آنالیز عملکرد کسب و کار بانک و ریسک بازار با به کار بردن DEA فازی The analysis of bank business performance and market risk—Applying Fuzzy DEA

۱٫ Introduction As financial institutions around the world become more internationalized and globalized, the trading activities of the financial industry continue to rise. The market structure is further complicated due to the diversity and innovativeness of products available. Therefore, the risk of investment for financial institutions likewise increases. With such changes in the economic state, banks no longer have the sole role of being the purely monetary intermediary. They must now develop a whole range of investment channels in order to survive under such conditions. However, bearing the objective of profit-making in mind, banks will naturally increase their investments in high-risk products or increase leveraged trading, which means that the high potential profits mask the high risks involved and increase the probability of a bank’s bankruptcy due to poor management. For this reason, more attention must be paid to the high risks attached to the high potential profits. The topic of Risk Adjusted Performance Measurement has, in recent years, gained increasing awareness and has become more widely discussed as people place more importance on risk management. From the perspective of efficiency measurement, Data Envelopment Analysis (DEA) takes into consideration both inputs and outputs. The mathematical method therefore provides a fair measurement of efficiency. Since this analytical model was first proposed, it has been widely applied in a whole range of industries. Most studies to date on bank efficiency have focused mainly upon the economies of scale and scope (Berger and Humphrey, 1991; Berger et al., 1987; Hunter and Timme, 1986; McAllister and McManus, 1993), total productivity (Aly et al., 1990; Favero and Papi, 1995; Fukuyama et al., 1999; Grabowski et al., 1993; Schaffnit et al., 1997; Zaim, 1995), and the efficiency effect (Barr et al., 1994; Casu and Molyneux, 2003; Cebenoyan et al., 1993; Chang, 1999; DeYoung and Hasan, 1998; Elyasiani et al., 1994). The fact that increasing importance is gradually being placed on risk management means that more attention is also given to DEA models that include risk in their equations. There are two issues concerning banks’ efficiency and risk. One issue treats risk as exogenous in order to analyze efficiency effects (Ataullah et al., 2004; Barr et al., 1994; Berger and DeYoung, 1997; Chang and Chiu, 2006; Cebenoyan et al., 1993; Elyasiani et al., 1994; Pastor, 2002). The above results show that the efficiency level is significantly correlated with the risk indicators. The other issue treats risk as endogenous in order to analyze banks’ efficiency (Altunbas et al., 2000; Chang, 1999; Chiu and Chen, 2008; Drake and Hall, 2003; Girardone et al., 2004; Hughes, 1999; Hughes et al., 2001; Mester, 1996; Pastor, 1999). However, the majority of literatures adopt the overdue loan ratio as the substitute variable for risks, which does not reflect the characteristic of uncertainty that risks display. Risk is defined as the presence of the characteristic uncertainty, and the degree of risk varies with the asset value fluctuation and the manager’s attitude toward risk. Risk may therefore either bring profit or loss to the asset value. The basic function of capital in this context is to help bear the possible loss incurred by taking risks. The appropriate provision of capital is therefore key to a stable fi- nancial structure, which can help prevent a situation of an inability to make payments. In 2002, the Basel Committee on Banking Supervision (BCBS) proposed the New Basel Capital Accord (Basel II), which sets out guidelines for international banks in terms of taking risks, and therefore, to prevent financial crises. In the section on minimum capital requirement outlined in Basel II, the internal rating uses Value at Risk (VaR) as the basis to estimate the maximum potential loss of the portfolio selection. In simple terms, the VaR ‘uses a single value to represent the maximum potential loss of an investment portfolio during a period of time, with a certain confidence level’. Hence, VaR is a prediction interval that provides different estimates according to the different confidence intervals, and therefore takes into account the characteristic of uncertainty that risks displays. While VaR is widely used to represent the level of risks entailed, the input and output values of the original DEA models are considered crisp values. This is a reoccurring issue encountered when using VaR to estimate the efficiency values of banks. Considering both domestic and foreign literatures, there have been none that have combined these two issues and provided an analytical discussion on the topic. Therefore, this paper seeks to combine the Slack-Based Measure of Efficiency (SBM) as proposed by Tone (2001), with the Fuzzy Measure Theory, and develops the non-radial Fuzzy Slack-Based Measure of Efficiency model (Fuzzy-SBM).