1 Bank Risk: Does Size Matter? David E. Allen Akhmad R. Kramadibrata Robert J. Powell Abhay K. Singh School of Accounting, Finance and Economics, ECU

Methodology: Four Measures of Risk 2 Value at Risk (VaR) Conditional Value at Risk (CVaR, which measures extreme risk beyond VaR) Distance to Default (DD) based on Merton’s structural model Conditional Distance to Default (CDD) (our own model) which applies CVAR techniques to the structural model to measure extreme credit risk

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Data 10 years data divided into 2 periods –Pre GFC(7 years data which corresponds with Basel requirements for advanced models) –GFC( ) All listed local banks in each country (excludes foreign banks) –Australia 13 –Canada 9 –Europe75 –USA 52 Daily equity data and balance sheet data from Datastream 4

Methodology – VaR & CVaR VaR: measures potential losses over a specific time period at a given level of confidence. We use 95% confidence level. CVaR : Average of losses beyond VaR (5% of worst losses). In order to exclude the possibility of distortion of results due to sensitivity to the method chosen, we use all 3 main methods: –The parametric method estimates VaR on the assumption of a normal distribution (σ x 1.645). –The historical method groups historical losses in categories from best to worst and calculates VaR on the assumption of history repeating itself (lowest 95 th percentile value over the period). –Monte Carlo Simulation simulates multiple random scenarios (we generate 20,000 random scenarios for both pre-GFC and post-GFC periods, then calculate VaR as the lowest 95 th percentile value for each period). 5

6 Methodology: Structural model Calculates distance to default (DD): Assumes default is triggered when value of borrower falls below it’s debt obligation Termed structural as it is based on debt/equity structure of the balance sheet Distance to default is number of standard deviations the firms value is away from default. In simplest format: V = Firm value F = Debt

7 Methodology Structural Model V = Firm value, based on market value plus liabilities F = Debt, based on current liabilities plus half of long term liabilities µ = asset drift, based on annual return T = Time period, usually modelled as 1 year σ = standard deviation N = cumulative standard normal distribution function

Methodology: Structural model Daily asset returns are obtained through a complex estimation and convergence process. The standard deviation of these returns are then applied to the DD and PD formulas per previous slides. 8

9 Methodology: CDD Cstdev is standard deviation of worst 5% of returns Again we use 3 methods. Parametric, Historical Monte Carlo (similar to VaR, but we are now applying these to asset returns instead of equity returns)

Methodology – testing for size impact Correlation between size and risk Split analysis between major / other banks Multiple regression to test size in conconction with other determinants 10

Correlation between size and risk 11

Major / Other Banks – Australia 12

Major / Other Banks – Canada 13

Major / Other Banks – Europe 14

Major / Other Banks – US 15

Fixed Effects Regression VaR it (or DD it ) = β 1 Size it + β 2 Equity it + β 3 ROE it + β 4 LA t + β 5 CLL it + β 6 INTI it + β 7 NPL it + β 8 GVaR it + α i + ε it Size:log of total balance sheet assets. Equity: total balance sheet equity / total balance sheet assets. ROE: net profit before tax / total balance sheet equity. LA:total balance sheet loans / total balance sheet assets. CLL:commercial (non-residential) loans / total loans. INTI:gross interest income / total income. NPL:non performing loans (impaired assets) / total loans. GVaR: Global Value at Risk, applied to Australia and Canada only, to assess the contagion effect of major market volatility of Global Banks - the measure used was the combined VaR of Europe and US 16

Regression - Notes We examined ROA as an alternative to ROE, and Tier 1 Capital ratio as an alternative to Equity ratio. We selected ROE and Equity as they provided a slightly better fit in term of R 2 than the alternates, and to avoid multicollinearity we excluded the alternate measures. CLL was applied to Australia only, due to insufficient availability of this data for other regions. A variety of lags were applied to each of the variables, but no lagging of variables significantly improved any of the outcomes and lags are thus not reported. R 2 shown at 3 levels; firstly excluding NPL and GVaR, secondly excluding GVaR only, thirdly including all variables. 17

Regression Results (Australia & Canada) 18

Regression Results (Europe & US) 19

20 Conclusions Neither correlation nor regression analysis show significance in association between size and risk. When splitting banks into ‘major’ banks and ‘other’ banks, size does have some significance, but the signs vary between regions. Overall, the study finds no conclusive evidence of association between size and risk.