Expected Losses and the Assets to Capital Multiple

My introductory piece on this topic was Bank Regulation: The Assets to Capital Multiple and later noted that the RY : Assets-to-Capital Multiple of 22.05 for 1Q08 was in excess of the usual guideline and in the 20-23 range where prior permission must be sought from OSFI.

When reviewing the RY Capitalization: 2Q08 I found the following note in their Supplementary Package:

Effective Q2/08, the OSFI amended the treatment of the general allowance in the calculation of the Basel II Assets-to-capital multiple. Comparative ratios have not been revised.

… and at the OSFI website I find the following Advisory regarding Temporary Adjustments to the Assets to Capital Multiple (ACM) for IRB Institutions and an accompanying letter. The advisory states:

This Advisory, which applies to banks, federally regulated trust and loan companies and bank holding companies incorporated or formed under Part XV of the Bank Act, complements the guidance contained in the Capital Adequacy Requirements (CAR) Guideline A-1, November 2007.

The CAR Guideline A-1 sets out capital adequacy requirements, including an asset to capital multiple (ACM) test. Upon the adoption of the Basel II framework, the ACM calculation changed for institutions using an Internal Ratings Based (IRB) approach. The change in the ACM calculation is a direct consequence of changes to the treatment of eligible general allowances used to calculate regulatory capital under the IRB framework and the distinction between expected and unexpected loss. OSFI has decided to reverse this unintended change to the ACM for IRB institutions until a comprehensive review of the ACM has been completed.

Adjustments should be made to both the numerator (total assets) and denominator (total capital) of the ACM in order to reverse the Basel II inclusions in and deductions from capital related to general allowances. This will allow IRB institutions to continue with the Basel I treatment of general allowances for the purposes of calculating the ACM.

Specifically, the amounts reported as Net on- and off-balance sheet assets and Total adjusted net tier 1 and adjusted tier 2 capital on Schedule 1 of the BCAR reporting forms should be adjusted as follows:
• Any deduction related to a shortfall in allowances should be added.
• For IRB institutions that have been given prior approval to include general allowances in capital, the amount of general allowances included under Basel II should be subtracted and the amount of general allowances taken by the institution should be added, up to maximum of 0.875% of Basel I risk-weighted assets.

The OSFI Rules are available for download. Link corrected 2008-6-13. There is also a Guideline to the Capital Adequacy Requirements

The advisory is interesting, particularly in light of the fact that RY is currently in the grey zone. The effect on RY’s capital multiple from this change is approximated as:

Effect on 1Q08 RY ACM of OSFI Advisory
Item 1Q08
As Reported
Change 1Q08
Capital 27,113 471 27,584
Assets 597,833 471 598,304
Multiple 22.05   21.69

It’s a significant change! But what does it mean?

As I noted in the introductory post, the variation in Assets:Risk-Weighted-Assets ratios between banks was enormous; the IMF pointed out that institutions with higher ratios appear to have been punished for this by the equity markets; I drew the conclusion that UBS had been “gaming the system” by leveraging the hell out of assets with a low regulatory risk weight … such as, f’rinstance, AAA subprime paper.

Now, the idea that the Basel II RWA calculations could possibly be gamed – or, even without conscious effort, be simply misleading – should not come as a surprise. Overall capital adequacy under preliminary guidelines was criticized in a 2005 speech by Donald E. Powell, FDIC Chair:

The magnitude of the departure from current U.S. norms of capital adequacy is illustrated by the observation that a bank operating with tier 1 capital between one and two percent of assets could face mandatory closure, and yet, according to Basel II, it has 25 percent more capital than needed to withstand a 999-year loss event.1 For 17 of the 26 organizations to be represented under Basel II as exceeding risk based minimums by 25 percent, when they would face mandatory supervisory sanctions under current U.S. rules if they were to operate at those levels of capital, is evidence that Basel II represents a far lower standard of capital adequacy than we have in the U.S. today.

Further, the FDIC argued that Basel II was incomplete without an ACM cap in its Senate Testimony:

My testimony will argue that the QIS-4 results reinforce the need to revisit Basel II calibrations before risk-based capital floors expire and to maintain the current leverage ratio standards. Leverage requirements are needed for several reasons including:
• Risks such as interest-rate risk for loans held to maturity, liquidity risk, and the potential for large accounting adjustments are not addressed by Basel II.
• The Basel II models and its risk inputs have been, and will be determined subjectively.
• No model can predict the 100 year flood for a bank’s losses with any confidence.
• Markets may allow large safety-net supported banks to operate at the low levels of capital recommended by Basel II, but the regulators have a special responsibility to protect that safety-net.

Some comment is also needed about the possibility of using the allowance for loan and lease losses (ALLL) as a benchmark for evaluating the conservatism of ELs. The aggregate allowance reported by the 26 companies in QIS-4 totaled about $55 billion, and exceeded their aggregate EL, and this comparison might suggest the ELs were not particularly conservative and could be expected to increase. We do not believe this would be a valid inference. The ALLL is determined based on a methodology that measures losses imbedded over a non-specific future time horizon. Basel II ELs, in contrast, are intended to represent expected one-year credit losses. Basel II in effect requires the allowance to exceed the EL (otherwise there is a dollar for dollar capital deduction to make up for any shortfall). More important, the Basel II framework contains no suggestion that if the EL is less than the ALLL, then the EL needs to be increased—on the contrary this situation is encouraged, up to a limit, with tier 2 capital credit.

In the view of the FDIC, the leverage ratio is an effective, straightforward, tangible measure of solvency that is a useful complement to the risk-sensitive, subjective approach of Basel II. The FDIC is pleased that the agencies are in agreement that retention of the leverage ratio as a prudential safeguard is a critical component of a safe and sound regulatory capital framework. The FDIC supports moving forward with Basel II, but only if U.S. capital regulation retains a leverage-based component.

Which is not to say that imposition of an ACM cap is universally accepted. After all, such a thing never made it into Basel II – perhaps due to this argument against leverage ratio:

As a final point, the U.S. applies an even more arbitrary “Tier 1 leverage” ratio of 5% (defined as the ratio of Tier 1 capital to total assets) in order for a bank to be deemed “well-capitalized”. As we have noted in our prior responses, the leverage requirement forces banks with the least risky portfolios (those for which best-practice Economic Capital requirements and Basel minimum Tier 1 requirements are less than 5% of un-risk-weighted assets) either to engage in costly securitization to reduce reported asset levels or give up their lowest risk business lines. These perverse effects were not envisioned by the authors of the U.S. “well-capitalized” rules, but some other Basel countries have adopted these rules and still others might be contemplating doing the same.

ALLL should continue to be included in a bank’s actual capital irrespective of EL. As we and other sourcesfootnotes 3,4,5 have noted, it is our profit margins net the cost of holding (economic) capital that must more than cover EL. As a member of the Risk Management Association’s (RMA) Capital Working Group, we refer the reader to a previously published detailed discussion of this issue that we have participated with other RMA members in developingfootnote 4. This issue is also addressed at length in RMA’s pending response to this same Oct. 11, 2003 proposal.

Speaking in general terms, I am all in favour of a second check on the adequacy of bank capital. Looking at problems in different ways generally leads to a conclusion that is better overall than the sum of its parts. HIMIPref™, for instance, uses 23 different valuation measures and applies them in a non-linear fashion to the question of trading. No single measure has veto power; some of the valuation measures turn out to be of negligible independent importance; but the system as a whole provides answers that are better than the sum of its parts.

In this particular instance, it is not the ACM, per se, that we are examining, but the effect of deducting from capital the shortfall of provisions actually taken relative to the Expected Loss (EL) defined in the Basel II accord:

384. As specified in paragraph 43, banks using the IRB approach must compare the total amount of total eligible provisions (as defined in paragraph 380) with the total EL amount as calculated within the IRB approach (as defined in paragraph 375). In addition, paragraph 42 outlines the treatment for that portion of a bank that is subject to the standardised approach to credit risk when the bank uses both the standardised and IRB approaches.

385. Where the calculated EL amount is lower than the provisions of the bank, its supervisors must consider whether the EL fully reflects the conditions in the market in which it operates before allowing the difference to be included in Tier 2 capital. If specific provisions exceed the EL amount on defaulted assets this assessment also needs to be made before using the difference to offset the EL amount on non-defaulted assets.

386. The EL amount for equity exposures under the PD/LGD approach is deducted 50% from Tier 1 and 50% from Tier 2. Provisions or write-offs for equity exposures under the PD/LGD approach will not be used in the EL-provision calculation. The treatment of EL and provisions related to securitisation exposures is outlined in paragraph 563.

EL is calculated as:


where EAD is Exposure at Default; PD is Probability of Default; and LGD is Loss Given Default.

The FDIC provides a good explanation of the number:

A final determinant of required capital for a credit exposure or pool of exposures is the expected loss, or EL, defined as the product of EAD, PD and LGD. For example, consider a pool of subprime credit card loans with an EAD of $100. The PD is 10 percent – in other words, $10 of cards per year are expected to default, on average. The LGD is 90 percent, so that the loss on the $10 of defaults is expected to be $9. The EL is then $100 multiplied by 0.10 multiplied by 0.90, that is, $9. EL can be interpreted as the amount of credit losses the lender expects to experience in the normal course of business, year in and year out. If the total EL for the bank, on all its exposures, is less than its allowance for loan and lease losses (ALLL), the excess ALLL is included in the bank’s tier 2 capital (this credit is capped at 0.6 percent of credit risk-weighted assets). Conversely, if the total EL exceeds the ALLL, the excess EL is deducted from capital, half from tier 1 and half from tier 2. In this example, the EL that would be compared to the ALLL was a very substantial 9 percent of the exposure. The example is intended to illustrate that for subprime lenders or other lenders involved in high chargeoff, high margin businesses, the EL capital adjustment may be significant.

In the negotiations that resulted in Basel II, a major point of contention was the difference between expected losses and unexpected losses. It was agreed that unexpected losses (UL) could not really be modelled – by definition! – and that the purpose of bank capital was to guard against UL. On the other hand, EL could be calculated in accordance with credit models at any time as a routine part of the lending process, with provisions taken as necessary to reduce capital (and profit).

A major bone of contention was … what to do when a bank’s provisions were not equal to the Expected Loss as calculated? According to the BIS press release and final paper:

The Committee proposed in October 2003 that the recognition of excess provisions should be capped at 20% of Tier 2 capital components. Many commenters noted that this would provide perverse incentive to banks. The Committee accepted this point and has decided to convert the cap to a percentage (to be determined) of credit risk-weighted assets.

In order to determine provision excesses or shortfalls, banks will need to compare the IRB measurement of expected losses (EAD x PD x LGD) with the total amount of provisions that they have made, including both general, specific, portfolio-specific general provisions as well as eligible credit revaluation reserves discussed above. As previously mentioned, provisions or write-offs for equity exposures will not be included in this calculation. For any individual bank, this comparison will produce a “shortfall” if the expected loss amount exceeds the total provision amount, or an “excess” if the total provision amount exceeds the expected loss amount.

Shortfall amounts, if any, must be deducted from capital. This deduction would be taken 50% from Tier 1 capital and 50% from Tier 2 capital, in line with other deductions from capital included in the New Accord.

Excess provision amounts, if any, will be eligible as an element of Tier 2 capital. The Tier 2 eligibility of such excess amounts is subject to limitation at supervisory discretion, but in no case would be allowed to exceed a percentage (to be determined) of credit risk weighted assets of a bank.

The existing cap on Tier 2 capital will remain, Thus, the amount of Tier 2 capital, including the amount of excess provisions, must not exceed the amount of Tier 1 capital of the bank.

The basis of the difference (between EL and ALLL) is tricky to understand – possibly on purpose. Some of it may be due to correllations – as explained in a comment letter from Wachovia:

Removal of EL from required capital further highlights the problems with the retail capital functions that we and other banks have discussed in our previous letters. Assuming a 100% LGD for the “other retail” category, capital actually decreases after removing EL from the capital formula when PD increases from 2.6% to 4.6%, as shown in Figure 2 below. The correlations decline so rapidly that they more than offset the increase in PDs.

Our proposed solution is to reduce the asset value correlations at the high quality (low PD) end of the spectrum. For example, the curve smoothes out if the maximum correlation is lowered to the .08 to .10 range.

Remember correllations? That’s what makes pricing CDOs so interesting!

Another rationale (echoing that presented with WaMu’s arguments against any ACM in the first place, quoted above) was provided in a discussion by Price Waterhouse:

It is therefore clear that the calculation of expected losses is still relevant to the Basel IRB capital calculation in order to identify these shortfalls or excesses. Unless a bank has explicitly captured expected losses within its future margin income and can demonstrate this to be the case, the regulator will need to understand the amount of cushion that is in place to manage expected losses – either within capital or as part of provisions. In theory the regulator should not mind where this cushion for expected losses is positioned – future margin income, provision or capital – just as long as it is somewhere!

While this makes a certain amount of sense, it doesn’t sit well with me on a philosophical basis. All that’s happening – when expected losses are presumed to be covered by margin – is that the bank is stating that the loan is expected to be profitable. Well, holy smokes, we can assume that anyway, can’t we? Applying this rationale over a block of loans would mean that capital is equally unaffected by a stack of safe loans made at a small margin, or an equally sized stack of risky loans made at a fat margin … it makes much more sense to me to deduct the expected losses from capital (via provisioning) when the loans are made and subsequently to realize a greater proportion of the interest spread as profit as time goes on.

I’m certainly open to further discussion on this point – but that’s what it looks like from here, from the perspective of a fixed income investor to whom capitalization and loss protection is of more importance than equity stuff like income.

I am not particularly impressed by the explanation given in the TD Bank Guide to Basel II:

Referring to page 24 lines 14 and 21 of the Supp-pack, how is the “50% shortfall in allowance” derived?

The shortfall under Basel II is a regulatory calculation. The methodology is prescriptive and builds in possible, but not necessarily probable, assumptions. Examples could include downturns in the economy, sectors that experience particular challenges, among other items. Our current general allowance methodologies are in accordance with GAAP and approved by OSFI. We believe the existing allowance reported on the Balance sheet is adequate and we are comfortable with our current allocation.

This doesn’t make a lot of sense to me. TD’s EL is entirely under their control; they, not the regulators, determine the EAD, PD and LGD for each loan (subject to approval of methodology by the regulator). I will write them for more information on this matter.

Remember the OSFI advisory? The thing that this post is (allegedly) about? I’m deeply suspicious of the sentence OSFI has decided to reverse this unintended change to the ACM for IRB institutions until a comprehensive review of the ACM has been completed. They’re saying they want to do this now, and that the change was unintended? Not only have they spent the last year bragging about how hard they worked, but

  • The Expected/Unexpected losses thing was a major issue, that actually held up the signing of the Basel II accord. I would have expected anything to do with these effects to have be subject to more scrutiny than other elements, not less.
  • The ACM cap is exclusive to North America (as far as I know). Again, surely all elements of this measure must have been scrutinized with more care than others.

I will certainly be following their “comprehensive review of the ACM” with great interest – and, for what my two cents are worth, lobbying for the divisor to be Tier 1 Capital, as it is in the States, not Total Capital.

Here’s a summary of the differences as of the end of the second quarter. Kudos to BMO, who seem (seem!) to have bitten a bullet that has frightened off the competition.

Provisions vs. Expections & Total Capital
Bank Excess
RY (383) 28,597 (1.33%)
BNS (1,014)* 25,558 (3.97%)
BMO 0 21,675 0%
TD (478) 22,696 (2.11%)
CM (122)* 16,490 (0.74%)
NA (403)* 7,353 (5.48%)
*BNS, CM, NA – deduction may include securitization deductions, etc.; the figure is not adequately disclosed.

Update: The following eMail has been sent to BMO Investor Relations:

I note from page 19 of your 2Q08 Supplementary Package that “Expected loss in excess of allowance – AIRB approach” is zero, implying that your provisions for expected loan losses (ALLL) is equal to your Basel II EL = EAD * PD * LGD.

(i) Is this equality deliberate? Is there a policy at BMO that states a desired relationship between ALLL and EL?

(ii) Do you have any discussion papers or written policies available that will explain BMO’s policy in computing ALLL and/or EL?

(iii) Has the bank determined a position regarding the “comprehensive review of the [Assets to Capital Multiple]” announced by OSFI in their advisory of April, 2008?

Update, 2008-6-5: The following eMail has been sent to TD’s Investor Relations Department:

I note that in your discussion of Basel II at http://www.td.com/investor/pdf/2008q1basel.pdf you state: “The shortfall under Basel II is a regulatory calculation. The methodology is prescriptive and builds in possible, but not necessarily probable, assumptions. Examples could include downturns in the economy, sectors that experience particular challenges, among other items.”

However, I also note that in testimony to the US Senate Donald Powell stated that ALLL should normally be – and should be encouraged to be – greater than EL due largely to a shorter time horizon for the latter measure of credit risk. It is also my understanding that the factors of EL (EAD, PD and LGD) are entirely within your control.

What specific differences in assumptions are applied by TD when computing ALLL as opposed to EL? Do you have a reconciliation between the two figures that shows the effect of these assumptions? Do you have any policies in place that would have the effect of targetting a relationship between the two measures?

Update, 2008-6-5: The following eMail has been sent to OSFI:

I have read your April Advisory on the captioned matter (http://www.osfi-bsif.gc.ca/app/DocRepository/1/eng/guidelines/capital/
advisories/Advisory_Temp_Adjust_ACM_e.pdf) with great interest. I have a number of questions:

(i) Why does OSFI enforce the ACM using total capital instead of solely Tier 1 Capital, the latter being the practice in the United States?

(ii) Was testing of the ACM incorporated in any run-throughs and pro-forma financial tests performed by OSFI prior to implementation of the Basel II accord? Were the effects of provision shortfalls simply missed or have they changed significantly in the interim?

(iii) It is my understanding (from Donald Powell’s 2005 Senate testimony, published at http://banking.senate.gov/public/_files/ACF269C.pdf) that in the States it is expected that ALLL will normally exceed EL, due to differences in the desired effects of these two measures. Are you aware of any methodological or philosophical differences that have led to this situation being reversed in Canada for five of the Big-6 banks as of 2Q08?

(iv) I also understand that ACM is normally regarded as being a more stringent constraint on bank policies that Tier 1 Capital and Total Capital Ratios. Is this the view of OFSI?

(v) I understand that some justification for ALLL being lower than EL is that some proportion of EL is expected to be made up as a component of gross loan margin. Is this rationale accepted by OSFI?

(vi) Should the answer to (v) be affirmative, it seems to me that two similar banks could each make a basket of loans having the same value, with Bank A’s basket being lower-margin, lower-risk than Bank B’s basket. The EL for Bank B would be higher, but ALLL for both banks could be the same if Bank B determined that their higher margin justified a shortfall of ALLL relative to EL. Under the rules effective 1Q08, the effect of the ACM cap would be more constraining than they currently are after giving effect to the advisory; that there is currently no effect of risk on the ACM cap (although there is an effect on the Capital Ratios). Is this the intent of the advisory?

(vii) Will OSFI be dedicating a section of its website to the “comprehensive review of the ACM”? Will draft papers, requests for comments and responses from interested parties be made public in this manner? Have the terms of the comprehensive review yet been set?

4 Responses to “Expected Losses and the Assets to Capital Multiple”

  1. […] PrefBlog Canadian Preferred Shares – Data and Discussion « Expected Losses and the Assets to Capital Multiple […]

  2. […] He supports the views of Powell – former FDIC Chairman – but for different reasons. Powell’s views were referenced in PrefBlog in the post Expected Losses and the Assets to Capital Multiple. […]

  3. […] One reason why the Canadian financial sector has been relatively untroubled is because whenever an institution got into trouble, the rules were changed to let them off the hook. The change with MFC was not isolated: when it became apparent that OSFI’s incompetent testing of the effect of Basel 2 had created unexpected effects in the Assets-to-Capital Multiple they changed the rules. […]

  4. […] there could be trouble at the margins, particularly with specialty lenders; additionally, OSFI has shown in the past that it is incapable of running stress tests that include attention to the […]

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