Measuring bank risk. Abstract: Keywords:

Measuring bank risk Abstract: Keywords: This paper looks at different approaches to use of the Risk Index or z score as measures of bank risk, having regard to the time over which it is measured and the frequency of observations over which it is measured. We identify advantages in using quarterly data, if it is available, and also note that use of annual data can be problematic over short time periods. Where researchers are limited to annual data, it may be preferable to use the range between the maximum and minimum values as a volatility measure. Banking, Risk measurement, Risk index, z score 1

Introduction The Global Financial Crisis (GFC) has revived attention to risk in the banking sector and the ways in which it can be measured. One important strand in this regard has been a measure based originally on work by Roy (1952), revived as the Risk Index by Hannan & Hanweck (1988) and the Z score by Boyd et al (1993), with both measures for practical purposes identical. These measures have subsequently been subject to some additional analytical review by Lepetit & Strobel (2013, 2015). Because, as commonly specified, it relies only on accounting data, it is able to be used as a risk measure where share market derived information (share prices) are not available. The basic principle of this measure is to relate a bank s capital level to the variability in its returns, so that one can know how much variability in returns can be absorbed by capital without the bank becoming insolvent. The variability in returns is typically measured by the standard deviation of Return on Assets (ROA) as the denominator of a ratio, while the numerator of the ratio is typically defined as the ratio of capital to assets plus a measure of ROA (on the assumption that those will be available to support the bank remaining in business, or in the case of loss, to adjust the capital level downwards). The assumption is made that the point at which a bank becomes unable to continue in business is when its capital level reaches zero. This is, of course, not realistic in practice, in that banks need a positive minimum level of capital to persuade counterparties to do business with them (see, for example, Berger et al, 1995). This means that there is another potential line of research in terms of identifying distance not to default per se, but to a minimum level of capital below which a bank cannot operate. An important consequence of the way this risk measure is defined is that a low risk bank will have a high value for its Risk Index or z score, indicating that a drop in returns by a large number of standard deviations would need to occur for the bank to become insolvent. The counterpart to this is that a lower value for the Risk Index or z score indicates a high risk bank. Key questions for this research which have not been the subject of particular focus in prior research are the way in which a bank s risk profile might change through time, and the consequent relative stability of risk measures. Sometimes in the literature we find that risk has been measured over as short a period as three years (e.g Boyd et al, 2006; Yeyati & Micco, 2007), although other researchers have looked at 5 (e.g. Hannan & Hanweck, 1988) or 6 years (e.g. Laeven & Levine, 2009). In their U.S sample, Boyd et al (2006) used quarterly observations to estimate the mean and standard deviations of bank ROAs, as did Yeyati & Micco (2007), while Hannan & Hanweck (1988) 2

used semi annual data. Some other researchers have used Bankscope as a data source, which has generally limited them to annual observations. Lepetit & Strobel (2013) also note that a variety of approaches have been applied to specifying the capital ratio to be used in analyses. A common approach is to use capital as at the current date, but some authors have looked at an average ratio of capital to assets over a period of time. This paper focuses primarily on use of New Zealand bank data, which has been available on a quarterly basis since the beginning of 1996, and for which we thus have a particularly extensive data series. This allows us to experiment with a number of options, including providing a comparison of risk index measures estimated using annual and quarterly data. We will also look at some of the Australian major banks, for which we have more than 20 years of annual data. The next section of the paper looks in more detail at the results that we might expect to find, given the sorts of data that we are going to explore. The following section look at the data that we use and the method we employ to analyse it, while the next section reports results. The final section provides some summary discussion and conclusion. Some expectations for our research Prior to embarking on our empirical analysis, however, we want to formalise a set of views as to the results that might be expected from different choices. These should help is to design our analysis better. Some of these issues have already been addressed by Lepetit and Strobel (2013), but there are still a number of other issues for us to explore. The first point to discuss in this context is the measurement of equity capital. Since we are concerned about potential bank insolvency, it strikes us that a bank s current level of capital is what is important, rather than the average over some preceding period. Lepetit and Strobel (2013) also found this to be a superior measure. We are also going to confine ourselves to accounting measures of equity, consistent with the leverage ratio approach being adopted in many jurisdictions (although not New Zealand) under Basel III. An alternative capital strength measure might be the ratio or regulatory capital to risk weighted assets, but there are two reasons not to utilise this, at least in the current research. Firstly, regulatory capital often includes elements which would not normally be regarded as equity available 3

to support losses, which is one of the reasons why regulators have moved to strengthen the definition of capital under Basel III. Secondly, the measurement of risk weighted assets has changed with the adoption of Basel II, which would cause inconsistencies in measurement through time, particularly for banks that use internal models. A further capital measure, the use of which was proposed by Boyd (1993), is the market value of equity. Such a measure is usable only where banks have share market listings, and we cannot therefore use it in New Zealand as we have only one listed bank (and that only since 2012). Such a measure can, however, be used in other environments (such as in looking at the major Australian banks). We should generally expect quarterly data to show more variability than annual data, particularly following the adoption of IFRS which has generally led to more volatile outcomes, reflecting items such as mark to market fair value adjustments being processed through the income statement. Annual data is also more likely to be smoothed than quarterly data, which is not generally the subject of so much focus by analysts. If quarterly data is used, the standard deviation of ROA should be expected to be higher than if annual data were used, although we have no prior view as the size of the effect, and thus what the impact would be on the Risk Index, other than to increase it. We have no reason to suppose that the standard deviation should vary greatly with the length of the time window used to estimate it, although short windows, particularly where annual data is used, are likely to lead to greater variation in the standard deviation and thus greater volatility in the Risk Index. Current ROA, which is one component of the numerator of the ratio, may be measured as an annualised spot number for the most recent period, or an average over a longer period (although presumably not for a window longer than that for which the standard deviation has been estimated). The longer the period over which it is measured the less variable it is likely to be (subject to major strategic shifts in the bank s direction and performance) and the less variability there will be in the estimated value of the Risk Index. It would be straightforward enough to introduce a leverage ratio requirement into this structure if one wished to. The numerator could be adjusted by subtracting the required leverage ratio from the ratio of capital to assets, so that the numerator was, in effect, measuring the capital buffer. With such a variation, a significantly lower value should be observed for the Risk Index ratio. 4

Data and method Since the beginning of 1996, a major pillar of the banking supervisory regime in New Zealand has been public disclosure. This entails banks being required to publish a year to date income statement and balance sheet at the end of every quarter, which allows one to develop a quarterly income statement and balance sheet, and thus to calculate relevant performance ratios. The key performance ratio for this study is the return on assets (ROA), specified as the net profit after tax divided by average total assets, which we annualise in all cases. For our equity ratio we use shareholders equity only, not including any subordinated debt. In practice our data sets is somewhat constrained, in that the analysis can only be conducted for banks that are incorporated in New Zealand, and not for the branch operations of foreign banks. We have also had banks entering and leaving the New Zealand market, so that there only 4 banks for which we have data for the whole period of the study, from the September quarter of 1996 up to the September quarter of 2014. These ae the ANZ Bank New Zealand Ltd (ANZ), ASB Bank Ltd (ASB), Bank of New Zealand (BNZ) and TSB Bank Ltd (TSB). We are able, however, to broaden our data set by including some banks that have been incorporated and registered more recently, and for some more recent periods we report results for up to 7 banks. The additional banks are Westpac New Zealand Ltd (WNZL), Kiwibank Ltd (Kiwi) and SBS Bank (SBS). Risk indices are calculated for each of the banks as reported in the next section the paper. We start by looking at 4 year windows of quarterly observations, with various different approaches to specifying ROA, and then compare these with results from 3, 5 and 6 year windows, and with figures estimated from annual observations only. We also analyse some data for the four major Australian banks, which we have on an annual basis only, from 1993 through to 2014. We use this as a basis for comparing the standard deviations of annual ROA data with the range between the minimum and maximum values over the period of the relevant window. The four banks studied, which by the end of 2014 accounted for close to 80% of the assets of the Australian banking system, are the Australia and New Zealand Banking Group Ltd (ANZ), the Commonwealth Bank of Australia (CBA), the National Australia Bank (NAB) and the Westpac Banking Corporation (WBC). 5

Results To provide comparisons more straightforwardly, the paper reports results only for the financial yearend quarter, as this allows us to report results for annual data alongside those for quarterly data. Full results are available from the authors on request. Table 1 shows the results for the different four year window for the four banks for which we have a full data set. [Insert Table 1 about here] Some key effects are evident from these results. For most banks, risk tended to decrease during the early to mid 2000s, reflecting the generally benign views for the economy as residential property prices were rising (in New Zealand and elsewhere in the world). Risk then increased significantly in 2009 as banks were impacted by events around the GFC, which was seen in New Zealand through increased funding costs and higher levels of bad and doubtful debt expense. Use of the Risk Index is thus generating results consistent with what we would expect. Another striking effect is the figures estimated on the basis of bank annual results only, many of which are significantly higher (and some of which differ from preceding and following observations by large amounts). The difference here is with the standard deviation of ROA, as this is how these figures vary from those recorded in the columns of the table that show the annual ROA with the standard deviation of quarterly ROA. When one considers how the standard deviation is estimated, however, it becomes apparent that a standard deviation of four numbers should not be expected to provide a reliable measure. A standard deviation of 16 numbers, obtained from a four year window of quarterly data should be expected to be a more meaningful measure of volatility. The quarterly data is more volatile (as predicted), making the standard deviation higher (and the Risk Index lower), but its overall effect is to provide a less extreme set of results. The quarterly results are also much more consistent with each other than with the annual figures. A further implication of the results using only the annual figures is that, if one was obliged to restrict analysis to annual observations, a more useful approach might be to measure volatility as the range between the minimum and maximum values over the relevant period. We report the results of a test reflecting this later in the paper. Observers may also note the generally much lower Risk Index values (and thus implied higher risk) for BNZ. It has had much more volatile income since the adoption of IFRS, with these effects 6

exacerbated since the GFC, with these appearing to relate to mark to market value adjustments through the income statement. This would appear to reflect a much higher proportion of both its assets and liabilities being valued at fair value than is the case for any other banks. In fact, as of February 2015, BNZ has a credit rating of AA from Standard & Poor s, the same as for ANZ and ASB. As a result of this exploratory analysis, our preferred approach for ongoing analysis will be to use quarterly ROA data to estimate the standard deviation, and we will also use average ROA across a year rather than the whole data window (the best alternative), as preferred by Lepetit & Strobel (2013). The impact on the estimated Risk Index is small (with the ROA figure in the numerator not contaminated for as long by unusual outcomes for as long), and such a measure should be useful and acceptable for bank management. Our next comparative analysis therefore looks at the effects of using different time windows, of three, four, five and six years, using our initial data set of four New Zealand banks. Results are reported in Table 2. [Insert Table 2 about here]. What we find here is that the Risk Index generally decreases in value as the size of the window increases, indicating higher risk, as can be seen in the mean values shown in the bottom row of Table 2. On the other hand, as the window extends, the period for which unusual results are evident for BNZ also extends (although the unusual results are not as low as for shorter windows), and it is not obvious what criteria might be applied to specify an optimal window length. Was the BNZ s position as weak in 2014 as it was in 2009, or was the hangover (in terms of the effect on the Risk Index) of the poor performance in the June 2009 quarter no longer relevant? Once we have quarterly observations to allow a meaningful number to be generated for the standard deviation, is it reasonable to propose that a four or five year window is sufficient (although this will of course depend on the availability of data, which may not be as readily obtained as it can be in New Zealand)? Other things being equal, we would be inclined to prefer the four year window, as that provides more scope to recognise changes occurring within the banks to change their risk profiles. For a final check, following on from a point above about annual observations, we use some data for the four major Australian banks, which we have back as far as 1992. Because the observations are annual, we limit ourselves to the study of 5 and 6 year windows, so that we can have reasonable 7

sized data set for estimating a more meaningful standard deviation, and we also contrast the standard deviation as a volatility measure with the range between the minimum and maximum values over the window. Results are reported in Table 3. [Insert Table 3 about here]. As might be expected, the risk indices estimated using the range are lower than for those estimated using the standard deviation as the volatility measure, while the indices estimated from 6 year windows also generate lower values than those estimated over five years. We see a relatively low value for NAB in particular for the period following the GFC, which would generally seem to reflect poorer profitability performance (and higher risk?). As a robustness check, we ran an analysis using a 10 year window and the standard deviation, but that did not appear to be particularly useful, while there has to be considerable doubt as to whether events 10 years previously should have a major impact on current assessments of risk. Overall, it would look as if the measures generated using the range would be likely to be more useful, but it is also clear that, if more frequent data can be obtained, they are likely to generate more meaningful measures. Summary and conclusion On the strength of what we ve done, we can now look at data for the broader range of New Zealand banks, using a four year window, quarterly data, annual average mean and the standard deviations measured across the whole window. Results are shown in Table 4. [Insert Table 4 about here]. We can see how banking sector risk has been improving as banks have recovered from the effects of the GFC. We consider it to have been a valuable exercise to review the range of ways in which the Risk Index or z score can be calculated, in terms of the options around data frequency and the length of the window over which it is estimated. For the New Zealand case, we consider that the four year window and quarterly data give us the most satisfactory results, but for other jurisdictions where 8

data are available with lower frequency, these measures may not be feasible. If annual data have to be used, it is likely to be better to use the range between the minimum and maximum observations. We have also identified an opportunity for future research, in terms of seeing how banks sit relative the proposed leverage ratio under Basel III. We note, however, that the quite low values for the risk index for some banks might make their adherence to leverage ratios problematic, unless they were to increase their capital but that is one of the outcomes expected under Basel III. References: Berger, A. N.; Herring, R. J. & Szegö, G. P. (1995, June). The role of capital in financial institutions. Journal of Banking and Finance, 19. 393 430. Boyd, J. H.; De Nicolo, G. & Jalal, A. M. (2006). Bank Risk Taking and Competition Revisited: New Theory and New Evidence. IMF Working Paper 06/297. International Monetary Fund; Washington DC. Boyd, J. H.; Graham, S. L. & Hewitt, R. S. (1993). Bank holding company mergers with nonbank financial firms: effects on the risk of failure. Journal of Banking and Finance. 17. 43 63. Hannah, T. H. & Hanweck, G. A. (1988). Bank insolvency risk and the market for large certificates of deposit. Journal of Money, Credit and Banking. 20 (2). 203 211. Laeven, L. & Levine, R. (2009). Bank governance, regulation and risk taking. Journal of Financial Economics. 93. 259 275. Lepetit, L. & Strobel, F. (2013). Bank insolvency risk and time varying Z score measures. Journal of International Financial Markets, Institutions and Money. 25. 73 87. Lepetit, L. & Strobel, F. (2015, forthcoming). Bank insolvency risk and Z score measures: a refinement. Finance Research Letters. Roy, A. D. (1952). Safety first and the holding of assets. Econometrica. 20 (3). 431 449. Yeyati, E. L. & Micco, A. (2007). Concentration and foreign penetration in Latin American banking sectors: impact on competition and risk. Journal of Banking and Finance. 31. 1633 1647. 9

Table 1 Risk Index for New Zealand banks, estimated using four year windows Current quarter ROA Standard deviation of Quarterly ROA Annual ROA Standard deviation of Quarterly ROA Four year average ROA Standard deviation of Quarterly ROA Annual data Standard deviation of Annual ROA ANZ ASB BNZ TSB ANZ ASB BNZ TSB ANZ ASB BNZ TSB ANZ ASB BNZ TSB 2000 29.5 76.0 34.0 28.6 30.5 75.3 34.0 28.7 29.8 74.9 34.2 28.8 28.4 137.8 37.5 200.5 2001 24.3 72.9 49.1 40.1 23.9 73.5 49.8 42.2 22.8 72.5 49.6 41.6 23.5 88.6 116.1 118.4 2002 28.7 71.7 25.0 41.2 29.7 71.0 26.3 41.3 28.8 70.0 25.5 41.3 29.7 71.1 36.0 113.9 2003 34.7 78.0 25.5 48.3 34.5 78.0 26.3 49.5 34.2 76.8 25.8 49.3 42.3 84.4 37.1 119.3 2004 44.0 98.8 22.8 49.2 44.0 100.1 24.2 50.4 45.5 99.7 24.6 50.6 107.8 125.5 40.6 258.1 2005 33.7 126.5 25.6 75.8 33.7 126.5 25.4 76.9 34.7 126.3 25.7 76.5 36.5 201.4 47.1 239.4 2006 43.1 145.7 39.1 72.4 43.2 145.4 39.1 73.5 43.1 145.5 39.4 73.2 42.2 483.8 65.5 228.8 2007 65.0 106.0 44.7 81.2 64.3 106.9 44.9 82.4 63.9 106.3 44.6 82.2 56.6 302.0 225.8 215.3 2008 49.6 40.8 47.0 71.5 51.4 43.2 47.8 73.8 51.7 44.1 47.6 73.5 74.5 70.3 537.4 566.8 2009 17.5 21.1 3.7 52.1 19.2 21.7 3.5 53.7 20.5 23.0 4.5 53.8 21.5 26.6 6.7 281.9 2010 21.0 12.2 4.0 40.4 21.9 11.1 4.4 42.2 22.1 11.9 4.5 42.3 24.5 17.5 7.1 250.4 2011 25.0 14.9 5.4 30.2 24.4 14.7 4.9 30.3 23.9 14.2 4.7 31.4 28.7 23.8 7.9 42.5 2012 23.0 15.0 5.6 33.1 23.2 15.3 6.0 33.5 22.3 14.6 5.8 34.0 26.3 21.1 11.5 45.4 2013 43.9 16.8 17.7 42.8 44.0 17.0 18.0 43.4 43.3 16.5 17.8 43.5 53.3 22.4 102.8 55.8 2014 48.8 56.8 20.5 70.8 48.6 57.7 20.0 70.4 47.5 56.7 19.6 70.7 56.3 63.4 58.1 150.0 10

Table 2 Risk Index for New Zealand banks, estimated using different window lengths and quarterly data. Three year window for average and standard deviation of ROA Four year window for average and standard deviation of ROA Five year window for average and standard deviation of ROA Six year window for average and standard deviation of ROA ANZ ASB BNZ TSB ANZ ASB BNZ TSB ANZ ASB BNZ TSB ANZ ASB BNZ TSB 2002 30.2 96.9 22.9 45.3 29.7 71.0 26.3 41.3 22.4 70.6 27.1 46.2 21.7 67.6 28.5 31.3 2003 46.2 104.8 24.2 46.8 34.5 78.0 26.3 49.5 31.9 59.6 28.9 44.8 23.4 58.9 28.9 48.9 2004 39.3 105.0 21.9 72.3 44.0 100.1 24.2 50.4 46.4 78.4 26.1 52.4 48.4 60.5 28.3 47.4 2005 38.8 139.7 36.7 70.6 33.7 126.5 25.4 76.9 35.7 114.1 27.3 55.8 38.2 86.2 28.9 56.5 2006 78.1 134.2 42.8 75.7 43.2 145.4 39.1 73.5 36.5 135.5 27.0 77.8 37.6 123.0 28.8 59.6 2007 58.1 110.2 66.1 93.5 64.3 106.9 44.9 82.4 42.8 117.4 41.2 79.2 36.0 113.9 28.7 82.3 2008 49.4 37.3 41.7 66.7 51.4 43.2 47.8 73.8 56.5 47.2 38.9 71.5 41.0 51.2 37.0 71.5 2009 17.6 19.8 3.1 48.6 19.2 21.7 3.5 53.7 21.6 23.6 3.9 58.8 23.7 25.3 4.2 59.7 2010 21.5 10.5 4.0 37.0 21.9 11.1 4.4 42.2 22.8 11.9 4.9 45.9 25.0 12.8 5.3 49.6 2011 23.4 13.5 4.5 29.2 24.4 14.7 4.9 30.3 24.9 15.2 5.3 33.3 25.6 16.1 5.8 35.6 2012 39.7 13.3 15.0 36.2 23.2 15.3 6.0 33.5 24.7 16.6 6.5 33.1 25.7 17.3 6.9 35.2 2013 58.5 62.7 17.4 94.4 44.0 17.0 18.0 43.4 25.5 18.6 7.2 38.7 27.1 19.9 7.6 37.2 2014 54.0 76.8 20.0 64.7 48.6 57.7 20.0 70.4 38.1 18.4 19.8 43.7 24.3 19.4 8.0 39.2 Mean 42.7 71.1 24.6 60.1 37.1 62.2 22.4 55.5 33.1 55.9 20.3 52.4 30.6 51.7 19.0 50.3 11

Table 3 Risk Index for Australian banks comparing alternative volatility measures 5 year window with standard deviation as volatility measure 6 year window with standard deviation as volatility measure 5 year window with range between maximum and minimum as volatility measure 6 year window with range between maximum and minimum as volatility measure ANZ CBA NAB WBC ANZ CBA NAB WBC ANZ CBA NAB WBC ANZ CBA NAB WBC 1998 61.6 44.9 29.0 55.9 24.1 28.3 30.3 18.2 27.3 18.6 11.8 21.2 8.6 10.4 11.8 6.9 1999 63.3 62.8 36.9 188.3 69.2 46.9 36.6 62.0 31.2 25.9 13.9 76.5 31.2 18.4 13.9 21.8 2000 49.3 36.6 48.7 117.5 52.7 40.7 38.0 116.8 21.5 14.3 17.6 47.0 21.5 14.3 13.0 45.2 2001 44.2 36.6 30.4 107.0 49.4 40.9 28.3 108.7 21.1 14.4 12.5 43.3 21.1 14.4 10.1 43.3 2002 43.0 37.8 35.6 87.7 39.8 39.4 34.7 97.9 15.7 13.9 14.4 37.6 15.7 13.9 12.8 37.6 2003 75.6 34.3 38.7 105.8 47.2 34.4 42.6 91.6 32.3 12.5 16.1 49.7 17.1 12.5 16.1 37.2 2004 95.8 29.2 42.7 132.1 78.8 32.3 44.2 124.8 40.6 11.2 16.5 53.0 31.1 11.2 16.5 53.0 2005 69.3 45.0 45.6 136.9 75.5 32.4 47.9 144.8 31.5 18.5 16.9 53.5 31.5 11.4 16.9 53.5 2006 73.6 33.6 51.1 126.0 72.7 36.8 31.7 138.5 30.2 13.6 23.3 49.9 30.2 13.6 11.6 49.9 2007 80.4 36.3 53.7 105.1 72.3 38.6 52.1 90.4 33.1 14.0 21.3 39.6 28.7 14.0 21.3 33.3 2008 32.4 47.3 16.8 58.9 32.4 38.4 18.6 65.8 12.5 17.4 6.8 23.1 11.6 13.2 6.8 23.1 2009 28.1 31.7 13.6 33.1 27.7 33.3 15.1 35.4 12.7 11.5 6.5 13.0 11.1 11.5 6.5 13.0 2010 30.6 40.8 16.0 41.6 32.4 32.4 15.3 40.4 13.2 19.5 7.1 16.0 13.2 12.3 6.8 14.2 2011 36.1 48.6 21.6 45.1 33.6 45.4 17.7 45.2 13.8 21.1 8.2 18.7 13.0 19.9 7.0 16.0 2012 49.3 71.3 50.0 47.2 39.9 56.3 26.1 49.7 20.1 28.7 18.9 19.0 13.7 21.9 9.1 19.0 2013 50.0 98.8 48.3 47.3 53.0 79.4 52.1 52.7 20.3 44.1 19.6 19.2 20.3 29.7 19.6 19.2 2014 199.2 96.1 82.2 95.0 51.9 84.2 50.4 49.0 80.0 35.6 31.4 36.8 19.2 31.7 18.3 18.3 12

Table 4 Risk index values for a broader spectrum of New Zealand banks, using a four year window and quarterly data Quarter ending ANZ ASB BNZ WNZL TSB Kiwi SBS September 2012 23.2 15.4 6.0 37.0 43.9 23.7 45.1 December 2012 23.3 16.1 6.0 36.7 44.1 24.3 49.8 March 2013 23.2 16.5 6.3 37.9 43.4 24.7 53.4 June 2013 24.0 17.0 15.2 44.3 57.8 29.0 53.8 September 2013 44.0 47.2 18.0 45.5 62.5 28.0 51.9 December 2013 44.0 48.9 17.8 43.6 69.1 27.7 53.3 March 2014 47.5 58.1 18.2 45.5 70.4 28.6 57.3 June 2014 49.3 57.7 18.0 39.8 72.5 29.2 58.2 September 2014 48.6 51.8 20.0 44.9 72.1 28.6 57.9 13