Discrete Dynamics in Nature and Society

Volume 2016 (2016), Article ID 2967830, 5 pages

http://dx.doi.org/10.1155/2016/2967830

## Does Diversification Affect Banking Systemic Risk?

School of Economics and Management, Southeast University, Nanjing 211189, China

Received 14 July 2016; Accepted 6 November 2016

Academic Editor: Ricardo López-Ruiz

Copyright © 2016 Shouwei Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper contributes to the understanding of the linear and nonlinear causal linkage from diversification to banking systemic risk. Employing data from China, within both linear and nonlinear causality frameworks, we find that diversification does not embody significant predictive power with respect to banking systemic risk.

#### 1. 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 [1–3] 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 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 [19–23], 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.

#### 2. 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., [24–26]). We adopt the method proposed by Elsas et al. (2010). Moreover, we use the unweighted average diversification of banks () and the weighted average diversification of banks () to measure banking diversification, where the weight is the individual market-capital weight. Elsas et al. (2010) classify bank’s non-interest-related activities into net commission revenue, net trading revenue, and all other net revenue and illustrate the diversification indicator of bank at time as follows: where denotes gross interest revenue, net commission revenue, net trading revenue, and all other net revenue, respectively. indicates total operating revenue, which is equal to the sum of the absolute values of , and .

##### 2.2. 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 [19–23]. Therefore, we also use the unweighted average DD series () and weighted average DD series () to measure banking systemic risk, where the weight is the individual market-capital weight.

Similar to Singh et al. (2014), , 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 the volatility of bank equity capital, respectively.

##### 2.3. 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. 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 . In the null hypothesis that does not Granger cause , Diks and Panchenko (2006) find that there is the following equation: where is the probability density function. Let indicate the local density estimators of a -variate random vector at by where ; is an indicator function and is the presetting bandwidth depending on the sample length . Then, the new test statistic can be expressed as Diks and Panchenko (2006) demonstrate that converges to the standard normal distribution under certain conditions.

#### 3. Data and Empirical Results

##### 3.1. Data and Preliminary Analysis

Considering the difference of the listed times, in this paper we analyze 14 listed banks in China, where their stock codes are 600000.SH, 600015.SH, 600016.SH, 600036.SH, 601009.SH, 601166.SH, 601169.SH, 601328.SH, 601398.SH, 601939.SH, 601988.SH, 601998.SH, 000001.SZ, and 002142.SZ, respectively. Data employed in this paper stem from the Wind Database and the quarterly reports of banks, where the Wind Database is a leading integrated service provider of financial data in China. The time interval is from October 2007 to June 2014. In this paper, is one year; is total liabilities of banks; is set as the one-year deposit interest rate during the trading period; 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.