Variables

While the following paragraphs provide detailed discussion on the variables used in this chapter in terms of variable construction, expectations on the regressions signs, and etc., a summary of variable definitions is presented in Appendix 1.A. The correlation matrix is reported in Appendix 1.B.

3.3.2.1 Dependent variable: 𝑳𝒏𝒁

It is widely accepted that 𝒁𝒔𝒄𝒐𝒓𝒆 could be employed to measure a bank’s

overall risk, the theory discussion of which can rely on Boyd and Graham (1986).

Theoretically, 𝒁𝒔𝒄𝒐𝒓𝒆 is an indicator that measures the probability of

banks or bank holding companies to fail. The 𝒁𝒔𝒄𝒐𝒓𝒆 comes from a profitability

indicator (𝒓) and another risk indicator (𝑺), the standard deviation of 𝒓, which

measures the variability of profit. Let 𝒊 denote an individual bank, 𝒋 denote a

year, and 𝒏 denote the length (in years) of the sample period, then the empirical

mean rate of return can be specified as:

𝒓̅𝒊= ∑𝒏𝒋=𝟏(𝒓̃𝒊𝒋⁄ )𝒏 (3.1) Thus, 𝒓̅_𝒊 is a sample estimate of the true mean of 𝒓̃_𝒊𝒋 distribution.

Therefore, the estimated standard deviation of 𝒓 for the 𝒊th bank is:

𝑺_𝒊 = {∑𝒏_𝒋=𝟏[(𝒓̃_𝒊𝒋− 𝒓̅_𝒊)𝟐⁄(𝒏 − 𝟏)]}𝟏/𝟐 (3.2)

Finally, for 𝒁𝒔𝒄𝒐𝒓𝒆, which measures the probability of a consolidated

bankruptcy, should be:

𝒑(𝝅̃ < −𝑬) = 𝒑(𝒓̃ < 𝒌) = ∫_−∞𝒌 𝝓(𝒓)𝒅𝒓 (3.3)

where 𝝓 is the probability density function of 𝒓̃, 𝝅 is the consolidated profits, 𝑬 is consolidated equity, and 𝒌 = −𝑬/𝑨, in which 𝑨 is the consolidated

asset. Normal distributions are completely characterized by a location and a dispersion parameter, which means Euqation (3.3) may be simplified by changing

coordinates. Therefore, if 𝒓̃ is normally distributed, then

𝒑(𝒓̃ < 𝒌) = ∫_−∞𝒁 𝑵(𝟎, 𝟏)𝒅𝒛 and 𝒛 = (𝒌 − 𝝆)/𝝈 (3.4)

where 𝝈 is the standard deviation of rate of return on assets. Here 𝒛 is the

principal risk measure, except that the sample estimate S is substituted for 𝝈 and

the sample estimate 𝒓̃is substituted for 𝝆, and −𝒛 is the risk variable that stands

for overall risk, 𝒁𝒔𝒄𝒐𝒓𝒆. This Zscore is an estimate of the number of standard

deviations below the mean that consolidated profits would have to fall to make consolidated equity negative, which means it is an indicator of the probability of a consolidated bankruptcy.

To be simplified, the specific calculation of z-score could then could be transferred into:

𝒁𝒔𝒄𝒐𝒓𝒆 =𝑹𝑶𝑨+𝑬/𝑨

𝒔𝒅𝑹𝑶𝑨 (3.5)

where 𝑹𝑶𝑨 is bank's net income after tax as a percentage of average

assets, 𝑬/𝑨 is equity capital and minority interests to total assets, and 𝒔𝒅𝑹𝑶𝑨 is

the standard deviation of 𝑹𝑶𝑨. A higher level of 𝒁𝒔𝒄𝒐𝒓𝒆 corresponds to a lower

𝒁𝒔𝒄𝒐𝒓𝒆 has been widely employed in banking literature because it reflects

many parts of the potential risk. Firstly, Boyd and Graham (1986) indicate that

𝒁𝒔𝒄𝒐𝒓𝒆 is strongly associated with commercial paper ratings as reported by

Moody's Investors Service. Secondly, this measurement contains bank profitability

(𝑹𝑶𝑨, return on assets), bank risk (standard deviation of 𝑹𝑶𝑨) and bank safety

(𝑬/𝑨, equity to assets ratio), which has a synthetic explanation of the overall risk.

In the research of exploring the relationship between ownership structure and

overall risk, Barry et al. (2011) employ 𝒁𝒔𝒄𝒐𝒓𝒆 and find a significant association

between them. (More empirical literatures about z-score can refer to: Boyd et al., 1993; Altman and Saunders, 1997; Konishi and Yasuda, 2004; Demirguc-Kunt et al., 2008; Garcia-Marco and Robles-Fernandez, 2008; Graham et al., 2008; Lepetit et al., 2008; Santos and Winton, 2008; Laeven and Levine, 2009; Pathan, 2009; Uhde and Heimeshoff, 2009; Demirguc-Kunt and Huizinga, 2010; Houston et al., 2010)

Theoretically, the distribution of dependent variable should follow the

normality assumption, which means a new dependent variable 𝑳𝒏𝒁 will be

employed here. According to the basic mathematics knowledge, considering the

feature of natural logarithm, the trends of 𝑳𝒏𝒁 should follow 𝒁𝒔𝒄𝒐𝒓𝒆, which

means a higher 𝑳𝒏𝒁 value still stands for a lower probability of default, or to say,

overall risk. Following the methodology of Beck, De Jonghe and Schepens (2011), Michalak and Uhde (2012), as well as Anginer, Demirguc-Kunt and Zhu (2013), this

study also employs a three- and five-year rolling 𝑳𝒏𝒁.1

3.3.2.2 Securitization measures

Researches on securitization so far can be categorized in the following groups. Some researchers prefer to discuss the general influence of securitization, where they mainly define the regressor of securitization as total securitized assets to total assets, as in Mandel et al. (2012). Recently, more studies began to focus on the differences among securities. For example, Solano et al. (2006), when discussing the effects of securitization on the value of banking institutions, distinguish mortgage-backed securities (MBS) and asset-backed securities (ABS). Moreover, another group of researches classify detailed categories of

1 _{The results are robust with different rolling windows, from four to six years, when calculating} the standard deviation of ROA.

securitization. For example, Cheng et al. (2008) employ four different securitization variables, ABSt (total securitized assets divided by total assets),

MBSt (securitized 1-4 family residential mortgages scaled by total assets), CONSBSt

(securitized consumer loans scaled by total assets) and COMMBSt (securitized

commercial loans scaled by total assets) to study the relationship between securitization and opacity of banks. The key independent variable in this research is𝑺𝒆𝒄𝒖𝒓𝒊𝒕𝒊𝒛𝒂𝒕𝒊𝒐𝒏 𝒓𝒂𝒕𝒊𝒐, which is defined as the ratio of the outstanding principal

balance of assets securitized over total assets for a given type (i.e., mortgage or non-mortgage loans).

3.3.2.3 Control variables

This study controls for several bank specific characteristics.

𝑹𝒆𝒕𝒂𝒊𝒏𝒆𝒅 𝒊𝒏𝒕𝒆𝒓𝒆𝒔𝒕 𝒓𝒂𝒕𝒊𝒐 is defined as the total amount of retained interest

divided by the total amount of securitization assets of a given type, including the aggregate retained interests into credit enhancements, liquidity provisions, and seller’s interest. The incentive of securitizers to carefully monitor loans could increase by providing enhancements which may decrease bank risk (Downing, Jaffee, and Wallace, 2009).

𝑩𝒂𝒏𝒌 𝒔𝒊𝒛𝒆 is the natural logarithm of total assets. DeMiguel et al. argue

that size plays a significant role in the performance of banks. Haan and Poghosyan (2012) prove bank size reduces return volatility. However, the factor of scale could have negative impacts, which means banks do better by reducing their size (Gennotte and Pyle, 1991). Recently, papers also support this point of view, that larger companies tend to have riskier portfolios, which could increase the overall risk (Demzets, 1999). The relationship between bank risk and bank size, Hakenes and Schnabel (2011), Haan and Poghosyan (2012), and DeMiguel et al. (2013) suggest a negative relationship, while Gennotte and Pyle (1991) support a positive relationship.

𝑫𝒊𝒗𝒆𝒓𝒔𝒊𝒇𝒊𝒄𝒂𝒕𝒊𝒐𝒏indicates the diversification level of banks, which is

calculated as noninterest income divided by total operation income, following the approach of Stiroh (2004). Previous research on diversification of portfolios shows positive influence, as the investors are more likely to be better off when holding a large number of low quality stocks than a smaller number of high quality stocks,

and the return on the former portfolio will be higher (Wagner and Lau, 1971). Recently, empirical research on large Austrian commercial banks over the period of 1997-2003 also provides a decline of banks' realized risk, as well as increases profit efficiency when regarding to diversification effects, though it may impact cost efficiency negatively.

𝑳𝒊𝒒𝒖𝒊𝒅𝒊𝒕𝒚 𝒓𝒂𝒕𝒊𝒐 is an indicator for banks' liquidity, specified as liquid

assets divided by total assets. Liquidity impacting on banks is not a one-way method, in fact, it sometimes could help managers to weaken the potential risks. Bolton et al. (2011) propose a dynamic model of investment, financing and risk management for financial institutions, and then find that liquidity significantly associated with banks' performance. Meanwhile, this model also supports the opinion that liquidity management is one of the complementary risk management tools.

𝑵𝒐𝒏 𝒊𝒏𝒕𝒆𝒓𝒆𝒔𝒕 𝒆𝒙𝒑𝒆𝒏𝒔𝒆 𝒓𝒂𝒕𝒊𝒐 is an indicator of banks’ efficiency, defined

as non-interest expenses divided by total assets. Non-interest expenses are usually not associated with targeting customers to deposit funds; therefore, they are more likely to increase risk level (Lepetit et al., 2008).

𝑵𝒐𝒏 𝒑𝒆𝒓𝒇𝒐𝒓𝒎𝒊𝒏𝒈 𝒍𝒐𝒂𝒏𝒔 𝒓𝒂𝒕𝒊𝒐, computed as the amount of loans past due

90 days divided by total assets, reflects the risk management situation. Because non-performing loans are either in default or close to being in default, bank risk level can be positively related to the proportion of non-performing loans. For

example, Affinito and Tagliaferri (2010) define non-performing loans as “bad

loans” in their research to estimate the motivations of banks to choose securitization in Italian banking industry. Other researches which employ this control variable could refer to Calomiris and Mason (2004), Cardone-Riportella et al. (2010), Jiangli and Prisker (2008), and Minton, Stulz and Williamson (2009) for examples.

Following Berger and Bouwman (2013), I also control for banks’

𝒍𝒐𝒄𝒂𝒍 𝒎𝒂𝒓𝒌𝒆𝒕 𝒑𝒐𝒘𝒆𝒓 as the deposit concentration for the local markets in which

the bank operates. The larger the local market power, the greater a bank’s market

power and concentration in its surroundings. This is a standard measure of competition used in antitrust analysis and research in the U.S. (Berger and

Bouwman, 2013). Moreover, using deposits for this purpose because it is the only vairbale for which location is known. Following Berger and Bouwman (2013), this research uses the new local market definitions based on Core Based Statistical Area (CBSA) and non-CBSA county.

This study uses a bank holding company dummy (𝑩𝑯𝑪 𝒅𝒖𝒎𝒎𝒚) to control

for whether it belongs to a bank holding company. 𝑩𝑯𝑪 𝒅𝒖𝒎𝒎𝒚 equals one if the

bank belongs to a bank holding company, and zero otherwise. Within a short-time window, banks belonging to a BHC are more likely to take more risk, as they have

this “backup” (Jiang, Lee, and Yue, 2010).

Finally, a metropolitan statistical area dummy (𝑴𝑺𝑨 𝒅𝒖𝒎𝒎𝒚), which

equals one if the bank is located in a metropolitan area, and zero otherwise, is

used to identify individual banks’ locations. Competition may be fiercer in metropolitan areas, and banks in suburban areas are more likely to have a more stable environment.