Capital Ratio Calibration for the New Zealand Banking Sector

Ref #7879822 v1.0 MEMORANDUM FOR Financial System Oversight Committee FROM Financial Policy (Susan Guthrie) DATE 13 November 2018 SUBJECT Capital Ratio calibration FOR YOUR Decision Summary Note:  This paper has been circulated prior to being considered by BSG, so elements of the paper may need to be revised in light of BSG’s discussion on 16 Nov 2018.  FSO has previously approved the risk appetite framework that is to be used for setting the capital target.  We have applied the framework as outlined in the earlier paper, with a primary focus on Tier 1 capital, systemic banks and credit-related risks (although nevertheless briefly addressing capital held for operational and market risk, and Tier 2 capital).  Our analysis has focused on estimating risks for the New Zealand banking sector, although our views have been informed by, and our findings compared with, findings from overseas jurisdictions.  This paper is silent on the timeframe for implementing our recommendations. We envisage a period of at least 5 years would be required, while acknowledging that the higher the target the more implementation time one might want to allow. Agree:  The Tier 1 target should be set between 14.5% and 16% of RWA (using the new definition of RWA for IRB banks).  We recommend this be made up of a 6% minimum Tier 1 requirement with 8.5% to 10% consisting of buffers (the nature of the regulatory response to breaches of the buffers is not the subject of this paper).  The level of Tier 2 should remain at its current setting of 2.0%, but reviewed during 2019 once APRA’s current consultation on TLAC concludes.  We should continue to monitor and assess the capital held for operational and market risk.  A leverage ratio of 3.0% should be introduced for all banks.

2 Ref #7879822 v1.0 The risk appetite framework for bank capital policy

1. This paper applies the previously-presented risk-appetite framework to the capital ratio policy decision. To summarise the risk appetite framework, a complex relationship between capital, financial stability and expected output leads to a relationship between stability and expected output that can be illustrated as follows:
2. The horizontal axis measures the probability the banking sector will retain market confidence even though subject to an extreme shock. Implicit in this is the banking sector remaining solvent in the face of such a shock.
3. The vertical axis measures expected output (or expected material standard of living). It is ‘expected’ because it is the weighted average level of output of two future states of the world (the state that is in crisis, and the state that isn’t). The level of capital matters for the probabilities that are used to calculate the weighted average (the more capital there is the lower the probability of a crisis), and for the output level in each state. As one moves from the left to the right of the graph, capital and financial stability are increasing and, depending on the starting point, expected output may be increasing, static or decreasing.1
4. If the starting position is such that output and stability can be increased by moving to the right (i.e. increasing capital) the starting position is ‘inefficient’ and increasing capital is an efficient act (increasing capital increases two things of value, output and stability).
5. If the starting position is such that stability can only be increased by forgoing expected output it means society is very risk averse and, despite already achieving a high level of stability, wants more. There is nothing inherently wrong or inefficient in society being risk averse and targeting a level of stability that means expected output is not maximised.
6. The risk appetite framework generates a two-step decision process. First, we identify the level of capital that achieves our stability goal (delivering ‘soundness’). Secondly, and subsequently, we explore whether, at the target level of capital, there are opportunities to increase stability further without any loss of expected output (delivering ‘efficiency’).

1 Because these states of the world lie in the future, they are discounted and thus measured in present value terms.

3 Ref #7879822 v1.0 7. The primary focus of our analysis, and the main subject of this paper, is Tier 1 capital. However we do recommend a target for Tier 2 capital later in the paper. Delivering soundness 8. Delivering the soundness objective requires forming a view about the relationship between capital and the probability of a banking crisis. We approached this aspect, firstly, through the lens of solvency, exploring what capital might be required to ensure banking sector solvency with varying probability. When we had established a range of capital levels that might cap the probability of a crisis at 0.5% did we consider the additional capital needed to ensure the banking sector retains the confidence of the market. 2 9. As will be explained in detail later in the paper, we focused our analysis on credit risk (for the purposes of this work we have assumed the level of capital currently held in the banking sector for operational and market risk will continue to be required). 10. We used a variety of approaches for assessing the capital needed to deliver soundness. We looked at overseas studies but wanted to reflect the New Zealand￾specific context. In order to do this we used the Value-at-Risk (VaR) Basel III capital equation, as an analytical tool. This allowed us to estimate the relationship between capital and the probability of crisis using various input values drawn from New Zealand data (where available). For more information about this aspect of our approach refer Appendix 1.3 11. Under Basel III all IRB banks are required to use the Basel III capital equation to estimate the capital needed to cover unexpected asset class losses (for more on this equation see Appendix 2). We applied the equation to the New Zealand banking sector as a whole (modelling the sector as a single systemic bank), finding the equation a useful way to explore the New Zealand-specific context (for example the potential for asset values in New Zealand to be quite correlated with real output). 12. Other regulators have used regression analysis to estimate the relationship between capital and the probability of a crisis, and we reviewed this literature. In the chart below we show the Federal Reserve’s equation for the relationship between CET1 capital and the probability of bank failure (the Federal Reserve’s equation relates to US banks with assets above US$50bn). 4 For comparison purposes, we also show the relationship we have estimated for Tier 1 capital, using our ‘base case’ assumptions applied to the Basel equation. Note, while our modelling and recommended targets relate to Tier 1 capital we envisage CET1 capital making up more or less then entire Tier 1 capital value going forward, thus we find this to be a useful comparison for sense-checking purposes.

2 We considered two values for the cap on the probability of a crisis – 0.5% and 1% - but in the final analysis opted for the more conservative option 0.5%. 3 We did not include the maturity adjustment, hence the Basel III capital equation, as we used it, was a simple VaR model based on a normal distribution and three inputs. 4 The Federal Reserve’s equation relates CET1/RWA to the probability of bank failure. The Federal Reserve also reports that the ratio of RWA to unweighted assets that they use in their analysis is 0.66. In order to draw this chart we used the Fed’s equation to calculate the probability for a given CET1/RWA, then converted the CET1/RWA to CET1/unweighted assets using a factor of 0.66. The Fed’s equation requires a setting for ‘f’, the CET1/RWA value at which failure is deemed to occur. We set this at 4.5% for the purpose of mapping the Fed’s equation.

4 Ref #7879822 v1.0 13. When we vary assumptions for the three inputs in the Basel equation the curvature evident in the chart above changes, but not the fundamental relationship (which is one of a declining marginal impact of capital on the probability of a crisis as capital increases). 14. A key benefit of using the Basel capital equation is that we can vary the underlying assumptions and monitor the effect, enabling us to test how sensitive our results are to the assumptions we’re making. 15. In addition to setting our risk appetite (which is how confident we want to be the banking sector will be solvent after an extreme shock), the Basel equation requires us to form a view about three variables: a. the long run average probability of loan default in New Zealand (‘PD’); b. the loss given default in New Zealand (‘LGD’); and c. the correlation between the value of a borrower’s assets and economic output (correlation ‘R’). 16. We settled upon base case assumptions for these variables, and considered a risk tolerance of 0.5% and 1% (i.e. a target confidence level of 99% and 99.5%), and explored the impact of varying our assumptions either side of the base case. 17. For example, setting LGD to 40% and focusing on a confidence level of 99.5%, we found that, in order to deliver on our soundness objective in the face of credit-related shocks, Tier 1 capital should be set somewhere between 7.5% and 12% of unweighted assets. 18. Amongst the large four banks 0.6% of unweighted assets is held as capital for operational and market risk. Hence we added 0.6% to our estimates of the capital needed in the banking sector as a whole to cover unexpected losses. The range of potential capital targets therefore becomes 8.1% of unweighted assets (7.5% plus 0.6%) to 12.6%.

5 Ref #7879822 v1.0 19. After considering the impacts of the different potential targets on quantum of new Tier 1 capital required, our recommended Tier 1 target is between 9% and 10% of unweighted assets (as indicated in red in the table below). 20. Using an updated RWA calculation (using our preferred setting for the IRB output floor and scaler), and after rounding, these targets translate to 14.5% to 16% of RWA. In comparison, currently actual Tier 1 capital is 12.6% of RWA across the whole banking sector and 12.3% among the big four banks. 21. We have a number of options as to how we allocate the Tier 1 target between the small sector and large banks. This could be done on the basis of their respective RWA value, for example, their unweighted assets or something else. We will raise this issue in the consultation paper and develop a policy which is informed by submissions. For more information refer to Appendix 3. 22. Our results are dependent on the risk appetite chosen. If we sought to cap the probability of insolvency at 1%, rather than 0.5%, our target for Tier 1 capital would be 12% and 13% of RWA (refer Appendix 4). Sense-checking the recommended capital target 23. The recommended Tier 1 target protects the sector as a whole from a shock loss of $51bn to $56bn. This loss is equivalent to 10% to 11% of unweighted assets (or 16% to 17.5% of RWA).5 Comparing the unexpected loss that corresponds to our Tier 1 target with the losses experienced in other countries’ during crises provides us with one sense check on our capital target.

5 The shock loss estimate is larger than the target capital level due to banks making some provisions for loss in advance (these are anticipated expense items).

6 Ref #7879822 v1.0 24. It is difficult to estimate the losses incurred in banks during crises because the losses can be removed from the banks’ balance sheets during resolution, realised only many years later or averted through a government-funded bailout. Nevertheless, there are some reports available. 25. An investigation ten years on from the GFC estimates the cumulative net losses of the 11 main banks in Ireland, for example, reached 25% of unweighted assets, suggesting our capital target might be on the light side.6 As will be discussed later in the paper, using other metrics Ireland does not appear to be an outlier in terms of the GFC loss experience. 26. Evidence from other countries, and drawing on more than the GFC, suggests a wide range of potential shock loss rates. Using losses expressed relative to RWA, the BIS reported losses ranging from under 5% in Japan (1997) and the US (GFC), to between 10% and 15% for Finland (1991) and nearly 25% for Korea (1997).7 The Irish experience suggests we should be cautious in using the numbers relating to the US and the GFC as the report was written soon after the crisis, in 2010, and additional losses have been reported since then. 27. In comparison, the current actual level of Tier 1 capital is equal to 12.6% across the whole banking sector and 12.3% among the big four banks. For more information on how the small banking sector would be impacted by these targets please see Appendix 4. 28. We outline the information we used to form the assumptions that led to these results later in the paper. Banks maintaining the confidence of the market 29. Having identified the Tier 1 capital needed to meet our solvency objective in the face of a shock arising from credit, operational and/or market risk, we need to consider the capital needed to ensure market confidence in the bank when it is emerging from the shock. 30. It is possible that, after incurring a large shock, our large banks would continue to earn profits at the same rate as they have achieved historically. This would generate new retained earnings and thus provide a flow of new capital. Based on historical averages, annual net profits earned by the large four banks collectively amount to

6 Refer the Irish Times, Sep 2018 “Irish banks’ loan losses hit €140bn in 10 years after the crash”. 7 BIS (2010) Calibrating regulatory minimum capital requirements and capital buffers: a top-down approach. October 2010. Tier 1/RWA target (low line corresponds to lowest recommended target when the risk appetite is 1%, the high line corresponds to the highest recommended target when the risk appetite is 0.5%)

7 Ref #7879822 v1.0 around $4bn per annum and, if retained, would potentially be able to contribute a sizeable new source of capital. One finding from the stress tests is that banks do envisage continuing to earn sizeable profits after large stress events. Caution should be exercised too, it would seem overly optimistic to rely on new retained earnings to engender the confidence of creditors in a bank emerging from a shock. 31. Rather than aim to shore up market confidence in shocked banks with additional, pre￾emptive, Tier 1 capital, we propose addressing it with Tier 2 capital and supervisory actions. Alternatively, an amount could be added to our Tier 1 targets to address this. We now turn to the efficiency issue (and, later in the paper, make recommendations about Tier 2 capital target). Delivering efficiency 32. There is a considerable literature which looks at what level of capital would maximise expected output. This literature does not adopt a risk appetite framework in its analysis, implicitly accepting whatever probability of crisis emerges from the output￾maximising analysis. The results from these studies are thus not directly applicable. However, this way this literature conceives of the relationships between capital and output, and stability and output, aligns with our own and this literature is a valuable source of information that we used in the second step, which is the efficiency analysis.8 9 33. In order to assess whether, at our target Tier 1 capital levels, there might be opportunities to increase stability further without any reduction in expected output, we need to form a view on two additional relationships – (i) the impact of capital on lending rates, lending and thus output and (ii) the impact of a banking crisis on output. The impact of capital on lending rates and thus output 34. In the literature there is a well-established method of estimating the impact on lending rates of a 100 bps increase in the ratio of equity to debt in the banking sector. First, the impact on the bank’s average cost of capital is estimated. There is conventional approach to this estimation which includes a focus on Tier 1 capital and the assumption of a 50 percent Modigliani-Miller offset10. We have used this conventional approach and New Zealand-based estimates for the return on equity (14.4% per annum), the return required by holders of bank debt (2.9%) and the tax rate. In calculating these values we used information about the four large banks, and a Federal Reserve adjustment to debt costs the still-present impact of the GFC on global lending rates. 35. We estimate that a 100 bps increase in the Tier 1 ratio would increase the weighted average cost of capital by 6.6 bps with a flow-through effect on lending rates (which we estimate would increase by 8.2 bps).

8 Our illustration of our risk appetite framework, which shows how stability and output are related, is based entirely on this large body of literature. 9 As well, for some studies, we can extract from the recommended capital level what probability of crisis is associated with it. In the case of the Federal Reserve (2015) for example, they identified the output-maximising CET1/RWA ratio as being 13% to 25%. This corresponds to a probability of crisis of approximately 0.6% (using their estimates of the US relationships) to 0.03%. 10 The Modigliani-Miller ‘offset’ arises in the context of a bank having a capital restructure, with the ratio of equity to debt funding increasing. The ‘offset’ refers to the extent to which the bank’s eventual weighted average cost of funding does not rise by as much as the pre-capital restructure relative returns on equity and debt would suggest.

8 Ref #7879822 v1.0 36. The return on equity of New Zealand's systemic banks is very high compared to countries such as the US and the UK. Hence the estimated impact on lending rates tends to be a fraction higher than what is estimated in those jurisdictions. 37. The Federal Reserve reports that their macroeconomic modelling indicates the relationship between lending rates and GDP is linear, with every 1 bps increase in lending rates leading to a fall in GDP of 1.07 basis points. Hence, their estimate of the impact on GDP of a 100 bps increase in the equity ratio was to reduce annual GDP by 7.4 bps (1.07 x 6.9 bps). 38. We have not done our own macroeconomic modelling, but have used the Federal Reserve's assumption of a linear relationship with a coefficient of 1.07. Hence we assume an increase of 100 bps in the ratio of Tier 1 capital to unweighted assets is to reduce annual GDP by 8.8 bps (1.07 x 8.8 bps). The impact of a crisis on output 39. Estimates of the output impact of a crisis vary widely, depending on whether the impacts are expected to be permanent or not. If the effect is permanent, it means even though the economy returns to growth at some point, perhaps soon after the crisis was triggered, growth is from a permanently lower base. Hence, in this case, the estimated output effects are high. The case where output effects are permanent is illustrated in the figure below, with the orange line showing the output trajectory post-crisis. Source: Federal Reserve 2017-034 40. Because the output effects of a crisis occur can occur over an extended period of time, the impact of a crisis on output is measured in present value terms. Estimates of the NPV of the output cost of a crisis range from 19% to 158%. The range is wide

9 Ref #7879822 v1.0 partly because the various studies use different discount rates, and partly because views as to the permanence of the output effects vary. 41. In the studies reported in the table below, in every case the discount rate is lower than what is currently required of public projects (other than accommodation and office buildings) by the NZ Treasury, for example. This suggests that the output cost of a crisis reported in these studies would be less if the costs had been discounted using the rate currently prescribed by the NZ Treasury. 42. A further complicating factor is that these impact estimates are invariant with the level of capital. In the theoretical literature there are some studies that suggest the output impacts of a crisis will be smaller the more capital is held in the system at the time of the crisis (in other words, it is not just the probability of a crisis that is related in a non￾linear way to capital, the output impacts of a crisis are too). 43. In terms of assessing whether or not there are opportunities to simultaneously reduce risk and increase expected output, we have accepted the approach of the studies reported in the table and used the BCBS's mid-point estimate of output losses equal to 63% of GDP. Identifying if any win-win opportunities are available at our Tier 1 target

44. While there is uncertainty around the setting of values for any of the three inputs into the Basel capital equation, a particularly important decision is the value to use for R.
45. There is considerable uncertainty around the value to use for R. 0.6 is our estimate of the long-run correlation between house prices and real GDP in New Zealand whereas 0.3 is the value we settled on for our base case assumption. Basel III includes a cap on R of 0.24 but, based on the data available, we believe that is too low for New Zealand.
46. In the two charts below we have estimated the output-stability curve for New Zealand using either R=0.3 or R=0.6. In both cases the banking sector’s current ratio of Tier 1 capital to unweighted aggregate assets (7.7%) is shown. The capital required to cap the probability of a crisis to 0.5% differs depending on the value of R.
47. What these charts indicate is that, irrespective of whether R=0.3 or 0.6, at the Tier 1 target there are some win-win opportunities remaining (it is possible to increase stability with no loss of expected output). 11

11 The reason the curve turns down so sharply on the far right is that so much stability has been achieved already. A this point, increasing capital delivers only a tiny benefit in terms of averting crisis-related output losses and so it is exceeded by the output cost impact of increased lending rates.

10 Ref #7879822 v1.0 48. Note the numbers reported in the chart relate to Tier 1 capital relative to unweighted assets. A value of 10% (chart on the left), for example, corresponds to Tier 1 capital equal to 16% of RWA (using the new RWA definition for IRB banks). A value of 16% (chart on the right) corresponds to Tier 1 capital equal to 27% of RWA). 49. In the remainder of the paper we outline the information available to inform our settings for PD, LGD and R, contrast our estimates for NZ with those of other countries and do sensitivity analysis. A long run average PD for New Zealand 50. There is impaired loan ratio data for New Zealand banks going back to 1988, and non-performing loan (NPL) ratios going bank to 1996. We can construct relative frequency distributions for these ratios and average ratio values. 51. The ratio of impaired loans to total loans, or non-performing loans to total loans, indicates the probability any outstanding loan is impaired (or non-performing). The average long run value of these ratios can be used as a guide to the long run average probability of default (PD) for NZ. We find the average ratio values varies from 1.5% (NPL) to 2.8% (impairment ratio).

11 Ref #7879822 v1.0 52. The NZ impaired loan data includes large losses from BNZ in 1992. At the time BNZ was NZ’s largest bank by a considerable margin. Five large banks dominated the banking sector and, among them, BNZ had 40% market share. In 1992 BNZ had an NPL ratio of 25%. It was state-owned and received substantial capital injections before being sold. Despite the size and systemic importance of the bank, and the need for capital injections, the BNZ episode is not considered to constitute a ‘crisis’. This appears to be because the fiscal injections were relatively modest relative to GDP and there was limited contagion to other banks (BNZ’s losses did not appear to cause systemic problems, although some other small banks incurred large losses around this time). Given the impairment data includes the resolution of NZ’s largest bank at the time, it seems a relevant data set to use for modelling purposes. 53. BNZ’s NPL ratio in 1992 was on par with NPL ratios incurred by countries that have experienced systemic crises. For example, BNZ’s peak NPL ratio was on par with the peak aggregate NPL ratio prevailing in Ireland as a result of the GFC. 54. Despite the BNZ episode, NZ has had no systemic banking crisis and this is reflected in the historical impairment and NPL record. The relative frequency of high NPL ratios is much higher in countries that have had banking crises. For example, NZ’s NPL record is contrasted with that of Ireland. Ireland’s average NPL ratio over 1998 to 2017 is 7.7% compared to NZ’s average of 1.5% (1996 to 2017).

12 Ref #7879822 v1.0 55. While Ireland’s losses were high, as indicated in the earlier cross-country chart, it is not an outlier. This is confirmed by the recapitalisation costs incurred by the government in Ireland. 56. Other sources of information that were considered in arriving at our base case PD value include: • The PDs our large banks use for their key portfolios • The BoE’s 2015 review of the probability of default based on global data • Federal Reserve modelling of non-systemic banks failure rates • Other countries loss experiences 57. Factoring in all of the above, we opted to use a PD of 2.8% in our base case (this is the long term average impairment ratio for NZ). For sensitivity analysis purposes we used PD’s ranging from 1.5% to 3%.

13 Ref #7879822 v1.0 An LGD input for New Zealand 58. Previous analysis led to prescribed LGD values for different types of loans. The maximum prescribed value (which applies to high LVR farm loans) is 42.5%. In our view this analysis is supportive of a base case LGD input of 40%. 59. Supporting a base case LGD value of 40% are the results from the stress tests, held with the big four banks, in 2015 and 2017. The 2017 large bank stress test outcomes for asset class losses give us some information which can be used to arrive at an LGD input assumption. Based on the aggregate loan exposure of the four large banks, the weighted average LGD rate was 31% (4.3/13.8). The estimate from 2014 was slightly higher, at 37% (5/13.7). 60. It is difficult to use historical crises to extract LGD estimates because losses can take a long time to materialise, and may be obscured by restructuring efforts (for example, if ‘bad debts’ get placed in a separate entity, the losses will not be recorded in the stressed banks accounts). 61. We used 40% for our base case LGD input, with 35% to 45% used for sensitivity analysis. NZ’s R assumption 62. In the Basel equation Correlation R measures the relationship between the borrower’s asset value and economic output. 63. The Basel capital equation models R as a function of PD, and has been criticised for this.12 As well, in Basel III the equation is required to be applied to asset classes (which are assumed to be collections of homogenous loans). Because it applies to only one asset class, the correlation is assumed to be relatively low (it is capped at 0.24 in Basel III). 64. In New Zealand house prices and GDP are quite highly correlated. The correlation between the annual % change in GDP (either nominal or real) and the annual percent change in house prices is 0.63.

12 Refer Moody’s (2010)

14 Ref #7879822 v1.0 65. New Zealand’s correlation appears high relative to other countries. Country 1990 to 2007 1990 to 2017 Full sample available Full sample result NZ 0.52 0.63 1990 to 2017 0.63 UK 0.37 0.62 1976 to 2018 0.47 Canada 0.24 0.26 1971 to 2018 0.31 Norway 0.40^ 0.44^ 1993 to 2018 0.44 Ireland 2006 to 2018 0.44 ^ starting year for Norway is 1993, Source: Federal Reserve of St Louis, RBNZ 66. We are applying the model to the combined value of all loans in the economy, not an individual assets class. In this case, we believe it is appropriate to input R as a distinct variable (i.e. not allow it to be dictated by PD). We also believe the appropriate value of R will exceed the 0.24 cap imposed by Basel. 67. We used 0.3 as our base case, but explored a range of R values (0.24 to 0.6). ‘Base case” PD, LGD and R for NZ 68. Our base case values are indicated in the table below: Equation input Base value Range  PD 2.8% 1.5% to 3%  LGD 40% 35% to 45%  Correlation R 0.3 0.24 to 0.6  Confidence level 0.995 0.99, 0.995 Sense check on NZ LGD and R assumptions 69. We can explore the potential relevance of our LGD and R assumptions using the Irish experience. Using Ireland’s peak NPL ratio of 7.7% for the PD input, can our LGD and R base case assumptions do a reasonable job of projecting Ireland’s actual GFC loss rate? 70. Using a confidence range of 99% to 99.5%, the model projected a total loss rate of 17% to 20% of unweighted assets. Actual realised losses from Irish banks, 10 years on from the crisis, are estimated to be 25% of the initial value of unweighted assets (Irish Times report 2018). So our input assumptions led to an underestimate of the losses experienced in Ireland. Increasing the R value to 0.5 meant the model could reproduce the actual result.

15 Ref #7879822 v1.0 71. A further check was to compare out estimated shock losses with realised losses from countries other than Ireland. This was discussed earlier in the context of BIS crisis loss estimates. 72. A third sense check was to compare our estimated relationship between Tier 1 capital and the findings of other regulators. For example, we used the Federal Reserve’s capital function described earlier. For completeness we repeat here the chart showing the Fed’s results versus our base case. Sensitivity analysis 73. The impact of varying our risk appetite, and assumptions about PD, LGD and R, was explored. The results from some of this analysis are represented in the table below where PD and R vary, but not LGD and our risk appetite (set at 40% and 0.5% respectively). Possible criticisms of our approach 74. One objection to our analysis might be that the Basel equation is designed on the basis of annual losses. In the real world losses due to a shock can take years to materialise. In this case, shouldn’t our PD and LGD estimates in particular reflect annual losses, not cumulative ones? 75. Our response is that we agree the realisation of losses following a shock can take some time, reflecting delays in reporting cycles, accounting methods and so on. As well, borrowers themselves will try and respond to the shock and it will be some time before they succumb. But in an economic sense, the loans lost their value at the time of the shock – that was when the assets lost value. This reality merely materialised later. For modelling purposes it is not unreasonable to adopt the view that the (subsequent) cumulative losses occurred at one point in time, namely the time of the shock (as we do in our analysis).

16 Ref #7879822 v1.0 76. Another criticism might be that we have placed too much emphasis on the Basel equation at the expense of overseas research. Firstly, we used the equation as a tool for our thinking, exploring various potential scenarios that apply to New Zealand. The equation enabled us to do sensitivity analysis which is valuable for informing an important decision that ultimately requires considerable judgement (we are setting capital for an unknowable future event). We also looked at overseas data and results and used these as a sense check on our analysis. Hard minimum versus buffers 77. The Tier 1 target could be met entirely with a hard minimum but our preference is to keep the hard minimum close to current requirements, with the balance made up with buffers. This is because the hard minimum signals the capital level at which we would act to place a bank in resolution and realistically, that will occur only when Tier 1 capital reaches 6% on an RWA basis. 78. Thus we propose setting the hard minimum for Tier 1 capital equal to 6% of RWA, with the balance (8.5% to 10% of RWA, depending on which target is settled upon) made up with soft buffers. This is a significant increase in buffers. Currently the ‘conservation buffer’ is set at 2.5% and the ‘countercyclical buffer’ is set at 0%. 79. Note that Tier 2 capital only plays a role once a bank has been deemed non-viable. Leverage ratio 80. The arguments for a Leverage ratio were made in previous papers, and FSO agreed to include this policy in the consultation. Our recommendation is Tier 1 capital equal to 3% of the leverage base (which is calculated differently than total unweighted assets). Setting of the output floor 81. We propose setting the output floor and scaler such that the RWA for the large four banks is $280bn (up from $253bn currently, and an 11% increase). The time frame for implementation 82. This paper is silent on the timeframe for implementing our recommendations. We envisage a period of at least 5 years would be required, while acknowledging that the higher the target the more implementation time one might want to allow.

17 Ref #7879822 v1.0 Recommendations 83. We recommend:  Setting the output floor and scaler such that the RWA for the large four banks is $280bn (up from $253bn currently, and an 11% increase).  Setting the Tier 1 target to between 14.5% and 16% of RWA (using the new definition of RWA for IRB banks).  We recommend this be made up of a 6% minimum Tier 1 requirement with 8.5% to 10% consisting of buffers (the nature of the regulatory response to breaches of the buffers is not the subject of this paper).  The level of Tier 2 should remain at its current setting of 2.0%, but reviewed during 2019 once APRA’s current consultation on TLAC concludes.  We should continue to monitor and assess the capital held for operational and market risk.  We recommend a leverage ratio of 3.0% for all banks.

18 Ref #7879822 v1.0 Appendix 1 The conceptual framework for our credit-risk analysis

1. We are assuming the banking sector is made up of a single systemic bank that holds assets in the same proportion as the present day banking sector as a whole and is exposed to the operational and market risks that our present day systemic banks face.
2. We assume the hypothetical bank owns all the loan assets of the economy, and loans are secured by the same items (e.g. residential property) as is true currently.
3. We are the regulator setting capital requirements for the bank.
4. We require the bank to hold enough capital to survive an unexpected loss that has a probability of occurrence less than 0.5% (also explored 1%).
5. We approach the problem as per Basel III, only using the VaR model, only using the entire loan pool in the economy not individual asset classes held within individual banks.
6. We use the Basel Capital equation to estimate the capital required.
7. We do not use the R = f(PD) approach of Basel, but instead use our own fixed estimate.
8. Our sensitivity analysis uses the Basel cap on R of 0.24.
9. Inputs are PD, LGD and R deemed to be appropriate for the NZ-wide pool of loans.
10. We estimate losses and required capital relative to unweighted assets (i.e. akin to the leverage ratio).

19 Ref #7879822 v1.0 Appendix 2: the VaR Basel III capital equation Box 1: The Value at Risk (VaR) model Banks expect to lose money on some loans during normal business times. This potential for loss is factored into loan pricing but, as well, provision is made for future losses. When a loan is originated an expense item (a ‘provision’) is created at the same time, equal to the average loss the bank expects to incur from this type of loan. Aggregate provisions enter the bank’s balance sheet as a liability. The effect of provisions is to reduce volatility in the value of the bank’s net equity (when a loan incurs a loss, an offsetting amount is deducted from provisions). Banks can estimate expected losses in a variety of ways, using historical experience, for example, or theoretical modelling. Banks do not typically make provisions for extreme events, instead focusing on losses likely to occur during a typical business cycle. If a bank’s aggregate loan loss provisions are always sufficient to cover future loan-related losses, the bank will never become insolvent. However, the scale of future losses cannot be known with any certainty. The depth and duration of historical business cycles may be a poor guide to future cycles, and unexpected shocks that occur independently of any business cycle are a possibility. If a bank was to rely only on credit pricing and aggregate provisions, it would be exposed to a non-negligible risk of insolvency. Hence, bank owners can be expected to willingly commit some long term equity capital to the bank, so it is able to absorb unexpected losses (i.e. future loan losses for which no accounting provisions have been made). The essential problem that capital regulation addresses is that, in the absence of regulation, bank owners are believed to be willing to commit less equity capital than is socially optimal. Capital regulation is about requiring banks to hold capital sufficient to match some unexpected losses. It is unrealistic to expect banks to hold capital against extremely large losses because the level of capital needed to match the loss would be so high as to make lending non-viable (the income needed to pay as dividends to the bank’s owners would exceed the revenue able to be generated by the loans). Hence, in simple terms, the core task facing regulators when setting capital policy is to identify the largest potential future loss they deem to be unacceptable. The amount of capital required of the bank can be directly inferred from this loss value by taking account of provisions. 1 The regulators’ task can be illustrated graphically. Loss rates are arrayed in an ascending order along the horizontal axis, with the expected frequency represented on the vertical axis. Losses up to the level marked ‘A’ are expected to occur during a usual business cycle, and are matched exactly by bank loan loss provisions. Shareholders are willing to provide capital to match losses that are larger than ‘A’ and as much as ‘B’. The regulator has decided that losses beyond ‘B’ and up to ‘C’ are unacceptable, but losses beyond ‘C’ are either too expensive to match with capital or are a sufficiently remote risk they can be ignored. Hence the bank is required to hold capital equal to ‘C’ minus ‘A’. Should a loss of magnitude ‘C’ eventuate the bank will remain solvent because the loss is matched by the combined value of provisions and bank capital.

20 Ref #7879822 v1.0 Appendix 3 Allocating the Tier 1 target We have options when it comes to allocating the Tier 1 target between the small bank sector and the large banks. We could allocate the target across the two sectors based on their relative RWA, their aggregated unweighted assets, or something else. In the table below we firs allocate the target based on RWA, and then below we allocate it based on unweighted assets. Given the smaller banks convert each dollar of unweighted assets into a higher RWA dollar value, compared to large banks, the impact of basing the allocation on RWA requires more capital from small banks than the alternative. How to allocate the Tier 1 target is an important issue that can be addressed via a D-SIB requirement imposed only on large banks, and other methods.

21 Ref #7879822 v1.0 Appendix 4: Recommendation if one were to tolerate more risk If we were to aim to cap the probability of a crisis to 1%, rather than 0.5%, we require less capital of the system. Retaining the same base case assumptions and methodology produces a target for Tier 1 capital of 7.5% to 8% of RWA which translates to 12% to 13% of RWA (after rounding).