A risk-averse bank might choose (select) to fund its loans with a higher ratio of financial capital-to-deposits than a risk-neutral bank. Since financial capital is typically more expensive than deposits, this might lead one to conclude that the risk-averse bank produces its output in an allocatively inefficient manner, when actually it is the risk-preferences that differ. In order to control for these differences in risk-preferences, Mester (1996) claims that the level of financial capital should be included in the cost function. Chang (1999) presents (demonstrates) a non-parametric approach to incorporate three risk factors (elements) (non-performing loans, allowance for loan losses, and risky assets) into the measurement of technical efficiencies of the major financial intermediaries in rural Taiwan. Her test results support the idea that incorporating risk as an undesirable output has significant (significantly) impacts on the ranking of efficiency performance. Altunbas et al. (2000) investigate (investigates) the impact of risk on bank efficiency for a sample of Japanese commercial banks between 1993 and 1996. They use loan loss provisions, financial capital to control risk. Their findings suggest that optimal bank size is considerably smaller when risk factors are taken into account, and the level of financial capital has the largest influence on the scale efficiency estimates.
During the period of 1999-2004, Iannotta et al. (2007) use (uses) the ratio of loan loss provision to total loans as a proxy for both asset quality and risk to compare the performance and risk of a sample of 181 large banks from 15 European countries. They present that public sector banks are on average less profitable and riskier than other banks, while mutual banks have better loan quality and lower asset risk than both private and public sector banks. Pasiouras (2008) uses DEA to investigate the efficiency of the Greek commercial banking industry over the period 2000’2004 and indicates that the inclusion of loan loss provisions as an input increases the efficiency scores. It seems that most studies in the existing literature mainly use credit risk indicators, including non-performing loans and allowance for loan losses and risky assets, to explain bank efficiency scores, but do not consider other kinds of risks associated (related to) with bank efficiency. However, loaning funds to the demand side is no longer the main business of banks. They are exposed to various sources of risks, which may be due to exogenous circumstances. In January 2001 the Basle Committee divides calculating bank risks into three major parts (components): credit risk, operational risk, and market risk. Credit risk is the risk of loss due to a debtor’s non-payment of a loan or other lines of credit. Operational risk is the risk arising from the execution of a company’s business functions. It is a very broad concept including fraud risks, legal risks, physical or environmental risks, etc. More specifically, Basel II defines operational risk as the risk of loss resulting from inadequate or failed internal processes, people and systems, or from external events. Market risk is the risk that the value of an investment will decrease due to moves in market factors including equity risk, interest rate risk, and currency risk. Thus, the non-performing ratio is no longer the only index to evaluate (measure) the risks of banks. The literature also includes the estimates of bank efficiency using market or operational risk though they are somewhat incomplete.
Armah and Park (1998) believes that agricultural banks face three major sources of risks. Default risk arises when borrowers cannot repay their loans and accrued interests. Liquidity risk derives from the uncertainty about banks’ abilities to maintain enough funds to meet customers’ loan demands. Interest rate risk is the hazard of banks refinancing their long-term loans at interest rates above the rates they receive.
Eisenbeis et al. (1999) find (discovers) evidence that the stochastic frontier scores are more closely related to risk-taking behavior, managerial competence, and stock returns. They use the standard deviation of daily stock returns to measure the total systematic and nonsystematic risks of the banking firm’s common stocks. They use the standard deviation of residuals from the market model to measure the non-diversifiable idiosyncratic risk. They also use the ratio of loan charge-offs to loans outstanding in order to measure the banking firm’s exposure to credit risk. Gonz??lez (2005)analyzes the impact of bank regulation on bank charter value and risk-taking. He measures credit risk with the ratio of nonperforming loans to total bank loans and measures overall risk with the standard deviation of daily bank stock returns. The results indicate that regulatory restrictions increase banks’ risk-taking incentives by reducing (decreasing) their charter value. Chiu and Chen (2009) consider not only credit risk, but also market and operational risk factors such as the foreign exchange rate, the interest rate, and the economic growth rate to analyze Taiwanese bank efficiency. Only a few studies examine how ROA’s (Return on Assets’) volatility affects bank efficiency. For example (instance), by using data on US banks over the period 1990’1995, Berger and Mester (1997)finds a negative relationship between cost efficiency and the standard deviation of ROA. A similar result is found for the standard deviation of ROE (Return on Equity). They interpret the results as bad managers are poor at both operations and risk management. However, more recent studies using international data find some results contradicting the earlier findings for the USIsik and Hassan (2002) show that the standard deviation of ROE is positively related to input efficiency in the Turkish banking industry. Havrylchyk (2006) investigates the determinants of bank efficiency using non-parametric DEA on a sample of Polish banks between 1997 and 2001. Her result shows that the volatility of ROA significantly affects bank efficiency positively. She then runs regressions with ROA as a dependent variable and the variance of ROA as an explanatory variable. A positive correlation between ROA and variance of ROA suggests that riskier banks are not only more efficient, but also more profitable on average. The circumstance above is somehow difficult to understand. If there is a trade-off between risk and efficiency, then banks that are poor at operations might also be poor at risk management. Furthermore, inefficient banks tend to have higher risk in stock returns, which means that stocks of inefficient banks tend to underperform their more efficient counterparts.