El método kantiano

This study first examines how different approaches as described above impact on the construction of time-varying z-scores, with the main focus on approaches Z1 and Z2. To highlight the trends and volatilities of z-scores, Figure 1 (a) and (b) plot time-varying z-scores for the six New Zealand banks (named “individual z-score”), using approaches Z1 and Z2, respectively.

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(b) Approach Z2

Figure 1 – Trends of individual z-scores for New Zealand banks

This figure shows the time series of individual z-scores for New Zealand banks. Individual z- scores are computed using approaches Z1 and Z2, respectively.

It is obvious that individual z-scores measured by approaches Z1 and Z2 follow similar trends, although individual z-scores measured by approach Z2 are much smaller in values. This is not unexpected, as approaches Z1 and Z2 both use rolling windows to compute the elements of z-score. Values of the individual z-score using approach Z2 are much lower, as the range-based volatility measure is greater in value than the standard deviation of ROA.

The individual z-scores vary through time, indicating the variability of bank risk throughout the sample period. Before the GFC, more specifically up until 2007Q2, the individual z-scores followed an upward trend or stayed at a relatively high level27, although with fluctuations. This reflects greater banking stability. The individual z-scores decreased substantially during 2008-2010, reflecting higher bank risks. This is due to sharp decreases of ROA, combined with a high level of standard deviation of ROA. This also coincided with the banking crisis in the GFC. BNZ was extremely risky during 2009Q2-2013Q1, which is owing to BNZ’s low levels of (or even negative) ROA during the GFC. BNZ also has higher volatility in ROA. The individual z-scores gradually recovered from the beginning of 2011.

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Table 1 reports the summary statistics (Observations, Mean values, Standard deviation, and Coefficient of Variation) of individual z-scores of the six New Zealand banks, using both approaches Z1 and Z2. The sample covers the period from March 2000 to June 2015.

Table 1 – Summary statistics of individual z-scores for New Zealand banks, quarterly data

This table reports summary statistics of individual z-scores for the New Zealand banks, using approaches Z1 and Z2. Z-score is computed as ROA plus equity-to-asset ratio divided by the standard deviation of ROA. Approach Z1 uses moving mean and standard deviation of ROA over previous 16 quarters, combined with current period value of equity-to-asset ratio. Approach Z2 uses the range between maximum and minimum ROA over previous 16 quarters as a volatility measure, combined with moving mean of ROA over 16 quarters and current period value of equity-to-asset ratio. The sample covers the period from March 2000 to June 2015.

ANZ NZ ASB BNZ Kiwi TSB WNZL

Panel (a) - Approach Z1

Obs. 62 62 62 26 62 19 Mean 33.4 69.1 24.0 26.0 51.5 36.6 St. dev. 11.8291 37.9150 14.3330 5.8071 17.6518 10.0954 Coe. Var. 35.42% 54.87% 59.72% 22.34% 34.28% 27.58% Panel (b) - Approach Z2 Obs. 62 62 62 26 62 19 Mean 9.1 21.0 5.7 7.4 14.4 10.5 St. dev. 3.8875 11.3928 3.4112 1.6481 4.8145 3.0801 Coe. Var. 42.72% 54.25% 59.85% 22.27% 33.43% 29.33%

Both approaches agree that ASB and TSB are safer individually, represented by higher values of their individual z-scores. ASB generally had stable ROA through time, except the GFC period. This results in its overall high levels of individual z-score, which significantly decreased during the GFC. In other words, the values of ASB’s individual z-scores have moved through a broader range, and this explains its high levels of standard deviations of z- score (with the values of 37.9150 or 11.3928 in approaches Z1 and Z2 respectively) across the time period studied.

On the other hand, BNZ is always identified as the riskiest bank. BNZ has much more volatile income, especially since the adoption of the International Financial Reporting Standards

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(IFRS), with these effects exacerbated since the GFC. This may be related to mark-to-market value adjustments through its income statement items. BNZ has a higher proportion of assets and liabilities being valued at fair value than is the case for other banks28. In fact, as of October 2017, BNZ has a credit rating of AA- from Standard & Poor’s, the same as for the other three large banks (ANZ NZ, ASB and WNZL).

Meanwhile, although this study is mainly developed using quarterly data, prior z-score literature often uses Bankscope as a data source, which only provides annual financial statement data. Consequently, it is common for z-score studies to be limited to annual observations. As a comparison, this study further constructs time-varying z-scores for the New Zealand banks using annual data. Summary statistics are reported in Table 2.

Table 2 – Summary statistics of individual z-scores for New Zealand banks, annual data

This table reports summary statistics of individual z-score for the major New Zealand banks. Z-scores are computed using approaches Z1 and Z2, but based on annual data. The sample covers the period 2000-2014.

ANZ NZ ASB BNZ Kiwi TSB WNZL

Panel (a) - Approach Z1

Obs. 15 15 15 5 15 4 Mean 45.1 120.5 88.1 28.0 31.4 38.9 St. dev. 22.0696 124.9520 138.7649 4.3834 17.2674 8.4893 Coe. Var. 48.88% 103.72% 157.44% 15.65% 55.02% 21.84% Panel (b) - Approach Z2 Obs. 15 15 15 5 15 4 Mean 19.7 53.0 41.7 13.3 14.3 17.2 St. dev. 9.1566 53.8574 65.2940 2.0563 7.8911 3.5879 Coe. Var. 46.39% 101.69% 156.65% 15.46% 55.19% 20.86%

As shown in Table 2, the most striking effect is that z-scores estimated on the basis of annual data are significantly greater in value than those on the basis of quarterly data, especially in approach Z1. The difference arises from the standard deviation of ROA. The standard deviation computed from 4 annual numbers is much smaller than that computed

28 _{According to quarterly disclosure statements, BNZ has around 40% of assets and liabilities being valued at}

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from 16 quarterly numbers. It is apparent that a standard deviation of 4 numbers should not be expected to provide a reliable measure, as it is computed using relatively few observations (Alizadeh et al., 2002). This supports the advantage of using quarterly data in constructing time-varying z-score. The quarterly data is more volatile (as predicted), making the standard deviations of ROA higher and thus the z-score values lower, but its overall effect is to provide a more stable series of z-score estimates, as shown by coefficient of variation. Z-scores computed with annual data have much greater coefficient of variation. An implication of these results is that, for studies that are limited to annual data, it may be advisable to use the range between the maximum and minimum of ROA as a volatility measure.

To sum up, approaches Z1 and Z2 are both meaningful in theory, as the use of a rolling window is consistent with the change in a bank’s risk profile. Empirical results of the New Zealand banks support the effectiveness of approach Z1 in capturing bank risk through time. Approach Z2 is a preferable method if analysis is restricted to annual observations.

4.3.2 Comparison between z-score and accounting-based risk measures, New