VaR and Capital VaR and Capital AllocationAllocation

Eric FalkensteinEric Falkenstein

Senior Vice President - KeyCorpSenior Vice President - KeyCorp

International Association of Financial International Association of Financial Engineers Engineers

September 16, 1998 September 16, 1998

2

Moving risk measures from Moving risk measures from reportingreporting to to capital estimationcapital estimation brings a brings a heightened degree of relevanceheightened degree of relevance

VaR measurement can help your VaR measurement can help your bank reduce its capital chargebank reduce its capital charge

VaR can highlight better Balance VaR can highlight better Balance Sheet Strategies, though allocating Sheet Strategies, though allocating capital is difficultcapital is difficult

HighlightsHighlights

3

Ordinal Vs. Cardinal Risk MetricsOrdinal Vs. Cardinal Risk Metrics

It is one thing to numerically estimate It is one thing to numerically estimate risk, another to map this measurement risk, another to map this measurement into a dollar amountinto a dollar amount

Mapping VaR into capital is the first step Mapping VaR into capital is the first step in taking risk measures from reporting in taking risk measures from reporting to managing riskto managing risk• The first step in apples-to-apples The first step in apples-to-apples

comparisoncomparison

4

One should always be checking One should always be checking various assumptionsvarious assumptions

Usually VaR measures risk on an end-Usually VaR measures risk on an end-of-day portfolio. Using historical P&Ls, of-day portfolio. Using historical P&Ls, we can refine VaR estimates to we can refine VaR estimates to adequately capture :adequately capture :

Intraday tradingIntraday trading• speculative, not flow tradesspeculative, not flow trades

Peculiar nonlinearities and spreadsPeculiar nonlinearities and spreads Particular liquidity of the trader portfolioParticular liquidity of the trader portfolio

5

Validation is KeyValidation is Key

Validation is required for use of VaR as a Validation is required for use of VaR as a measure of capital by regulatorsmeasure of capital by regulators

Validation also helps one understand the Validation also helps one understand the relative importance of various VaR refinementsrelative importance of various VaR refinements

Each portfolio or trader will have different Each portfolio or trader will have different relevant risk factors and pricing models, and it relevant risk factors and pricing models, and it is the risk manager’s job to find and quantify is the risk manager’s job to find and quantify these risksthese risks

6

VaR and Regulatory CapitalVaR and Regulatory Capital

FDIC, OCC and Federal Reserve all stand behind the Basle FDIC, OCC and Federal Reserve all stand behind the Basle Capital AccordCapital Accord

Use 99% 10-day VaR (one tail); greater of previous day or Use 99% 10-day VaR (one tail); greater of previous day or average over the past 90 daysaverage over the past 90 days

Regulatory capital for market risk = VaR x Regulatory capital for market risk = VaR x factorfactor

factorfactor is the following: is the following:Number of exceptionsNumber of exceptions FactorFactor<=4<=4 3355 3.43.466 3.53.577 3.653.6588 3.753.7599 3.853.85>=10>=10 44

Exceptions are the number of times that the P&L loss is greater Exceptions are the number of times that the P&L loss is greater than the than the

daily daily 99% VaR in a quarter.99% VaR in a quarter.

7

The BIS guidelines suggest estimating The BIS guidelines suggest estimating capital by using 3 or 4 times the VaR capital by using 3 or 4 times the VaR plusplus Specific Risk Specific Risk

Specific risk is either the Standardized Specific risk is either the Standardized amount or that from internal models amount or that from internal models (not to be less than 50% of the (not to be less than 50% of the Standardized amount)Standardized amount)

VaR and Regulatory CapitalVaR and Regulatory Capital

8

The Standardized Regulatory Capital The Standardized Regulatory Capital Approach for Specific Risk CapitalApproach for Specific Risk Capital

8% against most assets8% against most assets 1.6% against OECD bank debt1.6% against OECD bank debt 0% against OECD government debt0% against OECD government debt 4% against liquid equity portfolio4% against liquid equity portfolio 2% against equity indexes2% against equity indexes apply to both long and short positionsapply to both long and short positions

9

Internal Models Calculation of Internal Models Calculation of Specific Risk CapitalSpecific Risk Capital

If no specific credit risk measurement is If no specific credit risk measurement is operational, 4xMVARoperational, 4xMVAR

If a model demonstrably isolates If a model demonstrably isolates spread, event, and default risk, 3xSVARspread, event, and default risk, 3xSVAR

If a model can capture some but not all If a model can capture some but not all of specific risk, 4xSVARof specific risk, 4xSVAR

10

Standardized Vs. Internal ModelsStandardized Vs. Internal Models

For For individualindividual security holdings, the security holdings, the standardized regulatory approach allocates standardized regulatory approach allocates allocates less capital for speculative grade allocates less capital for speculative grade bonds and equitiesbonds and equities

For portfolios, the internal models approach For portfolios, the internal models approach generates lower capital requirementsgenerates lower capital requirements

The BIS has therefore created an The BIS has therefore created an employment program for quantsemployment program for quants

11

Use 99% VaR over reasonable and flexible time-to-close Use 99% VaR over reasonable and flexible time-to-close assumption assumption

Take into account dynamic strategies in the form of loss Take into account dynamic strategies in the form of loss limitslimitsThink of an unused loan commitment: Think of an unused loan commitment:

One translates this into a One translates this into a Loan Equivalent ExposureLoan Equivalent Exposure, , taking into account the probability of being used in the taking into account the probability of being used in the future.future.Example:Example: Trader A Trader A VaRVaR Loss LimitLoss Limit

$45$45 $120 $120

Capital=VaR+Capital=VaR+VaR Equivalent Unused CommitmentVaR Equivalent Unused CommitmentCapital=VaR+factor(Loss Limit - VaR)Capital=VaR+factor(Loss Limit - VaR)Capital=$45+.5*(120-45)=$82.5Capital=$45+.5*(120-45)=$82.5

Economic Risk Economic Risk CapitalCapital

12

How does one allocate while accounting for diversification?How does one allocate while accounting for diversification?Example: Example: VaR VaR VaR-Equivalent VaR-Equivalent Stand-Alone Stand-Alone Unused Commitment Unused Commitment Capital Capital

Trader ATrader A $42 $26$42 $26 $68 $68Trader BTrader B $23$23 $13 $13 $36$36TotalTotal $50$50 ? ? ? ?

We will suppose the total We will suppose the total VaR-Equivalent Unused Commitment VaR-Equivalent Unused Commitment is reduced similar to the VaR: is reduced similar to the VaR: 50/(42+23)=.77 50/(42+23)=.77 Total VaR is 77% the sum of Total VaR is 77% the sum of the partsthe parts

Stand-Alone Capital Allocated CapitalStand-Alone Capital Allocated CapitalTrader ATrader A $68 $68 $52(=68x.77) $52(=68x.77)Trader BTrader B $36 $36 $28(=36x.77) $28(=36x.77) Total Total $80 $80

Loss Limit Risk is Loss Limit Risk is Diversifiable TooDiversifiable Too

13

Key PointKey Point

Unused trading authority necessitates Unused trading authority necessitates risk capital. VaR calculation alone will risk capital. VaR calculation alone will miss this.miss this.

If a trader doesn’t like this charge, they If a trader doesn’t like this charge, they can have their limits reducedcan have their limits reduced

14

Important NotesImportant Notes

Using VaR and Loss Limits and tying this Using VaR and Loss Limits and tying this to a capital charge explicitly incents to a capital charge explicitly incents traders to minimize risk by both lowering traders to minimize risk by both lowering their daily VaR and loss limits.their daily VaR and loss limits.

Economic capital different than VaR used Economic capital different than VaR used in regulatory reporting. It is much more in regulatory reporting. It is much more forward looking, in that it takes into forward looking, in that it takes into account a trader’s discretionary account a trader’s discretionary capabilities. capabilities.

15

Adding Accountability to the MixAdding Accountability to the Mix

Capital charges are an incompleteCapital charges are an incomplete ex ante ex ante incentive. incentive. Holding people accountable Holding people accountable ex posteex poste is a useful way to is a useful way to minimize operating risk. minimize operating risk.

If a trader blows by their loss limit,assuming a truly If a trader blows by their loss limit,assuming a truly unforeseeable event did not occur (e.g., October 19, unforeseeable event did not occur (e.g., October 19, 1987, other 0.1% events), culpability resides in 2 places:1987, other 0.1% events), culpability resides in 2 places:

Risk ManagersRisk Managers

The Trader’s ManagerThe Trader’s Manager

Risk managers should only be held accountable for items Risk managers should only be held accountable for items they sign off on.they sign off on.

16

Integrating Regulatory and Integrating Regulatory and Economic CapitalEconomic Capital

Case 1Case 1Regulatory Capital = Economic CapitalRegulatory Capital = Economic CapitalNo problemNo problem

Case 2Case 2Regulatory Capital < Economic CapitalRegulatory Capital < Economic CapitalNot clear how to charge for regulatory vs. Not clear how to charge for regulatory vs. economic capital, since the fact that economic capital, since the fact that regulatory capital can bind tomorrow makes it regulatory capital can bind tomorrow makes it relevant todayrelevant today

Case 3Case 3Economic Capital < Regulatory CapitalEconomic Capital < Regulatory CapitalSuboptimal, should take more riskSuboptimal, should take more risk

17

Regulatory Regulatory andand Economic Economic Requirements Affect Capital CostsRequirements Affect Capital Costs

Credit spreads by rating and issuer typeCredit spreads by rating and issuer type

Sovereign Sovereign BankBank Corporate Corporate

AAAAAA -2bp-2bp +2bp+2bp +10bp+10bp

AAAA 0 0 +5bp+5bp +15bp+15bp

AA +5bp+5bp +12bp+12bp+22bp+22bp

18

Return on EquityReturn on Equity

Most successful traders generate exceedingly high ROEs. Most successful traders generate exceedingly high ROEs.

Nonetheless, ROE is a useful performance measure, Nonetheless, ROE is a useful performance measure, especially for new traders (e.g., writing calls on the S&P especially for new traders (e.g., writing calls on the S&P would have been very profitable over many consecutive would have been very profitable over many consecutive months, yet on an ROE basis would have been very weak)months, yet on an ROE basis would have been very weak)

P&L still reigns supreme in performance measurement, P&L still reigns supreme in performance measurement, and is essential for validation. Risk managers need to and is essential for validation. Risk managers need to know a trader’s P&L and their incentive compensation know a trader’s P&L and their incentive compensation plan.plan.

19

2 Ways that Bad Traders2 Ways that Bad Tradersare Exposedare Exposed

Blow out. A quiescent market can allow a negative Blow out. A quiescent market can allow a negative NPV strategy to produce seemingly large returns NPV strategy to produce seemingly large returns with low risk for many consecutive months (e.g., with low risk for many consecutive months (e.g., Orange County).Orange County).

Profit drip. A trader might have very low risk, yet Profit drip. A trader might have very low risk, yet have locked in a negative carry (e.g., Joseph Jett at have locked in a negative carry (e.g., Joseph Jett at Kidder).Kidder).

In both cases, accurate monthly P&L In both cases, accurate monthly P&L helps highlight these problems, though helps highlight these problems, though the former is usually more painful.the former is usually more painful.

20

What can we Learn from What can we Learn from These?These?FirstReported Company Estimated loss (millions)11/92 Dell $82/93Showa Shell $1,7007/93Nippon Steel $1281/94Metallgesellschaft $1,3001/94Codelco $2003/94Askin Capital Management $6003/94Minnetonka Fund/Cargill $1004/94Mead Corp $74/94Procter & Gamble $1574/94Gibson Greetings $235/94Air Products $695/94ARCO $226/94Dell $356/94Virginia Retirement System $666/94Florida Treasurer's Office $1756/94Pain Webber Mutual Fund $337/94Glaxo Holdings $1007/94CS First Boston Inv't Mgt. $408/94Piper Jaffray $7008/94Charles County $2

FirstReported Company Estimated loss (millions)8/94 Colonia (Germany) $769/94 Shoshone Indians $59/94 Investors Equity Life $909/94 Odessa College TX $1110/94 Community A Mgmt. $4410/94 Portage County OH $810/94 Sears $23711/94 Todyo Securities Co. $35611/94 3 Farm Credit Banks $2312/94 Orange County CA $1,70012/94 Chemica Bank $702/95 Barings $1,2003/95 Wisconsin Inv. Board $953/95 MCN Corp $105/95 Morgan Stanley clients $287/95 First Capital Strategists $1378/95 Postipankki (Finland) $11010/95 Daiwa $1,100

21

Asset and Liability VaRAsset and Liability VaR

A Balance Sheet Management department A Balance Sheet Management department has a different risk profile than a trader, has a different risk profile than a trader, as A&L trading horizons are typically 3 as A&L trading horizons are typically 3 months to 1 year in durationmonths to 1 year in duration

Accounting measures of risk are the Accounting measures of risk are the industry normindustry norm

Deposits will not be marked-to-market Deposits will not be marked-to-market anytime soon, making VaR more abstract anytime soon, making VaR more abstract than accounting risk measuresthan accounting risk measures

22

Balance Sheet VaRBalance Sheet VaR

Like trading risk, capital should be Like trading risk, capital should be allocated against the current risk allocated against the current risk profile, plus a portion of the maximum profile, plus a portion of the maximum feasible risk exposure under corporate feasible risk exposure under corporate policypolicy

Often duration limits of 1 or 5 years act Often duration limits of 1 or 5 years act as the maximum interest rate risk limitas the maximum interest rate risk limit

23

Main Risk FactorsMain Risk Factors

3 Factors of Yield Curve risk (shift, 3 Factors of Yield Curve risk (shift, twist, curvature)twist, curvature)

Spread riskSpread risk

Prepayment riskPrepayment risk

Parameter uncertaintyParameter uncertainty

24

Benchmarks for BSM VaRBenchmarks for BSM VaR

Call Reports are not very informativeCall Reports are not very informative

Most banks have a duration between 1 Most banks have a duration between 1 and 5 yearsand 5 years

When is a noisy VaR worse than an When is a noisy VaR worse than an accounting measure of Risk?accounting measure of Risk?

25

Do Banks Have a ComparativeDo Banks Have a ComparativeAdvantage in Riding the Yield Curve?Advantage in Riding the Yield Curve?

ROE must be greater than cost of equity ROE must be greater than cost of equity capital, or, an agency problem existscapital, or, an agency problem exists

The answer is probably a little of bothThe answer is probably a little of both

26

An Application of BSM VaRAn Application of BSM VaR

The average return of short funding a long The average return of short funding a long maturity bond is positive, as the yield curve maturity bond is positive, as the yield curve is usually upward slopingis usually upward sloping

The Sharpe ratio of this risk-return The Sharpe ratio of this risk-return relationship can help one see the relative relationship can help one see the relative attractiveness of this strategyattractiveness of this strategy

With derivatives one can see how to With derivatives one can see how to optimize a common, simply strategyoptimize a common, simply strategy

27

1 5 10 20

4

5

6

7

8

Yield Curve ReviewYield Curve Review

MATURITY

YIE

LD

(%

) RISKPREMIUM

EXPECTEDYIELD

28

Returns to Riding the Yield Returns to Riding the Yield CurveCurve

29

1/83-7/98 Performance1/83-7/98 Performance

Return from being long the specific Return from being long the specific maturity, maturity,

and short a 6 month security, in basis and short a 6 month security, in basis pointspoints

1yr1yr 3yr3yr 5yr5yr 10yr10yr 30yr30yr

Avg. ReturnAvg. Return 3636 121121 209209 300300 438438

Avg. VolatilityAvg. Volatility 7373 161161 423423 601601 876876

Sharpe RatioSharpe Ratio .49.49 .75.75 .49.49 .50.50 .50.50

30

Replicating the 30 Year Risk, using a 3 Year Replicating the 30 Year Risk, using a 3 Year Bond, in a Bond, in a Zero-cost Strategic AlternativeZero-cost Strategic Alternative

31

Applications are ImportantApplications are Important

Wholesale replacement of accounting based Wholesale replacement of accounting based measures of Balance Sheet risk will not occur measures of Balance Sheet risk will not occur soonsoon

Tying Balance Sheet VaR to Capital used in Tying Balance Sheet VaR to Capital used in an ROE is an unsolved issuean ROE is an unsolved issue

In the meantime, piecemeal applications of In the meantime, piecemeal applications of VaR to balance sheet management VaR to balance sheet management strategies are quite fruitfulstrategies are quite fruitful

32

ConclusionConclusion

Capital allows a VaR manager to take their Capital allows a VaR manager to take their numbers to a higher degree of relevancenumbers to a higher degree of relevance

Regulatory capital also is of interest, and to Regulatory capital also is of interest, and to avoid marginalization one should learn these avoid marginalization one should learn these rulesrules

The lack of mark to market accounting makes The lack of mark to market accounting makes estimating VaR for the Balance Sheet difficult for estimating VaR for the Balance Sheet difficult for both political and statistical reasons. Stick to both political and statistical reasons. Stick to isolated applications.isolated applications.