Robustness analysis

This study employs logistic regression analysis to identify significant variables and the optimum cut-off rates of each markup interval. The incorporation of insignificant variables can affect the accuracy of the π values.

Therefore, after eliminating the insignificant variables, we conduct logistic regression analysis on the significant variables to calculate the π values with greater accuracy. The results in Table 16 indicate that, excluding the deposit performance variable, all variables have a significant influence on defaults under the mutual effects of the 10 significant variables.

We take the 10 significant variables as a basis to calculate the π value of the various borrowers and use the profit calculation formula mentioned above (the profit functions 1 to 4) to identify the optimum cut-off rates (Table 17). The results show that compared to the previous points or locations for cut-off rates, the locations calculated during this analysis – namely, 0.76, 0.64, 0.56, and 0.43 - are more concentrated. This indicates that when the value of a borrower is 0.76, the bank offers the benchmark interest-rate markup of 4.5%; when the value is between 0.76 and 0.64, the markup is 3%; when the value is between 0.64 and 0.56, the markup is 2.5%; when the value is between 0.56 and 0.43, the markup is 2%; and when the value is less than 0.43, 1% is added to the benchmark

Rate (%)

Cut-off

Figure 2

The optimum cut-off rates

This figure shows the optimum cut-off rates of each interest-rate markup interval. The vertical axis denotes the interest-rate markups, and the horizontal axis denotes the cut-off points from 0 to 1.

Table 16

Logistic regression analysis — Robustness test

This table presents the results of logistic regression after robustness analysis. A total of 804 valid samples are analyzed, and the variables include annual income, government preferential policies, loan period, number of guarantors, occupation, deposit performance, the period of credit-granting business, and the period of active bank accounts (9 items). B is the regression coefficient, and S. D. is the standard deviation.

Variable B S. D. T Significance

Constant -4.700 0.792 -5.831 0.001

Annual income -0.001 -0.001 -1.913 0.015**

Government preferential policies -0.598 0.250 -2.777 0.005**

Loan periods 0.108 0.179 2.503 0.004**

Number of guarantors 0.299 0.213 2.198 0.013**

Occupation 0.711 0.219 3.681 0.001**

Deposit performance 0.002 0.003 0.989 0.158

The period of credit-granting business 0.098 0.049 1.854 0.051*

The period of active bank accounts -0.102 0.058 -1.798 0.075*

The holding of credit cards -0.215 0.127 -1.060 0.158

** denotes a 0.05 significance level; * denotes a 0.10 significance level.

0

158Rationality of the personal loan interest-rate markups of banks Table 17 The optimum cut-off rates — Robustness test This table presents the profits of the bank within each cut-off rate after robustness analysis (the significant variables are selected). 𝐶𝐶1, 𝐶𝐶2, 𝐶𝐶3, and 𝐶𝐶4are the cut-off rates of the five interest-rate markup intervals. 𝐿𝐿𝑙𝑙is the number of loans that had equivalent low forecast and actual interest rates. 𝐿𝐿

ℎis the number of loans that had a forecast interest rate greater than the actual interest rate. 𝐻𝐻𝑙𝑙is the number of loans that had a forecast interest rate of less than the actual interest rate. 𝐻𝐻ℎis the number of loans that had equivalent high forecast and actual interest rates. Profit is the sum of the profits of each cut-off rate. Probability is the number of loans in the various conditions divided by the total number of loans. Cut- off𝑪𝑪𝟏𝟏𝐶𝐶2𝑪𝑪𝟑𝟑𝑪𝑪𝟒𝟒 𝐿𝐿𝑙𝑙𝐿𝐿ℎ𝐻𝐻𝑙𝑙𝐻𝐻ℎProfit 𝐿𝐿𝑙𝑙𝐿𝐿ℎ𝐻𝐻𝑙𝑙𝐻𝐻ℎProfit 𝐿𝐿𝑙𝑙𝐿𝐿ℎ𝐻𝐻𝑙𝑙𝐻𝐻ℎProfit 𝐿𝐿𝑙𝑙𝐿𝐿ℎ𝐻𝐻𝑙𝑙𝐻𝐻ℎProfit (Probability)(Probability)(Probability)(Probability) 0.99210024600.0049310014600.013939206400.022742802800.0265 (0.46)(0.00)(0.54)(0.00)(0.68)(0.00)(0.32)(0.00)(0.86)(0.00)(0.14)(0.00)(0.94)(0.00)(0.06)(0.00) 0.90210024330.0052310014330.014239206130.023142802620.0269 (0.46)(0.00)(0.53)(0.01)(0.68)(0.00)(0.31)(0.01)(0.86)(0.00)(0.13)(0.01)(0.94)(0.00)(0.05)(0.01) 0.80210024060.0055310014060.014639205860.023542802260.0277 (0.46)(0.00)(0.53)(0.01)(0.68)(0.00)(0.31)(0.01)(0.86)(0.00)(0.13)(0.01)(0.94)(0.00)(0.05)(0.01) 0.762100232140.00633100132140.0155392050140.0245424418100.0279 (0.46)(0.00)(0.51)(0.03)(0.68)(0.00)(0.29)(0.03)(0.86)(0.00)(0.11)(0.03)(0.93)(0.01)(0.04)(0.02) 0.702100226200.00693100126200.0162385450160.0240419917110.0275 (0.46)(0.00)(0.50)(0.04)(0.68)(0.00)(0.28)(0.04)(0.84)(0.01)(0.11)(0.04)(0.92)(0.02)(0.04)(0.02) 0.642101215300.00783082117290.0170385940220.02464092016110.0262 (0.46)(0.01)(0.47)(0.07)(0.68)(0.00)(0.26)(0.06)(0.84)(0.02)(0.09)(0.05)(0.90)(0.04)(0.04)(0.02) 0.602083207380.00843056110350.01733781537260.02433953514120.0245 (0.46)(0.01)(0.45)(0.08)(0.67)(0.01)(0.24)(0.08)(0.83)(0.03)(0.08)(0.06)(0.87)(0.08)(0.03)(0.02) 0.5620410182600.01013001690500.01823583631310.02243617211120.0200 (0.45)(0.02)(0.40)(0.13)(0.66)(0.04)(0.20)(0.10)(0.78)(0.08)(0.07)(0.07)(0.79)(0.16)(0.02)(0.03) 0.5019819157820.01152834072610.01733415825320.020231911510120.0144 (0.44)(0.04)(0.34)(0.18)(0.62)(0.09)(0.16)(0.13)(0.75)(0.13)(0.05)(0.07)(0.70)(0.25)(0.02)(0.03) 0.43196191161250.01552537061720.015129510520360.01492951408130.0115 (043)(0.04)(0.25)(0.28)(0.56)(0.15)(0.13)(0.16)(0.65)(0.23)(0.04)(0.08)(0.64)(0.31)(0.02)(0.03) 0.4018567751290.01382309558730.012429411014360.01472551816140.0064 (0.41)(0.15)(0.16)(0.28)(0.50)(0.21)(0.13)(0.16)(0.65)(0.24)(0.3)(0.08)(0.56)(0.40)(0.01)(0.03) 0.30150108501480.012019014540810.008424016611390.0081180257415-0.0034 (0.33)(0.24)(0.11)(0.32)(0.42)(0.32)(0.09)(0.17)(0.53)(0.36)(0.02)(0.09)(0.40)(0.56)(0.01)(0.03) 0.2094132701600.008415618029910.0056155250744-0.0020145292316-0.0078 (0.21)(0.29)(0.15)(0.35)(0.34)(0.39)(0.06)(0.20)(0.34)(0.55)(0.01)(0.10)(0.32)(0.64)(0.01)(0.03) 0.1063158581770.0070882591099-0.0017124280646-0.005693345117-0.0145 (0.14)(0.35)(0.13)(0.38)(0.19)(0.57)(0.02)(0.22)(0.27)(0.62)(0.01)(0.10)(0.20)(0.76)(0.00)(0.04) 0.0131184322090.0071452897115-0.004552350054-0.013642395019-0.0209 (0.07)(0.40)(0.07)(0.46)(0.10)(0.63)(0.01)(0.25)(0.11)(0.77)(0.00)(0.12)(0.09)(0.87)(0.00)(0.04)

interest rate as the interest rate (see Figure 3). After eliminating the insignificant variables, the forecast π values are more accurate. Therefore, the identified cut-off rates are more accurate than those of the previous and the profits are greater than those of the previous calculation.

6. Conclusions

Based on the principle of profit maximization, we develop a model for optimizing the interest-rate markups of bank loans. We take 804 personal loan cases sourced from a Taiwan bank as the research samples and analyze the practical credit evaluation items used by banks for personal loans or credit-granting to identify the significant variables influencing personal credit-granting quality. Furthermore, we identify the rational interest-rate markups of loans using the model developed by the linear formula, which can provide a reference for bank loan officers to develop credit-granting strategies

Rate (%)

Cut-off

Figure 3

Robustness analysis－The optimum cut-off rates

This figure shows the optimum cut-off rates of each interest-rate markup interval for the robustness analysis. The vertical axis denotes the interest-rate markups, and the horizontal axis denotes the cut-off points from 0 to 1.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0 0.43 0.56 0.64 0.76 1

1%

2%

2.5%

3%

4.5%

and maximize bank profits.

The purpose of this study is to develop a model that can be a reference for banks. On the premise of competition, we hope to find the optimal interest rate on loans not only to avoid a rate that is too low and affects profits, but one that is too high and drives potential customers to other competitors. Doing analysis and screening of regular customers to find the optimal interest rate, of course we see that the better the conditions of the customer are, the lower the interest rate offered. However, we need to develop a model to discover the most optimal one.

For this study we reference the extent literature and the variables used in existing loan evaluation mechanisms of banks to select empirical variables. The significant variables are selected based on the empirical results and include government preferential policies, interest rates, loan periods, the number of guarantors, occupation, deposit performance, the period of credit-granting business, the period of active bank accounts, and the holding of credit cards.

Regarding rationality of the interest-rate markups, under the premise and goal of profit maximization, we employ the sample information and the model developed from the linear formula to calculate the optimum cut-off rates of each markup interval. The higher the cut-off rate is, the higher the markup.

The empirical results of this study have two primary contributions to the literature. First, the results can reduce the default risk of credit-granted customers and reduce bank default rates. Second, this unprecedented study has explored the rationality of interest-rate markups. By targeting profit maximization, we utilize the model developed from the linear formula to calculate the optimum cut-off rates to determine the interest-rate markups of loans.

The management implications of this study are to develop applicable models to provide banks with the most objective and accurate method for evaluating the optimal interest rate of their loans, so as to not lose loyal customers due to a high interest rate nor lose profits due to a low interest rate. This method can serve as a calculation tool for the credit-granting unit of banks to calculate rational interest-rate markups and loan amounts. Additionally, banks can use the profit calculation formula developed herein as well as their policy needs to establish markup standards to improve the accuracy of the markup amounts for loans. This will enable the credit-granting unit of banks to offer more accurate and rational interest-rate markups for loans. Furthermore, borrowers can use this empirical

model to examine the rationality of the interest rates offered by various banks when applying for loans.

Although we have conducted this study as rigorous as possible, there are still some limitations. The samples were difficult to find, and so the number of cases was not really adequate. Building up another out-of-sample case to verify our model has some difficulties. The clients included in the study were also selected and reviewed by the credit-granting unit of banks, which may also have an effect on the accuracy.

Because of the differences of loan business in several types of banks (such as public banks, SME banks, commercial banks, global banks), we recommend researchers who are interested in this topic to conduct follow-up analyses. One can compare different behaviors when speaking of a raise in the interest rate between banks, expand the numbers of samples to reduce variation, pick cases that reflect actual situations better, and use the non-performing loan ratio in order to make the study more practical.

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