Grigore Bace

Ioan Batrancea

Larissa Batrancea

Sorin Borlea

English

Research Papers in Economics

International Conference on Emerging Economic Issues in a Globalizing World, Đzmir, 2008 
 
  166 
Statistic Study of Banking Efficiency Ratios 
 
 
Ioan Batrancea 
Babes-Bolyai University, Romania 
 
Larissa Batrancea 
Babes-Bolyai University, Romania 
 
Sorin Borlea 
Babes-Bolyai University, Romania 
 
Grigore Bace 
Romanian National Bank, Romania 
 
 
 
 
Introduction 
In  order  for  a  more  relevant  financial-economic  analysis,  we  realized  a  statistic 
processing  of  data  resulted  from  financial  statements  for  the  period  2001-2006. 
Essentially,  the  statistic  study  has  concentrated  around  “RETURN  ON  EQUITY” 
(ROE) indicator, which in our opinion, is the main financial efficiency criterion.  The 
number  of  values  registered  for  each  statistic  variable  is  relevant,  taking  into 
consideration  that  the  data  from  the  six  annual  balance  sheets  are  highlighted  at 
quarterly level.     
Data and methods  
Due  to  presentation  reasons,  which  correspond  to  statistic  links,  we  shall  use  the 
following  symbols  for  the  financial-economic  indicators  from  the  annual  financial 
statements: 
ROE   - Financial Profitability Ratio; 
RACADEPA  - Assets Covering with Attracted Deposits Ratio; 
DOBACTIV - Active Interest; 
DOBPASIV - Passive Interest; 
GAP - Gap between Active and Passive Interest; 
FDCLNEBA - Funds attracted from non-banking customers; 
DATORII – Total Attracted Funds; 
FLUXNUM - Total Cash-Flow; 
PROVR_CH - Provisions; 
CREANTE - Receivables; 
DATORII - Debts; 
RACTLICH - Current Assets Ratio; International Conference on Emerging Economic Issues in a Globalizing World, Đzmir, 2008 
 
  167 
LUXFIN - Financing Cash-Flow; 
GESTRLIC - Liquidity Risk Financial Administration; 
FLUXINV - Investment Cash-Flow; 
INDSOLV1 - Solvency 1Indicator; 
CAPNIV1 - Level 1 Equity; 
CAPNIV2  - Level 2 Equity; 
CAPNIV3  - Level 3 Equity. 
In the following, we shall analyze some of the most significant statistic links which 
have been identified at many Romanian banks level, based on the data from the annual 
financial statements, during the period 2001-2006.  
Results 
Another factor which influences ROE variance by almost 50% is the ratio of assets 
covering  with  attracted  deposits  (RACADEPA).  The  following  information  is 
significant in this issue: 
The regression result for the dependent variable: ROE 
R = 0.7228;  R
2 = 0.5224;   R
2adjusted = 0.4985; 
F(1.20)  = 21.883;   p < 0.00014;   standard estimation error: 1.5493 
  coef. ai  St. ERR     
    For  ai  t(20)  p-level 
a0  37.03123  7.499546  4.93720  0.000079 
RACADEPA  -0.42407  0.090655  -4.67790  0.000145 
CORRELATIONS 
  RACADEPA  ROE 
RACADEPA  1.00  -0.72 
ROE  -0.72  1.00 
COVARIANCE 
  RACADEPA  ROE 
RACADEPA  13.9  -5.9 
ROE  -5.9  4.8 
The econometric model between ROE and RACADEPA is: 
ROEt =  37.03 – 0.42 . RACADEPAt + εt  
Which means that for an increase by one percent of RACADEPA, ROE decreases by 
0.42 %. International Conference on Emerging Economic Issues in a Globalizing World, Đzmir, 2008 
 
  168 
Figure 1: ROE and RACADEPA Correlation 
Scatterplot (DATE.STA 27v*24c)
y=37,031-0,424*x+eps
RACADEPA
R
O
E
-1
0
1
2
3
4
5
6
7
74 76 78 80 82 84 86 88 90 92
 
The statistic links between the ROE variance and the following elements are interesting: 
active  interest,  passive  interest,  and  the  difference  between  them  (GAP).  In  the 
following,  we  present  information  which  resulted  from  data  processing,  in  order  to 
analyze their significance.    
The regression result for the dependent variable: ROE 
R = 0.9108;  R
2 = 0.8296;   R
2adjusted = 0.8211; 
F (1.20) = 97.419;   p < 0.0000;   standard estimation error: 0.9853 
  coef. ai  St. ERR     
    For  ai  t(20)  p-level 
a0  -2.63217  0.507519  -5.18635  0.000045 
DOBACTIV  0.14873  0.015069  9.87013  0.000000 
CORRELATIONS: 
  DOBACTIV  ROE 
DOBACTIV  1.00  0.91 
ROE  0.91  1.00 
There is a direct link between ROE and DOBACTIV, meaning that with an increase by 
one percent of active interest, ROE will increase by an average 0.14 %. DOBACTIV 
influences ROE variance by 82%. Moreover, there is a high level of correlation between 
the two indicators.   
In order to analyze the link between ROE and passive interest we use the information 
below. 
The regression result for the dependent variable: ROE International Conference on Emerging Economic Issues in a Globalizing World, Đzmir, 2008 
 
  169 
R = 0.9066;  R
2 = 0.8219;   R
2adjusted = 0.8180 
F(1.20)  = 92.349;   p < 0.0000;   standard estimation error: 0.94596 
  coef. ai  St. ERR     
    For  ai  t(20)  p-level 
a0  -2.19204  0.479001  -4.57628  0.000183 
DOBPASIV  0.18426  0.019174  9.60985  0.000000 
The link between ROE and DOBPASIV is almost equivalent to that previously studied, 
between ROE and DOBACTIV. In the last case, the model is the following: 
ROEt = -2.19 + 0.18. DOBPASIVt + εt  
This means that ROE variance is slightly sensitive to DOBPASIV variance (a1 = 0.18 
%). Beside this, both the correlation level and the percent through which the factor 
explains ROE variance are almost the same.  
Figure 2: ROE and DOBPASIV Correlation 
Scatterplot (DATE.STA 27v*24c)
y=-2,192+0,184*x+eps
DOBPASIV
R
O
E
-1
0
1
2
3
4
5
6
7
4 10 16 22 28 34 40
  
ROE variance in correspondence with GAP can be analyzed as following: 
The regression result for the dependent variable: ROE 
R = 0.7313;  R
2 = 0.5349;   R
2adjusted = 0.5116; 
F(1.20)  = 23.002;   p < 0.00011;   standard estimation error: 1.5290 
  coef. ai  St. ERR     
    For ai  t(20)  p-level 
a0  -2.02471  0.897001  -2.25720  0.035337 
GAP  0.47868  0.099808  4.79603  0.000110 
 International Conference on Emerging Economic Issues in a Globalizing World, Đzmir, 2008 
 
  170 
CORRELATIONS 
  GAP  ROE 
GAP  1.00  0.73 
ROE  0.73  1.00 
COVARIANCES 
  GAP  ROE 
GAP  11.2  5.85 
ROE  5.5  4.79 
The  difference  between  active  and  passive  interest  explains  by  51%  ROE  variance. 
Although there is a strong correlation between the two indicators, the link between them 
is the following: 
ROEt =  -2.02 + 0.47 . GAPt + εt  
With an increase by one percent of the gap between the two interests, the financial 
profitability ratio increases by 0.47 %. 
Figure 3: ROE and GAP Correlation 
Scatterplot (DATE.STA 27v*24c)
y=-2,025+0,479*x+eps
GAP
R
O
E
-1
0
1
2
3
4
5
6
7
2 4 6 8 10 12 14 16
 
Another factor which influences ROE variance is represented by the funds attracted 
from non-banking customers. The effect analysis is conducted based upon the following 
information: 
The regression result for the dependent variable: ROE 
R = 0.7167;  R
2 = 0.5137;   R
2adjusted = 0.4849; 
F(1.20)  = 21.233;   p < 0.00017;   standard estimation error: 1.5634 
 International Conference on Emerging Economic Issues in a Globalizing World, Đzmir, 2008 
 
  171 
  coef. ai  St. ERR     
    For  ai  t(20)  p-level 
a0  6.481126  1.033644  6.27017  0.000004 
FDCLNEBA  -0.000405  0.000088  -4.59711  0.000175 
CORRELATIONS 
  FDCLNEBA  ROE 
FDCLNEBA  1.00  -0.72 
ROE  -0.72  1.00 
The model which relates the two variables has the following structure: 
ROEt = 6.48 – 0.000405. FDCLNEBAt + εt  
It is observed that for an increase by a million lei of the funds attracted from non-
banking customers, the financial profitability ratio decreases by an average 0.00405 %. 
There is a high enough correlation between the two indicators (ρ = -0.72). Based upon 
the data above, it is observed that FDCLNEBA factor influences ROE variance by 49%. 
Obviously, there are also many other factors which influence ROE variance.  
Figure 4: ROE and FDCLNEBA Correlation 
Scatterplot (DATE.STA 27v*24c)
y=6,481-0*x+eps
FDCLNEBA
R
O
E
-1
0
1
2
3
4
5
6
7
2000 6000 10000 14000 18000 22000
 
The  total  funds  attracted  by  the  bank  (DATORII)  represent  another  factor  which 
influences  ROE  variance.  For  the  analysis  we  take  into  consideration  the  following 
information: 
The regression result for the dependent variable: ROE 
R = 0.6363;  R
2 = 0.4049;   R
2adjusted = 0.3751; 
F(1.20)  = 13.609;   p < 0.00145;   standard estimation error: 1.7295 
 International Conference on Emerging Economic Issues in a Globalizing World, Đzmir, 2008 
 
  172 
  coef. ai  St. ERR     
    For  ai  t(20)  p-level 
a0  6.831070  1.364906  5.00479  0.000068 
DATORII  -0.000338  0.000092  -3.68898  0.001454 
CORRELATIONS 
  DATORII  ROE 
DATORII  1.00  -0.64 
ROE  -0.64  1.00 
The link between the two variables is: 
ROEt = 6. 83 – 0.000338. DATORIIt + εt  
 It is observed that the DATORII influence effect upon ROE is almost the same as in the 
case of the FDCLNEBA factor. For an increase by one million lei of DATORII factor, 
profitability ratio decreases by 0.000338 %. The accounting effect can be converted to a 
more convenient form, if DATORII factor is transformed in billion lei. Only 37% of 
ROE  variance  is  explained  through  DATORII.  Between  the  two  indicators,  the 
correlation level is above average, ρ = -0.64. 
Figure 5: ROE and DATORII Correlation 
Scatterplot (DATE.STA 27v*24c)
y=6,831-0*x+eps
DATORII
R
O
E
-1
0
1
2
3
4
5
6
7
6000 10000 14000 18000 22000 26000
 
Possible influences of factors which can influence ROE variance are also important for 
study. In this way, we analyzed the following correlations which allow us to quantify 
one  factor  variance  effect  upon  others.  In  order  to  study  the  correlation  between 
DATORII and FDCLNEBA we use the following information: 
The regression result for the dependent variable: DATORII 
R = 0.9688;  R
2 = 0.9385;   R
2adjusted = 0.9358; 
F(1.22)  = 336.27;   p < 0.0000;   standard estimation error: 1047.8 International Conference on Emerging Economic Issues in a Globalizing World, Đzmir, 2008 
 
  173 
  coef. ai  St. ERR     
    For  ai  t(20)  p-level 
a0  2834.793  680.9076  4.16326  0.000405 
FDCLNEBA  1.036  0.0565  18.33759  0.000000 
CORRELATIONS 
  FDCLNEBA  DATORII 
FDCLNEBA  1.00  0.97 
DATORII  0.97  1.00 
The interaction between the two variables can be studied with the help of the model: 
DATORIIt =  2834.793 + 1.036  . FDCLNEBAt + εt  
  This  means  that  if  funds  which  are  attracted  from  non-banking  customers 
increase by one million, then debts increase by 1.036 millions. FDCLNEBA explain 
DATORII variance by 53%. It is observed that there is a high correlation level between 
the two indicators, ρ = 0.97. 
Figure 6: DATORII and FDCLNEBA Correlation 
Scatterplot (DATE.STA 27v*24c)
y=2834,793+1,036*x+eps
FDCLNEBA
D
A
T
O
R
I
I
6000
10000
14000
18000
22000
26000
2000 6000 10000 14000 18000 22000
 
The analysis of the link between active (passive) interest and funds which are attracted 
from non-banking customers makes the object of an interesting study. The dependence 
between DOBACTIV and FDCLNEBA is based on the following: 
The regression result for the dependent variable: FDCLNEBA 
R = 0.6524;  R
2 = 0.4257;   R
2adjusted = 0.3996; 
F(1.22)  = 16.310;   p < 0.00055;   standard estimation error: 2997.6 
 International Conference on Emerging Economic Issues in a Globalizing World, Đzmir, 2008 
 
  174 
  coef. ai  St. ERR     
    For ai  t(20)  p-level 
a0  17330.79  1580.083  10.96828  0.000000 
DOBACTIV  -193.69  47.960  -4.03855  0.000549 
CORRELATIONS 
  DOBACTIV  FDCLNEBA 
DOBACTIV  1.00  -0.065 
FDCLNEBA  -0.65  1.00 
DOBACTIV influence upon FDCLNEBA can be summarized in the following model: 
FDCLNEBAt =  17330.79 – 193.69 . DOBACTIVt + εt  
If the active interest increases by 1%, then the funds attracted from the non-banking 
customers decrease by 193.69 million lei. FDCLNEBA variance is explained through 
the DOBACTIV variance by 40%. The correlation level between the two indicators is: ρ 
= -0.65.  
Figure 7: FDCLNEBA and DOBACTIV Correlation 
Scatterplot (DATE.STA 27v*24c)
y=17330,79-193,69*x+eps
DOBACTIV
F
D
C
L
N
E
B
A
2000
6000
10000
14000
18000
22000
5 10 15 20 25 30 35 40 45 50
 
The  correlation  between  FDCLNEBA  and  DOBPASIV  is  studied  based  on  the 
information below. 
The regression result for the dependent variable: FDCLNEBA 
R = 0.6389;  R
2 = 0.4082;   R
2adjusted = 0.3813; 
F(1.22)  = 15.178;   p < 0.00078;   standard estimation error: 3042.9 
 
 International Conference on Emerging Economic Issues in a Globalizing World, Đzmir, 2008 
 
  175 
  coef. ai  St. ERR     
    For  ai  t(20)  p-level 
a0  16597.,30  1460.525  11.36392  0.000000 
DOBPASIV  -233.82  60.017  -3.89590  0.000777 
CORRELATIONS 
  DOBPASIV  FDCLNEBA 
DOBPASIV  1.00  -0.64 
FDCLNEBA  -0.64  1.00 
The econometric model which links the two variables is the following: 
FDCLNEBAt =  16597.30 – 233.82 . DOBPASIVt + εt  
which means that, for an increase by one percent of the passive interest, an average 
decrease by 233.82 million lei of funds which are attracted from non-banking customers 
is registered. Passive interest explains the variance of these funds by 38%. Correlation 
level between the two indicators is of -0.64. 
Figure 8: FDCLNEBA and DOBPASIV Correlation 
Scatterplot (DATE.STA 27v*24c)
y=16597,3-233,818*x+eps
DOBPASIV
F
D
C
L
N
E
B
A
2000
6000
10000
14000
18000
22000
4 10 16 22 28 34 40
 
Conclusions  
Although  ROE  is  influenced  by  many  factors,  a  study  concerning  ROE  variance 
regarding various factors, in the same time, cannot be conducted. This is also observed 
from the independent analysis of influence factors which emphasize a strong co linearity 
phenomenon.  
 
 
 International Conference on Emerging Economic Issues in a Globalizing World, Đzmir, 2008 
 
  176 
References 
Cade E. – Banking Risks, Fitzroy Dearborn Publishers, Chicago, 1999  
Crouhy M., Galai D., Mark R. – Risk Management, McGraw-Hill, New York, 2001 
Fabrozzi F.J, Petersen P.P. – Financial Management & Analysis, John Wiley &Sons, 
Inc., USA, 2003 
Johnston  J.,  Dinardo  J.,  Econometric  Methods,  Fourth  Edition,  the  McGraw  –  Hill 
Companies, Inc., New York, 1997 
Needles B.E. Jr., Anderson H.R., Caldwell J.C., Principles of Accounting, Houghton 
Mifflin Company, Boston, 1987. 
 

Banking Risks, Fitzroy Dearborn Publishers,

Proceedings of the Conference on Emerging Economic Issues in a Globalizing World

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