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The impressive development of riskmanagement models in the pastdecade was mainly driven by twothings. The regulators, aiming at increas-ing the security of financial markets toavoid crises caused by insolvent banks;and increasing market competition, withshareholders/investors looking for the fi-nancial institution (FI) with the best risk-return profile. The former reason led tothe implementation of the Basel I Accordfor credit risk (1988) and market risk(1996), requiring banks to hold minimumamounts of capital against their credit andmarket risk. This will be enhanced by theBasel II Accord in the near future, whichwill incorporate operational risk into thecapital framework. The second reason ini-tiated the development of internal risk-based (IRB) models, affecting not only anFIs profitability but also pricing, securiti-sation and business strategy.

Economic capital models overviewTo meet the regulators two main re-quirements, most FIs developed two riskmanagement systems one for the ex-ternal risk supervision and regulatory re-porting and one internal risk model as abasis for further management decisions.Internal models typically developed intoeconomic capital models, where the eco-nomic capital of an FI defines the needfor capital as a buffer against all financialrisks on a common solvency standard.Economic capital typically functions as acommon currency for risk, overcomingthe inconsistencies in the regulatory cap-ital adequacy framework (see below).

Since the development of economiccapital models started in the mid-1990s oreven later, market benchmarks are quiterare, and were pursued only very recent-ly, for example in Sarraf (2003) analysing 61 European financial organi-sations; Oliver, Wyman (2001) focusingon global banking/insurance conglomer-ates; CMRA (2001) investigating majorbanks across the world; and ERisk (2002) analysing economic capital-based risk-adjusted return on capital (Raroc) modelsin 17 major banks, to investigate best-practice standards and the sophistication

of different models, which was found tovary considerably.

It turned out in all surveys that morethan two thirds of major FIs in Europe andthe USA use internal economic capitalmodels. The key reasons named for theirimplementation were (in the order of de-creasing importance) regulators, ratingagencies, shareholders and equity ana-lysts, that is, all external drivers. It is quitesurprising to see regulators as a key fac-tor, proving that their influence and su-pervision already exceeds the control ofcapital adequacy according to the Basel Iframework. Under the Basel II framework,to be implemented till 2006 (Basel Com-mittee on Banking Supervision, 2002), wecan expect this tendency to increase evenmore, since under Pillar 2 the regulatorysupervision will be further enhanced, al-lowing regulators to require banks to es-timate and hold capital requirementsbeyond Pillar 1 measures. Regulators in-tention to increase the sophistication ofcapital adequacy models is also reflectedin various studies and research papers ofthe Basel Committee (Joint Forum on Fi-nancial Conglomerates, 1999).

The main features of economic capi-tal models can by summarised as:1

Quantification of all financial risks ofan FI endangering its equity, includingcredit risk, market risk, operational risk(with two sub-categories business riskand event risk2) and (if applicable) insur-ance risk. The basic idea is to quantify therisk of an adverse change of the FIs eq-uity E in a certain time-period T, whichis:

(1)

Market liquidity risk of assets is includ-ed in the market risk category, whereasliquidity risk in the sense of the banksavailable liquid funds is not included ineconomic capital models, since it is notdirectly endangering the equity of thebank.

AE assets liabilitiesMarket ALM

credit riskInsur

= ( ) ( )/ /

1 24 34aancerisk

Businessrisk

Net income in T

1 244 344

1 2444 3444+ ( )

Economic valuation of assets and lia-bilities (mark-to-market/mark-to-modelrather than book values). Consistent measurement of differentrisk-types by using a value-at-risk typeapproach with the same holding periodand confidence level. The economic cap-ital figure of an FI is the (negative) valueof E from equation (1) on a certain con-fidence level, where the probability dis-tribution of E is calculated taking intoaccount correlations between assets, li-abilities and net income streams, allow-ing diversification benefits whenaggregating different risk categories. The confidence level of the economiccapital model is typically linked to the tar-get debt rating of the FI on a one-yeartime horizon, for example, a 99.9% capi-tal level corresponds to a single-A rating.

Typical confidence levels range between99% and 99.98% (Sarraf, 2003). The one-year time horizon is the industry standard,since most budgeting and allocationprocesses also relate to one year. Raroc-based performance measure-ment and capital allocation processes.The Raroc of a portfolio is defined as theexcess return over the risk-free rate overthe corresponding economic capital, al-lowing not only for a risk-adjusted per-formance comparison but also enablingthe use of the results for capital allocationdecisions or pricing.

According to Capital Market Risk Ad-visors (2001), most FIs include marketrisk (including ALM) and credit risk (76%and 79% of all FIs respectively) in theireconomic capital model, whereas only55% of the banks include operational risk,showing that not only the regulatory riskframework delayed the inclusion of op-

Economic capital versus regulatorycapital a market benchmarkGuido Giese sets out to provide a market benchmark for the relationship between economic andregulatory capital models currently used or developed across different financial institutions, andto analyse the market forces driving the development of economic capital models

Since the development of economiccapital models started in the mid-1990s or even later, marketbenchmarks are quite rare

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erational risk in capital adequacy model-ling. In Oliver, Wyman (2001) and Capi-tal Market Risk Advisors (2001), thetypical risk profile of major organisa-tions was outlined (see figure 1).

Figure 1 shows the average (stylised)economic capital breakdown in major uni-versal banks (where credit risk domi-nates), non-life insurance (whereinsurance risk prevails due to the unpre-dictability of casualties) and life insurances(where insurance risk is small due to thehigh predictability of the mortality rate, butmarket risk is high, since the stock quotain the asset portfolio is usually very highdue to the long-term investment horizonof life insurances). See Oliver, Wyman(2001) and Capital Market Risk Advisors(2001).

Most banks (more than 80%) allocateeconomic capital (EC) at enterprise andbusiness level, but only half go down tothe desk level. Further, most banks thatuse Raroc methods do so on a businesslevel (about 40%, where another 37% an-nounced to do so in the close future),whereas very view banks do so on a desklevel (about 13%), showing that Rarocmodels on a business level develop rapid-ly to a best practice approach (Sarraf,2003, and Capital Market Risk Advisors,2001).

Economic capital models implementation Economic capital models can compensateseveral weaknesses of the Basel I and IIframework, that is: The incompleteness of financial riskstaken into account, for example, interestrate risk in the banking book is not in-cluded in the Basel capital requirements.Moreover, the regulatory capital model (in-cluding Basel II) views banks as silos forassets and liabilities and neglects incomestreams that can be highly correlated withassets or liabilities, that is, business risk isneglected. The inconsistent risk measurement of dif-ferent risk categories. A consistent method-

ology requires a full VAR approach with thesame confidence level and holding periodfor all risk areas. Even under the Basel IIIRB approach for credit risk, the capital re-quirement calculation is not a full VAR ap-proach, since the model is based on theassumption of a portfolio of infinite gran-ularity (Wilde, 2001, Wilson, 1997), ne-glecting portfolio diversification and riskconcentration effects. The inconsistency inthe regulatory capital framework has vari-ous consequences, for example: Inefficient capital allocation process inthe economy due to an unfair pricing ofloans; Regulatory arbitrage, since the sameeconomic risk exposure can have differ-ent regulatory capital requirements with-in a financial group, depending on theentity in which it is booked. Uneconomic aggregation of risk. Ag-gregation of risks has to take place underconsideration of correlation and can beperformed on the following three levels,that is, aggregation (Oliver, Wyman, 2001)i. within a certain risk factor, for exam-ple, market risk in the trading portfolio(Level I)ii. across different risk factors within abusiness line for example, combiningmarket and credit risk within a bankingdivision (Level II)iii. across different business lines, for ex-ample, aggregating banking and insurancerisk within a financial group (Level III).

Level I aggregation takes place for theregulatory Basel model approach for mar-ket risk (BIS (1996)) and partially for cred-it risk under the Basel II IRB approach forcredit risk (limited by the aforementionedgranularity assumption). Aggregation oflevel II and level III including correlationand diversification effects will not be pro-vided under Basel II.

Most economic capital models current-ly perform a sufficient aggregation on LevelI, for example, due to the use of VAR formarket risk (currently two out of threebanks use VAR models for market risk andthe remaining third intends to do so in the

future (Capital Market Risk Advisors,2001)) or portfolio/VAR-based credit risktools such as KMV Portfolio Manager,CRisk+ or CreditMetrics, which take intoaccount industry and geographic diversifi-cation/concentration and credit correla-tions.3 These approaches are already usedby more than 50% of financial institutionswithin their economic capital model, andthis number is growing. For operationalrisk models using VAR-type approachesthat are not yet well developed, the pre-vailing methodology is a heuristic scenario-analysis, showing a clear accuracy gapbetween market/credit risk and opera-tional risk on the Level I calculation.

Industry benchmarking showed (Oliv-er, Wyman, 2001) that Level II and espe-cially Level I aggregation can revealsignificant diversification benefits of (to-gether) up to more than 50%, whereas thebenefits from Level III diversificationamounts to at most 10%, showing thatonly neglecting the latter effect within aregulatory or internal model is justifiable.

Concerning a correlated Level II andLevel III aggregation, there are broadlytwo approaches (see figure 2): A factor model (also called econo-metric or statistical model) that defines aset of deep economic factors (GDPgrowth, interest rates, indexes, etc) thatinfluence all risk types using an econo-metric function to model the dependen-cy of the loss distribution function foreach risk type (market risk, credit risk,etc) which can then be aggregated to agroup-wide loss distribution function tocalculate the total VAR (economic capi-tal) of the bank. Direct estimation of the correlation be-tween risk types based on internal ex-perience. Put simply, instead ofcalculating the economic capital as a cer-tain percentile of the banks global lossdistribution, one calculates the correla-tion of the N VAR figures per risk type,requiring estimating a correlating matrixof size N N only.

Figure 2 is an example of an economiccapital model with common risk factors forall risk categories. The aggregation can ei-ther be based on a direct approach, calcu-lating a total VAR as a correlation of thesingle VAR figures per risk category, usinga heuristic correlation matrix ij, or on a sta-tistical approach, aggregating the key riskfactors to a bank-wide total loss distribu-

Universal bank Non-life insurance Life insurance

MarketCreditOp riskInsurance

1. Average (stylised) economic capital breakdown

1 Not all FIs reached the same level ofsophistication and hence this list can be viewedas a target most models seem to converge to2 The risk of suffering losses due to internal orexternal incidents (see Oliver, Wyman &Company, 2001)3 For a comparison of these methods, seeKoyluoglu & Hickman (1998)

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tion and then taking the VAR. The directapproach is currently the most commonlyused often with the simplification to asimple sum of the individual VAR figures,similar to the Basel II framework. Also, itis usually only market and credit risk andsometimes insurance risk that are modelledby a statistical approach; operational risk isusually modelled by heuristic approaches.

Banks often use a simple correlationmatrix for only three risk categories: cred-it, market and op risk a market average(Oliver, Wyman, 2001) is the matrix:

showing that Level II and III aggregationtogether recognises significant diversifica-tion benefits between credit, market andop risk, unlike the regulatory framework.

The econometric aggregation ap-proach is theoretically profound and canbe statistically accurate, but hard to im-plement, the direct approach is relativelyeasy to implement but is nothing morethan a guesstimate.

=

1 0 8 0 40 8 1 0 40 4 0 4 1

. .

. .

. .

Use of economic capitalAbout 60% of financial institutions (Sarraf,2003) use economic capital for internalrisk reporting, performance measurementand planning/budgeting purposes, butonly about 40% include economic capitalin the pricing of products.

Almost all financial institutions in-cluded in the surveys either already usea Raroc-based performance measure-ment system or intend to implement oneas soon as internal capital modelling iscomplete (Capital Market Risk Advisors,2001). The main driver for Raroc-basedperformance measurement and capitalallocation are investors and sharehold-ers, who seem to reward banks per-forming Raroc-based profitability andallocation disclosure, according to ERisk(2001). Since a bank-wide Raroc capitalallocation based on sophisticated ECmodels allows us to optimise returns ona fixed level of risk, EC can be viewed asthe best tool to find the optimal trade-offbetween the conflicting interests ofshareholders on the one hand, who aretrying to avoid over-capitalisation to op-timise profitability and debt holders andpolicyholders on the other, who fear

under-capitalisation due to the impliedrisk of insolvency.

An important finding in Sarraf (2003)is the fact that more than 90% of the fi-nancial institutions under considerationclearly stated their wish to use their in-ternal credit capital model for regulatorycapital calculations in the future, provid-ed they are sufficiently tested and reliable.Even if regulators and auditors might findgood arguments against such a step, na-tional policy makers will face an increas-ing pressure from the market to allow theuse of internal models for regulatory cap-ital adequacy purposes, since oncethese models are reliable it implies sev-eral advantages for an economy, that is,a fully risk/return efficient capital alloca-tion process and a possible competitiveadvantage over those countries that keepthe old system. However, a convergenceof both regulatory capital models and eco-nomic capital models to one unifiedmodel is not reasonable, since both ap-proaches view risk from a different basis regulatory capital is typically based onthe book value of assets and liabilities,whereas economic capital models (in thestrict sense) focus on an economic value

Common Risk Factors (GDP growth, inflation, interest rates,

indices etc.)

Common risk factors (GDP growth, inflation, interest rates,

indexes etc)

Asset RiskAsset risk Liability RiskLiability risk Operational RiskOperational risk

CreditCredit MarketMarket BusinessBusiness EventEventNon-LifeNon-life LifeLife

V1 V2 V3 V4 V5 V6

Total Economic Capital(Direct Aggregation Approach)

Total economic capital(direct aggregation approach) Total Economic Capital(Statistical Aggregation Approach)

Total economic capital(statistical aggregation approach)

VARijjji

iVVVAR =,

2. Economic capital: statistical versus direct aggregation approach

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of balance sheet items.A comparison of the absolute amounts

of economic capital and regulatory capi-tal across different financial institutionsshown in figure 3 reveals two results (Cap-ital Market Risk Advisors, 2001): On average, the regulatory capitalframework seems to overestimate the fi-nancial risk of banks, because of the ne-glecting of diversification benefitsbetween different risk categories, since allbanks (13%) that reported a higher eco-nomic capital than regulatory capital alsoneglect these benefits in their internalmodel, so their economic capital must beclearly overstated, especially because itincludes various risk types that the regu-latory framework neglects.

The relationship between economiccapital and regulatory capital differs sig-nificantly among different financial insti-tutions for two reasons:i. The Basel regulatory capital frameworkis inconsistent, that is, not risk-sensitive,so the relationship between regulatorycapital and economic capital strongly de-pends on the banks business.ii. There are significant differences be-tween different banks economic capitalmodels.

Figure 3 displays EC versus regulato-ry capital (RC). Banks that reported ahigher EC than RC do not take into ac-count diversification benefits betweendifferent risk categories (simple sum ap-proach see above).

Problems with economic risk capitalA main problem is the fact that apart frommarket risk, where VAR models are wellestablished and a back-testing of the mod-els is straightforward due to a sufficientpool of market data, VAR-type models arenot very well developed for other typesof risk, that is, for credit risk tools such as CreditMetrics or CRisk+ back-testing tech-niques were developed only recently(Granger & Huang, 1997) and an inten-sive back-testing of these methods, whichis absolutely necessary to confirm themodels confidence level, is not as simpledue to the lack of data and the longer timeperiod considered in credit risk. In oper-ational risk and business risk, the devel-

opment of VAR-type models is even fur-ther behind. Hence, it is clear that the ac-curacy of models for the aforementionedrisk types differs considerably.

An important problem is the valua-tion approach that the statistical loss dis-tribution is based on, except for assetsthat are traded on a liquid market witha well-defined market price. For non-traded assets, for example, loans, thereare two different approaches for the cal-culation of economic capital: the mark-to-market approach (for example,CreditMetrics) calculating a marketprice for loans using the yield curve forthe corresponding counterparty ratingand hence including migration and de-fault risk into the EC calculation; and thedefault model (for example CRisk+),using the book value perspective andmodelling default risk only (Saunders,1999). It is arguable as to whether thepure default approach is reasonableunder the economic capital methodolo-gy, since the latter is usually based onan economic perspective. This problemespecially arises when capital adequacyor capital allocation and profitability is-sues are investigated based on econom-ic capital, since the latter relies on aneconomic picture, whereas capital is typ-ically only known from a book valuepoint of view.

A major problem arising when aggre-gating different risk types is the use of anadequate time horizon, which usually dif-fers significantly among different risk cat-egories. For example, for market risk VARcalculations, a time-horizon of one to 10trading days is used, for credit risk andbusiness risk typically one year and for

insurance risk up to 30 years (life insur-ance). Hence, an adequate scaling of thetime-horizon has to be developed, whichis difficult, especially for market risk, sincethe assumption of a constant trading port-folio over a one-year horizon is not real-istic, as traders typically react tomovements in market indexes, for exam-ple when they re-hedge portfolios. Hence,a certain effort is necessary in quantita-tive modelling to take into account the be-haviour of actively managed portfolios.

ConclusionRecent market surveys demonstrate thateconomic capital is evolving into the stan-dard model for a comprehensive and con-sistent monitoring of the financial risks ofa financial institution, avoiding the incon-sistency and incompleteness of the regula-tory capital framework, including Basel II.But the level of sophistication of internalcapital models varies significantly, and cur-rently there seems to be no financial insti-tution that uses a fully statistical aggregationapproach on all levels to explicitly modelall interactions between different risk typeson the basis of a common set of key riskindicators.

A key driver for economic capital be-sides the influence of the regulators isclearly investors, which seem to rewardbanks using risk-adjusted profitability analy-sis. In this sense, a Raroc strategy based oneconomic capital as a risk measure is turn-ing out to be a key weapon for banks abil-ity to compete in financial markets.

Guido Giese is head of market risk man-agement, business advisory services at

KMPG Zurich

Bank for International Settlements, 1996Amendment to the capital Accord toincorporate market risksJanuaryBasel Committee on Banking Supervision, 2002Quantitative impact study 3 technicalguidanceOctoberCapital Market Risk Advisors, 2001Economic capital surveyAvailable at www.cmra.comERisk, 2002Economic capital bank survey methodologyAvailable at www.erisk.comGranger C and L Huang, 1997Evaluation of panel data models: somesuggestions from time-seriesDiscussion paper 97-10, Department ofEconomics, University of California at SanDiegoJoint Forum on FinancialConglomerates, 1999Supervision of financial conglomeratesA collection of papers, February

Koyluoglu H and A Hickman, 1998Reconcilable differencesRisk October 1998, pages 5662Oliver, Wyman & Company, 2001Study on the risk profile and capital adequacyof financial conglomeratesFebruarySarraf H, 2003KPMG European capital survey 2002Credit Risk InternationalSaunders A, 1999Credit risk measurementJohn Wiley & SonsWilde T, 2001IRB approach explainedRisk May 2001, pages 8790Wilson T, 1997Portfolio credit riskRisk September 1997, pages 111117, andOctober 1997, pages 5661

EC significantly less than RCEC less than RCEC equals RCEC higher than RCNo EC calculated

3. Economic capital versus regulatory capital

References