S22 CREDIT RISK ● RISK OCTOBER 2002 ● WWW.RISK.NET

Basel II and SMEs

The current proposal for the newBasel capital Accord (Basel II) aimsat greater risk sensitivity by using

ratings. The ratings might originate inter-nally from the banks or externally fromagencies. While it is desirable to be rat-ings-sensitive, a possible downside ofthis, especially in the internal ratings-based (IRB) approach, could be that itleads to pro-cyclical capital requirements(see, for example, Credit Risk October2001, page S28). During difficult eco-nomic times, commercial banks would berequired to have more capital for eachloan on average than during quiet times,because the general rating of their port-folio would be lower. This could lead tocredit crunches that might worsen eco-nomic recessions. Basel II would thustrigger a new systemic risk on its own.

We believe this unwelcome pro-cyclical capital effect could be especial-ly dramatic for small to medium sizedenterprises (SMEs) – now under heavydiscussion and political dispute. Banks’internal ratings of SMEs rely heavily onyearly financial statements. These obvi-ously tend to fluctuate over economiccycles. Furthermore, banks assign a borrower to ‘default’ as soon as it is expected to be unable to repay capitalor interest in due time, even if that borrower still pays trustfully. As a consequence, the probability of default(PD) varies more with changing eco-nomic conditions.

The pro-cyclical effect could be feltstrongly despite a Basel II-proposed risk-weight curve that becomes flatter withhigher PDs – and even if the overall levelof regulatory capital is reduced, on aver-age over time, for IRB-abiding banks.

We suggest the pro-cyclicality short-comings stem from a ‘double-counting’of the risks. According to Basel II, cap-ital is derived as a multiple of the ex-pected loss. This works in quiet times,when expected losses are near average.The requested capital is significantlylarger than the expected loss, reflectingthe possibility that much more difficulttimes might come. But when a severerecession strikes, the bank enters the tailof the loss distribution, so obtaining thecapital by multiplying the much larger

expected losses for this year by the samefactor makes little sense. It would implythat one still expects increasingly worsetimes to come.

This observation holds if one believesin the mathematical distribution selectedby Basel to describe the distribution ofcredit losses, and to derive the risk fac-tors. If Basel does not believe in its curve,it has to revise it. Assuming the curveholds, then the conclusion is inescapablethat a double-counting occurred by de-riving capital through multiplying the ex-pected losses of crisis times by the samefactor as that of quiet times.

To escape the bottleneck of risk dou-ble-counting, we propose two alterna-tives – a weaker and a stronger one. The

weaker alternative would be to define arule leading to constant regulatory capi-tal along the economic cycle, compara-ble to a long-term average, where cycleeffects would be smoothed out. Thiswould provide a stability similar to thatof Basel I, albeit with ratings included.The second, stronger alternative we sug-gest would be to define anti-cyclical cap-ital. Capital would be allowed to comeup in good economic times and go downin difficult times, to serve as a buffer. Thissecond possibility would assume thatcapital is really a safety cushion. Bothschemes offer the advantage that bankswith different risk profiles will need tohave different capital levels at any timealong the cycle.

Avoiding pro-cyclicality David Cosandey and Urs Wolf argue that, for small to medium-sized enterprises, Basel II is pro-cyclical because of double-counting of the risks. They present two main directions for possiblecapital rules that would circumvent the pro-cyclicality problem

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Basel II and SMEs

A constant capitalDefining capital requirements relying onratings but not changing in time can bedone in several ways. We propose twopossibilities here, but there could be manymore. The idea is to always smooth-outeconomic cycles, to obtain a long-termaverage view.

A first possibility would be to scale alldefault probabilities internally calculatedby a bank by a factor reflecting the stateof the economy. This factor would becountry-wide, unique for all exposureslinked to this country. It would typicallybe derived from the corporate failure rateof the last year measured over the wholecountry. The PDs associated with the dif-ferent ratings would then have to be di-vided by this national factor. The equationwould read:

where:

With the exception of this correction,all present rules of Basel II would remainthe same.

That first methodology has the limita-tion that all PDs are divided by the samefactor, although some rating classes aremore volatile than others. This would bean approximation, but still, it would re-duce pro-cyclicality effects on capital. Toimprove on it, banks could rely on sev-eral failure rates, one for each rating class.With sufficiently long (internally mea-sured) time series of defaults, banks couldthen extract a long-term average, andhence an alpha factor, for each rating class.

An even more refined possibilitywould be to define a national rating mi-gration matrix each year – a return-to-av-erage migration matrix. This matrix wouldreflect how much the present distributionof all companies in the country differ fromthe long-term average distribution alongthe rating axis. This matrix would be thesame for all exposures and banks withinthe country. Applying the matrix on thebank’s portfolio (by matricial multiplica-tion on the position vector) would leadto the long-term-average expected loss ofthe portfolio. The formula would read:

ELL = VxMxV

where ELL = long-term expected loss, V = vector of a bank’s credit exposure, one component per rating class, and M = national (regulatory) return-to-

alpha factor

national corporate failurerateof current yea r

long term averageof corporate failurerate

=

−

regulatory PD for ratingi

PDof current year for ratingi

alpha facto=

rr for current year

average rating migration matrix for cur-rent year.

The return-to-average migration matrixfor the current year would have to be de-termined according to the state of the econ-omy, for example, with the help of theGDP growth of the preceding year. Thismatrix would actually be the inverse of the‘shift-operator’ used in Tom Wilson’s cred-it risk model ‘CreditPortfolioView’. Thisoperator transforms a long-term-averagerating migration matrix into a matrix validfor the current year. To build this opera-tor, the model compares the current year’sdefault rates per rating class with the long-term-average default rates. But getting anational return-to-average matrix mightnot be straightforward, since the rating sys-tems differ from bank to bank.

In practice, neither of these two cal-culation rules (national default rate andreturn-to-average migration matrix)would lead a static portfolio to a perfect-ly constant capital requirement, becauseof inaccuracies in ratings, in the nationalreturn-to-average matrix, etc. But it wouldcome much closer to a constant capitalthan the present Basel II rules.

Both suggested rules would satisfy anessential requirement, namely that bankswith different risk profiles within the samecountry receive different capital require-ments. Banks with higher risk profileswould be requested more capital, sincethe return-to-average transition matrix andthe alpha factor will maintain the originalgap in the risk profile between both banks.

Anti-cyclical capitalThe second option we propose to allevi-ate the pro-cyclicality problem of Basel IIgoes further. Here, we question the im-plicit assumption that more capital shouldbe required in bad times. If capital is meantfor covering unexpectedly large risks indifficult situations, then it might not be souseful to increase it right then. With this inmind, regulators should allow capital tofluctuate, that is, to come down in badtimes, whereas it should rise in good times.

An obvious counter-argument is: whatif a deep economic slump lingers longerthan expected, longer than any crisis be-fore (so that the default rate distributionassumed by Basel II was too optimistic)?Won’t banks lowering their capital be dri-ven to disaster? The obvious answer isyes, of course, but in such a situation oflong and extreme economic decline, bankfailures will follow anyway, whatever theregulatory rules.

Clearly, this issue brings us back to thefundamental question: what does capitalactually stand for? If one accepts the viewof capital as being, functionally speaking,

a reserve, then regulators should allow cap-ital to be lowered when bad times strike.To calculate exactly how much, we sug-gest the following possible methodology:a bank should start with Basel I regulatoryrequirements. Every year, the bank shouldadd or subtract capital according to the gen-eral state of the economy. When the econ-omy is doing fine, it has to add capital.When the economy is going down, it is au-thorised to reduce capital. To determinehow much to add or subtract each year, thebank estimates the long-term average losson its credit portfolio, and adds/subtractsexactly the difference between last year’sloss and the long-term average yearly loss.To estimate the long-term average loss, thebank applies the preceding formulas (ei-ther relying on national default rates perrating or using a return-to-average matrix).The formulas read:

δCi = Llong-term – Li – 1

Ci = Ci – 1 + δCi

where Ci = capital in year i, δCi = capitalchange in year i, Llong-term = long-term av-erage portfolio loss and Li = effective lossin year i.

This is nothing new, actually. Age-oldwisdom says good times should be ex-ploited to prepare reserves for bad times.

Could a sell-out of capital happen in arecession? Regulatory capital representsonly a minimum. Many banks will stillmaintain more capital on their balancesheet than requested by regulators. Morecapitalised banks enjoy lower risk premi-ums. Moreover, the banks would know thatthe following year could bring a higher cap-ital requirement, making a sell-off quicklycounter-productive. Thus no material at-tack on capital would be necessary. Butpro-cyclicality systemic risk embedded inthe present Basel II rules would be signif-icantly reduced.

ConclusionVariable, anti-cyclical capital might be a longway off, but constant, long-term-averagecapital should not be so far-fetched. Thusit seems reasonable to suggest that Basel IIadopt the option of a credit risk capital thatis rating-sensitive, but smoothed-out overeconomic cycles. ■■

David Cosandey is head of asset liabili-

ty management at Zurich Cantonal

Bank. Urs Wolf is head of credit portfo-

lio management analysis and models at

Credit Suisse Financial Services. The

views expressed in this article reflect

the authors’ personal views and are not

in any way tied to or reflect the official

companies’ views