The data set reflects the outlook of proposed creditability measures of 1000 samples of the Australian bank. On the view point of their performances and performances of other parameters, the bank would decide whether it would provide creditability or not.
The necessary cost-profit portfolio analysis is being executed with the help of this data. Most of the data variables are categorical (ordinal or nominal). For purpose of analysis, we transformed the numerical data set into categorical variables too.
The Jasp (version 0.8.6.0) software or tool is utilised in this analysis for solving the assignment. However, we have taken the help of MS Excel (the format in which data set is given) in some instances of the calculation or execution, where Jasp software faced failure.
Firstly, the three numerical variables of the data set are merged in categorical variables. Credit amount is transformed into categorical variable (credit amount < $2000 = “1”, $2000<= credit amount <$4000 = “2”, $4000 <=credit amount < $6000 = “3”, credit amount => $6000 = “4”). Age is transformed to age group (age < 25 = “1”, 25<age<50 = “2,” 50<=age <=75 = “3”). Duration of monthly credit (months <20 = “1”, 20<=months<40 = “2”, 40 <=months<60 = “3”, 60<=months<80 = “4”).
The recoding is not possible in Jasp software. Therefore, we took the help of MS Excel.
2. Splitting the dataset into Training and Testing data set:
By random sample drawing process, we have drawn the random samples in MS Excel and out of then 80% (800 samples) are chosen for training data set and 20% (200 samples) are selected for testing data set. This operation is also not possible in Jasp tool. Therefore, in this case also, the help of MS Excel is also taken.
The descriptive statistic of Creditability, Account balance, Payment Status of Previous credit and Purpose of training data indicates that the average values are 0.693, 2.539, 2.556 and 2.804 respectively (Altman and Bland 1996). The standard deviations of these categorical variables are 0.462, 1.252, 1.097 and 2.749 respectively. The Creditability, Account balance, payment Status of Previous Credit vary from 0 to 1, 1 to 4, 0 to 4 and 0 to 10 level respectively.
The descriptive statistic of Value Savings/Stocks, Length of current employment, Instalment per cent and Sex & Marital Status of training data shows that the average values are 2.07, 3.395, 2.958 and 2.672 respectively. The standard deviations of these categorical variables are 1.562, 1.207, 1.113 and 0.713 respectively. The Value Savings/Stocks, Length of current employment, Instalment per cent and Sex & Marital Status vary from 1 to 5, 1 to 5, 1 to 4 and 1 to 4 level respectively.
The descriptive statistic of Guarantors, Duration in Current Address, most valuable available asset, Concurrent Credits and Type of apartment of training data shows that the average values are 1.144, 2.886, 2.377, 2.674 and 1.921 respectively. The standard deviations of these categorical variables are 0.475, 1.093, 1.062, 0.706 and 0.539 respectively. The Value Guarantors, Duration in Current Address, most valuable available asset, Concurrent Credits and Type of apartment vary from 1 to 3, 1 to 4, 1 to 4, 1 to 3 and 1 to 3 level respectively.
The descriptive statistic of Number of Credits at this bank, Occupation, number of dependents, Telephone and Foreign Workers of training data shows that the average values are 1.413, 2.875, 1.156, 1.389 and 1.036 respectively. The standard deviations of these five categorical variables are 0.583, 0.661, 0.363, 0.448 and 0.187 respectively. The Number of Credits at this bank, Occupation, number of dependents, Telephone and Foreign Workers vary from 1 to 4, 1 to 4, 1 to 2, 1 to 2 and 1 to 2 level respectively
The descriptive statistic of Duration of monthly credit, Amount of Credit and Age group of training data shows that the average values are 1.524, 1.964 and 1.915 respectively. The standard deviations of these categorical variables are 0.638, 1.059 and 0.548 respectively. The Duration of monthly credit, Amount of Credit and Age group vary from 1 to 3, 1 to 4 and 1 to 3 level respectively.
Out of 800 people, 30.75% people are not credit worthy and rest of 69.25% people are credit worthy.
Out of 800 people, 28.375% people have no balance or debit followed by 27.875% people have no running account. A highest percentage of 38% people have checked out $200 for at least 1 year.
A highest percentage of 52% people have no previous or pending credits followed by 30.125% people who had paid back previous credits at this bank. Only 4.25% and 4.875% people are facing hesitant payment of previous credits and problematic running account.
A highest percentage of 27.875% people need credit for purchasing items and furniture followed by the 24.375% people require credit for purchasing other purposes. It is notable that the percentage of people who need credit for purchasing used cars (9.875%) is also satisfactory.
Among 800 chosen people, mostly (61.375%) people have no available savings followed by 17.625% people who have more than $1000 savings.
Only 6.125% people are currently unemployed. 34.25% people are employed for 1 to 4 years followed by 25.625% people who are employed for more than 7 years.
A significant number of 46.5% people are under the Instalment percent less than 20%.
53.875% people are either single or widowed male. Only 9.25% people are females.
90.75% people has no guarantor of their credits.
42.5% people are living in their current addresses for more than 7 years followed by 29.625% people who are living in their current addresses for only 2 to 4 years.
More than 33% people have savings contract with building society or life insurance.
A very high percentage of 81.25% people prefer to run no further credits.
More than 70% people are living in owner-occupied flat with highest percentage and only 10.875% people are living in rented flat with least frequency.
More than 62% people have only one credit in this bank and only 0.75% people have six or more credits in this bank.
The people who are asking for credit in this bank are either skilled worker or skilled employees and minor civil servants. Only 2.625% unemployed or unskilled labour will no permanent resistance are asking for credit.
84.375% employees have 3 or more dependents.
61.125% people are using telephones whereas 38.875% people are not using telephones.
96.375% people are foreign workers whereas 3.625% people are not foreign workers.
The duration if credits of employees less than 40 months is for 55.5% people, followed by the duration of credits of employees less than 60 months but greater than 40 months is for 36.625% people.
The frequency of people is highest for the people whose amount of credit is less than $2000 (42.875%) followed by the frequencies with credit amount more than $2000 but greater than $4000 (32.875%).
Major number of people belong to the age-group 25 years to 50 years with percentage almost 70%.
The statistically significant associations with explanatory variable Creditability is found in case of the following variables-
1) Account Balance (r = 0.358, p-value <0.001): Moderate positive correlation (Lee Rodgers and Nicewander 1988)
2) Payment Status of previous credits (r = 0.249, p-value <0.001): Weak positive correlation
3) Value savings/stocks (r = 0.174, p-value <0.001): Weak positive correlation
4) Length of current employment (r =0.124, p-value<0.001): Weak positive correlation
5) Most valuable available assets (r = -0.13, p-value<0.001): Weak negative correlation
6) Concurrent Credits (r = 0.141, p-value <0.001): Weak positive correlation
7) Duration of monthly Credits (r = -0.175, p-value <0.001): Weak negative correlation
8) Credit amount (r = -0.112, p-value = 0.001): Weak negative correlation.
This test help to find the equality of averages of any numerical variable (here, Creditability) with respect to different levels of categorical variables (here, age and sex). For calculation, we transformed the level 1,2 and 3 to the level “Males” and level 4 to the level “Females”. This recoding is not possible in Jasp software. Therefore, we have incorporated this in MS Excel.
The independent sample t-test produces the t-value 0.62 with 998 degrees of freedom and p-value 0.535. The mean creditability of 92 females is 0.728 and 908 males are 0.697.
The p-value greater than 0.05, indicates that the averages of creditability with respect to both the genders is significantly different to each other. Therefore, it is 95% evident that the averages of creditability are different for males and females (Heeren and D’Agostino 1987).
Training data
|
Coefficients |
Wald-Chi-square |
|
(Intercept) |
11.33423872 |
|
Account Balance |
56.25 |
|
Payment Status of Previous Credit |
16.24837921 |
|
Purpose |
1.525951557 |
|
Value Savings/Stocks |
9.460284665 |
|
Length of current employment |
2.963627624 |
|
Instalment per cent |
14.87755102 |
|
Sex & Marital Status |
2.743164063 |
|
Guarantors |
2.078280811 |
|
Duration in Current address |
0.003460208 |
|
Most valuable available asset |
4.364376042 |
|
Concurrent Credits |
8.150104058 |
|
Type of apartment |
1.205222117 |
|
No of Credits at this Bank |
1.289571962 |
|
Occupation |
0.011531012 |
|
No of dependents |
0.516601563 |
|
Telephone |
3.058274405 |
|
Foreign Worker |
2.698979592 |
|
Duration_of_monthly_Credit |
4.794589774 |
|
Credit_Amonth |
3.398412098 |
|
Age_group |
2.891921223 |
(Source: Fears, Benichou and Gail 1996)
The logistic regression model takes into consideration “Creditability” as dependent and all other variables as independent variables. The logistic regression model interprets that that significant factors that influence the rate of Creditability are Account balance, payment Status of Previous Credits and Instalment per cent. Rest of the factors do not significantly impact the dependent factor- Creditability. It could be suggested that variables like Duration in current address (Wald statistic = 0.003), Occupation (Wald statistic = 0.0115) and number of dependents (Wald statistic = 0.5) could be easily omitted from the model.
The AIC value is 814.369. It indicates that the model is not badly fitted. The significant p-value (p < 0.001) indicates that the model is well fitted (Harrell 2001).
The logistic regression on testing data indicates that the model is also good fitted (p-value <0.001) with AIC value = 215.79. However, only Account balance is found significant in the logistic model of testing data with significant p-value less than 0.001. In this logistic regression model, the Wald Chi-square statistic also validates that Purpose (Wald statistic = 0.49), Duration in current address (Wald statistic = 0.005), Age group (Wald statistic = 0.69), foreign workers (Wald statistic = 0.0001) and Occupation (Wald statistic = 0.001) are unnecessary predictors present in the variable. These variables should be eliminated from the logistic model.
Therefore, it could be said that the logistic regression model executed on training data do not completely validates the logistic regression on testing data.
|
Coefficients |
Wald Chi-square |
|
(Intercept) |
0.000225 |
|
Account Balance |
13.77036 |
|
Payment Status of Previous Credit |
5.653374 |
|
Purpose |
0.49 |
|
Value Savings/Stocks |
7.716049 |
|
Length of current employment |
2.626635 |
|
Instalment per cent |
0.756144 |
|
Sex & Marital Status |
3.114915 |
|
Guarantors |
2.528843 |
|
Duration in Current address |
0.005262 |
|
Most valuable available asset |
0.671978 |
|
Concurrent Credits |
0.979275 |
|
Type of apartment |
1.367808 |
|
No of Credits at this Bank |
3.356839 |
|
Occupation |
0.001072 |
|
No of dependents |
0.206612 |
|
Telephone |
0.409489 |
|
Foreign Worker |
0.000168 |
|
Duration_of_monthly_Credit |
0.046172 |
|
Credit_Amonth |
4.548889 |
|
Age_group |
0.690305 |
When a bank rejects an applicant with a good credit risk who are likely to repay the loan, then it results loss in business and also when a bank accepts an applicant with a bad credit risk, then also it results the financial loss in business. The two decisions that might bring causes of loss and profit are said two be wrong and correct decisions. The analysis incorporates the total credit amount is $3271248. As per fitted logistic model of training data, we find the probabilities of credit risk of the whole data set (1000 samples). If the credit risk probabilities are found greater than equal to 0.5, then we consider it risky and level it by “1”. If credit risk probabilities are found lesser than 0.5, then we consider it non-risky and therefor level it “0”. For, equality of levels of “Creditability” and “Credit risk” (1 or 0 for both cases), we consider wrong decision and otherwise correct decision. Further, the revenues for correct decisions are accounted as 135% and for wrong decisions are accounted as 0%. The total revenue is found $1256545.9. The deficit is calculated as $2014703. The bank would face a loss if they would not verify their creditability procedure (Ray and Das 2010). Note that, Cost-profit analysis is almost impossible by Jasp software. Therefore, we executed it by MS Excel.
References:
Altman, D.G. and Bland, J.M., 1996. Detecting skewness from summary information. British Medical Journal, 313(7066), pp.1200-1201.
Fears, T.R., Benichou, J. and Gail, M.H., 1996. A reminder of the fallibility of the Wald statistic. The American Statistician, 50(3), pp.226-227.
Harrell, F.E., 2001. Ordinal logistic regression. In Regression modeling strategies (pp. 331-343). Springer, New York, NY.
Heeren, T. and D’Agostino, R., 1987. Robustness of the two independent samples t?test when applied to ordinal scaled data. Statistics in medicine, 6(1), pp.79-90.
Lee Rodgers, J. and Nicewander, W.A., 1988. Thirteen ways to look at the correlation coefficient. The American Statistician, 42(1), pp.59-66.
Ray, S.C. and Das, A., 2010. Distribution of cost and profit efficiency: Evidence from Indian banking. European Journal of Operational Research, 201(1), pp.297-307.
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