Risk Analysis of Scheduled Commercial Banks of India

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Decision, Vol. 37, No.3,December, 2010

Risk Analysis of Scheduled Commercial Banks of India

Kalpataru Bandopadhyay

Souvik Kumar Bandyopadhyay

Introduction

Risk might be defined as uncertainties arising out of adverse impact against the expectedoutcome on the basis of planned objective. The standalone profitability of a business entityis not very meaningful unless it is accounted for along with risk. Banks are no exception.

Banks are basically financial intermediaries which are confronted with several types of risk.After economic liberalisation, banks were open to discriminate pricing policies and offereddifferential products which carry different types of risks not dealt with by the banks previously.We understand that a transition of risk profile of the banks has taken place and thus, theimportance of risk management and risk analysis has increased. Again, for the implementationof BASEL II, a robust integrated risk management system should be required in place for eachbank.

In the year 2000, there were one hundred and two scheduled commercial banks comprisingState Bank of India (SBPSU) and its seven subsidiaries, nineteen Public Sector Banks (PSU),forty-two foreign banks and thirty-three Indian private banks. However, as on 31st March,2007 only eighty eight banks reported to the Reserve Banks of India.

During the period, the group comprising of SBPSU and PSU has increased from twenty-seven

to twenty eight due to the inclusion of IDBI Ltd. On the other hand, in India, the number ofNew Private Banks (NPVT), Old Private Bank (OPVT) and Foreign Banks (FOR) reduced byfifteen. There were a few cases where merger like Global Trust Banks and ANZ Grinlays had

Overall risk of a bank depends on many factors. In this paper, we investigate how group characteristics andbank-wise individual factors (credit policy, extent of hedging) influence the risk of a bank and how theyvary with time. Initially we used coefficient of variation and K-means cluster analysis to explore the natureof the data. Further, we attempted a mixed modeling strategy to model the net interest margin values,treated as a surrogate of the exposed risk of a bank. The estimates of mixed model suggested that although

there was an observed group-wise disparity in the level of risk, risk is more sensitive towards the individualcharacteristics of the bank. It was also observed in the study that the temporal effect on group-wisecharacteristics and individual bank characteristics is minimal in determining their influence on the exposedrisk of a bank. The study indirectly demonstrates why Indian banks are almost unperturbed even in thebackdrop of collapse of big banks in US and Europe.

Key words: Coefficient of Variation (C.V), cluster analysis, mixed model, net interest margin (NIM), PanelData, Risk

Kalpataru Bandopadhyay, Natunpally East, Ambagan, P.O. & Dist: Burdwan 713101, West Bengal(Email: [email protected])

Souvik Kumar bandyopadhyay, Dept. of Statistics, Memari College, Burdwan, West Bengal(Email: [email protected])
mailto:[email protected])mailto:[email protected])mailto:[email protected])mailto:[email protected])


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Risk Analysis of Scheduled Commercial Banks of India 49


taken place but those do not explain the whole situation. Again, the mergers in both theaforementioned cases were caused by inefficiency in operation. The other banks that havenot reported their accounts for the year 2006-07 to the regulatory apex body, which is mandatory,either stopped working in India or their accounts were not in a position to be submitted evenup to 31stMarch, 2008. Thus, from the reduction in number of banks we can perceive that riskintrinsically lies in the banking business.

We have conducted a comparative analysis of total risk of bank at group level as well asindividual level on the basis of study of variation in Net interest margin. The paper is organizedas follows. In the following part of this section, we define the various facets of risks associatedwith banking environment. In the next section, we present a literature review of the work donein this area both in the context of India as well as internationally. The third section describesthe data and the methodology as well as the analysis used. Interpretations are discussed inthe fourth section followed by a conclusion.

Comparative Analysis

The assessment of risk in absolute terms would not be very meaningful. In fact, Beckers(1998) commented that risk is always a relative concept and managers are continuouslyevaluated against their peer group. The absolute risk analysis leads to risk inherent in thebenchmark and the active risk added on the benchmark by the respective manager. So, theabsolute quantification of risk turns out to be unreliable. Thus, an attempt has been made tocompare the risks among scheduled commercial banks of India.

A bank has to deal with various types of risks. These are broadly divided into credit risk,market risk, liquidity risk, operational risk etc. Again, all these risks club into overall risk ortotal risk.

Total Risk and Risk Philosophy

A bank like any other business entity sets its risk tolerance according to its risk philosophy.A firm should ensure that plans related to risk-bearing activities coincide with or complementother aspects of corporate business. The actual management of risks tends to occur at a desklevel or business unit level. A firm should review the totality of its risk when seeking to defineits risk philosophy. By verifying how total risks might act to affect total operations, it coulddefine its tolerance level with greater accuracy and can define risk tolerance in different unitsand functional levels. A review of risk at individual enterprise level can reveal important macroconsiderations during a critical point in the risk philosophy phase (Banks, 2002).

There are two broad approaches for developing risk management strategies (Hull, 2007). Oneapproach is to identify risks one by one and handle each separately. There are various typesof risks a bank has to deal with. These are broadly divided into credit risk, market risk, liquidityrisk, operational risk etc. Again, all the risks can be divided into further sub-classes. This issometimes referred to asrisk decomposition. There are a number of techniques to assess thedifferent kind of risks. The other approach for framing risk management is called riskaggregation. Sadakkadulla (2001) conducted a theoretical study on an integrated riskmeasurement framework. He arithmetically added three types of risk, viz. market risk, credit


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risk and operational risk to arrive at the overall risk estimate. In USA, Federal Reserve hasapproved the procedure for adoption for internal risk management. However, Dembo (1998)observed that one cannot take Risk Metrics value and add it to Credit Metrics value andobtain a risk statistic that combines credit and market risk. He observed that the methodologiesfor generating scenarios might not be compatible. Kumar et al. (2007) commented that differentcategories of risk are interdependent and overlapping. As such the risks must not be viewedand assessed in isolation not only because a single transaction might have a number of risksassociated with it but also because one type of risk triggers other risks. In such a casecombination of individual risk might not be exactly the same as the overall risk of bankingbusiness. Again, arithmetical aggregation does not take into account the power ofdiversification arising out of existence of negative correlation among different kinds of risks.

We do not subscribe to the idea of combining different functional risk to find out total risk.Rather, instead of managing the individual functional risk on a standalone basis, a bankshould monitor its individual risk in such a manner that the overall risk does not go beyondcontrol. Here, in this paper, an attempt has been made to compare the total risk of differentscheduled commercial banks. The total risk could also be analysed from the viewpoint ofvarious layer or levels.

Levels of Risk

The existing literature has assessed risk at the micro level i.e. at the bank level. These studieshave carried an analysis taking one particular aspects of risk. In this paper, we observe riskfrom the macro level and then analyze at the bank level. The risk of an individual bank couldbe divided into four levels viz. risk at global level, risk at country level, risk at group level and

risk at individual level.

In fact, r =f (g, s, c, i)

where,

r = Overall risk of a bank

g = Global level risk

s = Sovereign risk

c = Risk characterised by different group or category

i = Risk specific to an individual bank

There is hardly any economy in the world which is now insulated from global economicmovement. The global level risk is almost equivalent for all the banks in India. The sovereignrisk is almost equivalent for all categories of banks in India except for the foreign banks whoseimpact on sovereign risk might be less because of their operation networked in differentcountries. However, Choi et. al. (2006) found that geographical diversification does not affectrisk of a bank. The different group of banks are promoted and managed by different kinds ofpromoters. So, it is possible that they have different philosophy as far as risk appetite isconcerned.


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Laeven & Levine (2006) observed that their sample of the largest banks in each countrydemonstrates that ownership and management structure exerts influence on risk taking. Wefound that several components like the unsecured advances to total advances, unapprovedsecurities to total investment, economic equity ratio and unsecured advances to total advancesare characteristically different for different category of bank. As there is problem of additivemeasure, we cannot add up different risk component to arrive at total risk. So, we took resortto an overall indicator that would reflect the risk directly or indirectly for all the bankingactivities it carries.

Total income of a bank consists of interest income and non-interest income. But, non-interestincome is in no way within the principle activity of a bank. In fact, a bank cannot survivedepending only on its non-interest income. A survey (Ramsastri et al., 2004) observed thatless than 17% of the total income arises out of non-interest income in India. The non-interestincome does not have any definite line of operation. Again, due to continuous introduction ofnew services and severe competition the non-interest income changes randomly. Smith,Chirstos and Geoffery (2003) also observed that characteristically non-interest income wasmore unsTable than interest income in other countries as well. Any non-stochastic statisticalapplication would not be very meaningful under that circumstance. So, we have consideredassessing the risk inherent in the principle income component of banking activities i.e. oninterest income. For this many authors (Kumar et al., 2007) have observed that variability ofnet interest income (NII) or net interest margin (NIM) as the indicator of risk. But, continuousaddition of fresh capital especially in last two-three years by many of the banks in Indiaimproves the asset base and as such the net income might have increased but the riskundertaken by them might be same. Therefore, variability of net interest income might not

adequately manifest the risk. On the other hand, variation of NIM might be a better parameterto assess risk.

Variation of Net interest margin (NIM)

The net interest income is defined as the difference between total interest income over totalinterest expenses.

Net Interest Income =Total Interest Income Total Interest Expenses

The Net interest margin (NIM) is defined as net interest income divided by average totalassets. In our article, however, we have considered closing total assets instead of averagetotal assets as prescribed by Reserve Bank of India. Thus,

Net interest margin =Net Interest Income / Total Assets =(Total Interest Income Total

Interest Expenses)/Total Assets If net interest income fluctuates without adding any otherassets, it might be considered that the risk undertaken by bank has increased. As such weprefer variability of NIM over net interest income to be treated as a measure of risk form.

The net interest income of banks mostly from the spread maintained between total interestincome and total interest expenses. The higher the spread, the higher the NIM will be. Weunderstand that the decline in net interest income (and Thus, NIM) increases the risk. Again,


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in a competitive environment, spread will be thin, competitive and would not allow earningabove normal return and hence, above average NIM would imply involvement in the activitywith greater risk exposure. The increment in NIM might be a result of acceptance of higher risklevel. So, both upward and downward departure of NIM from the average might reflect theincrease in risk.

The financial management of a bank views the risks as a set of interrelationships that must beidentified, coordinated and managed as an integral system to control the interest income andexpenses and the resulting NIM on an ongoing basis. So, in other words, the main function ofthe financial management of the bank is, therefore, to manage NIM to ensure that its level ofrisk is compatible with risk-return objective of the bank.

Instead of total spread, some authors considered partial spread. Evanoff and Wall (2001)found that sub-debt yield spreads as bank risk measures has higher prediction error andfurther work is required to refine the risk measure. Birchler and Hancock (2004) providedevidence that a banks subordinated debt yield spread is not by itself a sufficient measure ofdefault risk.

Finally, interest income is the core banking income of a bank. All the risk that is undertaken forthe core banking activities should be reflected finally in the net interest margin either directlyor indirectly, at least, in the long run. The variability of NIM reflects all sorts of risk togethera bank is concerned with. So, in this paper, we are focusing on the variability of NIM.

Literature Survey

There is some literature on risk measurement in the field of business. However, before 1970s

risk management was largely based on experience and judgment. Later on several techniquesand models were developed (e.g. concept of standard deviation, concept of beta, option-pricing models, credit link swap, interest swap, cross asset risk exposure etc.) to tackle theissue of risk in business activities. Some of these techniques and models had been used toassess the risk of banks as well. During mid-1990s at the initiation of J . P. Morgan Chase,value-at risk (VaR) has been developed to measure portfolio risk of a business entity. Thebanks preferred VaR to measure the market risk and portfolio risk. J aschke (2002) and Saita(2007) found the limitations of VaR. Saita (2007) is of the opinion that while the highly technicalmeasurement techniques and methodologies of VaR have attracted huge interest, much lessattention has been focused on how VaR and the risk-adjusted performance measures [such asRAROC] are to be used to manage risk. Anthony (1996) reported about several risk managementtechniques in the banking industry. He reported the standard practices and evaluated how

and why it is conducted in the particular way chosen. He also mentions the elements missedin the existing methodology. Macdonald (1998) described the scope of carrying out quantitativemonitoring of banks on the basis of consolidated financial statements and off-balance sheetitem. He concluded that bank supervision must respond to the challenge of new developmentsfor banks and consequent additional risks they represent for depositors. There are somestudies that dealt with different issues of risk in banks. Applying option-pricing model,Robinovitch (1989) found that the banks in his study have very low insolvency risk. Kotrozo


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& Choi (2006) used Herfindahl Index (HHI) to measure diversification and found that total riskis increased for those banks that focused on their revenue activities. On the other hand, Boydet al. (2006) observed that there is no relationship between the banks risk of failure andconcentration. They further observed that competition fosters the willingness of banks tolend. DeYoung & Roland (2001) conducted a study on different product mix and earningvolatility of commercial banks using leverage model. Smith, Chirstos and Geoffery (2003)demonstrated the relationship between non-interest income and income stability. Morton etal. (2005) introduced a general and flexible framework for asset allocation to manage risk usingMonte Carlo techniques.

In India, there is dearth of studies on risk of banking. After deregulation, among one of thevery few studies in this field, Rao & Ghosh (2008) rightly pointed out that India bankingsector is still in its preparatory stage in implementing a sound operational risk managementdue to lack of quantification. Das (1999) attempted to measure risk preference of differentcategories of banks. Ramsastri et al. (2004) had conducted a study on scheduled commercialbanks and concluded that though average net interest income declined, the stability of incomeof commercial banks has improved during the period 1997 to 2003. On the other hand, Ghoshet al. (2008) analysed the firm specific abnormal returns using cross-sectional regression.Sadakkadulla (2001) arithmetically added up different types of risk to find out overall risk.Chattopadhyay & Mazumdar (2006) conducted a study on seventeen banks and concludedthat the risk of PSU banks have come down significantly while Indian Private Banks assumesto be more risky. On the basis of extensive ratio analysis, Bandopadhyay & Dutta (2006)assessed risk and found that the risk level is low in case of PSU Banks in comparison to Indianprivate banks.

Risk cannot be measured directly. It is the derivative of fluctuations of some parameters. InIndia, there is no serious study to analyze the overall risk of a bank. Hence, in this paper ourendeavor is to compare risk of different categories of banks using the mixed model approach.In mixed model, it would be possible to capture the random effect generated by the group andby the respective individual bank which in turn would help to have the risk analysis with moreaccurate predictive value.

Data & Methodology

The dataset consists of measurements of NIM of eighty eight Indian banks categorised intofive groups. Demonstrating a comparison between long-term and short-term risk models forUS and UK markets, Beckers (1998) found that the explanatory power of a long-term riskmodel is significantly higher than the short-term risk model. Hence, we dealt with data spanning

for as high as twenty-eight quarters. NIM values for each bank were obtained for all thequarters between periods 2000-2001 to 2006-2007. Some NIM values were not available mainlybecause some banks stopped working in India which results the dataset to be unbalanced. Allthe data have been collected from Reserve Bank of India web site [http://www.rbi.org.in].Themethodology adopted by this paper is as follows:


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(i) In the first subsection, we calculate group-wise NIM and its standard deviation to comparerisk among different group of banks.

(ii) In the second subsection, we compute the coefficient of variation and perform Analysisof Variance (ANOVA) to confirm group level risk.

(iii)Cluster analysis to verify individual bank level variation of NIM within a group is performedin the third subsection.

(iv)The final subsection reports application of Mixed Effects Model to quantify the extent ofvariation due to the group and also measure the extent of variation due to individualcharacteristics of the bank.

AnalysisThe group wise and year wise mean and standard deviations of the NIM values are reportedin Table 1. The higher the variation in NIM, higher is the risk of that bank. We observe thatyear wise mean NIM for Foreign banks, PSU banks and SBPSU banks are on the higher sideranging from 2.7 to 3.3. But the mean NIM of NPVT and OPVT banks are at 2.8 or below duringthe period of study. On the contrary, standard deviations of NIM of foreign banks were neverbelow 1.0 whereas the same data for PSU banks and SBPSU were never above 0.4. Thestandard deviations of NIM of both types of private banks were in between 0.6-0.9.

Group wise and year wise mean and standard deviations of Net interest margins Indian banks. The figure in

the brackets indicates the standard deviations.

The net interest income may vary widely due to the size of the bank. But, NIM itself is astandardized measure as far as size is concerned. So, standard deviation itself is a decentmeasure to capture deviation and to compare risk among different group.

To find out more about the variation in a concrete manner, we used coefficient of variation(C.V.). We obtained the C.V. of NIM for each year of each group. Figure 1 shows the bardiagram representing our findings. Figure 1 shows some interesting findings. The C.V. of NIMfor foreign banks and private sector banks (both new and old) are predominantly much higherthan that of public banks (both for PSU and SBPSU). It is further observed that C.V. of foreignbanks has a declining trend. The C.V. of PSU and SBPSU banks have also declined marginally

Table 1

YEAR FOR NPVT OPVT PSU SBPSU

2000-2001 3.258 ( 2.030 ) 2.142 ( 0.794 ) 2.622 ( 0.687 ) 2.848 ( 0.431 ) 3.163 ( 0.504 )

2001-2002 2.983 ( 1.999 ) 1.877 ( 0.736 ) 2.342 ( 0.768 ) 2.714 ( 0.380 ) 3.007 ( 0.373 )

2002-2003 3.173 ( 1.825 ) 2.355 ( 0.999 ) 2.434 ( 0.617 ) 2.99 ( 0.365 ) 3.056 ( 0.363 )

2003-2004 2.997 ( 1.600 ) 2.532 ( 0.709 ) 2.623 ( 0.842 ) 3.075 ( 0.344 ) 3.111 ( 0.319 )

2004-2005 2.619 ( 1.195 ) 2.526 ( 0.929 ) 2.724 ( 0.631 ) 3.075 ( 0.347 ) 3.171 ( 0.291 )

2005-2006 2.743 ( 1.039 ) 2.583 ( 0.829 ) 2.765 ( 0.689 ) 2.943 ( 0.289 ) 2.943 ( 0.376 )

2006-2007 3.142 ( 1.197 ) 2.452 ( 0.946 ) 2.834 ( 0.613 ) 2.746 ( 0.363 ) 2.687 ( 0.281 )


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G roup Net interest mar gi n dur ing 2001-2007

A.M . S.D. C.V.

SBPSU 2.86 0.15 5.24

PSU 2.90 0.14 4.83

OPVT 2.61 0.16 6.13

NPVT 1.97 0.42 21.32

FOR 3.49 0.19 5.44



over the period. But the variation of their NIM of both types of private banks has almost notrend.

Figure 1

Bar diagram of year wise Coefficient of Variation of the bank groups

Now let us combine the average NIM, their standard deviation and coefficient of variationtaking all the twenty-eight quarters at a time. We understand that the PSU banks remain in theleast risk domain where as the new private banks are most risky.

Table 2

Combined standard deviation and Co-efficient of Variation of Net interest margin

We further went on to perform two factor analyses of variances (ANOVA) (Scheff, 1959)without replications at 95% level of significance on the NIM values. The two factors takenwere groups and years. Table 3 shows the results of ANOVA.


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Table 3Analysis of Variance Table for the NIM

Table-3 ascertains that there exists statistically significant group level variation (P-value


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Noting the fact that there are only six and eight banks in the new private bank and state bankgroups respectively, we slightly modify our data set by merging the

new private banks and old private banks as a single group and denoting the group asprivate sector banks (PVT)

State banks and public sector banks as a single group and denoting the group as publicsector banks (PSU)

Thus, we had a modified data with the same number of banks and three groups. On thismodified NIM data we carried out 3-mean cluster analysis. Table 5 describes the resultsobtained from the analysis.

Table 5Cluster composition of 3-means cluster analysis on the modified NIM data

There are some revealing results in Table 5. The composition of cluster-1 did not change fromthat of Table-4 but the most significant change comes in cluster-2 where all the twenty sevenpublic sector banks belong. The NIM of foreign banks is widely dispersed. The NIM of PSU

banks forms a pure cluster demonstrating the consistency within the group. The NIM withinvarious private banks is also inconsistent to some extent.

Both C.V. and cluster analysis confirmed the presence of variation between groups and betweenbanks in a group. The pertinent question is to infer about the extent of variation andquantification of the variation by finding out the group level and bank within group levelvariance. For this we further analyze the data using mixed models. We take the advantage ofthe fact of two special characteristics of the data. The NIM data is a panel data containing amultilevel or nested grouping (Goldstein, 1995) structure. Both these features can be exploitedusing a mixed model.

In financial data analysis, an analyst confronts a situation where multiple measurements(returns/ profit /interest etc) are obtained from each subject (bank/portfolio etc) at different

times and possibly under different conditions. The main interest of such panel data is usuallyin characterizing the way the outcome changes over time, and the predictors of that change.In this study, we used panel data which is the combination of time series with cross-sectionsdata and can enhance the quality and quantity of data in ways that would be impossible usingonly one of these two dimensions (Gujarati, 2003). A note on panel data and its applicabilityfor our study can be had in note 2.

A mixed-effects model (Laird & Ware, 1982) is a widely accepted approach to analyse the

GROUP Cluster-1 Cluster-2 Cluster-3 TOTAL

FOR 5 14 9 28

PSU 0 27 0 27

PVT 0 14 9 23

T OT AL 5 55 18 78


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combination of time series with cross-sections. The mixed model approach is to simply writeout a single regression model for each observation. The model has the usual linear regressionpredictor for the mean response, but has two types of random error terms: between-subjecterrors and within subject errors. All of the observations on the same subject will have thesame between-subject errors; their within-subject errors will differ, and can be correlatedwithin a subject. Both within and between-subject errors are assumed independent fromsubject to subject, Thus, observations on different subjects are independent.

Let ijkNIM denote the NIM measured from the ith (i=1, 2,., nk) bank at jthperiod (j=1,2,,

tik) of the kth categorized group (k =1,2,5. ). It is quite reasonable to presume that the

observed NIM is subjected to two levels of variations. One is the variation between the

different groups i.e. the within group variation and the other is the variation in the banks of the

same group i.e. between group variation. The linear mixed model relating ijkNIM with ijt

incorporating the above variation is

(2))tb()b(NIMor,

(1)tNIM

ijkij1ik1k0ik0kijk

ijkij1ik0ikijk

++++=

++=

Where 0ik and 1ik are the individual intercept and slope of the ithbank belonging to the kth

group. In equation (2) both the individual intercept and slope is divided into two components.

0k and

1kare the intercept and slope for the kthgroup while

0ikb and

1ikbare the random

intercepts and slopes for the ithbank belonging to the kthgroup. Furthermore the group levelslope and intercept can be decomposed as

(3)bandb 1k101k0k000k +=+=

00 and 10 represents the fixed effect regression estimates of the intercept and slope and

0kb and 1kb are the random intercepts and slopes for the kthgroup. Using (1), (2) and (3) the

full model is

(1)

(2)

(3)


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)N(0,~and

),0(N~b

bb

),,0(N~b

bb

thatsassumptionwith the

(4))tbb()bb(NIM

2ijk

2~

2

1ik

0ikik

1~

2

1k

0k

k

ijkij1k1ik1k0k0ik00ijk

=

=

++++++=

We assume that bothkb and ikb follow a bivariate normal distribution with covariance

matrices1 and 2 respectively. We take ijt to be the years centered at 2000 i.e.

2000yeart ijji = . kb is the group-level random-effects vector.. ikb is the bank within

group level random effects model. ikb are assumed to be independent for different k and are

assumed to be independent for differenti,k. ijk the withingroup error is assumed to follow

a normal distribution with zero mean and variance 2 . ijk are assumed to be independentfor i,j andkand of the different random effects. Also, we do not assume a special structure

for1 and

2 . We assume

1and

2 to be symmetric and positive definite only..

The mixed model analysis of the data has been performed using the lme function of thenlme package (Jose Pinheroet al., 2007) for the statistical software system R (R developmentcore team, 2007).

Table 6

Fixed effects estimate of model described in equation 4

Fixed Effects Value Standard Error P-value

00 2.808 0.1862 0

10 0.0012 0.02469 0.9488

.....................................................(4)


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The evident feature is suggested by the fact that fixed effect of time has no impact on NIM as

is been reflected by small estimate of 10 an insignificant p-value (0.9488) but the intercept

has a statistically significant effect with p-value (0) less than 0.05.

Interesting findings were obtained for the random effects. The maximum likelihood estimates

of1 and 2 , denoted by 1 and 2 are

1

2

0.0331668772 -0.00001748587-0.00001748587 0.0005272087

2.0900127140 -0.05755-0.05755 0.0306970562

=

=

The maximum likelihood estimate of came to be 0.5290638. From the group level predicted(Best Linear Unbiased Predictor) random effects [see Appendix-1] we observed that foreignbanks, PSU banks and SBPSU banks have positive intercept and negative slope but NPVTand OPVT has negative intercept with positive slope. From the above estimates, it can beobserved that for group-level and bank within group level variation, both the intercept andslope are negatively correlated. In fact the estimated correlation between the intercept andslope group level is -0.991 and the same for bank within group is -0.897. In both cases thepredicted random effects associated with intercept and slope is highly correlated in opposite

direction. So, if the entity (group or bank) has a higher NIM value (i.e. higher intercept), therate of growth (slope) of NIM has a diminishing trend and vice-versa.

Again, the slope level variation for both (group level and individual bank level) the cases aresmall indicating that temporal effect has minimal existence in the variation of NIM. The interceptvariation is small for group level as compared to the intercept variation for the bank withingroup level, which is quite high, implying that most of the observed variation in NIM is majordue to the banks and minor due to groups. The plotting of observed and predicted datashows a strong linear trend demonstrating higher degree of predictability.

Interpretation & Discussions

The coefficient of variation of foreign banks and private sector banks (both new and old) arehigher indicating higher risk level than that of public sector banks. With the help of ANOVA,

we found that there exists statistically significant group level variation. This finding is inconsonance with Laeven & Levine (2006) that the ownership and management philosophyexerts influence on risk taking. After confirming the group level variation, we went on to checkwhether there exists individual (i.e. intra group) level inconsistency. We carried out k-meancluster analysis. None of the bank group solely forms a composition of the cluster under 5-meancluster analysis. On the modified NIM data we further carried out3-meancluster analysis.


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The finding of cluster analysis reveals that there exists bank level variation in the data and thepublic sector banks tend to be more similar on the basis of NIM whereas the NIM of foreignbanks is the dispersed most. The variation of NIM within Indian private banks is in betweenthe variation of PSU banks and foreign banks. This fact can also be corroborated from the bardiagram (Figure-1) where the dimension of the bars for public sector banks and state bankpublic sectors are more or less same in contrast to foreign banks and private banks. To assessthe magnitude of variation in both the cases we applied Mixed Effect Models. It is observedthat variation of NIM is caused by group level variation and individual bank level variation.However, mostly the variation is major due to operation of individual bank and minor due tothe group they belong. It is further observed from the group-wise random effects and bank-wise random effects that the intercepts and slopes are highly correlated in opposite direction

in both the cases. It implies that if the entity (group or bank) have a higher NIM value (i.e.higher intercept), the rate of growth (slope) of NIM have a downward direction. We cancorroborate the verity from Table-1. It explains the fact that the banks with higher NIM as awhole were either deliberately forced to reduce the spread or their spread reduced followingthe law of normal rate of return. This situation indicates the existence of competition inbanking industry. Ramsastri et al. (2004) demonstrated that volatility in net interest incomedeclined after economic liberalisation (1997-2003). However, it is observed in our study, thatthe slope level variations (for bank level as well as group level) are very small indicating thattime factor has minimal effect in the variation of NIM. The economic liberalisation has madethe PSU banks more efficient (Rammohan & Roy (2004), Bandopadhyay & Dutta (2006),Chattopadhyay & Mazumdar (2006) etc.) which might have intensified the competition in thebanking sector. But, the study infers that the competition did not affect the risk of the industry

significantly at least since 2000. We understand when NIM gets reduced, the banks startaccepting more risk in its operation for higher profitability and again when NIM gets higher,the banks reduces its risk exposure even sacrificing its earning but there was no significanttrend found in the period of study. This phenomenon indicates existence of proactive riskmanagement in place. So, in spite of remaining at comparatively high-risk domain afterliberalisation, this paper cannot infer that the risk management of foreign banks and privatebanks are less efficient.

From the bank-wise risk analysis one can move forward to find out Risk-adjusted Return onAsset (RAROA) for each bank to assess that whether risk assumed by the bank is incommensurate with return they earn in comparison to its peers.

The present study has taken variation of NIM to assess the risk. But, further research couldbe conducted taking different components of NIM to check how each component contributes

to the overall risk measures. In fact, we intend to conduct a study to analyse the role ofinterest/discount on advances/bills and interest on investment in the overall risk of a bank.

Conclusion

The performance of a bank from the viewpoint of profitability is not very meaningful unlessthe same is accounted for along with the risk. After economic liberalization, the banks werefree to introduce new products and free to charge price their products with varying risk


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associated with the instrument. During the period of study, the interest rate has also changedseveral times forcing spread structure to change. All these issues have enhanced the importanceof risk analysis of a banking firm. In this paper, instead of focusing on one component of riskwe have made an attempt to analyze overall risk of a bank. We considered NIM of all eighty-seven banks categorized into five groups spreading over twenty-eight quarters staring from2000.

Standard deviation and co-efficient of variation of NIM of foreign banks and both typesprivate banks are higher than both type of public sector banks and ANOVA confirms theexistence of group level variation. Cluster analysis further substantiates the existence of banklevel variation within the groups. The application of mix models validates the group levelvariation and individual bank level variation. It has also been found that risk arises due toindividual level operation is more prominent than the risk arises due to group level variation.The model further indicates the existence of competition by demonstrating negative correlationbetween intercept and slope of NIM. However, the model suggests that the time factor hasalmost no impact on the variation of NIM. So, we understand that economic liberalisationmight have increased competition but has not led to change the level of risk. This in turnproves prevalence of proactive risk management system in place in Indian Banking System.

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NOTES

Note 1:

Steps of Clustering Process:

Any clustering process typically consists of the following three steps

1. We have p measurements (variables) on n objects (data matrix). For the abovedata we have n =78 banks (in fact we had 87 banks but ignored those banks fromwhich one or more of NIM values were not available.) and p =7 measurements.

2. The data matrix is transformed into n n similarity or distance matrix (computedbetween pairs of objects across the p measurements (variables))

3. Cluster formation using a clustering algorithm to form either

a) Mutually Exclusive Clusters

b) Hierarchical Clusters

Clustering algorithms are rules concerning how to cluster the objects into clusters on the

basis of inter-object similarity. A variety of clustering algorithms have been proposed forcluster analysis purpose.
http://www.r-project.org./http://www.rbi.org.in./http://www.rbi.org.in./http://www.r-project.org./


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Group-wise Random Effects

Intercept Slope (Year 2000)

FOR 0.121967982 -0.01537706

NPVT -0.078844556 0.009940291

OPVT -0.095503166 0.012040518

PSU 0.008067985 -0.00101717

SBPSU 0.044311756 -0.00558658

Appendix-1

Bank Group-wise random effects



K-means cluster

MacQueen (1967) suggest the termsK-meansfor describing the algorithm that assigns eachitem to the cluster having the nearest mean. AK-meansalgorithm can be described as follows.

Step-1

Partition the items arbitrarily intoKinitial clusters.

Step-2

Proceeding through the list of items, assign an item to the cluster whose mean isnearest to that cluster (Distance is usually computed using Euclidean distances).Cluster composition changes. Recalculate the new mean for each cluster.

Step-3

Repeat step-2 until no more reassignment takes place.

Note2:

The objectives of panel data analysis are to examine and compare responses over time. Thedefining feature of such data model is its ability to study changes over time within subjectsand changes over time between groups. For example, panel data models can estimate individual-level (subject-specific) regression parameters and population-level regression parameters.Panel data sets differ from time series data sets because panel data usually consists of a largenumber of a short series of time points. On the other hand, time series data sets usuallyconsist of a single, long series of time points.


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Appendix -2Bank-wise Estimated Random effects

ABN-AMRO Bank N.V. 1.47585595 -0.123905514

Bank of Nova Scotia -0.65355986 -0.03962973

Bank of Tokyo-Mitsubishi UFJ 3.03868971 -0.391500574

Barclays Bank PLC -1.72342022 0.181436822

BNP Paribas -0.58741076 0.099760539

Ceylon Bank -1.46484998 0.100504055

Chinatrust Commercial Bank 3.58786894 -0.376126413

Citibank N.A. 1.14975198 -0.000380342

Deutsche Bank AG 0.81910776 -0.254839972

DBS Bank Ltd. 0.66650636 -0.122962004

HSBC Ltd. -0.17555225 0.131322201

Abu Dhabi Commercial Bank Ltd. -2.3569019 0.170234103

ING Bank N.V. -1.85602603 0.170827108

JPMorgan Chase Bank 0.51416078 -0.101167754

Krung Thai Bank Public Co. Ltd. 5.25669266 -0.546836973

Mashreqbank psc -1.52500029 0.317903461

Mizuho Corporate Bank Ltd. -0.05648201 0.01962775

Oman International Bank S.A.O.G. -4.81734051 0.454139507

Shinhan Bank 4.81258399 -0.660073625

Societe Generale -1.6526672 0.142932671

Sonali Bank -1.31614223 0.052955747

Standard Chartered Bank 0.90476926 0.003340681

American Express Bank Ltd. 0.14933839 0.034678213

State Bank of Mauritius Ltd. -0.01825398 -0.004065156

UFJ Bank Ltd. 1.26450646 -0.056994667

Antwerp Diamond Bank 0.31391841 -0.071170436

Arab Bangladesh Bank Ltd. 2.64811067 -0.181963027

Bank Internasional Indonesia -0.12952215 0.026623254

Bank of America NA -0.20859932 0.065852386

Bank of Bahrain & Kuwait B.S.C. -1.77874252 0.180688566

Bank of Ceylon 0.67527649 -0.097795861

Bank Name Intercept Slope (year 2000)


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Axis Bank -1.60358398 0.165285579

Bank of Punjab Ltd. -0.14263498 0.00207199

Centurion Bank of Punjab Ltd. -0.34076787 0.136967363

Development Credit Bank Ltd. -0.89665413 0.029449526

HDFC Bank Ltd. 0.08737961 0.079808103

ICICI Bank Ltd. -1.56119598 0.108888368

IndusInd Bank Ltd. -0.92791084 0.025830225Kotak Mahindra Bank Ltd. 1.2944575 -0.116207829

Yes Bank Ltd. -1.3930081 0.078849531

Bank of Rajasthan Ltd. 0.11839628 -0.06318149

Karnataka Bank Ltd. -0.9024303 0.088155445

Karur Vysya Bank Ltd. 0.79281799 -0.064211205

Lakshmi Vilas Bank Ltd. -0.44559436 0.002567629

Lord Krishna Bank Ltd. -1.76263577 0.166808533

Nainital Bank Ltd. 1.16354414 -0.049994341

Ratnakar Bank Ltd. 0.14204964 0.009307104

Sangli Bank Ltd. -0.03422197 -0.051298616SBI Com. & International Bank Ltd. -1.45686237 0.172237699

South Indian Bank Ltd. -0.26120998 0.019273651

Tamilnad Mercantile Bank Ltd. 0.77907825 0.04296009

Bharat Overseas Bank Ltd. -0.12930102 0.041499313

United Western Bank Ltd. -0.94772348 0.068049803

Catholic Syrian Bank Ltd. -0.26670165 0.071330029

City Union Bank Ltd. -0.07393181 0.054047728

Dhanalakshmi Bank Ltd. -0.39861948 0.064499176

Federal Bank Ltd. -0.01857568 0.017307323

Ganesh Bank of Kurundwad Ltd. -1.07924113 -0.022834216ING Vysya Bank Ltd. -1.22541851 0.157153616

Jammu & Kashmir Bank Ltd. 0.24893592 -0.054821367

Allahabad Bank 0.37434084 -0.052201669

Indian Bank -1.00106465 0.187866103





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Indian Overseas Bank 0.13440582 0.04465309

Oriental Bank of Commerce 0.5010968 -0.081350034

Punjab & Sind Bank -0.33753742 0.123171697

Punjab National Bank 0.54807168 -0.019418487

Syndicate Bank 0.99577393 -0.143387614

UCO Bank -0.37051472 0.015066375

Union Bank of India 0.28440724 -0.04944226

United Bank of India -0.16652488 0.047468964

Vijaya Bank 0.56459948 -0.060739374

Andhra Bank -0.03609515 0.038927811

Bank of Baroda 0.11020922 -0.01531644

Bank of India -0.12170812 -0.0303488

Bank of Maharashtra -0.09104751 0.009680742

Canara Bank -0.06543251 -0.011081639

Central Bank of India 0.41246316 -0.028112222

Corporation Bank 0.1834861 -0.007253723

Dena Bank -0.30754683 0.038823934

State Bank of India -0.23192512 0.04858578

State Bank of Bikaner & J aipur 0.4721722 0.000157753

State Bank of Hyderabad 0.246201 -0.050412026

State Bank of Indore 0.31779953 -0.054956733

State Bank of Mysore 0.54760307 -0.055453272

State Bank of Patiala 1.29711326 -0.218109304

State Bank of Saurashtra 0.20568795 -0.025885952

State Bank of Travancore -0.18113692 0.045853525


Documents

Risk Analysis of Scheduled Commercial Banks of India