In the fast changing financial circumstances of nowadays, in avoiding the crisis of closing down, financial institutions are concerned about the efficiency and risk strictly in the meantime. Therefore, efficiency and risk
management are goals for a financial institution administrator. Data Envelopment Analysis (DEA) is a
non-parameter approach to evaluate the performance of DMU's efficiency and the variables used in the
DEA are all accurate values. However, when the input or output variables are fuzzy, the performance of
DMUs must proceed by the Fuzzy-DEA. On the basis of risk uncertainty, this research plans to apply the
expanding model of Fuzzy Slack-Based Measurement (Fuzzy SBM). The efficiency scores estimated by
Fuzzy SBM model are subordinate to functional form, which provides efficiency value region in different degrees of confidence, conforms to the characteristic of risk anticipation, and estimates the management
achievement of Taiwan banking under market risk.
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 andoutputs. 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 thiscontext 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).
With the increasing frequency of financial disasters and its devastating impact over the recent years, countries around the world have
begun to pay much more attention to financial risk management. The
fact that the financial industry is the supporting structure to a
country's economic. This researchfirstly derives models from the theories, using trigonometry as the basis to develop the Fuzzy-SBM
model for the empirical study. Subsequently, banks in Taiwan were
used as the sample for the study, with the research carrying out interval estimation of VaR values for use as the input variables. We then
used the Fuzzy-SBM model to estimate the upper and lower bounds
of the efficiency value for the banks, while varying the a-cut value
to represent the effect of risk volatility on the efficiency value. Empirical results from the research show that: 1) The performance of most
DMUs varies according to the risk factor. 2) The a-cut value affects
the efficiency value, and therefore risk volatility affects the efficiency
value. The higher volatility leads to a greater difference between the
upper and lower bounds of the efficiency value, while conversely,
no volatility in risk means that the efficiency value is fixed. 3) For
some DMUs, regardless of the a-cut value, their upper and lower
bounds of efficiency value are equal, meaning that risk volatility
does not affect their efficiency values and the risk variable does not
affect their efficiencies. 4) The risk variable is a factor in the estimation of efficiency values and in the determination of the ranking of
efficiencies.
The Fuzzy-SBM model derived in this research paper uses trigonometry as the basis to estimate efficiency values as triangular membership
functions. This model conforms to the characteristic of forecasting VaR
and differs from traditional DEA models in that the results it produces
can better demonstrate the implications of risk and the effects of risk
on efficiency. The majority of literatures adopt the overdue loan ratio
as the substitute variable for risks proxy variable, which does not reflect
the characteristic of uncertainty that risks display (Altunbas et al., 2000;
Chang, 1999; Chiu and Chen, 2008; Drake and Hall, 2003Girardone et
al., 2004; Hughes, 1999; Hughes et al., 2001; Mester, 1996; Pastor,
1999). Thus, the main contribution of this article consists of the utilization of VaR as risk variables to reflect the features of riskfluctuation encountered by banks. Besides, in this article, the efficiency values
calculated using the Fuzzy-SMB are membership functions, so theevaluated efficiency value is in fact an interval value with the function
of anticipating the prospective efficiency performance. The results
obtained differ from that calculated by traditional DEA models as a
constant.
Data Envelopment Analysis (DEA) is a non-parameter approach to
evaluate the performance of DMU's efficiency and the variables used
in DEA are all accurate values. However, when the input or output
variables are fuzzy, the performance of DMUs must proceed by the
Fuzzy-DEA. The limitations of this study consist in the risk assessment
method suggested by Basel II. The method is able to produce the approximate estimations of the VaR of the banks in Taiwan; nevertheless, influenced by the limitations of incomplete data, this study
simply can evaluate a part of the risk conditions. In addition, due to
the different financial environment in each nation and the great diversity of banks' investment deployment, the situations of Taiwanese
banks may not reflect the actual financial environment in other countries. This article, therefore, provides a more applicable DEA assessment method for reference.
