Research on Investment Value of Bank Stocks Based on Factor Analysis Model

Data

Considering the requirements for data length, sample size, and data stability, this paper selects 16 banks listed on the Shanghai A-shares before 2016. These 16 banks are further divided into 5 state-owned banks and 11 non-state- owned banks. The 5 state-owned banks are Agricultural Bank of China, Bank of Communications, Industrial and Commercial Bank of China, China Construction Bank, and Bank of China. The 11 non-state-owned banks are Ping an Bank, Bank of Ningbo, Shanghai Pudong Development Bank, Huaxia Bank, China Minsheng Bank, China Merchants Bank, Bank of Nanjing, Industrial Bank, Bank of Beijing, China Everbright Bank, and China CITIC Bank. By analysing data from the first three quarters of 2022, the relevant sample data mainly come from each bank’s quarterly data available in the Tonghuashun database.

Based on the factors influencing bank stock investment value, this paper constructs an index system from four aspects reflecting the growth ability, expansion ability, operating ability, and solvency of banks. It selects 11 indicators, including net profit, year-on-year growth rate of net profit, total operating income, growth rate of total operating income, basic earnings per share, earnings per share, capital reserve per share, undistributed profit per share, return on equity, diluted return on equity, and asset-liability ratio, to form a comprehensive evaluation index system of bank investment value [21] as shown in Table 1.

Before conducting factor analysis on the data, pre- processing is necessary. Firstly, among the 11 indicators, the asset-liability ratio is a negatively oriented indicator, while the rest are positively oriented indicators. Therefore, the asset-liability ratio needs to be positively oriented. The formula for positive orientation is 1/|X-X ̅|. Secondly, standardization processing is performed on individual time cross-section data.

The Model

The basic idea of factor analysis is dimensionality reduction. This involves studying the internal structure of the correlation matrix of variables to identify a few key variables that can describe the relationships among multiple variables. Variables are then grouped based on the size of their correlations, with higher correlations within the same group and lower correlations between different groups. The aim is to synthesize the complex relationships of the variables into a smaller number of factors that represent the original variables’ relationships with the factors. The specific steps are as follows:

1. Suppose there are n samples and m observations, and the original data is represented as matrix V = (V1,⋯,Vm).
2. Standardize the original data to eliminate differences in scale among variables.
3. Construct the correlation matrix R of variables and perform principal component analysis on R.
4. Perform the Kaiser-Meyer-Olkin (KMO) test and Bartlett’s test to determine whether factor analysis is appropriate for the data.
5. Calculate the eigenvalues λ1≥λ2≥⋯≥λp and corresponding unit eigenvectors of R.

Generally, select the number of common factors based on eigenvalues greater than 1 and cumulative variance contribution rate greater than 80%. Extract the first P eigenvalues and their corresponding eigenvectors to form the loading factor matrix A, A=[A]

m×p. 6. Apply varimax orthogonal rotation to matrix A. 7. Compute factor scores.

Standard factor analysis typically applies to cross- sectional data only. Based on panel data and an improved factor analysis model incorporating Topsis [21], the calculation steps are as follows:

Standard factor analysis typically applies to cross- sectional data only. Based on panel data and an improved factor analysis model incorporating Topsis [21], the calculation steps are as follows: 1. Establish the indicator system, with the set of objects under study denoted as Sti (i=1,2,⋯,n), the set of indicators denoted as Utj (j=1,2,⋯,m), and n representing the number of evaluation objects, t∈[t1,t2 ]. If the evaluation period spans years, then I=t1-t2+1. 2. Conduct factor analysis on Sti using cross-sectional data, obtaining the factor composite score yt1, yt2,⋯,ytn for each object set, where represents the time point, thus obtaining the (Yti)n×l matrix. 3. Apply the Topsis method to evaluate the final factor composite score (yti) of object set Sti (i=1,2,⋯,n). The specific steps are as follows:

The factor analysis scores of cross-sectional data for each quarter serve as an evaluation indicator system for bank investment value. This forms a new indicator system, consisting of l indicators, n evaluation objects, and (yti) data points.

First, normalize the l indicators as shown in Equation 1:

Y Z Y = = ∑

ti ti n (1)

2 ti i

1 Second, normalize the matrix, where the optimal and worst vectors are composed of the maximum and minimum values of each column, respectively, as shown in Equations 2 and 3 below.

( ) 1 2 , , , max max maxi Z Z Z Z + = Λ (2)

( ) 1 2 , , , min min minl Z Z Z Z −= Λ (3)

Third, the distance between the ith evaluation object and the optimal/worst solutions is calculated as shown in Equations 4 and 5 below.

l ( = = − ∑ (4)

2 1 1 ) i max ji j D Z Z +

l ( = = − ∑ (5)

2 1 1 ) i min ji j D Z Z −

Fourth, the proximity degree C between the ith evaluation object and the optimal/worst solutions is determined as shown in Equation 6 below.

i i − D C D D

+ − = + (6) i i

If Ci is larger, it indicates that the investment value of the ith bank from the first quarter to the third quarter of 2022 is higher; conversely, it indicates that the value is lower.

Cross-Sectional Data Factor Analysis

1. The KMO (Kaiser-Meyer-Olkin) and Bartlett tests were conducted on the standardized data using SPSS software, and the results are shown in Table 2 below.

Generally, the KMO statistic should not be less than 0.5. As shown in Table 2, the KMO statistics for all three quarters are greater than the minimum requirement of 0.5. The accompanying probabilities for Bartlett’s test are all 0, indicating a small probability event. Therefore, the hypothesis that the correlation matrix is an identity matrix is rejected, leading to the conclusion that there are significant correlations among the 11 factors. It is thus considered appropriate to conduct dimensionality reduction using factor analysis.

2. With the assistance of SPSS, factor analysis was conducted separately on the cross-sectional data for the first, second, and third quarters of 2022. The principal factor eigenvalues, contribution rates, and cumulative contribution rates are presented in Table 3 below.

From Table 3, it can be observed that through factor analysis, 11 eigenvalues were obtained. For the first quarter, the first eigenvalue is 5.483, explaining a variance contribution rate of 35.665%; the second eigenvalue is 2.359, explaining a variance contribution rate of 24.618%; the third eigenvalue is 1.561, explaining a variance contribution rate of 23.762%; and the fourth eigenvalue explains a cumulative variance contribution rate of 9.349%. At this point, the cumulative variance contribution rate reaches 93.394%, so the first four common factors are selected.

For the second quarter, the first eigenvalue is 4.932, explaining a variance contribution rate of 28.078%; the second eigenvalue is 2.683, explaining a variance contribution rate of 27.184%; the third eigenvalue is

1.516, explaining a variance contribution rate of 22.139%; and the fourth eigenvalue explains a cumulative variance contribution rate of 13.541%. At this point, the cumulative variance contribution rate reaches 90.942%, so the first four common factors are selected.

For the third quarter, the first eigenvalue is 5.192, explaining a variance contribution rate of 30.538%; the second eigenvalue is 2.292, explaining a variance contribution rate of 26.784%; the third eigenvalue is 1.64, explaining a variance contribution rate of 24.219%; and the fourth eigenvalue explains a cumulative variance contribution rate of 9.471%. At this point, the cumulative variance contribution rate reaches 91.012%, so the first four common factors are selected.

In factor analysis, the larger the absolute value of the coefficient between a variable and a factor, the closer the relationship between the variable and that factor.

Analysing the coefficient matrices of the first, second, and third quarters, as shown in Table 4, it can be observed that: The first component primarily explains factors zx5, zx6 and zx8, corresponding to variables such as return on equity, basic earnings per share, net asset per share, and undistributed profits per share, reflecting primarily the bank’s expansion capability [25]. The second component mainly interprets factors zx1, zx2, zx3 and zx4, corresponding to variables such as year-on-year growth rates of net profit, operating income, return on equity, and diluted return on equity, predominantly reflecting the bank’s growth capability [26]. The third component mainly explains factors zx7, zx9 and zx10, corresponding to variables such as capital reserves per share, net profit, and operating income, primarily reflecting the bank’s profitability [27]. The fourth component mainly explains factor zx11, corresponding to the variable asset- liability ratio, primarily reflecting the bank’s solvency [28].

3. Based on the factor score results, calculate the scores of each common factor for each quarter.

0.12 0.137 ... 0.083 0.021 F

=− − + + +   = + + + +  = + + + +   =− − + − − 

1 ZX ZX ZX ZX

1 2 10 11 (8) (8)

0.408 0.426 ... 0.084 0.178 F

2 ZX ZX ZX ZX

1 2 10 11

According to Table 5, in the first quarter, from the expansion capability factor (F1), it can be observed that the top three are China Merchants Bank, Industrial Bank, and Ningbo Bank, while the bottom three are Agricultural Bank of China, Bank of Communications, and China Everbright Bank. From the growth capability factor (F2), it is evident that the top three are Nanjing Bank, Ningbo Bank, and Ping An Bank, whereas the bottom three are China Everbright Bank, Huaxia Bank, and Minsheng Bank. From the profitability factor (F3), the top three are China Construction Bank, Industrial and Commercial Bank of China, and Agricultural Bank of China, while the bottom three are Ping An Bank, Ningbo

Bank, and Huaxia Bank. From the debt-paying ability factor (F4), it is apparent that the top three are Shanghai Pudong Development Bank, Agricultural Bank of China, and China Construction Bank, whereas the bottom three are Bank of Beijing, Minsheng Bank, and China Merchants Bank.

According to Table 6, in the second quarter, from the expansion capability factor (F1), it can be observed that the top three are China Merchants Bank, Industrial Bank, and Ningbo Bank, while the bottom three are Bank of China, Agricultural Bank of China, and China Everbright Bank. From the growth capability factor (F2), it is evident that the top three are Ningbo Bank, Nanjing Bank, and Ping An Bank, whereas the bottom three are Shanghai Pudong Development Bank, Huaxia Bank, and Minsheng Bank. From the profitability factor (F3), the top three are Industrial and Commercial Bank of China, China Construction Bank, and Agricultural Bank of China, while the bottom three are Ningbo Bank, Huaxia Bank, and Bank of Beijing. From the debt-paying ability factor (F4), it is apparent that the top three are China Merchants Bank, Nanjing Bank, and China Everbright Bank, whereas the bottoms three are Industrial Bank, Shanghai Pudong Development Bank, and Ping An Bank.

According to Table 7, in the second quarter, from the expansion capability factor (F1), it can be observed that the top three are China Merchants Bank, Industrial Bank, and Ningbo Bank, while the bottom three are Agricultural Bank of China, China Everbright Bank, and Nanjing Bank. From the growth capability factor (F2), it is evident that the top three are Nanjing Bank, Ping An Bank, and Ningbo Bank, whereas the bottom three are Huaxia Bank, Minsheng Bank, and Shanghai Pudong Development Bank. From the profitability factor (F3), the top three are Industrial and Commercial Bank of China, China Construction Bank, and Agricultural Bank of China, while the bottom three are Huaxia Bank, Shanghai Pudong Development Bank, and Ningbo Bank. From the debt- paying ability factor (F4), it is apparent that the top three are China Construction Bank, Ping An Bank, and Shanghai Pudong Development Bank, whereas the bottom three are Minsheng Bank, Bank of Beijing, and China Merchants Bank.

1. The comprehensive evaluation score F can be obtained by weighting the contribution rates of each main factor’s variance relative to the cumulative contribution rate of the four main factors and summing them up. The formula for the first quarter is as follows:

( ) 1 2 3 4 35.665 24.618 23.762 9.349 F 93.349 F F F F + + + = (10

The formula for the second quarter is as follows:

( ) 1 2 3 4 28.078 27.184 22.139 13.541 F 90.942 F F F F + + + = (11)

The formula for the third quarter is as follows:

( ) 1 2 4 30.538 26.784 24.219 9.471 F 91.012 F F F + + + = (12)

Finally, the comprehensive evaluation scores of cross- sectional factor analysis for the first quarter, second quarter, and third quarter are obtained, as shown in Table 8 below.

According to Table 8, the top three banks in terms of composite factor scores for the first quarter are Industrial and Commercial Bank of China, Agricultural Bank of China, and China Construction Bank, while the bottom three are China Merchants Bank, Bank of Communications, and Bank of China; for the second quarter, the top three banks are Industrial and Commercial Bank of China, China Construction Bank, and Agricultural Bank of China, while the bottom three are China Merchants Bank, Bank of China, and Bank of Communications; and for the third quarter, the top three banks are Industrial and Commercial Bank of China, China Construction Bank, and Agricultural Bank of China, while the bottom three are China Merchants Bank, Bank of Communications, and Bank of China.

Based on Panel Data and Topsis-Improved Factor Analysis

Luo G, et al. [29] and Xiao Hongfei [30] calculated the evaluation results of stock investment value for 16 banks in the first, second, and third quarters of 2022 using a factor analysis model based on panel data and Topsis improvement, as shown in Table 9.

According to Table 9, among the 16 banks, the top three are Industrial and Commercial Bank of China, China Construction Bank, and Agricultural Bank of China, while the bottom three are Bank of Communications, Shanghai Pudong Development Bank, and China Merchants Bank. Among the top three banks, two are state-owned banks, while among the bottom three banks, all are non-state-owned banks. The ranking of state- owned banks among the 16 banks is 3rd, 5th, 8th, 9th, and 12th, corresponding to China Construction Bank, Industrial and Commercial Bank of China, Agricultural Bank of China, Bank of China, and Bank of Communications, respectively.