As the core of the financial system, financial institutions are playing a significant role in financial stability in the process of development; traditional analysis mainly discusses the institution’s revenue of assets. However, the current financial stability system pays more attention to financial institution risk behavior and operational efficiency; to solve the previous two issues, we propose the two-stage model. Firstly, we measure the dynamic financial institution’s risk behavior coefficient based on the volatility and return principle for different institutions. Secondly, according to the cross-efficiency principle, different financial institution operation efficiencies that assimilate risk behavior will be obtained, and the institution risk behavior valve is also given. Finally, we analyze the 31 banks listed in China to verify the validity and applicability of the two-stage model; the model has made a certain theoretical contribution to the financial institution analysis model, especially when we consider the risk behavior and multiple indexes. Therefore, the two-stage model that we built can help investors make a portfolio in banking enterprises; it also can help financial institutions evaluate their risk behavior for making an optimal decision and help government agencies to supervise banks based on their risk behavior.

1. Introduction

Current government agencies’ supervision of financial institution risk behavior is shown mainly from quantitative and qualitative perspectives. Quantitative indicators mainly include the nonperforming loan ratio, debt-to-asset ratio, liquidity ratio, return on total assets, revenue growth rate, and the target value of other related indicators or target range. However, even though qualitative data are crucial for the analysis of financial institutions’ risk behaviors, it is difficult to quantify qualitative descriptions in real cases. As a profitable institution, with a higher intensity of supervision, the financial institution’s risk behavior will be lower; on the other hand, the risk behavior will be higher. However, judging from the risk behavior information that is announced by each financial institution such as banks, there is no one who declares that he/she is a risk enthusiast.

In addition, risk and return are the subjects of eager attention in the field of institutions. Financial institutions have been a significant unit in the stability of the financial system and the adjustment of operating mechanisms. What is more is that risk behavior and operational ability are essential and stable strategies for an institution to keep on its core competitiveness. Facing the complex and changeable economic environment, institutions will encounter various financial risk problems in the process of continuous development. Accurate measurement and control of an institution’s risk behavior have become essential conditions for the stability of the financial system. In addition, benefits have closely related to risks and there is a positive correlation between them. How to deal with their problem has become a very significant issue to assess the institution’s operational abilities. Although the decision-makers and stockholders of institutions are mainly concerned with the institution’s returns, many elements also need to be considered, such as the institution’s dynamic risk behavior and various operational evaluation indicators. In addition, finance institution risk behavior is dynamic in different development periods, and many reasons lead to this situation. To address those issues, we propose a two-stage model to measure institution risk behavior based on the idea of cross-efficiency evaluation and evaluate the operating efficiency of the institutions. The model we put forward to analyzing institutions’ risk behavior is also useful to other enterprises; it can set multiple types of indicators to evaluate them, which is helpful for operators to make optimal decisions, and investors also can choose the long-term optimal investment products based on their efficiency. To verify the effectiveness and feasibility of the research method, we make an empirical study by using the data from 31 commercial banks listed on Shenzhen Stock Exchange and Shanghai Stock Exchange.

From the perspective of financial institution risk behavior, it comes from the portfolio theory area. Usually, the risk behavior of financial institutions can be divided into five categories from low to high. For example, risk behavior was used to analyze the field of corporate management later, especially in commercial bank operation management [1, 2]. Bank managers want to obtain different kinds of returns, so their risk behaviors are changed by policies and the economic environment [3]. For this problem, Hutcheson and Sharpe [4] take the relationship between income and liabilities to test bank risk behavior first and Kenyon et al. [5] take potential future exposure (PFE) as a standard risk metric for managing business unit counterparty credit risk and propose a risk behavior for PFE and suggest that this is uniquely consistent with the bank’s risk behavior framework as required by sound governance. Bekaert and Hoerova [6] find that the variance premium contains a substantial amount of information about risk aversion whereas the credit spread has a lot to say about uncertainty, so they link risk aversion and uncertainty estimates to practitioner and “academic” risk aversion indices. In addition, Kim et al. [7] explore the effect of bank risk behavior and transparency on risk diversification from the perspective of financial crises. Nowadays, risk behavior has become the object of cross-analysis of economics, management, mathematics, system science, and other disciplines. After decades of development, relevant research on bank risk behavior transformation has been emerging [814].

Among various indicators of the financial institution and compared with other economic indicators, risk behavior determines the direction of an institution from a macro perspective, so it is important in the area of the financial system. For example, Haisley et al. [15] propose risky allocation in the combination and experience sampling conditions, which is mediated by three indicators-decreased risk perception, increased confidence in the risky fund, and a lower estimation of the probability of a loss. Chen et al. [16] believe that risk behavior has a profound impact on credit default, and a reasonable risk behavior helps reduce credit risk and financial leverage; Caselli et al. [17] conclude that the lower risk behavior and the degree of ownership diversification will be higher and the impact of exogenous monetary policy on the probability of institution default will be lower; Kanga et al. [18] put forward that bank risk behavior is likely to reflect the integration of the management team risk behavior; the article shows that controlling the bank macro risk behavior is the diversification of institution system indirectly, and risk behavior of each staff will be well controlled, such as [1921] gives similar conclusions. However, institutional risk behavior is dynamically changing. A large number of current research studies about institution risk behavior are qualitative but lack a systematic measurement plan, and this article tries to avoid this shortcoming.

In financial institution evaluation system-related research, traditional theory mainly focuses on revenue and the achievement of financial products, and the evaluation index is relatively single [2224] (Kang, 2019 [25]). The financial institution’s operation efficiency evaluation system is mainly based on the comparison of input with output, and the indices in the evaluation system are complex and diverse. Therefore, appropriate indicators for evaluation have become a hot issue in research recently [26, 27] (Kang, 2019). Other scholars have studied the relationship between regulation and institution efficiency; for example, as Asaftei and Kumbhakar [28] put it, for all types of banks, the cost of technical operation inefficiency decreases in the years following a tightening of regulation. Kara and Ozsoy [29] think that the interplay between banks and regulators leads to inefficiently low levels of risky assets and liquidity. Gaganis et al. [30] showed that more regulatory requirements decrease financial institution efficiency and so on. Due to these evaluating operation efficiency characteristics, it is significant to choose an immediate method for calculating operation efficient value. In addition, many studies mainly focus on risk indicators or profit indicators, such as Beck and Hesse [31], Abuzayed et al. [32], and Yurtsever and Firat [33]. Therefore, this paper integrates multiple indexes for calculating operation efficient values.

In general, the existing studies mainly focus on the indicator of profitability, such as financial product returns, but less attention is paid to institutions’ comprehensive index. In this paper, we construct the two-stage model by selecting both the performance index and profit index for evaluation; it not only can assess the risk characteristics of institutions effectively but also add the profit factor. It is obvious that combining the solution of risk behavior with the evaluation of multi-index institutions system is essential; we quantify the dynamic institution’s risk behavior and introduce them into the two-stage model. Finally, the paper evaluates the operational efficiency of the bank.

The content of this paper is organized as follows: The next section of this paper describes the risk behavior model. The two-stage evaluation model will be elucidated in Section 3. Section 4 provides an empirical analysis and illustrated examples, including an operation efficiency assessment over the last ten years. The fifth part gives conclusions and some research directions. The framework can be seen in Figure 1.

2. Institution Risk Behavior Coefficient Calculation in the First Stage

2.1. Implication of Institution Risk Behavior Coefficient

In a financially stable system, an institution’s risk behavior decides its revenue and risk; in other words, like in the capital market, high-risk behavior leads to greater risks and benefits, and low-risk behavior brings smaller risks and benefits. Risk behavior affects all aspects of institution operations. However, with the development of the financial products market, the risk behavior of institutions and multiple evaluation indicators are extremely important. To some extent, almost all institutions announce that their risk behavior is risk-neutral, but in the actual operation process, is this the case? This requires judging whether it is truly risk-neutral from the information proclaimed by the institution itself. In addition, institution risk behavior indicators are mostly qualitative indicators with fewer precise quantitative indicators; in the first stage, we put forward the institution risk behavior model to solve the behavior coefficient according to the institution’s instant information based on the thought of the capital asset pricing model. To build a comprehensive evaluation indicator system, we have combined risk indicators with profit indicators and integrated the institution’s risk behavior.

On the idea of cross-efficiency evaluation, we construct multiple profitability indicators and risk indicators to obtain different cross-efficiency evaluation efficiency values based on the two-stage model. Thereby, the value of fused institution risk behavior reflects the operating efficiency of each institute unit. Decision-makers can instantly calculate institution risk behavior in different periods and make corresponding business adjustments to diversify risk based on the two-stage model.

2.2. Institution Risk Behavior Coefficient Model

First, this paper built a financial risk behavior analysis model based on the capital asset pricing theory. As Markowitz’s portfolio theory puts it, the risk behavior of investors mainly depends on the utility function, the risk-free interest rate, and the expected rate of return.where is the utility of function; 0.5 is the parameter of (1) based on Bodie et al. [34]. is the coefficient of risk behavior, according to the value of . There are five levels of risk behavior ranging from risk aversion to risk enthusiasts and from low to high. Furthermore, is total assets revenue. and are and standard deviations of the portfolio. Combining the previous algorithm, the following can be obtained:

We maximize the utility of the previous formula to solve the optimal risk-asset ratio , and it is easy to get the following:

It can be seen from formula (5) that the risk behavior coefficient can be determined by the expected return rate of risk-free assets, the expected return rate of risky assets, the weight of risky assets, and the variance of risky assets portfolios. To simplify the calculation process, we use the CAPM model proposed by Cochrane [35]; the current price of the bank or other asset is equal to the discounted value of the future asset as follows:where stands for discount factor; , and are our future and current consumption utility functions, respectively. is a dividend, . We divide both sides of 1 by to get the following:

We can get this conclusion from (6) and (7): Although in the financial product market, the rate of return on different financial products is different. In an equilibrium state, the expected discounted total rate of return is always equal to 1. Equation (7) can be changed to the following equation:

The left side of (8) is the risk-neutral part and the right is the adjustment according to the different mapping of risk preference. is the rate of return on risk-free assets. . Taking it into (8), we can obtain the following:

In addition, we multiply both sides of formula (8) by , and we can get the following formula:

The left equal represents an excess return, which is also named as risk premium, which is risk measurement and risk price multiplication. Pericoli and Sbracia [36] consider that another risk behavior index derived from the CAPM model is very close to the actual risk behavior index; therefore, if we use to represent a measurement of each risk asset, the price of each risk asset is . Then, the previous formula can be expressed as follows:where represents the rate of return per unit of risky assets. In other words, its reciprocal is the risk behavior coefficient. The risk behavior of investors is inversely related to the excess return rate of financial products, and the degree of risk behavior depends on the preference uncertainty in future consumption.

3. Two-Stage Model Building Process

In this section, after we calculate the institution risk behavior coefficient, a two-stage model that contains risk behavior and multiple indexes will be proposed for calculating the evaluated value of the institution, and these indexes have risky revenue features. However, in the first stage, we calculate the risk behavior of an institution, and we use the operation efficiency evaluation model for calculating the value of the institution. Thus, the two-stage model solves double-level problems, both of which aim to evaluate institution risk behavior and operation efficiency, as shown in Figure 2.

3.1. Two-Stage Evaluation Model

Based on the idea of cross-efficient [37], the model assumes that the analysis object has contents, and often aims for different kinds of risky input variables and some profitable output variables. In our study, the contents we analyze represent institutions; the research system is also produced in institution evaluation, and evaluation unit refers to institutions. There is a total of institutions. The input and output indicators are as follows:where and are input and output variables, respectively, and the variables are all from the institution. Firstly, we calculate the self-evaluation efficiency value of the institution, and the institution’s self-evaluation efficiency value is represented by based on Data Envelopment Analysis (DEA). Then, this paper calculates with (14), which represents the cross-efficiency evaluation value of different decision-making units.where is the optimal weight of ; also, is the optimal weight-. Each variable in the algorithm is a real number, whose value is between 0 and 1. and refer to input and output objects. refers to the number of inputs and outputs. are each optimal weight . The efficiency value of the cross-evaluation is represented by .

The formula shows that the crossover efficiency value is equal to the ratio of the output and input optimal weight efficiency values. In addition, the average cross-efficient value is calculated by the following formula:Here, is the average cross-efficient value in different institutions, and the meaning of other variables is constant; although is the only target value, the optimal weight is not unique; to solve this kind of problem, risk behaviors are divided into radical and robust types, and aggressive and benevolent evaluation models are often used to analyze it. This paper uses the risk behavior coefficient to determine the weight value of the multi-index model so that we can reasonably evaluate the empirical object. Here, we first introduce aggressive and benevolent multi-index analysis models.

It also can change to another mathematical expression as follows:

The objective functions of Models (17) and (18) are different, and the constraints are the same, that is to say, the evaluation methods of the two are different. Model (8) refers to the average of other institutions participating in the evaluation under the premise that the evaluation of other banks remains unchanged. The efficiency value is the smallest. In addition, Model (16) maximizes the average cross-efficiency value of other institutions as much as possible while ensuring that the efficiency of self-evaluation remains unchanged. We closely combine Models (17) and (16) through the risk behavior coefficient; based on , Model (19) can be obtained by averaging with equal weights as follows:Here, represents an institution’s risk behavior return on total assets, operating income growth rate capital, and adequacy ratio, which were substituted into (19); represents the value of cross-efficiency.

Table 1 is descriptive statistics, Table 2 is the multipreference index, and Table 3 displays the changes in interest rates of 31 banks from 2012 to 2020, it easily obtained VAR through table 1, the value of bank risk behavior based on (19), and the average value. Figure 3 shows details. Furthermore, the red line in Figure 3 is calculated based on (11), which refers to the calculated value of each bank’s risk behavior. The bank with the highest risk behavior coefficient is 601166.SH and equal to 0.61, and the lowest risk behavior coefficient is 002839.SZ and equal to 0.112. This paper normalized the risk behavior coefficient to 0-1, when the bank risk behavior coefficient is less than 0.5, it is risk aversion, when the risk behavior coefficient is greater than 0.5, it is the risk behavior, and when it is equal to 0.5, it is the risk-neutral. The order of risk behavior from high to low is 601166.SH, 601166.SH, 002966.SZ, 601077.SH, 601328.SH, 000001.SZ, 601916.SH, 601998.SH, 600908.SH, 601988.SH, 601939.SH, 600036.SH, 600000.SH, 601288.SH, 601577.SH, 601009.SH, 600016.SH, 601128.SH, 600919.SH, 600015.SH, 601398.SH, 600926.SH, 600928.SH, 601818.SH, 002948.SZ, 601997.SH, 601658.SH, 000156.SZ, 601229.SH, 601169.SH, and 002839.SZ. In addition, the risk behavior coefficient of 000001.SZ, 002966.SZ, 600908.SH, 601077.SH, 601166.SH, 601328.SH, 601860.SH, 601916.SH, 601939.SH, 601988.SH, and 601998.SH is greater than 0.5; in other words, they are risk seekers, and this is not consistent with what the bank reports.

To explain risk behavior from the economic sense preferably, we take the reciprocal of the risk behavior coefficient calculated by (11), and the risk behavior of 31 banks can be obtained. It is displayed in Figure 4. From the overall behavior preference value, many banks’ risk behaviors are relatively stable, and all of the banks are from 1 to 9, which is consistent with the conclusion reached by many scholars; they solved by using the Capital Asset Pricing Model and theory like Chiarella and Xuezhong [38] and Kaplow [39].

Tables 48 offer the dataof empirical researchin 2016–2020 to demonstrate model running results in detail, based on [40] and Drakos et al. [41]; this paper expresses index Provision Coverage Ratio, Cost-to-Income Ratio, Net Interest Margin, Bad Loan Ratio, Asset Liability Ratio Liquidity Ratio, Return on Total Assets, Operating Income Growth Rate Capital and Adequacy Ratio as A, B, C, D, E, F, G, H, and I, respectively, where measurement unit is a percentage.

Figures 59 display the risk behavior value of each bank and volatility in 2016–2020, which is shown in the form of a thermal map. In the figure, the darker the color is, the higher the efficiency value of the corresponding evaluation unit is; otherwise, the efficiency value is low. In addition, if the efficiency values of the diagonal are 1, their evaluation units are efficient; otherwise, they are not.

In Figure 10, each color represents the average efficiency value of different types, and the corresponding coordinate is the security code of each bank. From this table, it is easy to see the operation efficiency value of different banks, the higher the average efficiency, the better the operation efficiency of the bank. In the figure, China Construction Bank Co., Ltd has the largest average efficiency value, that is, 0.909 in 2020, followed by Industrial Bank Co., Ltd, and so on. Bank of Beijing Co., Ltd has the smallest average efficiency, and the value is 0.615.

From the horizontal point of view, this paper makes a comparative analysis of the operation efficiency values of banks in different years. As shown in Figure 10, although operation efficiency values for each bank fluctuated widely, the overall trend increased over time.

As Figure 10 displays, the values of 2016 and 2019 have a higher crest and their fluctuation rate is larger. By sorting out the regulatory policies and business expansion of banks from 2016 to 2020, we found that in 2016, the securitization of nonperforming assets, the conversion of bank debt to equity resumed, and the impact and influence of Internet finance led to reduced efficiency of operation and management. Moreover, in 2019, Contractor Bank was taken over by the Central bank and China Banking and Insurance Regulatory Commission, and nearly 40 banking executives lost their jobs. Those series of factors deeply affect the development of the bank.

Furthermore, the third, sixteenth, and twenty-fourth banks have low operation efficiency values, which are Jiangsu Zhangjiagang Rural Commercial Bank (JARCB), Jiangsu Changshu Rural Commercial Bank (JCRC), and Postal Savings Bank of China (PSBC). The main reason that led to low operation efficiency for JARCB may be that it manipulated the market and was fined 5.5 billion yuan by the (China Banking Regulatory Commission) CSRC. Such institutional behavior leads to the reduction of internal organizational management efficiency, and securities investors hold a pessimistic attitude when they come to portfolio selection. However, the risk control, asset matching, and operation means of JCRC are insufficient, and the risk and cost of operation are higher as well. Wind Information also announced that PSBC’s illegal operation and lack of internal capital control and management limited its development efficiency. Above all, the causes of low efficiency in banking institutions mainly focus on capital management and internal control.

From the time of vertical perspective, this part compares and analyzes the banking institutions from the Industrial and Commercial Bank of China (dark blue), Agricultural Bank of China (saffron), Bank of China (yellow), China Construction Bank (purple), Bank of Communications(green), and average value(blue). Figure 11 reveals that the Agricultural Bank of China is the most operation efficient. According to the seventh national census, 36% of China’s population is in rural areas; China is still a largely agricultural country, compared to other banking services. Agricultural Bank of China mainly focuses on the construction of modern agriculture, serves the integration of urban and rural areas and farmers’ production and life, and promotes the coordinated development of regions; likely, the policy orientation of the Chinese government and the urgent need for agricultural development have led to its higher efficiency for other banks.

In addition, the Industrial and Commercial Bank of China (ICBC) and Bank of Communications have a smaller operation efficiency value, and both of them have below-average banking operation efficiency. Although ICBC is the largest bank in China, it may have a large cost due to the excessive number of branches and staff, while Bank of Communications is mainly focused on mobile banking; other banking services may be relatively backward.

On the other hand, joint-stock banks are the second category of commercial banks; we compare the operation efficiency of five joint-stock commercial banks. On the whole, the average operation efficiency of the five major joint-stock banks is more than 0.5, and the fluctuation of the efficiency value of China Merchants Bank is relatively small; however, Everbright Bank’s operation efficiency fluctuates greatly; Figure 12 shows the details. From the annual report, Everbright Bank and ICBC yield and business volume are expanding, which is more consistent with the operation efficiency value fluctuation. In addition, the average operation efficiency value in 2018 and 2020 is lower; in the past two years, we have seen trade frictions between China and the US and the COVID-19 pandemic; therefore, this is probably the reason for the lower operating efficiency.

Figures 13 and 14 reveal operation efficiency comparisons and volatility for different types of banks. The operation efficiency value of urban commercial banks is low and the volatility is large, while the operation efficiency value of state-owned banks and rural commercial banks is high and the volatility is small. Therefore, urban commercial banks should learn from state-owned banks to stabilize their efficiency.

4. Conclusions

Financial institutions are crucial in the financial stability mechanism. We take the bank risk behavior coefficient solution as a case in point; it is extremely important to measure the dynamic risk behavior of institutions. Because the risk behavior of institutions may change at any time due to internal or external factors, it is a dynamic change process, and almost all institutions’ reported risk behavior is risk-averse. However, that is unlikely to be the case in reality. To measure banks’ risk behavior more accurately based on the information they published, we take CAPM and efficiency evaluation ideas to develop a two-stage model, which solves bank risk behavior immediately and evaluates operation efficiency. Consequently, the objective bank’s risk behavior and the bank’s operating efficiency results will be obtained. In this research, some contributions from the perspectives of theoretical improvement and practical application have been made by our cooperator. Firstly, financial institutions’ behavior coefficients are measured by the two-stage model, and operators can make their development strategy appropriate to their own bank’s risk behavior. Secondly, this study evaluates the financial institution’s operation efficiency from the perspective of risk and profitability comprehensively. Thirdly, the new method we proposed has been applied to the bank data application to verify its feasibility and effectiveness.

Furthermore, there are still some limitations to the two-stage model. For example, the period is limited, and in the future research, we will use panel data to solve institution risk behavior, and more comprehensive indicators will be adopted.

Data Availability

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that they have no conflicts of interest.


This work was supported by the National Social Science Foundation of China: The ways of Financial Supervision Department to Punish Law-breaking Institutions and the research of Penalty Pricing, Project no. 19BJY251.