About Efficient Choice of Savings and Checking Account with Use of Discrimination Analysis

Uniwersytet SzczeciĔski

Summary

Nowadays possessing personal bank account in Poland is common or even nec-essary. It is well known, that “virtual” money plays important role not only for mul-tinational corporations, but also for every single person. Fulfilling customer needs for individual service is the key figure in fight for customer between banks and SKOKs. Because of wide offer of savings and checking accounts, customers are forced to use sophisticated tools in order to ensure themselves the best possible choice. The method, which is presented in the article, is based on algorithm, that discriminate objects according to chosen criterions and helps to make rational choice in case, where object is described by many attributes. Special attention has been devoted to attributes, that characterizes distinguished groups of products. Ac-count of article restrictions, conclusion is not based on results obtained in the way of order classification but only in the way of grouping.

Keywords: Efficient Choice of Savings, Discrimination Analysis, Multidimen-sional Data Analysis. Grouping of Clients

1. Introduction

The main object of interest for Polish society being concerned about raising funds is both, safety of money entrusted to the banks and possibility of facilitation in making everyday transac-tions. That kind of expectations can be fulfilled with savings and checking account called also personal bank account.

For the author, the object of interest is possibility of achieving the best choice of personal ac-count from the savings and checking acac-counts which are offered by Polish banks and SKOK (Pol-ish abbreviation for Cooperative Found of Savings and Loan).

Banks offer many kinds of personal accounts. Most popular ones are: youth account (designed for youngest customers), student account, standard account and business account – designed spe-cially for people that deposit bigger amounts of money in a bank and have higher requirements than average customer. This wide diversity in bank’s offer is a result of need to adjust it in the best way to the demands of different groups of clients.

In the times of great growth of Internet users and possibilities to make shopping via world wide web, more and more popular are personal accounts which can be managed on-line (Home Banking). In defiance of current opinion it is not only possibility to use an account over the Inter-net, but also with use of regular telephone or cellular phone. Beyond obvious comfort and time saving which comes from the lack of queues in banks and access to account in every place and at every time, most of the transactions made on-line is much cheaper in comparison to the same ac-tions made in a traditional way. This is possible because there is no need to pay anything to bank workers when transactions are made over the Internet.

In the present days almost every adult has personal bank account. This leads to a great compe-tition between banks in this sector. Therefore, every customer should consider the problem of best choice from the long list of available personal accounts on the market. For the customer, the best choice is savings and checking account, which is best adjusted to the customer needs.

Finding the solution to this problem is relatively difficult, because only collecting information about available accounts from a number of banks and SKOK takes time and money. Furthermore, after this first time-consuming step customer faces a choice based on multidimensional criterion.

One of the most important qualities regarding personal account is account interest rates. There are also other qualities that should be taken into consideration, like: accessibility to the funds gath-ered on the account, number of branches of the bank, in which customer can collect information and make transactions. Also very important is to have an opportunity to use consumer credit with relatively low interest rate. Classification of private accounts that are offered by financial institu-tions, then selection of the best one according to its qualities is possible due to use of multidimen-sional data analysis. In this article the discrimination analysis is used to make the order classifica-tion of savings and checking accounts that are offered by banks and SKOK in Poland.

2. Examination subject selection and diagnostic variable specification.

The fundamental aim of discrimination analysis is to attribute examined objects to specific group distinguished by one of the features (key-feature) that are important for the decision-maker. The most important phase in the process is selection of the key-feature, which enables division of all the accounts into groups. This selection mostly depends on individual preferences of decision-maker (customer). For the preliminary discrimination in this article there was taken more than one key-feature. Every selection was examined for accuracy of classification depending on the feature chosen.

Before creating the function of discrimination, there should be checked if chosen earlier vari-able fulfill certain assumption. There are two main assumptions1 regarding character of diagnostic variables:

- diagnostic variables represent multidimensional normal distribution, - variation and covariation matrixes of distinguished classes are equal. Apart from these two main assumptions there are also:

- averages and variations should not be correlated,

- variables used to discrimination of the groups should not be entirely redundant.

Research which has been done until now with use of discrimination function allows to con-clude, that if all assumptions mentioned above are not met, then the discrimination function still can be used successfully as classification method2.

Key features that are used in the article for classification of savings and checking accounts: - evaluation of accessibility to bank or SKOK branches (X1),

- minimal account interest rate offered by a particular bank or SKOK (X2),

- maximal account interest rate offered by a particular bank or SKOK (X3),

- consumer credit interest rate available with a particular savings and checking account (X4),

- evaluation of accessibility of cash dispensers that supports withdrawal from particular pri-vate account (X5).

Features X1 and X5 need additional attention. In case of both qualities evaluation of their level

mean amount of points given to their value according to rule: the bigger number of bank (SKOK) branches or cash dispensers was accessible for the customer, the bigger amount of points was granted. In cases where number of bank (SKOK) branches or cash dispensers was equal, then the amount of points granted was equal also.

Analysis has been prepared for 46 banks and SKOK (data from 17.03.2005r.) that are offering private bank accounts (Table 1). All the accounts allow to take consumer credit.

Table 1. Banks and SKOK whose savings and checking accounts were taken under examination.

No. Name of the Bank No. Name of the Bank No. Name of the Bank

 %DQN%3+  ,1*%DQNĝOąVNL  6.2.LP.RSHUQLND2UQRQWRZLFH  %DQN%36%DQN3ROVNLHM 6SyáG]LHOF]RĞFL  ,QYHVW%DQN  6.2.LP.UyORZHM-DGZLJL.UDNyZ  %DQN*RVSRGDUNL ĩ\ZQRĞFLRZHM  .UDNRZVND6.2.  6.2.LP=&KPLHOHZVNLHJR/XEOLQ

 %DQN0LOOHQQLXP  .UHG\W%DQN  6.2.LP6:\V]\ĔVNLHJR:U]HĞQLD

 %DQN2FKURQ\ĝURGRZLVND  /XNDV%DQN  6.2.-DQ.DQW\-DZRU]QR  %DQN3HNDR6$  0D]RZLHFNL%DQN5HJLRQDOQ\  6.2.0DáRSROVND6WDORZD:ROD  %DQN3RF]WRZ\  0XOWL%DQN%5(%DQN  6.2.0D]RZV]H:DUV]DZD  %DQN=DFKRGQL:%.  1RUGHD%DQN3ROVND  6.2.3LDVW7\FK\  %LHV]F]DG]ND6.2.6DQRN  2U]HVNR.QXURZVNL%6Z.QXURZLH  6.2.ĝOąVN5XGDĝOąVND  %,6(%DQN,QLFMDW\Z 6SRáHF]QR(NRQRPLF]Q\FK  3.2%3  6.2.:DUV]DZD  &LWLEDQN+DQGORZ\  3RGNDUSDFNL%66DQRN  6.2.:HVRáD0\VáRZLFH  'HXWVFKH%DQN3%&  3RZV]HFKQD6.2..QXUyZ  6.2.:RáRPLQ  'RPLQHW%DQN  3=6.2.:URFáDZ  6.2.=LHPL5\EQLFNLHM&]HUZLRQND

 )RUWLV%DQN  5DLIIHLVHQ%DQN3ROVND  :LHONRSROVND6.2.3R]QDĔ

 *HWLQ%DQN  6.2.LP(.ZLDWNRZVNLHJR7DUQyZ

 *RVSRGDUF]\%DQN

:LHONRSROVNL

 6.2.LP)6WHIF]\ND*G\QLD

Source: personal elaboration

Discrimination analysis has been made on a basis of preliminary classification criterion taken one after the another, such as: evaluation of accessibility to bank or SKOK branches (X1), minimal

account interest rate offered by a particular bank or SKOK (X2), maximal account interest rate

offered by a particular bank or SKOK (X3), evaluation of accessibility to cash dispensers that

sup-ports withdrawal from particular private account (X5). Because preliminary analysis showed weak

ability of discrimination function based on consumer credit interest rate available with a particular savings and checking account (X4), it has not been taken as a criterion in this article3.

Because of article size restrictions, in the text below, there will be shown only analysis based on evaluation of accessibility to bank or SKOK branches.

3. Savings and checking account classification based on criterion X1 (accessibility evaluation of bank and SKOK branches)

Determination of variable that divides into groups on satisfying level is subjective. Arithmetic mean is most often used as a measure of critical level, but in the case, that distribution of tested feature is not similar to normal distribution, then classical statistic measures can not be applied. It is recommended to use median as average measure. Choice of median in diagnosis process is justi-fied because it allows to distinguish two equally numbered groups4.

It is assumed for the needs of this analysis, that customer evaluates account positively only then, when amount of bank (SKOK) branches would be greater or equal to the median number of branches determined from all savings and checking accounts that were analyzed. Otherwise acces-sibility to savings and checking account would be recognized as insufficient.

With use of standard analysis discrimination function was estimated:

708

,

0

038

,

0

066

,

0

482

,

0

1168

,

1

=

⋅

X

−

⋅

X

−

X

−

X

+

f

( 1 )

Determined discrimination function is characterized by significant discrimination of savings and checking accounts by criterion X1, despite the fact that Lambda-Wilks statistic has quite high

level. Factors values after standardization for canonical variables (Table 2) show that the highest share in discrimination has minimal account interest rate (X2) and the lowest share has consumer

credit interest rate (X4).

Table 2. Factors after standardization for canonical variables

Variable Factor

minimal account interest rates 1,581103 maximal account interest rates -0,770430 consumption credit interest rates -0,166229 accessibility evaluation of cash dispensers -0,287273 Source: personal calculations

Estimated discrimination function is characterized by high precision of classification. Amount of cases, that has been correctly classified in group which does not fulfill preliminary criterion, is 28,26%. In the group, that by preliminary criterion is recognized as good, accuracy level achieved 69,57%. Common classification error aggregate 26,09%. It means, that percentage of correctly classified savings and checking accounts with use of discrimination function was 73,91%. Only seven savings and checking accounts were classified into “better” group wrongly and five of all were classified wrongly into “worse” group. A posteriori probabilities showing, that the account belong to particular group, with a priori probability assumption proportional to size of groups is showed in table 3.

Classification of savings and checking accounts into particular group based on discrimination function comes from range measures, which can be used in multidimensional space defined by model variables. This amount (called Mahalanobis range) is calculated between every single case and center of the group defined by suitable group averages for every variable. The nearer the case is to the center of group, it is more certain that it belongs to the group (bigger a posteriori prob-ability) – showed in table 3.

Table 3. A posteriori probability and Mahalanobis ranges for particular cases (wrongly classified objects are marked with a star)

Gupa 1; p=0,5 Grupa 2; p=0,5 Gupa 1; p=0,5 Grupa 2; p=0,5 Gupa 1; p=0,5 Grupa 2; p=0,5 Gupa 1; p=0,5 Grupa 2; p=0,5

1 0,955143 0,044857 10,23172 16,34850 * 24 0,580051 0,419949 3,74179 4,38776 2 0,643933 0,356067 1,52448 2,70943 25 0,326941 0,673059 6,59062 5,14651 3 0,973829 0,026171 15,60297 22,83612 26 0,863990 0,136010 4,57958 8,27724 4 0,784752 0,215248 2,40939 4,99654 27 0,689251 0,310749 7,18425 8,77748 * 5 0,332578 0,667422 3,56198 2,16889 28 0,148469 0,851531 4,93895 1,44564 6 0,842740 0,157260 4,94712 8,30465 29 0,338229 0,661771 2,78942 1,44702 7 0,729210 0,270790 1,55166 3,53290 30 0,617930 0,382070 5,31554 6,27707 8 0,877194 0,122806 1,43583 5,36808 31 0,443961 0,556039 2,28706 1,83685 9 0,138796 0,861204 5,79357 2,14292 * 32 0,209667 0,790333 3,47683 0,82297 10 0,302661 0,697339 5,36340 3,69408 * 33 0,523674 0,476326 3,86074 4,05027 11 0,776902 0,223098 3,31756 5,81296 * 34 0,618440 0,381560 9,19758 10,16345 * 12 0,650176 0,349824 2,57019 3,80982 * 35 0,064696 0,935304 9,21588 3,87353 * 13 0,297293 0,702707 3,27140 1,55096 36 0,158693 0,841307 4,43283 1,09686 * 14 0,573501 0,426499 5,49553 6,08783 37 0,408667 0,591333 1,71952 0,98056 15 0,798164 0,201836 1,94858 4,69830 38 0,386722 0,613278 6,25668 5,33445 16 0,413151 0,586849 3,71501 3,01310 39 0,169480 0,830520 4,27523 1,09660 17 0,759199 0,240801 2,40980 4,70639 * 40 0,443961 0,556039 2,28706 1,83685 18 0,728707 0,271293 0,58631 2,56245 41 0,271727 0,728273 2,96299 0,99123 19 0,180843 0,819157 4,46613 1,44484 42 0,111576 0,888424 10,07431 5,92481 20 0,775443 0,224557 0,88307 3,36168 * 43 0,338229 0,661771 2,78942 1,44702 21 0,891082 0,108918 7,52924 11,73291 44 0,320848 0,679152 7,35466 5,85491 22 0,457085 0,542915 3,29250 2,94833 45 0,312340 0,687660 2,20106 0,62265 * 23 0,187302 0,812698 5,28391 2,34864 46 0,171595 0,828405 4,28468 1,13595

No. A posteriori probability Mahalanobis range No. A posteriori probability Mahalanobis range

Source: personal calculations

With use of discrimination analysis, except for assigning surveyed objects to the one of the groups, there can be also made classification of all elements creating so called rating. However, fundamental assumption that has to be fulfilled is compliance of signs that stay near the particular variable in function with character of this variable. This compliance should concern particularly variables, that have the biggest share in discrimination process. If this assumption is not fulfilled, then it is legitimate to divide elements only to the groups. Particular element is classified in to one of two groups for which it has higher classification value. It means that in this matter, value calcu-lated with classification functions distinguished for groups, determines where particular element will be attributed.

In the survey process following classification functions have been obtained:

group 1

41

,

23

123

,

0

627

,

2

786

,

2

366

,

2

=

−

⋅

X

+

⋅

X

+

X

+

X

−

f

( 2 )

group 2

565

,

22

078

,

0

548

,

2

209

,

2

029

,

1

=

−

⋅

X

+

⋅

X

+

X

+

X

−

f

( 3 )

In range of every group, examined savings and checking accounts characterizes themselves with particular discrimination function explicative variables level. Determination of descriptive statistics measures allows to identify group attributes based on variables accepted to analysis.

On the first graph, there are positional measures of central tendency for minimal interest rate prepared for both groups distinguished by criterion functions. It can be observed, that average interest rate in the first group is definitely lower than in the second.

Whereas spread in the first group is larger. For the minimal interest rate, third quartile in the first group is slightly higher in comparison to the second quartile in the second group. It means, that the value of minimal interest rate, under which is classified 75% of personal accounts in group one, defines as well minimal interest rate value, above which is classified 75% of personal ac-counts from the group two. Median, estimated for maximal interest rate is also higher in the sec-ond group (Graph 2).

Median 25%-75% Min.-Max. 1 2 Group -1 0 1 2 3 4 5 6 m in im a l a c c o u n t in te re s t ra te Median 25%-75% Min.-Max. 1 2 Group -1 0 1 2 3 4 5 6 7 m a x im a l a c c o u n t in te re s t ra te

Graph 1. Positional measures of minimal account interest-rates by groups

Graph 2. Positional measures of maximal account interest-rates by groups

Median 25%-75% Min.-Max. 1 2 Group 10 12 14 16 18 20 22 24 c o n s u m e r c re d it in te re s t ra te Median 25%-75% Min.-Max. 1 2 Group 0 2 4 6 8 10 12 14 16 18 20 22 24 26 n u m b e r o f c a s h d is p e n s e rs ( e v a lu a tio n )

Graph 3. Positional measures for consumer credit interest rate by groups

Graph 4. Positional measures for evaluation of accessibility of cash dispensers by groups Source: personal elaboration Source: personal elaboration

In the first group majority of the accounts has lower maximal interest rate than median. Quar-tile spread in this group is larger then in the second group. It means, that in the group two is bigger diversity around the median value in range of 50% of nearest elements.

Median, first and third quartile, minimal and maximal value in groups was estimated also for consumption credit interest rate. Worth mentioning is the fact, that level of median minimal inter-est rate value and third quartile in both groups is almost equal. Whereas first quartile and maximal value are definitely different in both groups. In the second group consumption credit interest rate achieves up to 23% (SKOK im. Królowej Jadwigi, Kraków) but 25% of accounts in this group is characterized by a level of 13% or less.

While analyzing a graph (Graph 4) made for evaluation of cash dispensers accessibility, it can be seen quite high median level can be seen in the second group, which is equal to third quartile and maximal value for this feature. It means that 50% of savings and checking accounts in this group allows access to at least 760 cash dispensers.

Table 4. Savings and checking accounts categorized into first and second group 1 %DQN%3+ 5 %DQN2FKURQ\ĝURGRZLVND 2 %DQN%36%DQN3ROVNLHM6SyáG]LHOF]RĞFL 9 %LHV]F]DG]ND6.2.6DQRN 3 %DQN*RVSRGDUNLĩ\ZQRĞFLRZHM 10 %,6(%DQN,QLFMDW\Z6SRáHF]QR (NRQRPLF]Q\FK 4 %DQN0LOOHQQLXP 13 'RPLQHW%DQN 6 %DQN3HNDR6$ 16 *RVSRGDUF]\%DQN:LHONRSROVNL 7 %DQN3RF]WRZ\ 19 .UDNRZVND6.2. 8 %DQN=DFKRGQL:%. 22 0D]RZLHFNL%DQN5HJLRQDOQ\ 11 &LWLEDQN+DQGORZ\ 23 0XOWL%DQN%5(%DQN 12 'HXWVFKH%DQN3%& 25 2U]HVNR.QXURZVNL%6Z.QXURZLH 14 )RUWLV%DQN 28 3RZV]HFKQD6.2..QXUyZ 15 *HWLQ%DQN 29 3=6.2.:URFáDZ 17 ,1*%DQNĝOąVNL 31 6.2.LP(.ZLDWNRZVNLHJR7DUQyZ 18 ,QYHVW%DQN 32 6.2.LP)6WHIF]\ND*G\QLD 20 .UHG\W%DQN 35 6.2.LP=&KPLHOHZVNLHJR/XEOLQ 21 /XNDV%DQN 36 6.2.LP6:\V]\ĔVNLHJR:U]HĞQLD 24 1RUGHD%DQN3ROVND 37 6.2.-DQ.DQW\-DZRU]QR 26 3.2%3 38 6.2.0DáRSROVND6WDORZD:ROD 27 3RGNDUSDFNL%66DQRN 39 6.2.0D]RZV]H:DUV]DZD 30 5DLIIHLVHQ%DQN3ROVND 40 6.2.3LDVW7\FK\ 33 6.2.LP.RSHUQLND2UQRQWRZLFH 41 6.2.ĝOąVN5XGDĝOąVND 34 6.2.LP.UyORZHM-DGZLJL.UDNyZ 42 6.2.:DUV]DZD 43 6.2.:HVRáD0\VáRZLFH 44 6.2.:RáRPLQ 45 6.2.=LHPL5\EQLFNLHM&]HUZLRQND 46 :LHONRSROVND6.2.3R]QDĔ

No. Bank or SKOK - group 1 No. Bank or SKOK - group 2

Source: personal elaboration

However in the first group can be found the best savings and checking account selected by cri-terion of the highest number of cash dispensers and it is offered by PKO BP. Customers of this bank can use network of 1776 cash dispensers located in Poland.

4. Final remarks

Survey with use of positional measures in distinguished by criterion X1 groups show, that in the second group indifferently higher are values of stimulants and lower are values of de-stimulants. It is caused by signs of factors that are standing by discrimination function vari-ables. Private bank accounts that are in the first and second group are listed in table 4.

In the same way but with use of other criteria (accessibility to cash dispensers, maximal and minimal account interest rate) has been prepared analogical savings and checking account classifi-cation.

As a result, graphical presentation of chosen positional measures for all criteria indicates that: - regarding evaluation of branches accessibility better are savings and checking accounts from the second group,

- regarding maximal account interest rate better are savings and checking accounts from the first group,

- lower values of consumer credit interest rate can be found in the second group,

- regarding accessibility evaluation of cash dispensers better values have savings and checking accounts from first group.

Summarizing, discrimination analysis is very helpful tool in process of making decisions re-garding rational selection of personal account, which is described by many attributes. It is recom-mended to make detailed examination of objects accepted for the analysis, not only based on final classification, but also within distinguished in previous phases groups.

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MATEUSZ GRZESIAK Uniwersytet SzczeciĔski

Instytut Informatyki w Zarządzaniu ul. Mickiewicza 64

71-101 Szczecin

e-mail: mateusz.grzesiak@univ.szczecin.pl tel. kom.: 508233338