Analysis of Correlation of Variables

A summary of the selected set of financial indicators that have been analysed in the previous section is shown in Table 3.15.

Table 3.15: The Financial Indicators

Financial Ratios Variables for statistical

analysis

Capital adequacy ratio (CAR) R1

Regulatory capital to risk-weighted assets ratio R2 Regulatory Tier 1 capital to risk-weighted assets ratio R3

Equity to debt ratio R4

Debt to equity ratio (financial leverage) R5

Nonperforming loans to total gross loans ratio R6 Nonperforming loans net of provisions to capital ratio R7

Salary to assets ratio R8

Retained earnings to total assets ratio R9

Return on equity ratio R10

EBIT to total assets ratio R11

Net interest margin R12

Interest rate spread R13

Working capital to total assets ratio R14

Current ratio R15

Source: Author

As was noted in section 3.3.2 the selected sample is not normaly distributed (Appendixces 3B, 3C). This set of indicators gives a table of paired correlation coefficients calculated by Spearman. Spearman’s correlation matrix is used because it does not make any assumptions about the distribution of the data. It does not require a normal distribution (Zimmerman and Zumbo, 1993) (Table 3.16)

The correlation matrix is the table that shows all pairs of correlation coefficients for a set of indicators. It shows the correlation coefficients between each pair, for 15 variables, arranged so that each variable is identified on each row and on each column, with the coefficient listed in the cells and defined by the rows and columns. In SPSS, before finding a solution to a set of variables to make it more sensible, PCA is conducted in order to look at the intercorrelation between variables.

Table 3.16: Paired Correlation Coefficients of Selected Indicators (Spearman's rho) R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13 R14 R15 R1 1.000 0.882** 0.760** 0.994** -0.787** -0.247* -0.165 -0.044 0.070 -0.268* -0.113 0.217* 0.076 0.139 0.123 R2 0.882** 1.000 0.889** 0.882** -0.675** -0.256* -0.167 -0.094 -0.088 -0.446** -0.205 0.145 0.053 0.164 0.033 R3 0.760** 0.889** 1.000 0.745** -0.537** -0.343** -0.253* -0.020 -0.052 -0.407** -0.254* 0.023 -0.024 0.137 0.157 R4 0.994** 0.882** 0.745** 1.000 -0.793** -0.227* -0.147 -0.027 0.077 -0.263* -0.110 0.243* 0.085 0.149 0.108 R5 -0.787** -0.675** -0.537** -0.793** 1.000 0.035 0.353** -0.095 0.131 0.072 0.315** -0.048 0.095 -0.217* -0.075 R6 -0.247* -0.256* -0.343** -0.227* 0.035 1.000 0.784** -0.043 -0.240* 0.036 -0.043 -0.307** -0.576** 0.079 -0.028 R7 -0.165 -0.167 -0.253* -0.147 0.353** 0.784** 1.000 -0.192 -0.061 -0.135 0.183 -0.111 -0.378** -0.016 -0.043 R8 -0.044 -0.094 -0.020 -0.027 -0.095 -0.043 -0.192 1.000 0.169 0.231* 0.186 0.152 0.124 0.042 0.263* R9 0.070 -0.088 -0.052 0.077 0.131 -0.240* -0.061 0.169 1.000 0.739** 0.583** 0.326** 0.317** 0.081 0.283** R10 -0.268* -0.446** -0.407** -0.263* 0.072 0.036 -0.135 0.231* 0.739** 1.000 0.502** 0.023 0.056 0.012 0.179 R11 -0.113 -0.205 -0.254* -0.110 0.315** -0.043 0.183 0.186 0.583** 0.502** 1.000 0.226* 0.244* -0.060 0.160 R12 0.217* 0.145 0.023 0.243* -0.048 -0.307** -0.111 0.152 0.326** 0.023 0.226* 1.000 0.806** 0.058 0.006 R13 0.076 0.053 -0.024 0.085 0.095 -0.576** -0.378** 0.124 0.317** 0.056 0.244* 0.806** 1.000 -0.008 -0.095 R14 0.139 0.164 0.137 0.149 -0.217* 0.079 -0.016 0.042 0.081 0.012 -0.060 0.058 -0.008 1.000 0.237* R15 0.123 0.033 0.157 0.108 -0.075 -0.028 -0.043 0.263* 0.283** 0.179 0.160 0.006 -0.095 0.237* 1.000

**. Correlation is significant at the 0.01 level (2-tailed). *. Correlation is significant at the 0.05 level (2-tailed).

In order to do PCA, all selected variables should be correlated fairly well, but not perfectly correlated. Thus, a correlation matrix table can be used to check the pattern of relationships among the variables.

Table 3.16 shows mediocre correlation between most of the variables and significant relationships exist between some ratios. For example, the capital adequacy ratio (R1), regulatory capital to risk-weighted assets ratio (R2), regulatory Tier 1 capital to risk- weighted assets ratio (R3), equity to debt ratio (R4) and equity to debt ratio (R5) variables are highly correlated. From the economic point of view, it is understandable because these four indicators characterize capital adequacy.

Table 3.17 lists of the variables and their communality.

Table 3.17: Communality Coefficients

Initial Extraction

R1 Capital adequacy ratio (CAR) 1.000 0.902

R2 Regulatory capital to risk-weighted assets ratio 1.000 0.900 R3 Regulatory Tier 1 capital to risk-weighted assets

ratio 1.000

0.648

R4 Equity to debt ratio 1.000 0.587

R5 Debt to equity ratio (financial leverage) 1.000 0.727 R6 Nonperforming loans to total gross loans ratio 1.000 0.818 R7 Nonperforming loans net of provisions to capital ratio 1.000 0.590

R8 Salary to assets ratio 1.000 0.271

R9 Retained earnings to total assets ratio 1.000 0.953

R10 Return on equity ratio 1.000 0.406

R11 EBIT to total assets ratio 1.000 0.936

R12 Net interest margin 1.000 0.951

R13 Interest rate spread 1.000 0.957

R14 Working capital to total assets ratio 1.000 0.338

R15 Current ratio 1.000 0.549

Source: Author

By default, in the procedure of PCA, each variable has a unit value of communality. Communality coefficients estimate part of the variability in each variable that is shared with others, and which is not due to measurement error or latent variable influence on the observed variable. The values in the column extraction indicate the proportion of each variable’s variance that can be explained by the principal components. Variables with high values are well represented in the common factor space, while variables with low values are not well represented. The initial values can be ignored because in the PCA analysis the initial estimates for the communalities are all set to 1.

Table 3.17 lists the coefficients indicating the presence or absence of communalities in the variables.

It can be seen that the variables of the salary to assets ratio R8, the return on equity ratio R10 and the working capital to total assets ratio R14 have low correlation coefficients with other variables. However, the variables to use will be determined by PCA.

Table 3.18: KMO and Bartlett's Test

Kaiser-Meyer-Olkin Measure of Sampling Adequacy. 0.635

Bartlett's Test of Sphericity Approximate Chi-Square 2861.467

Df 105

Sig. 0.000

Source: Author

Table 3.18 lists the data of KMO and Bartlett's Test to verify the adequacy of sampling and the reliability of its results.

The KMO (Kaiser - Meyer - Olkin) selective adequacy measure and Bartlett's Test results are used to test the adequacy of sampling and the reliability of the result. The KMO is a measure characterizing the applicability of PCA to the sample. Kaiser (1974) interpreted the KMO test measure as follow:

> 0.9 – ‘marvelous’; 0.8 – 0.9 – ‘meritorious’; 0.7 – 0.8 – ‘middling’; 0.6 – 0.7 – ‘mediocre’; 0.5 – 0.6 – ‘miserable’ and < 0.5 – ‘unacceptable’.

Kaiser-Meyer-Olkin’s measure of selective adequacy is a value characterizing the applicability of PCA to this sample. The value of 0.635 means satisfactory adequacy of the sample.

Bartlett’s test of sphericity is the criterion for the degree of correlation of variables. A value of p-level (Sig) less than 0.05 indicates that the data are quite acceptable for PCA because correlations between variables essentially differ from 0.