
Federal Bank 
459.3485 (0.0000) 
0.049780 (0.0249) 
0.854490 (0.0000) 
0.80471 
0.012869 
HDFC Bank 
6.603240 (0.0025) 
0.012940 (0.0000) 
0.945291 (0.0000) 
0.932351 
0.006753 
ICICI Bank 
0.619479 (0.4746) 
0.031003 (0.0000) 
1.038101 (0.0000) 
1.007098 
0.013377 
IDBI Bank 
16.61563 (0.5424) 
0,007239 (0.6507) 
0.928425 (0.0000) 
0.935664 
0.020092 
IndusInd Bank 
0.957461 (0.6546) 
0.043653 (0.0020) 
0.940622 (0.0000) 
0.984275 
0.014340 
Kotak Mahindra Bank 
81.05523 (0.0000) 
0.411744 (0.0000) 
0.422210 (0.0000) 
0.833954 
0.020609 
Oriental Bank of Commerce 
35.34770 (0.0943) 
0.121593 (0.0095) 
0.695387 (0.0000) 
0.81698 
0.018138 
State Bank of India 
459.3312 (0.0000) 
0.049789 (0.0249) 
0.854369 (0.0000) 
0.80458 
0.012897 
* Value in parenthesis represents probability values
Table 27 presents the results of GARCH (1, 1) model in which sensitivity of banks conditional stock returns is examined with market returns and interest rate changes. α, measuring the effect of market returns on conditional stock returns which represents ARCH effect is statistically significant in 8 out of 11 cases whereas β the coefficient of interest rate sensitivity that represents GARCH effect is negative in 2 cases and statistically significant in all the 11 cases.
It can be observed that the impact of market returns on banks conditional stock returns is significant in 8 out of 11 cases and coefficient of interest rate sensitivity is significant in all the cases, so we cannot say that any one of them has a greater impact on stock returns. β the coefficient of interest rate sensitivity and represents GARCH effect is statistically significant in case of all the cases, that means interest rate sensitivity has a greater impact on banking sector stock returns. The possible reason for this may be that large amount of sums are required for investment in this industry. If risk free interest rate increases in the market, this will led to increase of investment in Fixed Deposits, Government bonds and securities and treasury bills , which will led to fall in demand of stocks and as a result stock returns will fall. It can be seen from the results that the magnitude of interest rate risk is very high on banks as total of α and β coefficient values are very close to 1 in all cases that means there a very strong sensitivity exists between the conditional stock returns and interest rate variable for banking sector in India.
In GARCH model the sum of the ARCH and GARCH effect is close to 1 representing volatility persistence which also holds true. Therefore, shocks to stock returns of banks are highly persistent and volatile to interest rate changes.
Table 28: Estimation of Average Banks conditional stock returns with GARCH (1, 1) model
Portfolio 
ϲ 
Α 
β 
α + β 
Adjusted R^{2} 
Banks Returns 
10.33479 (0.1488) 
0.027780 (0.1924) 
0.871421 (0.0000) 
0.899201 
0.020199 
Table 29: Estimation of Index conditional returns with GARCH (1, 1) model
Index 
ϲ 
Α 
β 
α + β 
Adjusted R^{2} 
S and P BSE 500 
1.301690 (0.3023) 
0.092655 (0.0096) 
0.877679 (0.0000) 
0.970334 
0.025103 
It is found out from the results derived, that both coefficient values of α and β values are positive and their total is greater than 0.50 and near to 1 which shows high level of persistence and volatility to interest rate changes. But GARCH effect is significant as p value is lesser than critical value (5%) but ARCH effect i.e. α is not significant. This means that high interest volatility led to volatility of banks' stock returns.
It is found out from the results derived, that both α and β values are positive and are significant as pvalue is lesser than 0.05. That is both ARCH and GARCH effect have a significant impact on volatility of S and P BSE 500 index. And total of α and β is highly significant as it is 0.970334 as it is highly close to 1 which shows interest rate sensitivity causes high level volatility in stock returns.
CONCLUSION:
The results of the study gives a empirical evidence that interest rate exhibits significant impact on stock returns of banking sector in India as interest rate changes have a negative effect on the stock returns which was also found out through correlation test, that there is negative relationship of interest rates with banks' stock returns i.e. if interest rate rises, then the investors will shift from capital market to banks, which will led to fall in stock prices due to fall decrease in the demand of shares. And also it was found out through GARCH model that the interest rate volatility led to banking sector stock returns volatility. And also Johansen's cointegration test shows that interest rates and banks stock returns have a long term association with each other.
The findings of the study depicts significant impact of interest rate changes on stock returns mplying that a major portion of bank’s stock returns is explained by the interest rate risk. Results of the present study lend support to the Stone (1974) twoindex model and attest the presence of interest rate as an extra factor in determining stock returns. Apart from interest rate there are also other macroeconomic variables that have a impact on stock returns like inflation, GDP and CPI should also be considered by investors and policy formulators.
The results derived from this study will prove to be useful and assist bank managers to frame risk management strategies and market participants to design investing and hedging strategies, but will also provide useful information for regulators in formulating policies.
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Websites and links:
· http://www.bseindia.com/markets/equity/EQReports/StockPrcHistori.aspx?expandable=7andflag=0
· https://www.rbi.org.in/scripts/annualPublications.aspx?head=Handbook%20of%20Statistics%20on%20Indian%20Economy
Received on 07.01.2019 Modified on 16.02.2019
Accepted on 18.03.2019 ©AandV Publications All right reserved
Res. J. Humanities and Social Sciences. 2019; 10(2): 359370.
DOI: 10.5958/23215828.2019.00062.7