Does Diversification Affect Banking Systemic Risk ?

The 2007–2009 financial crisis has shed light on the significance of systemic risk and has made the concern about systemic risk increased by academics, regulatory bodies, and central banks.There is a growing literature on systemic risk. It mainly analyzes two aspects of systemic risk: the measure of systemic risk [1–3] and factors that may cause changes in the level of systemic risk, such as hedge funds [4], the opaque [5], financial system consolidation [6], and network structures [7–10]. It is well known that individual risk can be reduced through diversification [11]. However, the relationship between diversification and systemic risk is less commonly known [12]. And it is widely accepted that diversification at financial institutions benefits the stability of the financial system [13]. In fact, diversification has its costs. It enables institutions to become more similar to each other and hence systemic risk becomes more likely, which is the dark side of diversification [12, 13]. In the case of full diversification or full risk sharing, Shaffer [14] and Ibragimov et al. [15] find that diversification may benefit individual institutions but often increases systemic risk. Wagner (2010) shows that any degree of diversification increases systemic risk. Raffestin [16] also confirms the negative effect of diversification and goes more in depth by considering any level of diversification and any number of failures. The above theoretical findings reveal the negative effect of diversification on systemic risk. Based on the linear and nonlinear causality tests, in this paper we aim to examine whether there is the causal relationship fromdiversification to banking systemic risk by using data from the Chinese banks. In fact, systemic risk is a complex phenomenon [17, 18]. In this paper, we focus on analyzing it from a technical-econometric point of view, which is useful to understand it from a different perspective. Similar to some studies [19–23], in this paper we measure banking systemic risk based on Contingent Claims Analysis. However, the purpose of this paper is different from theirs, and the novelties of this paper are as follows: the causal relationship from diversification to banking systemic risk is empirically tested; the causality tests are conducted within both linear and nonlinear frameworks; we conduct an empirical analysis for Chinese banking sector. After this introduction, Section 2 describes the methodology. Section 3 presents the data and empirical results, while Section 4 provides a conclusion.


Introduction
The 2007-2009 financial crisis has shed light on the significance of systemic risk and has made the concern about systemic risk increased by academics, regulatory bodies, and central banks.There is a growing literature on systemic risk.It mainly analyzes two aspects of systemic risk: the measure of systemic risk [1][2][3] and factors that may cause changes in the level of systemic risk, such as hedge funds [4], the opaque [5], financial system consolidation [6], and network structures [7][8][9][10].
It is well known that individual risk can be reduced through diversification [11].However, the relationship between diversification and systemic risk is less commonly known [12].And it is widely accepted that diversification at financial institutions benefits the stability of the financial system [13].In fact, diversification has its costs.It enables institutions to become more similar to each other and hence systemic risk becomes more likely, which is the dark side of diversification [12,13].In the case of full diversification or full risk sharing, Shaffer [14] and Ibragimov et al. [15] find that diversification may benefit individual institutions but often increases systemic risk.Wagner (2010) shows that any degree of diversification increases systemic risk.Raffestin [16] also confirms the negative effect of diversification and goes more in depth by considering any level of diversification and any number of failures.
The above theoretical findings reveal the negative effect of diversification on systemic risk.Based on the linear and nonlinear causality tests, in this paper we aim to examine whether there is the causal relationship from diversification to banking systemic risk by using data from the Chinese banks.In fact, systemic risk is a complex phenomenon [17,18].In this paper, we focus on analyzing it from a technical-econometric point of view, which is useful to understand it from a different perspective.Similar to some studies [19][20][21][22][23], in this paper we measure banking systemic risk based on Contingent Claims Analysis.However, the purpose of this paper is different from theirs, and the novelties of this paper are as follows: the causal relationship from diversification to banking systemic risk is empirically tested; the causality tests are conducted within both linear and nonlinear frameworks; we conduct an empirical analysis for Chinese banking sector.After this introduction, Section 2 describes the methodology.Section 3 presents the data and empirical results, while Section 4 provides a conclusion.

Methodology
2.1.Diversification Measures.In this paper, the diversification indicator is calculated from the perspective of banks' profitability.There are different calculation methods for diversification of banks (e.g., [24][25][26]).We adopt the method proposed by Elsas et al. (2010).Moreover, we use the unweighted average diversification of banks (ADIV) and the weighted average diversification of banks (WADIV) to measure banking diversification, where the weight is the individual market-capital weight.Elsas where INT denotes gross interest revenue, COM net commission revenue, TRAD net trading revenue, and OTH all other net revenue, respectively.TOR indicates total operating revenue, which is equal to the sum of the absolute values of INT, COM, TRAD, and OTH.

Systemic Risk Measures.
In this paper, we measure banking systemic risk based on Contingent Claims Analysis (CCA).It is a framework that combines market-based and balance sheet information to obtain financial risk indicators, such as Distance-to-Default (DD), probabilities of default, risk-neutral credit risk premia, and expected losses on senior debt [20].The CCA approach has been adopted to investigate banking systemic risk based on aggregated DD series [19][20][21][22][23]. Therefore, we also use the unweighted average DD series (ADD) and weighted average DD series (WADD) to measure banking systemic risk, where the weight is the individual market-capital weight.Similar to Singh et al. ( 2014), DD  , the distance-to-default of bank  at time , is calculated from the following equations: where  is the value of bank assets,  the time horizon of debt,  the face value of the debt,  the volatility of bank assets,  the risk-free rate,  the market value of bank equity capital, and σ the volatility of bank equity capital, respectively.

Linear and Nonlinear Granger Causality
Tests.Granger [27] defines causality between two variables in terms of predictability.The linear causal relationship between two variables can be tested within a VAR framework, where the null hypothesis of no causality is tested via the significant contribution that past values of one variable can offer in predicting current values of another [28].Since the linear Granger causality test cannot capture nonlinear and higher order causal relationships [29], we further consider a nonlinear Granger causality test, which was developed by Baek and Brock [30] and modified by Hiemstra and Jones [31].
Under certain variance conditions, Diks and Panchenko [32] find that the Hiemstra-Jones (HJ) test could overreject the null hypothesis.
where    = (‖  −   ‖ <   ); (⋅) is an indicator function and   is the presetting bandwidth depending on the sample length .Then, the new test statistic can be expressed as − f, (  ,   ) f, (  ,   )) . ( Diks and Panchenko (2006) demonstrate that   (  ) converges to the standard normal distribution under certain conditions.In this paper,  is one year;  is total liabilities of banks;  is set as the one-year deposit interest rate during the trading period; σ is calculated as the standard deviation of daily equity logarithmic returns multiplied by the square root of the number of trading days in a month.In addition, similar to Gropp and Moerman [33], Blundell-Wignall and Roulet [34], and Saldías (2013), the data from the quarterly reports of banks are interpolated to yield monthly observations by using a cubic spline.Through the calculation, the results of banking diversification and systemic risk are obtained and shown in Figures 1 and 2, respectively.

Empirical Results
. Before conducting the linear and nonlinear Granger causality tests, we apply Augmented Dickey-Fuller (ADF) test and Phillips-Perron (PP) test to analyze whether there are unit roots for all of the four variables, namely, ADIV, WADIV, ADD, and WADD.Table 1 illustrates the test results.In every case, we reject the null hypothesis of a unit root for the two tests.Obliviously, all of the variables are stationary and thus suitable for further statistical analysis with linear and nonlinear Granger causality tests.
We first investigate whether there is the linear causal relationship from diversification to banking systemic risk, by implementing the standard Granger causality test [27].The results are reported in Table 2.They reveal that the null hypothesis of linear causality running from diversification to banking systemic risk is never rejected for both tests.Therefore, there is no linear causality running from diversification to banking systemic risk.
Before testing for nonlinear Granger causality, we conduct the Brock-Dechert-Scheinkman (BDS) test to investigate whether the residual series are characterized by nonlinearities, where the residual series are from VAR models.We estimate the VAR model with the endogenous variables ADIV, ADD, WADIV, and WADD, respectively, where the lag of the VAR model is set based on Schwartz Information Criterion.We use these residual series so that any linear predictive power has been removed.Table 3 displays the results of the BDS tests.We can see from it that nonlinearities are in diversification and systemic risk.Such result signifies that nonlinear Granger causality test is appropriate in our study.Now we conduct the nonlinear causality test.Based on the standardized residuals of VAR models, we set the bandwidth as 1.5 and the embedding dimensions as 1 to 8, where the empirical results from the DP test are presented in Table 4.It can be seen from Table 4 that the null hypothesis of no nonlinear Granger causality from diversification to banking systemic risk is not rejected.Therefore, there is no nonlinear causality running from diversification to banking systemic risk.

Conclusion
Recently, the negative effect of diversification on systemic risk is analyzed in the some literature.This paper adopts both  linear and nonlinear Granger causality tests to examine whether there is the causal relationship from diversification to banking systemic risk.Based on the banking data from China, our empirical findings reveal that there is no linear or nonlinear causal relationship from diversification to banking systemic risk.A possible reason is that banking systemic risk is largely derived from the cyclical fluctuations of the macroeconomy, while diversification mainly affects banking nonsystemic risk.Overall, our results show that diversification does not affect banking systemic risk in China.

Figure 2 :
Figure 2: Banking systemic risk based on ADD and WADD.
To compensate this shortcoming, Diks and Panchenko (2006) propose a new test statistic (hereafter DP test).In this paper we adopt the DP test to check the nonlinear Granger causality.Suppose {  } and {  } are both strictly stationary time series, and   =  +1 .In the null hypothesis that  does not Granger cause , Diks and Panchenko (2006) find that there is the following equation:  ≡  [ ,, (, , )   () −  , (, )  , (, )] (⋅) is the probability density function.Let f (  ) indicate the local density estimators of a   -variate random vector  at   by
Notes: the numbers in parentheses refer to the  values.

Table 2 :
Linear Granger causality tests.: the VAR lag lengths were selected based on the Schwartz Information Criterion (SIC). Notes

Table 3 :
BDS tests for nonlinearity.: each column represents the test results of the VAR residuals for the corresponding variable as the dependent variable.The numbers represent the statistics and those in parentheses are the  values. Notes