**Research on the impact of loan portfolios on profitability of joint stock commercial banks - 9**

In general, through many empirical studies, the obtained results are quite consistent with the conclusion that the ratio of equity to total assets has a positive relationship with bank performance. This is consistent with the fact that banks with higher capital ratios have lower funding costs because of lower potential bankruptcy costs.

**Hypothesis H1: There is a positive correlation between the equity/total assets ratio and the bank's performance.**

**4.1.1.3 Bank Size (ASSET)**

Bank size is used to reflect the advantages or disadvantages of economies of scale in the market. The larger the bank size, the higher the profit . Empirical evidence shows a positive and statistically significant relationship between size and bank profitability (Akhavein et al. (1997), Smirlock (1985)). In addition, Short (1979) suggested that size is related to a bank's capital adequacy ratio, because large banks tend to be less likely to raise high-cost capital (equity), and therefore, will increase profits.

Arguing similarly, Haslem (1968), Bourke (1989), Molyneux and Thornton (1992), Bikker and Hu (2002), Goddar et al. (2004) also argue that as size increases, profits also increase. . However, in some situations, the bank's size is too large, which will reduce profits by beyond the control of the bank.

Berger et al. (1987) argue that large banks will face a size disadvantage, because as the size increases, the costs also increase. Similarly, Anna and Hoi (2007) with the study of internal bank factors as well as macro factors, financial structure affecting the profitability of banks in Macao in the period from 1993 to 2007 showed that Small-sized banks will have higher ROA than large banks in which the research data is that 5 banks account for 75% of total assets and have the same loan balance in Macao.

Not stopping there, Fotios and Kyriaki (2007) extended their research to many countries when conducting research on internal bank factors and economic environment affecting domestic and foreign bank profitability of 15 countries. European countries for the period 1995 to 2001. The total number of banks used in this study is 584 banks. The results show that the profitability of domestic and foreign banks is not only affected by internal factors in the bank but also by financial structure and macroeconomic conditions. In which, size plays an important role and has a negative impact on bank profitability.

Besides, to study the impact of internal factors on bank profitability in each period, Andreas and Gabrielle (2011) used GMM estimation technique to analyze data on 372 commercial banks. in Switzerland from 1999-2009, is divided into two periods: pre-crisis period from 1999-2006 and crisis period from 2007-2009. The results show that there is a huge difference in profitability between banks. In terms of size, there is ample evidence that small or large banks are more profitable than mid-sized banks in the pre-crisis period; but large banks are less profitable than medium and small banks in times of crisis because large banks have large provisioning rates for credit losses during times of crisis.

Contrary to the above opinions, Eichengreen and Gibson (2001) show that the effect of size on profitability is non-linear, i.e. returns initially increase with size, but then returns. reduced. In general, with many independent studies in different countries and periods, the impact of size on bank profitability is still controversial and has not come to a consistent conclusion. It can be the relationship in the same direction, in the opposite direction, or both together and in the opposite direction, or it may not work. That can be explained on the basis of differences between territories and economic, legal and periodical environments. Above all, the role of the underlying theory drawn from these empirical studies is enormous and undeniable.Summarizing the results of previous studies and based on the current situation of Vietnamese banks, the relationship between bank size and profitability is expected to have a positive relationship. In this thesis, the author uses Ln of total assets to describe this relationship.

**Hypothesis H2: Bank size has a positive effect on performance**

**4.1.1.4 Traditional Concentrations of the Hirshmann-Herfindahl Index (HHI):**

The HHI index views diversification as equally risky in all sectors.

This index is used by Benjamin M. Tabak, DimasM.Fazio and Daniel O.Cajueiro and many other researchers to measure industry concentration or the concentration of loans.

The objective of the thesis is to analyze and evaluate which industry banks are currently focusing on lending. Thereby, it will be seen the impact of the concentration of lending in one or more business sectors on the profitability of banks.

The HHI is calculated as the sum of the squares of the loan weights. The Bank's HHI at time t can be calculated as follows:

HHI bt= 2 bt

With

rbti = Outstanding loans of industry i / Total outstanding loans of the Bank at time t

**Hypothesis H3: Concentration is positively related to profitability**

**Table 4.1 Expectations of sign between independent and dependent variable**

Independent variables | Symbol | Calculation formula | Relation |

Equity /total assets ratio |
EQ | Total equity/Total assets | + |

Bank size | ASSET | Ln (Total assets) | + |

The level of competition | HHI | Calculated by HH index (Average | + |

between banks | weighted square of each | ||

in the money market | branch) | ||

get a loan |

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**4.1.2 Data collection and data processing**

The data of the thesis is collected based on financial statements, income statements, cash flow statements, notes to financial statements, annual reports... of joint-stock commercial banks in the period. the last 11 years, the period from 2004 to 2014 according to financial and securities data of the website: http://vietstock.vn The final sample of the group includes 282 year-by-year observations of banks according to orders. million dong or as a percentage depending on the variable.

**4.1.3 Research Methods**

According to Baltagi (Econometric analysis of Panel data, Third edition, 2005) the use of panel data estimation method brings many benefits such as:

- It is possible to consider the heterogeneity in the data sample by considering the individual-specific variables.

- Estimation by panel data gives us more information, less multicollinearity between variables and more efficient.

- Panel data is more suitable for studying the dynamics of change, panel data is better performing studies of changes that occur continuously.

- For micro variables that gather a lot of individuals, businesses or subjects, there will be a more accurate measurement. According to Blundell (1988) and Klevmarken (1989) the biased estimates will be reduced or eliminated when we use panel data.

Therefore, in order to be able to research the topic and analyze data on many domestic banks over the years in the most favorable way, the author decided to collect data, process it, and return it to panel data. ). Due to the uneven data set of banks, there are banks that fully report on outstanding loans by industry from 2004-2014, but there are some banks that cannot make complete statistics but only one over a period of several years, the panel data used in the study is an unbalanced panel data.

Currently, the domestic market has not had many empirical studies on this topic, so in order to determine the most accurate model with unbalanced panel data, the author runs the data on both 3 basic models, suitable for panel data and often used to handle different economic problems: pooled regression model (Pooled OLS), fixed effect model (Fixed Effect Result - FEM) and Random Effect Result (REM) model, then carry out the tests and consider the necessary indicators to choose the most suitable model.

**4.1.4 Correlation survey between independent variables**

Through the correlation coefficient matrix to find the pairs of variables with high correlation coefficients. Gujarat and Porter (2004) said that it is necessary to study the correlation coefficient between the variables, if they exceed 0.8, the regression model has multicollinearity problem.

**4.1.5 Constructing empirical equations and selecting models**

To test the relationship between factors affecting bank performance, the survey model is as follows:

(ROA) = f (EQ, RSK, ASSET, HHI)

According to Wooldridge (1997) and Hsiao (2003), the common regression methods with tabular data are pool regression model, fixed effect model and random effect model. The study will present the above models in turn.

**4.1.5.1 Pool . regression model**

As the simplest case, the model ignores the temporal and spatial array of panel data, and only estimates the ordinary least squares (OLS) regression model. In this model, the assumptions about autocorrelation, variable variance, spatial and temporal differences of each observed variable are not affected. Therefore, the slopes and slopes of the coefficients are assumed to be unchanged over time, space and even each variable. The regression model is shown as below:

Yit = β1 + β2*X2it + β3*X3it + … + βk*Xkit + µit (1) Where: i = 1, 2, 3, ….n; t= 1, 2, 3, ….T However, the disadvantage of this model is that the possibility of autocorrelation in the data is quite high. In addition, the assumption that the intercept in the model is the same for the observed objects, and the assumption that the estimated coefficients of the observed variables are the same for the observed objects distorts the real image. about the relationship between the Y variable and the X variable.

**4.1.5.2 Fixed Effect Model (FEM)**

The fixed effects model does not ignore time series effects and cross units, in other words, the slope of each cross unit is variable but still assumes the slope is fixed for each variable. . Then, the fixed effects model is represented as follows:

Yit = βit + β2*X2it + β3*X3it + ….+ βk*Xkit + µit (2) Model (2) can be split into two models:

Yit = β1t + β2*X2it + β3*X3it + ….+ βk*Xkit + µit (2.1) Yit = β1i + β2*X2it + β3*X3it + ….+ βk*Xkit + µit (2.2) Model 2.1 mock The slope determination is time-varying but the same across cross-units within the same year of observation, known as time-fixed-effects regression. In this model, fixed-time effects control for unobserved variables that are the same across cross-units but differ as time varies.

Model 2.2 assumes that the overall slope of the model changes, but the slopes of the diagonal units remain the same.

With a fixed cross-over, so the origin is different between the cross units, but it does not change over time. The effects of changing the base gradient may be due to differences in the characteristics or management style of each bank.

**4.1.5.3 Random Effect Model (REM)**

If in the fixed-effects regression model, the unobserved factors are considered as parameters and are estimated, in the random-effects model, they are considered as the result of the random variables. From model 2.2, we assume β1i as a random variable with mean β1 and the intercept of the cross unit is represented as follows:

β1i = β1 + Ɛi; Where i = 1, 2, …N and Ɛi are random errors.

We can rewrite Model 2.2:

Yit = β1i + β2*X2it + β3*X3it + ….+ βk*Xkit + it = β1 + β2*X2it + β3*X3it + ….+ βk*Xkit + µit + Ɛi = β1 + β2X2it + β3X3it + …. + βkXkit + wit where wit = µit + Ɛi is the error term combining the two components: Ɛi is the spatial error component and µit is the combined space and time series error component. This model helps to control for the unobserved effects of different cross-units that do not change over time.

Unobserved impacts such as characteristics, policies, human resources, etc. of the bank.

The model makes assumptions of fixed effects plus the additional requirement that unobserved effects are not correlated with all explanatory variables. This hypothesis is tested by Hausman (1978). According to Wooldridge (1997), if the random effects hypothesis is correct, the random effects estimate is more efficient than the pool model and also the fixed effects model. However, if we do not keep the assumption that the fixed effects are not correlated with the explanatory variables, then the fixed effects regression model is more appropriate than this model.

**4.1.5.4 Model selection**

The question is which model would be the right one: Pooled OLS, FE or RE. The concordance of the random and fixed effects estimates is verified on the basis of comparison with the rough estimates.