Bank size, competition and risk in the Turkish banking industry

Abstract

This paper investigates the impact of bank size and competition on earnings volatility and insolvency risk using quarterly data for commercial banks operating in the Turkish banking industry for the period 2002Q1–2012Q2. The main result of the paper indicates that bank size and earnings volatility are negatively related, suggesting that larger banks are less risky. The results also indicate that competition measured by the Boone indicator increases earnings volatility. The results further suggest that higher capitalized banks, banks with a higher share of non-interest income in total income and efficient banks face lower earnings volatility. Finally, insolvency risk measured by Z-score and bank size are positively related, suggesting that larger banks are more stable.

Appendix

To estimate Eq. (4) we need the computation of marginal costs for each bank and quarter. As marginal costs cannot be directly observed, we estimate them by using a translog cost function, which is common in the related literature since it does not require too many restrictive assumptions about the nature of the technology. The multi-product cost function for a given bank s at time t can be specified as follows:

$$ \begin{aligned} \ln tc_{st} & = \alpha_{0} + \sum\limits_{i = 1}^{3} {\alpha_{i} \ln y_{ist} } + \frac{1}{2}\sum\limits_{i = 1}^{3} {\sum\limits_{k = 1}^{3} {\alpha_{ik} \ln y_{ist} \ln y_{kst} } } + \sum\limits_{j = 1}^{2} {\beta_{j} \ln w_{jst} } \\ \quad + \frac{1}{2}\sum\limits_{j = 1}^{2} {\sum\limits_{m = 1}^{2} {\beta_{jm} \ln w_{jst} \ln w_{mst} + \sum\limits_{i = 1}^{3} {\sum\limits_{j = 1}^{2} {\delta_{ij} \ln y_{ist} \ln w_{jst} } + \sum\limits_{t = 1}^{T - 1} {\theta_{t} } D_{t} } } } + \varepsilon_{st} \\ \end{aligned} $$

(5)

where tc is the total cost and y denotes three outputs; total loans, other earning assets and non-interest income. The last output is a proxy for bank non-traditional activity.²² w represents two input prices: price of funds and a common price of labor and capital. Since personnel expenses are not reported in some quarters, we calculate a common price for labor and capital (see Hasan and Marton 2003). The common price is calculated as the ratio between operating costs and total assets. The price of funds is calculated by dividing total interest expenses by total deposits. Both financial and operating costs are included in the estimation of the cost function. In addition, D, which represents time dummies for each quarter, is included to capture technological progress, and $\varepsilon = v + u$ is a composite error term where v represents standard statistical noise and u captures inefficiency. To ensure that the estimated cost frontier is well-behaved, two standard properties of the cost function, symmetry and linear homogeneity, are imposed via parameter restrictions. The linear homogeneity conditions are imposed by normalizing total cost (tc) and the price of labor ($w_{1}$) by the price of funds ($w_{2}$). The symmetry condition requires $\alpha_{ik} = \alpha_{ki\;} \forall \;i,\;k$ and $\beta_{jm} = \beta_{mj\;} \forall \;j,\;m$.

The marginal costs for loans (l) can be obtained by taking the first derivative of the dependent variable in Eq. (5) with respect to output $y_{lst}$ as follows:

$$ MC_{st} = \frac{{\partial \ln (tc_{st} /w_{2} )}}{{\ln y_{lst} }} = \frac{{(tc_{st} /w_{2} )}}{{y_{lst} }}\left[ {\alpha_{l} + \alpha_{il} \ln y_{lst} + \sum\limits_{k = 1, \ldots ,K;k \ne l} {\alpha_{ik} \ln y_{ist} + } \phi_{j} \ln \left(\frac{{w_{1} }}{{w_{2} }}\right)} \right] $$

(6)

We also estimate cost efficiency using Jondrow et al. (1982) approach. Bank-specific estimates of inefficiency, u, can be computed by using the distribution of the inefficiency term conditional on the estimate of the composite error term. The random error term (v) is assumed to be normally distributed and the inefficiency term (u) is assumed to be one-sided.

The descriptive statistics of variables used in the translog cost function are reported in Table 4.

Table 4 Descriptive statistics

Table 5 Definitions, expected signs and data sources of the variables used in the analysis

Fig. 2

Earnings volatility (SD), bank stability (Z-score), capitalization, diversification, inefficiency, and size over the period 2003Q1–2012Q1. Standard deviations of earnings (ROA) are computed using a four-quarter rolling time windows. Total assets are in millions of US dollars. a Earnings volatility. b Bank stability. c Bank capitalization and diversification. d Bank inefficiency. e Total assets