Sampling and Data Description

Banks are the most crucial channels of the financial economic needs in most countries (Boldeanu and Tache, 2016, p.59). However, during the financial crises, banks incur declines in the credit activities that directly affect the availability of the financial resources that drive the economy of the countries. One of the causes that could into the financial crises is the collapse of some key players in the banking sector who are relied upon by other minor players (Wolfson, 2017). For instance, this report provides a valuation of the banks after the collapse of the Lehman Brothers that held nearly $40 billion assets before it declared itself bankrupt in 2008 (Schiereck, 2016, pp.291-297). The valuation was conducted on the largest banks across the world to determine the effects of the financial crises in the banking sector.

A sample size of 500 observations was considered for the analysis with the use of profitability and the risk factors as the major variables. The profitability variables selected were the Equity Returns, which is a measure of the shareholders Net Income, and the Income Diversity variable, which measures the diversity in the non-interest on the total income. The risk variables selected were the Capital Ratio variable, which defines the adequacy of total assets among the banks, and the Fragility variable that determines the likelihood of a bank to run as a short-term funding (Black, Correa, Huang, and Zhou, 2016, pp.107-125). The variables are summarized in the screenshot below.

The sampling formula used in MS Excel

In order to obtain the 500 observations for the study, the use of the Ablebits tools was used to come up with the random sample as demonstrated by (Kimball, 2016, pp.91-98). Below are the steps used;

Go to the Ablebits Tools Tab, under the utilities click on Randomize then Select Randomly

The number of rows indicates the sample size required. Input 500 as the sample size then click Enter. Copy paste the randomly selected sample into a new tab for analysis.

• The estimation of the mean and the standard deviation of the variables
  • Return on Equity (ROE)

Using the MS Excel, the mean/average and the standard deviation are given by

 Using the formula “=STDEV (G2:G501)” then “Enter”

• Income Diversity 

• Capital Ratio

• Fragility

• The estimation of the correlation of the pairs

The correlation coefficient is used to determine how two variables of a data set are correlated to each other, which is illustrated, by (Furlotte and Eskin, 2015, p.114). The coefficient value can be obtained in MS Excel using the formula “=CORREL (Array ‘A’, Array ‘B’)” the “Enter” where the arrays represent the data columns for the variables A and B. Using the formula, the correlation values between the pairs of the variables are shown below.

• ROE-Income diversity

• ROE-Capital Ratio

• ROE-Fragility

• Income diversity-Capital Ratio  

• Income Diversity-Fragility

• Capital Ratio-Fragility 

• The empirical distributions plot for the four variables

The relative frequency of the means of the variables is shown in the table

Variable	Mean	cumulative mean	Relative frequency (%)
ROE	7.22048	7.22048	5.0566
Income Diversity	43.74237	50.96285	35.6897
Capital Ratio	8.6983	59.66115	41.7812
Fragility	83.13307	142.7942	100

The empirical distribution obtained from the data is given below.

 H₁: Whether an open market cannot withstand the financial crisis

The first hypothesis is to test whether the open market (example the United States) could withstand the financial crises as the null hypothesis by using the variable average scores.

The overall means and the mean for the US banks

Variable	Overall Means	Mean for the US banks(Open market)
ROE		19.96344
Income Diversity		46.34982
Capital Ratio	8.6983	11.43067
Fragility	83.13307	91.16287

H1: Whether an open market cannot withstand the financial crisis

The values in the table above indicate that the mean for the variables for the United States banks are higher than the overall financial crises means indicating that the open market like the US could withstand the financial crises after the collapse of the Lehman Brothers. Therefore, the null hypothesis is accepted for the study.

• H0: Open economy (like US) compare to protected economy (like China)

 H1: Open economy (like US) does not compare to protected economy (like China)

The average values for the variables are given below

The means for the US banks and the Chines banks

Variable	Mean for the US banks	Mean for the Chinese banks
ROE	19.96344	19.17182
Income Diversity	46.34982	59.50669
Capital Ratio	11.43067	6.348182
Fragility	91.16287	81.43881

The ROE means are almost similar indicating that the bank profits for an open economy and a closed economy could be similar after the financial crisis. However, the income diversity for the non-interest is higher for a protected economy than for an open economy thus implying a higher profitability in a protected economy after the crisis. Concisely, the mean values for the Capital ratio and the Fragility are lower for a protected economy than the open economy thus indicating a higher financial risk for the protected economy during and after the crisis (Bordo, Redish, and Rockoff,  2015, pp.218-243).

• H0: State owned banks have better variable values than the no state ownership banks

H1: State owned banks have no better variable values than no state ownership banks

The values obtained for the US banks that have no state ownership using the pivot table in excel are shown below.

The mean for the state owned Chinese banks and the mean for privately owned US banks

Variable	Mean for the Chinese banks (State owned)	Mean for the US banks (No state owned)
ROE	19.17182	56.18857
Income Diversity	59.50669	57.01173
Capital Ratio	6.348182	14.6625
Fragility	81.43881	91.37316

From the results, the state owned banks have lower returns on equity of the shareholders compared to the privately owned banks during and after the financial crises. However, both cooperate entities exhibit similar diversity measures on the capital assets at the incidences of crisis. Contrary, the capital ratio and the fragility figures for the no state owned banks are higher than the state owned banks thus the private owned banks exhibit lower risks during financial crisis in the banking industry (Lazzarini, Musacchio, Bandeira-de-Mello, and Marcon, 2015, pp.237-253). Therefore, the null hypothesis false and thus rejected.

• H0: The variance of state owned is different between countries (UK and France)

H1: The variance of state owned is not different between countries (UK and France)

The variance for the state owned banks for France and UK are depicted in the table below.

The variance for the UK and France banks computed from Pivot tables

Variable	Variance for UK	Variance for France
ROE	49.0664	5.977267
Income Diversity	49.45004	27.54929
Capital Ratio	1.17769	0.030567
Fragility	189.7269	461.7661
Correlation function “=CORREL(A,B)”	0.968997

The relationship between the variances of the variables of the two countries can be demonstrated using correlation function in MS Excel as shown in Table 6. The value of the obtained correlation indicates that the variances are strongly correlated towards the positive thus making the hypothesis false. This relationship can be illustrated using the line graphs below.

1. Regression analysis
   • The regression for the hypothesis that Fragility and Capital ratio affect the ROE

The results for the analysis between Fragility and ROE are shown below

The F is a low value implying that there are chances that some of the regression value parameter are nonzero. This indicates that there is probability that the hypothesis model is true; therefore, the ROE could be slightly dependent on the fragility during the financial crisis as seconded by (Chaibi and Ftiti, 2015, pp.1-16).

The results for the analysis between Capital Ratio and ROE are shown below

H2: Open economy (like US) does not compare to protected economy (like China)

The significance F value is nearly one implying that the hypothesis model is true as thus indicating that the returns on equity of the shareholders is dependent on the capital ratio of the shareholders (Baselga-Pascual, Trujillo-Ponce, and Cardone-Riportella, 2015, pp.138-166).

• Regression analysis for the business model by introduction of income diversity as an additional control

The regression results for introduction of the income diversity to the ROE are shown below.

The Prob (F) and the F values from the regression analysis are 0.208807 indicating that there could be a probability of 208 chances in 1000 occurrences thus implying that the ROE of the shareholders is only partially dependent on the diversity of the income (Ho et al., 2016, pp.194-209).

• Regression analysis for the size, current ration, and z-score as the control measures
  • The analysis of size on the ROE

The F and P-values indicate a low probability that the ROE is dependent on the size of the banks during financial crises (Laeven, Ratnovski, and Tong, 2016, pp.25-34). Additionally, this is also indicated by a weak correlation relationship between the variables, Multiple R. This illustrates that the bank sizes in the banking market is vital for determining the amount of the shareholders returns in the industry and in economics.

• The analysis of NPL on the ROE

The significance value F indicates that the Non-performing loans as a control model slightly affects the ROE with 270 chances in 1000 occurrences, which is acknowledged by (Becker and Ivashina, 2017, pp.83-115). This is implies that the probability if the NPL to determine the shareholders ROE is 0.27 which can be used to reflect on the shareholders’ equity returns in the banking sector.

• The analysis of current ratio on the ROE

The significance value F is insignificant indicating that there would be higher risks on the ROE of the shareholders depending on the size of the current financial ratios during and after the crisis. The results indicate that the current ratios cannot be used as a control measure on the ROE of the shareholders in the economy of the banking sector (Vintila and Nenu, 2015, pp.732-739).

• The analysis of z-scores on the ROE

The significance value F indicates fair probability chances of controlling the risks on the returns of equity of the shareholders.

• Time fixed effect

All the variables, the ROE, the capital ratio, the income diversity, and fragility will remain significant with consideration of the time fixed effects since they are all dependent on the time factor (Martynova, 2015).

• Selection of the best model

The best model that describes the returns on equity of the shareholders in the banking industry is the capital ratio model, which has the highest significant value among all the models.

Conclusion

The banking sector is one of the factors that determine the economic growth of nations. However, for it to be success, it requires the coordination of factors such as the effective measures that could increase the returns of the shareholders on equity and an efficient framework that promotes income diversity for the bank to realize the profits. Failure in any of the aspects results in massive loses especially after a financial crises whereas both aspects have to be put in place to achieve the profit margins. Concisely, the capital ratio and the fragility factors should be set to higher standards for the banking industry to minimize the chances of risks during and after the financial crisis. These includes the bank assets, short-term funding, and higher rates of deposits from the customers.

References

Baselga-Pascual, L., Trujillo-Ponce, A. and Cardone-Riportella, C., 2015. Factors influencing bank risk in Europe: Evidence from the financial crisis. The North American Journal of Economics and Finance, 34, pp.138-166.

Becker, B. and Ivashina, V., 2017. Financial repression in the European sovereign debt crisis. Review of Finance, 22(1), pp.83-115.

Black, L., Correa, R., Huang, X. and Zhou, H., 2016. The systemic risk of European banks during the financial and sovereign debt crises. Journal of Banking & Finance, 63, pp.107-125.

Boldeanu, F.T. and Tache, I., 2016. The Financial System of the EU and the Capital Markets Union. European Research Studies, 19(1), p.59.

Chaibi, H. and Ftiti, Z., 2015. Credit risk determinants: Evidence from a cross-country study. Research in international business and finance, 33, pp.1-16.

Ho, P.H., Huang, C.W., Lin, C.Y. and Yen, J.F., 2016. CEO overconfidence and financial crisis: Evidence from bank lending and leverage. Journal of Financial Economics, 120(1), pp.194-209.

Kimball, R., 2016. Journal overlap analysis of the GeoRef and Web of Science databases. Science & Technology Libraries, 35(1), pp.91-98.

Laeven L, Ratnovski L, Tong H. Bank size, capital, and systemic risk: Some international evidence. Journal of Banking & Finance. 2016 Aug 1;69:25-34.

Martynova N. Effect of bank capital requirements on economic growth: a survey.

Schiereck D, Kiesel F, Kolaric S. Brexit:(Not) another Lehman moment for banks?. Finance Research Letters. 2016 Nov 1;19: 291-7.

Vintila, G. and Nenu, E.A., 2015. An analysis of determinants of corporate financial performance: Evidence from the Bucharest Stock Exchange listed companies. International Journal of Economics and Financial Issues, 5(3), pp.732-739.

Wolfson MH. Financial crises: Understanding the postwar US experience. Routledge; 2017 Jul 28.