Proxies for the BSFI

In line with the existing literature, we consider the non-performing financing (NPF) and the ratio of domestic credit to private sector proxies in order to measure the credit risk. In the literature, non-performing loans (NPL) and non performing financing are widely used and accepted as prominent determinants for credit risk both for conventional and Islamic banks (Berger and DeYoung, 1997; Firmansyah, 2015; Salim et al., 2017; Khan et al., 2020). The non-performing loans (NPL) in Shari’ah banking, in fact are calculated as non-performing financing (NPF) since Islamic banking is different from conventional banking in terms of financing. One should also note that NPF is directly related with Islamic Bank specific contracts such as Murabahah, Ijarah, Salam, Istisna’, Musharakah and Mudarabah. Therefore, including NPF as a credit risk proxy to measure fragility, our choice reflects the tenets of Islamic financing that are different from conventional banking.⁴⁵ A rising value of NPF adversely affects the health of the banking system thus increases the fragility of banks. Besides, the ratio of domestic credit to private sector is a commonly used proxy in the related literature to measure the financial debt reflecting the developments in the credit market (Baum et al., 2020; Beck et al., 2013; Levine and Zervos, 1998).

45 Note that, credit risk can be defined as the possibility that the counterpart might not be able to pay his/her obligations. Accordingly, credit risk in Islamic banking is directly related to the financial products as Murabahah, Ijarah, Salam, Istisna, Musharakah and Mudarabah. As already explained in the Section 3.5, Ijarah is a leasing contract where a property is leased to the customer in return for a rental payment for a certain period. Murabahah is a transaction where the trader buys a property to sell it to a buyer by placing a certain profit rate (where Islamic banks are the traders). In the context of Murabahah and Ijarah contracts, there is a risk that the customer might not make his/her payments on time (Akkizidis and Kumar, 2008). On the other hand, Salam means the prepaid sale of a well-defined product to be delivered in the future. Therefore, for Islamic banks the credit risk occurs due to Salam contracts, if the customer does not make the agreed payments and where the seller might not deliver the product on time or at agreed quality as well. In Istina contract, a producer creates a good of property based on a specific standard and price. It is an advance sale of a specific commodity that is not manufactured or constructed yet. Islamic banks are exposed to credit risk through Istisna’ contracts if the buyer is disable to buy the agreed product or if the buyer provides the installed payments after receiving the product. Mudarabah is a contract of partnership where one party provides capital and the other party provides labor and management. Musharakah is a mutual contract to establish a joint venture. One can see that in Mudarabah and Musharakah contracts, the relationship between the Islamic bank and the counterparts is partnership based. Therefore, credit risk occurs if the financial project does not bear the expected revenue (Akkizidis and Kumar, 2008).

For the liquidity risk, bank deposits variable is considered. In Islamic banking, the bank deposits are comprised of demand deposits (Wadia), saving deposits (Wadia and Mudarabah), and Time Deposits (Mudarabah 1, 3,6,12,>12 months). Bank deposits is a standard measure for liquidity risk and frequently used in Islamic banking literature (Kibritçioğlu 2003, Ahmad and Mazlan, 2015; Kusuma and Asif, 2016; Wiranatakusuma and Duasa, 2017).

In order to measure the market risk, banks’ real foreign liabilities and time interest earned ratio (TIER) are considered. As Kibritçioğlu (2003) explains, under the expectation that currency is not devaluated in the near future, the banking sector tends to obtain funds from international financial markets by taking excessive risk. In this respect, if banks hold a considerable amount of unhedged foreign currency debt, an unexpected devaluation increase the fragility of the domestic banking sector by decreasing the net worth of banks.

For this reason, foreign liabilities is a crucial proxy for measuring the market risk. On the other hand, following Dincer (2011) and Carey and Stulz (2007), we also measure the market risk through the size of the bank in terms of the assets. The authors suggest that bank size is negatively related to the sensitivity of market risk and decreases the fragility of the banks since larger banks have more diversified portfolios than the small banks.

In this thesis, one of our attempts is to investigate whether the profitability risk has any impact on the predictive power results of EWS for Islamic banks. To this aim, we use ROE since it is accepted as the most important indicator of a bank’s profitability and, also widely-used for Islamic banking (Moin, 2013; Srouji et al., 2015; Bilal et al., 2016; Ekinci and Poyraz, 2019). ROE can be defined as the ratio of net income to stockholders’ equity.

More explicitly ROE is the profit after tax over equity capital and, it is the net earnings per dollar of the Islamic bank’s equity capital. In order to calculate the net income for Islamic banks, expenses are subtracted from the gross income where expenses include salaries and other operating expenses, depreciation and provisions (Krueger, 2017).

Table 12 presents the proxies for each of the banking risk factors that are used in constructing banking fragility indices to define banking crises.

Table 12: The Proxies and Risk Factors Used in the Construction of BSFIs

Credit Risk Liquidity Risk Market Risk Profitability Risk

Model 1⁴⁶ NPF DEP TIER -

Model 2 NPF - TIER -

Model 3 BC - TIER -

Model 4 NPF DEP FL -

Model 5 BC DEP TIER -

Model 6 NPF - FL -

Model 7 NPF DEP TIER ROE

Model 8 NPF - TIER ROE

Model 9 BC DEP TIER ROE

Model 10 BC - TIER ROE

Model 11 NPF DEP FL ROE

Model 12 NPF - FL ROE

Model 13 BC - FL ROE

Model 14 BC DEP FL ROE

Model 15⁴⁷ BC DEP FL -

Model 16 BC - FL -

Model 17 BC DEP - -

Model 18 BC DEP - ROE

Model 19 NPF DEP - ROE

Model 20 NPF - - ROE

Model 21 BC - - ROE

Model 22 - DEP TIER ROE

Model 23 NPF DEP - -

Model 24 - DEP - ROE

Model 25 - - TIER ROE

Notes: BC defines the ratio of domestic credit to private sector; NPF defines non-performing financing;

DEP defines bank deposits; FL defines real foreign liabilities; TIER defines time interest earned ratio; ROE defines return on equity.

As it can be seen from the above table, we construct 25 different banking crisis definitions using the same risk factor proxies set. That is, the ratio of domestic credit to private sector (BC) and non-performing financing (NPF) are used as credit risk proxies. The liquidity risk is proxied by bank deposits. TIER and real foreign liabilities are used as a proxy for market risk of Islamic banking. Furthermore, the profitability risk is proxied by return on equity (ROE). To achieve a substantial banking crisis definition for Islamic banks which will improve the predictive power of the EWS, we construct alternative crisis definitions by using different combinations of the significant risk factors. Furthermore, in order to make robust analyses of whether the credit risk, market risk, liquidity risk and

46 Same as the BSFI of Ahmad and Mazlan (2015).

47 Same as the BSFI of Kibritçioğlu (2003).

profitability risk factors play significant effects on the predictive power of our EWS models, we alternately include and exclude these risk factors in alternating banking crisis definitions. Namely, while we construct BSFI in some definitions we omit one of the risk factors in question to investigate its impact on the prediction power of the EWS.⁴⁸ Based on these definitions, we develop twenty-five EWS models in total. The analyses are conducted with the same methodology, explanatory variable set, bank coverage and time period for all the models. Therefore, the models differ only in banking crisis definitions that enable us to observe the impacts of banking crisis definitions on the predictive power of the EWS. The BSFIs for each model are presented in Table 13:

48 For instance, while we define the banking crisis in Model 1 based on credit risk, liquidity risk and market risk; we exclude liquidity risk factor in the BSFI in Model 2 to examine whether it plays an important role in the prediction power of the EWS.

104 Table 13: BSFI by Model

Model 1

𝑩𝑺𝑭𝑰_𝒊,𝒕=

([(𝑵𝑷𝑭_𝒕− 𝑵𝑷𝑭_𝒕−𝟏) 𝑵𝑷𝑭⁄ _𝒕−𝟏] − 𝝁_𝑵𝑷𝑭

𝝈_𝑵𝑷𝑭 ) + ([(𝑫𝑬𝑷_𝒕− 𝑫𝑬𝑷_𝒕−𝟏) 𝑫𝑬𝑷⁄ _𝒕−𝟏] − 𝝁_𝑫𝑬𝑷

𝝈_𝑫𝑬𝑷 ) + ([(𝒕𝒊𝒆𝒓_𝒕− 𝒕𝒊𝒆𝒓_𝒕−𝟏) 𝒕𝒊𝒆𝒓⁄ _𝒕−𝟏] − 𝝁_{𝒕𝒊𝒆𝒓}

𝝈_{𝒕𝒊𝒆𝒓} )

𝟑

Model 2

𝑩𝑺𝑭𝑰_𝒊,𝒕=

([(𝑵𝑷𝑭_𝒕− 𝑵𝑷𝑭_𝒕−𝟏) 𝑵𝑷𝑭⁄ _𝒕−𝟏] − 𝝁_𝑵𝑷𝑭

𝝈_𝑵𝑷𝑭 ) + ([(𝒕𝒊𝒆𝒓_𝒕− 𝒕𝒊𝒆𝒓_𝒕−𝟏) 𝒕𝒊𝒆𝒓⁄ _𝒕−𝟏] − 𝝁_{𝒕𝒊𝒆𝒓}

𝝈_{𝒕𝒊𝒆𝒓} )

𝟐

Model 3

𝑩𝑺𝑭𝑰𝒊,𝒕=

([(𝑩𝑪_𝒕− 𝑩𝑪_𝒕−𝟏) 𝑵𝑷𝑭⁄ _𝒕−𝟏] − 𝝁_𝑩𝑪

𝝈_𝑩𝑪 ) + ([(𝒕𝒊𝒆𝒓_𝒕− 𝒕𝒊𝒆𝒓_𝒕−𝟏) 𝒕𝒊𝒆𝒓⁄ _𝒕−𝟏] − 𝝁_{𝒕𝒊𝒆𝒓}

𝝈_{𝒕𝒊𝒆𝒓} )

𝟐

Model 4

𝑩𝑺𝑭𝑰_𝒊,𝒕=

([(𝑵𝑷𝑭_𝒕− 𝑵𝑷𝑭_𝒕−𝟏) 𝑵𝑷𝑭⁄ _𝒕−𝟏] − 𝝁_𝑵𝑷𝑭

𝝈_𝑵𝑷𝑭 ) + ([(𝑫𝑬𝑷_𝒕− 𝑫𝑬𝑷_𝒕−𝟏) 𝑫𝑬𝑷⁄ _𝒕−𝟏] − 𝝁_𝑫𝑬𝑷

𝝈_𝑫𝑬𝑷 ) + ([(𝑭𝑳_𝒕− 𝑭𝑳_𝒕−𝟏) 𝑭𝑳⁄ _𝒕−𝟏] − 𝝁_𝑭𝑳

𝝈_𝑭𝑳 )

𝟑

105 Model 5

𝑩𝑺𝑭𝑰_𝒊,𝒕=

([(𝑩𝑪_𝒕− 𝑩𝑪_𝒕−𝟏) 𝑵𝑷𝑭⁄ _𝒕−𝟏] − 𝝁_𝑩𝑪

𝝈_𝑩𝑪 ) + ([(𝑫𝑬𝑷_𝒕− 𝑫𝑬𝑷_𝒕−𝟏) 𝑫𝑬𝑷⁄ _𝒕−𝟏] − 𝝁_𝑫𝑬𝑷

𝝈_𝑫𝑬𝑷 ) + ([(𝒕𝒊𝒆𝒓_𝒕− 𝒕𝒊𝒆𝒓_𝒕−𝟏) 𝒕𝒊𝒆𝒓⁄ _𝒕−𝟏] − 𝝁_{𝒕𝒊𝒆𝒓}

𝝈_{𝒕𝒊𝒆𝒓} )

𝟑

Model 6

𝑩𝑺𝑭𝑰_𝒊,𝒕=

([(𝑵𝑷𝑭_𝒕− 𝑵𝑷𝑭_𝒕−𝟏) 𝑵𝑷𝑭⁄ _𝒕−𝟏] − 𝝁_𝑵𝑷𝑭

𝝈_𝑵𝑷𝑭 ) + ([(𝑭𝑳_𝒕− 𝑭𝑳_𝒕−𝟏) 𝑭𝑳⁄ _𝒕−𝟏] − 𝝁_𝑭𝑳

𝝈_𝑭𝑳 )

𝟐

Model 7 𝑩𝑺𝑭𝑰_𝒊,𝒕

=

([(𝑵𝑷𝑭_𝒕− 𝑵𝑷𝑭_𝒕−𝟏) 𝑵𝑷𝑭⁄ _𝒕−𝟏] − 𝝁_𝑵𝑷𝑭

𝝈_𝑵𝑷𝑭 ) + ([(𝑫𝑬𝑷_𝒕− 𝑫𝑬𝑷_𝒕−𝟏) 𝑫𝑬𝑷⁄ _𝒕−𝟏] − 𝝁_𝑫𝑬𝑷

𝝈_𝑫𝑬𝑷 ) + ([(𝒕𝒊𝒆𝒓_𝒕− 𝒕𝒊𝒆𝒓_𝒕−𝟏) 𝒕𝒊𝒆𝒓⁄ _𝒕−𝟏] − 𝝁_{𝒕𝒊𝒆𝒓}

𝝈_{𝒕𝒊𝒆𝒓} ) + ([(𝑹𝑶𝑬_𝒕− 𝑹𝑶𝑬⁄ _𝒕−𝟏] − 𝝁_𝑹𝑶𝑬

𝝈_𝑹𝑶𝑬 )

𝟒

Model 8

𝑩𝑺𝑭𝑰_𝒊,𝒕=

([(𝑵𝑷𝑭_𝒕− 𝑵𝑷𝑭𝒕−𝟏) 𝑵𝑷𝑭⁄ 𝒕−𝟏] − 𝝁_𝑵𝑷𝑭

𝝈_𝑵𝑷𝑭 ) + ([(𝒕𝒊𝒆𝒓_𝒕− 𝒕𝒊𝒆𝒓𝒕−𝟏) 𝒕𝒊𝒆𝒓⁄ 𝒕−𝟏] − 𝝁_{𝒕𝒊𝒆𝒓}

𝝈_{𝒕𝒊𝒆𝒓} ) + ([(𝑹𝑶𝑬_𝒕− 𝑹𝑶𝑬⁄ 𝒕−𝟏] − 𝝁_𝑹𝑶𝑬

𝝈_𝑹𝑶𝑬 )

𝟒

106 Model 9:

𝑩𝑺𝑭𝑰𝒊,𝒕

=

([(𝑩𝑪_𝒕− 𝑩𝑪_𝒕−𝟏) 𝑩𝑪⁄ _𝒕−𝟏] − 𝝁_𝑩𝑪

𝝈_𝑩𝑪 ) + ([(𝑫𝑬𝑷_𝒕− 𝑫𝑬𝑷_𝒕−𝟏) 𝑫𝑬𝑷⁄ _𝒕−𝟏] − 𝝁_𝑫𝑬𝑷

𝝈_𝑫𝑬𝑷 ) + ([(𝒕𝒊𝒆𝒓_𝒕− 𝒕𝒊𝒆𝒓_𝒕−𝟏) 𝒕𝒊𝒆𝒓⁄ _𝒕−𝟏] − 𝝁_{𝒕𝒊𝒆𝒓}

𝝈_{𝒕𝒊𝒆𝒓} ) + ([(𝑹𝑶𝑬_𝒕− 𝑹𝑶𝑬⁄ _𝒕−𝟏] − 𝝁_𝑹𝑶𝑬

𝝈_𝑹𝑶𝑬 )

𝟒

Model 10

𝑩𝑺𝑭𝑰_𝒊,𝒕=

([(𝑩𝑪_𝒕− 𝑩𝑪_𝒕−𝟏) 𝑵𝑷𝑭⁄ _𝒕−𝟏] − 𝝁_𝑩𝑪

𝝈_𝑩𝑪 ) + ([(𝒕𝒊𝒆𝒓_𝒕− 𝒕𝒊𝒆𝒓_𝒕−𝟏) 𝒕𝒊𝒆𝒓⁄ _𝒕−𝟏] − 𝝁_{𝒕𝒊𝒆𝒓}

𝝈_{𝒕𝒊𝒆𝒓} ) + ([(𝑹𝑶𝑬_𝒕− 𝑹𝑶𝑬⁄ _𝒕−𝟏] − 𝝁_𝑹𝑶𝑬

𝝈_𝑹𝑶𝑬 )

𝟑

Model 11 𝑩𝑺𝑭𝑰_𝒊,𝒕

=

([(𝑵𝑷𝑭_𝒕− 𝑵𝑷𝑭_𝒕−𝟏) 𝑵𝑷𝑭⁄ _𝒕−𝟏] − 𝝁_𝑵𝑷𝑭

𝝈_𝑵𝑷𝑭 ) + ([(𝑫𝑬𝑷_𝒕− 𝑫𝑬𝑷_𝒕−𝟏) 𝑫𝑬𝑷⁄ _𝒕−𝟏] − 𝝁_𝑫𝑬𝑷

𝝈_𝑫𝑬𝑷 ) + ([(𝑭𝑳_𝒕− 𝑭𝑳_𝒕−𝟏) 𝑭𝑳⁄ _𝒕−𝟏] − 𝝁_𝑭𝑳

𝝈_𝑭𝑳 ) + ([(𝑹𝑶𝑬_𝒕− 𝑹𝑶𝑬⁄ _𝒕−𝟏] − 𝝁_𝑹𝑶𝑬

𝝈_𝑹𝑶𝑬 )

𝟒 Model 12

𝑩𝑺𝑭𝑰_𝒊,𝒕=

([(𝑵𝑷𝑭_𝒕− 𝑵𝑷𝑭_𝒕−𝟏) 𝑵𝑷𝑭⁄ _𝒕−𝟏] − 𝝁_𝑵𝑷𝑭

𝝈_𝑵𝑷𝑭 ) + ([(𝑭𝑳_𝒕− 𝑭𝑳_𝒕−𝟏) 𝑭𝑳⁄ _𝒕−𝟏] − 𝝁_𝑭𝑳

𝝈_𝑭𝑳 ) + ([(𝑹𝑶𝑬_𝒕− 𝑹𝑶𝑬⁄ _𝒕−𝟏] − 𝝁_𝑹𝑶𝑬

𝝈_𝑹𝑶𝑬 )

𝟑

107 Model 13

𝑩𝑺𝑭𝑰_𝒊,𝒕=

([(𝑩𝑪_𝒕− 𝑩𝑪_𝒕−𝟏) 𝑵𝑷𝑭⁄ _𝒕−𝟏] − 𝝁_𝑩𝑪

𝝈_𝑩𝑪 ) + ([(𝑭𝑳_𝒕− 𝑭𝑳_𝒕−𝟏) 𝑭𝑳⁄ _𝒕−𝟏] − 𝝁_𝑭𝑳

𝝈_𝑭𝑳 ) + ([(𝑹𝑶𝑬_𝒕− 𝑹𝑶𝑬⁄ _𝒕−𝟏] − 𝝁_𝑹𝑶𝑬

𝝈_𝑹𝑶𝑬 )

𝟑

Model 14 𝑩𝑺𝑭𝑰_𝒊,𝒕

=

([(𝑩𝑪_𝒕− 𝑩𝑪_𝒕−𝟏) 𝑵𝑷𝑭⁄ _𝒕−𝟏] − 𝝁_𝑩𝑪

𝝈_𝑩𝑪 ) + ([(𝑫𝑬𝑷_𝒕− 𝑫𝑬𝑷_𝒕−𝟏) 𝑫𝑬𝑷⁄ _𝒕−𝟏] − 𝝁_𝑫𝑬𝑷

𝝈_𝑫𝑬𝑷 ) + ([(𝑭𝑳_𝒕− 𝑭𝑳_𝒕−𝟏) 𝑭𝑳⁄ _𝒕−𝟏] − 𝝁_𝑭𝑳

𝝈_𝑭𝑳 ) + ([(𝑹𝑶𝑬_𝒕− 𝑹𝑶𝑬⁄ _𝒕−𝟏] − 𝝁_𝑹𝑶𝑬

𝝈_𝑹𝑶𝑬 )

𝟒 Model 15

𝑩𝑺𝑭𝑰_𝒊,𝒕=

([(𝑩𝑪_𝒕− 𝑩𝑪_𝒕−𝟏) 𝑵𝑷𝑭⁄ _𝒕−𝟏] − 𝝁_𝑩𝑪

𝝈_𝑩𝑪 ) + ([(𝑫𝑬𝑷_𝒕− 𝑫𝑬𝑷_𝒕−𝟏) 𝑫𝑬𝑷⁄ _𝒕−𝟏] − 𝝁_𝑫𝑬𝑷

𝝈_𝑫𝑬𝑷 ) + ([(𝑭𝑳_𝒕− 𝑭𝑳_𝒕−𝟏) 𝑭𝑳⁄ _𝒕−𝟏] − 𝝁_𝑭𝑳

𝝈_𝑭𝑳 )

𝟑

Model 16

𝑩𝑺𝑭𝑰_𝒊,𝒕=

([(𝑩𝑪_𝒕− 𝑩𝑪_𝒕−𝟏) 𝑵𝑷𝑭⁄ _𝒕−𝟏] − 𝝁_𝑩𝑪

𝝈_𝑩𝑪 ) + ([(𝑭𝑳_𝒕− 𝑭𝑳_𝒕−𝟏) 𝑭𝑳⁄ _𝒕−𝟏] − 𝝁_𝑭𝑳

𝝈_𝑭𝑳 )

𝟐

108 Model 17

𝑩𝑺𝑭𝑰_𝒊,𝒕=

([(𝑩𝑪_𝒕− 𝑩𝑪_𝒕−𝟏) 𝑵𝑷𝑭⁄ _𝒕−𝟏] − 𝝁_𝑩𝑪

𝝈_𝑩𝑪 ) + ([(𝑫𝑬𝑷_𝒕− 𝑫𝑬𝑷_𝒕−𝟏) 𝑫𝑬𝑷⁄ _𝒕−𝟏] − 𝝁_𝑫𝑬𝑷

𝝈_𝑫𝑬𝑷 )

𝟐

Model 18

𝑩𝑺𝑭𝑰_𝒊,𝒕 =

([(𝑩𝑪_𝒕− 𝑩𝑪_𝒕−𝟏) 𝑵𝑷𝑭⁄ _𝒕−𝟏] − 𝝁_𝑩𝑪

𝝈_𝑩𝑪 ) + ([(𝑫𝑬𝑷_𝒕− 𝑫𝑬𝑷_𝒕−𝟏) 𝑫𝑬𝑷⁄ _𝒕−𝟏] − 𝝁_𝑫𝑬𝑷

𝝈_𝑫𝑬𝑷 ) + ([(𝑹𝑶𝑬_𝒕− 𝑹𝑶𝑬⁄ _𝒕−𝟏] − 𝝁_𝑹𝑶𝑬

𝝈_𝑹𝑶𝑬 )

𝟑

Model 19

𝑩𝑺𝑭𝑰_𝒊,𝒕=

([(𝑵𝑷𝑭_𝒕− 𝑵𝑷𝑭_𝒕−𝟏) 𝑵𝑷𝑭⁄ _𝒕−𝟏] − 𝝁_𝑵𝑷𝑭

𝝈_𝑵𝑷𝑭 ) + ([(𝑫𝑬𝑷_𝒕− 𝑫𝑬𝑷_𝒕−𝟏) 𝑫𝑬𝑷⁄ _𝒕−𝟏] − 𝝁_𝑫𝑬𝑷

𝝈_𝑫𝑬𝑷 ) + ([(𝑹𝑶𝑬_𝒕− 𝑹𝑶𝑬⁄ _𝒕−𝟏] − 𝝁_𝑹𝑶𝑬

𝝈_𝑹𝑶𝑬 )

𝟑 Model 20

𝑩𝑺𝑭𝑰_𝒊,𝒕=

([(𝑵𝑷𝑭_𝒕− 𝑵𝑷𝑭_𝒕−𝟏) 𝑵𝑷𝑭⁄ _𝒕−𝟏] − 𝝁_𝑵𝑷𝑭

𝝈_𝑵𝑷𝑭 ) + ([(𝑹𝑶𝑬_𝒕− 𝑹𝑶𝑬⁄ _𝒕−𝟏] − 𝝁_𝑹𝑶𝑬

𝝈_𝑹𝑶𝑬 )

𝟐

109 Model 21

𝑩𝑺𝑭𝑰_𝒊,𝒕=

([(𝑩𝑪_𝒕− 𝑩𝑪_𝒕−𝟏) 𝑵𝑷𝑭⁄ _𝒕−𝟏] − 𝝁_𝑩𝑪

𝝈_𝑩𝑪 ) + ([(𝑹𝑶𝑬_𝒕− 𝑹𝑶𝑬⁄ _𝒕−𝟏] − 𝝁_𝑹𝑶𝑬

𝝈_𝑹𝑶𝑬 )

𝟐 Model 22

𝑩𝑺𝑭𝑰_𝒊,𝒕=

([(𝑫𝑬𝑷_𝒕− 𝑫𝑬𝑷_𝒕−𝟏) 𝑫𝑬𝑷⁄ _𝒕−𝟏] − 𝝁_𝑫𝑬𝑷

𝝈_𝑫𝑬𝑷 ) + ([(𝒕𝒊𝒆𝒓_𝒕− 𝒕𝒊𝒆𝒓_𝒕−𝟏) 𝒕𝒊𝒆𝒓⁄ _𝒕−𝟏] − 𝝁_{𝒕𝒊𝒆𝒓}

𝝈_{𝒕𝒊𝒆𝒓} ) + ([(𝑹𝑶𝑬_𝒕− 𝑹𝑶𝑬⁄ _𝒕−𝟏] − 𝝁_𝑹𝑶𝑬

𝝈_𝑹𝑶𝑬 )

𝟑 Model 23

𝑩𝑺𝑭𝑰_𝒊,𝒕=

([(𝑵𝑷𝑭_𝒕− 𝑵𝑷𝑭_𝒕−𝟏) 𝑵𝑷𝑭⁄ _𝒕−𝟏] − 𝝁_𝑵𝑷𝑭

𝝈_𝑵𝑷𝑭 ) + ([(𝑫𝑬𝑷_𝒕− 𝑫𝑬𝑷_𝒕−𝟏) 𝑫𝑬𝑷⁄ _𝒕−𝟏] − 𝝁_𝑫𝑬𝑷

𝝈_𝑫𝑬𝑷 )

𝟐

Model 24

𝑩𝑺𝑭𝑰_𝒊,𝒕=

([(𝑫𝑬𝑷_𝒕− 𝑫𝑬𝑷_𝒕−𝟏) 𝑫𝑬𝑷⁄ _𝒕−𝟏] − 𝝁_𝑫𝑬𝑷

𝝈_𝑫𝑬𝑷 ) + ([(𝑹𝑶𝑬_𝒕− 𝑹𝑶𝑬⁄ _𝒕−𝟏] − 𝝁_𝑹𝑶𝑬

𝝈_𝑹𝑶𝑬 )

𝟐

110 Model 25

𝑩𝑺𝑭𝑰_𝒊,𝒕=

([(𝒕𝒊𝒆𝒓_𝒕− 𝒕𝒊𝒆𝒓_𝒕−𝟏) 𝒕𝒊𝒆𝒓⁄ _𝒕−𝟏] − 𝝁_{𝒕𝒊𝒆𝒓}

𝝈_{𝒕𝒊𝒆𝒓} ) + ([(𝑹𝑶𝑬_𝒕− 𝑹𝑶𝑬⁄ _𝒕−𝟏] − 𝝁_𝑹𝑶𝑬

𝝈_𝑹𝑶𝑬 )

𝟐

Belgede CONSTRUCTING FRAGILITY INDICES FOR ISLAMIC BANKS: DEFINITION IMPACT ON THE PREDICTIVE POWER OF AN EARLY WARNING SYSTEM (sayfa 112-123)