M OTIVATION

What are the major trends of CARs of Taiwanese banks? Figure 1.1 shows the CARs of Taiwanese banks from the year 2002 to 2012. The volatility of the CAR range is between 10%

and 13%, expect for 2003 of 9.21% and 5.15% in 2004. When two banks were sold or merged, it caused the Taiwanese banks’ CARs to decrease between 2003 and 2004. Meanwhile, Taiwanese banks built up the independent Department of Risk Management to implement Basel II. The objects of this department is to identify, measure, monitor and report the bank’s credit risk, market risk, operation risk and other risks. A bank enhances CARs by a capital increase of cash, or issue of unsecured bonds as subordinated debt for raising Tier-II capital. It executes capital management strategy while the equity capital is limited by regulatory capital requirements. Risk Management Committees were established, responsible to the Board and held regular meetings. Moreover, they constructed each risk management IT system to manage the risks of their business lines. Therefore, the highest CAR was 13.02% in 2012 and the

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Figure 1.1 CAR of Taiwanese Banks from 2001-2012

Figure 1.2 shows the Taiwanese banks’ CAR in 2012. Most of their CAR falls between the

range of 10% and 15%. There is only one is below 10%; the others are above the 15%.

Figure 1.2 Taiwanese Banks’ CAR in 2012

Fig 1.2 raises a serious question. What is an adequate approach to measure the performance of the banking industry? Moreover, the Taiwanese banking industry has implemented the Basel II to carry out the risk-based capital requirement (CAR) above 8% from 2005. To answer this question, we searched for any possible ways to solve this problem from the components of the CAR’s formula to highlight the coming issues, as follows:



 ^{0 08}

Equity Capital

CRT RMK ROP  .

 

where CRT is defined as the RWA for credit risk.

RMK is defined as the RWA for market risk.

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Firstly, do banks have to adjust their specified risk weight to allocate their risk exposure assets? The risk-based capital regulation sets a minimum ratio between equity capital and RWAs that is composed of credit risk, market risk and operational risk. As we know, for tax and dividend reasons, equity capital is more expensive than issuing unsecured bonds as subordinated debt for raising Tier-II capital. This shows the possibility that banks would adjust their specified asset risk weight, with their risk exposure assets allocated from risky class to riskless class. This portfolio selection does not only merely reduce RWAs, but also increases the amounts of the total loans, while the equity capital is kept constant. For example, Shrieves and Dahl (1992), Jacques and Nigro (1997) and Antão and Lacerda (2011) studied the relationship between the risk and capital requirement, to see how banks adjust their asset risk weight by more riskless assets, and to distribute their RWAs, while the equity capital is kept constant.

Secondly, although RWAs are a key indicator of banks, would loans and investment be substituted by RWAs? Leslé and Avramova (2012) posit CAR as a critical indicator of a bank’s solvency and resilience. After a period of time, the regulatory capital framework has changed significantly but remains heavily dependent on RWAs. In addition, RWAs have at least three important functions: (i) provide a common measure for a bank’s risks; (ii) ensure that capital allocated to assets corresponds to the risks; and (iii) potentially highlights where destabilizing asset class bubbles are may arise.

Besides, in what kind of category these RWAs for Credit risk will be classified depends on transaction objects. They also include: the on-balance sheet items, off-balance sheet transactions and counterparty, and the component of categories. These components contain Sovereign Countries, Non-central Government Public Sector Entities (PSEs), Banks (including multilateral development banks, MDBs), Corporates (including securities firms), the Regulatory Retail Portfolios, Residential Property, Equities Securities Investment and Other Assets. Therefore, the loans, investments and commitments could be replaced by RWAs. They

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are more diverse and closer to risk control and portfolio selection. For example, several studies have explored the relationship between RWAs and a bank’s probability of failure (Avery and Berger, 1991; Bradley et al., 1991). Recently, theses have applied banks’ RWAs to examine the determinants of stock returns and market measures of risk (Das and Sy, 2012; Xiao and Huang, 2013).

Thirdly, should we specify the RWAs as intermediate processes? As aforementioned, the RWAs provide a common measurement for a bank’s risks, and guarantee the equity capital be allocated for corresponding risks. The banks’ risk control processes are as follows: (i) To identify the debt exposures category and level of risk weights. They will depend on a bank’s risk appetite and its portfolio selection in regard to the preference for risky assets or riskless assets. (ii) To measure the claim costs, especially in regard to the equity capital. (iii) To monitor all forms of debt exposure, to verify whether or not the limit has been exceeded. Then, the risk monitoring report is periodically submitted to top management, the Risk Management Committee and the Board of Directors. The abovementioned discussion shows that the risk control processes would be treated as intermediate processes. Hence, it helps the bank to select portfolios, as well as to examine the quality of the overall loan portfolio, risk cost and returns.

In addition to solving these optimal RWAs and risk weight of each category, the optimal CAR would be derived from a CAR’s formula.

Fourthly, in measuring bank performance, is the frontier efficiency analysis superior to financial accounting ratios? The regulators, managers, investors and analysts generally depend on financial accounting ratios to appraise the relative efficiency of banks. These ratios will be suitable if we apply them for comparison with similar-sized banks, to control for sector-specific characteristics, permitting the comparison of an individual bank’s ratios with some benchmark for the sector (Halkos and Salamouris, 2004). Though financial accounting ratios are simple to apply, they are relatively easy to understand. They are used to measure bank performance that is constrained by many disparagements. The financial ratios cannot

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explain the differences in the business undertaken by different banks, which will be reflected in turn by different combinations of inputs and outputs (Tripe 2004). Moreover, Berger et al.

(1993) comment that financial ratios may be misleading because they do not control for product mix or input prices. Owing to the aforementioned intricacies of the financial accounting ratios, frontier efficiency analysis obtained enormous popularity in measuring the efficiency of the banking industry. Bauer et al. (1998) proposed that frontier efficiency analysis is superior to financial ratio analysis.

Fifthly, why do we prefer the directional distance function of DEA to CCR (Charnes, Cooper and Rhodes, 1978) or BCC (Banker, Charnes and Cooper, 1984)? Chambers et al.

(1996a) propose that this function is a generalization of Shephard’s input and output distance function. Färe and Grosskopf (2000b) also support this argument. One advantage is enabling the estimation of efficient scores by incorporating all types of inputs and outputs. Therefore, it is possible to investigate the efficiency levels of the production agents even when the output consists of both desirable and undesirable goods. The other advantage allows an evaluation of the levels of efficiency in any direction from the observation points (Watanabe and Tanaka, 2007). These two advantages support our employing this directional distance function of DEA.

Färe et al. (2004) employ the directional distance function to determine the effect of risk-based capital requirements on the profit performance of US banks, but they do not explore the role of RWAs in the process of bank production.

Finally, why do we use the two-stage DEA to measure the bank’s efficiency? Several studies and a survey provided by Berger and Humphrey (1997) have measured bank performance that has applied DEA. They assumed a black box production structure. These inputs are thought to flow into it where they are converted into outputs. Recently, some investigations have “opened” the black box. Then the DMUs can be regarded as having a network structure. The complicated process of the whole production can be divided into several sub-processes or sub-stages. A two-stage DEA model allows one to further investigate the

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structure and processes inside the DMU, to identify the misallocation of inputs among sub-DMUs and to generate insights into the sources of inefficiency within the DMU (Färe and Grosskopf, 2000a; Li et al., 2012). Wang et al. (2014) argue that the production process of the banking system is a typical two-stage process.

In conclusion, our studies include the sub-processes of risk control & portfolio selection, and the sub-process of profit-earning. In the processes of risk control & portfolio selection, a bank uses personnel cost, total asset and loanable funds to identify the debt exposures and level of risk weight shown as RWAs. Meanwhile, it can measure the claim costs, and guarantee the equity capital allocated for corresponding risks. These RWAs are taken as intermediate products of banks. In the process of profit-earning, we treat the RWAs as the intermediate measures to link the processes of risk control and portfolio selection to raise profits through 8 categories of debt exposures accompanied with undesirable goods (NPLs).

Moreover, we apply the concept of Chen et al. (2010) and Fukuyama and Weber’s (2010, 2014) model which advocate solving the optimal intermediate measures by a two-stage DEA.

These optimal solutions will require that the weight of intermediate measures in both stages is the same, and the objective function value for their model is equal to zero (inefficiency score).

Then we would obtain that a DMU must be a frontier point for both stages.

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