The Volatility of European Banking Systems: A Two-Decade Study

Abstract

This paper examines the trends and composition of volatility across European banking systems from January 1988 to December 2010. While there is no evidence of a long-term trend in the average level of banking system volatility, there is a change in its composition resulting from the growing importance of International and European nonfinancial components, especially in the largest banking systems. We argue that the changing composition of banking system volatility is the effect of a long-term integration process (with a growing importance of cross-border activities) that has not been influenced by the introduction of the Euro. Our results highlight the increasing vulnerability of the European banking systems to International and European shocks and an increasing likelihood of cross-border banking crises, and the need for regulatory reforms that focus on effective cross-border crisis management and resolution so as to safeguard the systemic stability of European banking in the near future.

Appendix

Equation (2) is derived by assuming that the return of a European index of nonfinancial firms (${R_{{E_{it}}}}$), the return of an International banking industry index (${R_{I\_IN{D_{it}}}}$), the return of a European banking index (${R_{E\_IN{D_{it}}}}$) and the return on a Country index (${R_{{C_{it}}}}$) are generated as follows:

$$ {R_{{E_{it}}}} = {\delta_i} + {\eta_i}{R_{{I_{it}}}} + \varepsilon_{it}^E $$

(1A)

$$ {R_{I\_IN{D_{it}}}} = {\theta_i} + {\varpi_i}{R_{{I_{it}}}} + {\kappa_i}{R_{{E_{it}}}} + \varepsilon_{it}^{I\_IND} $$

(2A)

$$ {R_{E\_IN{D_{it}}}} = {\gamma_i} + {\lambda_i}{R_{{I_{it}}}} + {\phi_i}{R_{{E_{it}}}} + {\varsigma_i}{R_{I\_IN{D_{it}}}} + \varepsilon_{it}^{E\_IND} $$

(3A)

$$ {R_{{C_{it}}}} = {\varphi_i} + {\tau_i}{R_{{I_{it}}}} + {\omega_i}{R_{{E_{it}}}} + {\chi_i}{R_{I\_IN{D_{it}}}} + {\psi_i}{R_{E\_IN{D_{it}}}} + \varepsilon_{it}^C $$

(4A)

where ${R_{{I_{it}}}}$ is the return on an international index of nonfinancial firms and $\varepsilon_{it}^E,\varepsilon_{it}^{I\_IND},\varepsilon_{it}^{E\_IND}$ and $\varepsilon_{it}^C$ are mean zero error terms that are orthogonal to the right hand side variable in their respective regression and refer to country i and time t.

By replacing ${R_{{E_{it}}}}$in Eq. (2A) with (1A), ${R_{{E_{it}}}}$ and ${R_{I\_IN{D_{it}}}}$ in Eq. (3A) with (2A) and (1A), and ${R_{{E_{it}}}}$, ${R_{I\_IN{D_{it}}}}$, ${R_{E\_IN{D_{it}}}}$in Eq. (4A) with (3A), (2A) and (1A) we can also write that:

$$ {R_{I\_IN{D_{it}}}} = \theta_i^{I\_IND} + \varpi_i^{I\_IND}{R_{{I_{it}}}} + {\kappa_i}\varepsilon_{it}^E + \varepsilon_{it}^{I\_IND} $$

(5A)

$$ {R_{E\_IN{D_{it}}}} = \delta_i^{E\_IND} + \eta_i^{E\_IND}{R_{{I_{it}}}} + {\phi_i}^{E\_IND}\varepsilon_{it}^E + {\varsigma_i}\varepsilon_{it}^{I\_IND} + \varepsilon_{it}^{E\_IND} $$

(6A)

$$ {R_{{C_{it}}}} = \varphi_i^C + \eta_i^C{R_{{I_{it}}}} + \phi_i^C\varepsilon_{it}^E + \chi_i^C\varepsilon_{it}^{I\_IND} + {\psi_i}\varepsilon_{it}^{E\_IND} + \varepsilon_{it}^C $$

(7A)

where

• $\theta_i^{I\_IND} = \left( {{\theta_i} + {\kappa_i}{\delta_i}} \right)$

• $\varpi_i^{I\_IND} = \left( {{\varpi_i} + {\kappa_i}{\eta_i}} \right)$

• $\delta_i^{E\_IND} = \left( {{\gamma_i} + {\phi_i}{\delta_i} + {\varsigma_i}\theta_i^{I\_IND}} \right),$

• $\eta_i^{E\_IND} = \left( {{\lambda_i} + {\phi_i}{\eta_i} + {\varsigma_i}\varpi_i^{I\_IND}} \right),$

• ${\phi_i}^{E\_IND} = \left( {{\phi_i} + {\varsigma_i}{\kappa_i}} \right)$

• $\varphi_i^C = \left( {{\varphi_i} + {\omega_i}{\delta_i} + {\chi_i}\theta_i^{I\_IND} + {\psi_i}\delta_i^{E\_IND}} \right),$

• $\eta_i^C = \left( {{\omega_i} + {\omega_i}{\eta_i} + {\chi_i}\varpi_i^{I\_IND} + {\psi_i}\eta_i^{E\_IND}} \right)$

• $\phi_i^C = \left( {{\chi_i}{\kappa_i} + {\omega_i} + {\psi_i}{\phi_i} + {\psi_i}{\varsigma_i}{\kappa_i}} \right),$

• $\chi_i^C = \left( {{\chi_i} + {\psi_i}{\varsigma_i}} \right).$

The residuals series are, therefore, uncorrelated with our proxy for the ‘International’ market and are uncorrelated to each other.

Thus, if we denote as R _it the return on a banking index that refers to country i and we assume that this return depends on the International nonfinancial, European nonfinancial, International banking industry, European banking industry and Country components as follows

$$ {R_{it}} = {\alpha_i} + \beta_i^I{R_{{I_{it}}}} + \beta_i^E{R_{E{}_{it}}} + \beta_i^{I\_IND}{R_{I\_IN{D_{it}}}} + \beta_i^{E\_IND}{R_{E\_IN{D_{it}}}} + \beta_i^C{R_{{C_{it}}}} + {\varepsilon_{it}} $$

(8A)

where $\beta_i^I\beta_i^E,\beta_i^{I\_IND},\beta_i^{E\_IND}$ and $\beta_i^C$ express the sensitivity of the banking system in country i to these components, and ε _it represents the unexplained residual, under the assumption that Eqs. 1A, 2A, 3A and 4A are correctly specified, we can postulate that the “true” return generating model is based on the following equation²⁹

$$ {R_{it}} = {\alpha_i} + b_i^I{R_{{I_{it}}}} + b_i^E\varepsilon_{it}^E + b_i^{I\_IND}\varepsilon_{it}^{I\_IND} + b_i^{E\_IND}\varepsilon_{it}^{E\_IND} + b_i^C\varepsilon_{it}^C + {\varepsilon_{it}} $$

(9A)

where

• $b_i^I = \beta_i^I + \beta_i^E{\eta_i} + \beta_i^{I\_IND}\varpi_i^{I\_IND} + \beta_i^{E\_IND}\eta_i^{E\_IND} + \beta_i^C\eta_i^C;$

• $b_i^E = \beta_i^E + \beta_i^{I\_IND}{\kappa_i} + \beta_i^{E\_IND}{\varphi_i}^{E\_IND} + \beta_i^C\varphi_i^C;$

• $b_i^{I\_IND} = \beta_i^{I\_IND} + \beta_i^{E\_IND}{\varsigma_i} + \beta_i^C\chi_i^C;$

• $b_i^{E\_IND} = \beta_i^{E\_IND} + \beta_i^C{\psi_i};$

• $b_i^C = \beta_i^C.$