2. VaR and Capital Allocation Eric Falkenstein Senior Vice President - KeyCorp International Association of Financial Engineers September 16, 1998

3. 2 Moving risk measures from reporting to capital estimation brings a heightened degree of relevance VaR measurement can help your bank reduce its capital charge VaR can highlight better Balance Sheet Strategies, though allocating capital is difficult Highlights

4. 3 Ordinal Vs. Cardinal Risk Metrics b It is one thing to numerically estimate risk, another to map this measurement into a dollar amount b Mapping VaR into capital is the first step in taking risk measures from reporting to managing risk The first step in apples-to-apples comparisonThe first step in apples-to-apples comparison

5. 4 One should always be checking various assumptions Usually VaR measures risk on an end-of-day portfolio. Using historical P&Ls, we can refine VaR estimates to adequately capture : Usually VaR measures risk on an end-of-day portfolio. Using historical P&Ls, we can refine VaR estimates to adequately capture : b Intraday trading speculative, not flow tradesspeculative, not flow trades b Peculiar nonlinearities and spreads b Particular liquidity of the trader portfolio

6. 5 Validation is Key b Validation is required for use of VaR as a measure of capital by regulators b Validation also helps one understand the relative importance of various VaR refinements b Each portfolio or trader will have different relevant risk factors and pricing models, and it is the risk manager’s job to find and quantify these risks

7. 6 VaR and Regulatory Capital FDIC, OCC and Federal Reserve all stand behind the Basle Capital Accord b Use 99% 10-day VaR (one tail); greater of previous day or average over the past 90 days Regulatory capital for market risk = VaR x factor factor is the following: Number of exceptionsFactor <=43 53.4 63.5 73.65 83.75 93.85 >=104 Exceptions are the number of times that the P&L loss is greater than the daily 99% VaR in a quarter.

8. 7 b The BIS guidelines suggest estimating capital by using 3 or 4 times the VaR plus Specific Risk b Specific risk is either the Standardized amount or that from internal models (not to be less than 50% of the Standardized amount) VaR and Regulatory Capital

9. 8 The Standardized Regulatory Capital Approach for Specific Risk Capital b 8% against most assets b 1.6% against OECD bank debt b 0% against OECD government debt b 4% against liquid equity portfolio b 2% against equity indexes b apply to both long and short positions

10. 9 Internal Models Calculation of Specific Risk Capital b If no specific credit risk measurement is operational, 4xMVAR b If a model demonstrably isolates spread, event, and default risk, 3xSVAR b If a model can capture some but not all of specific risk, 4xSVAR

11. 10 Standardized Vs. Internal Models b For individual security holdings, the standardized regulatory approach allocates allocates less capital for speculative grade bonds and equities b For portfolios, the internal models approach generates lower capital requirements b The BIS has therefore created an employment program for quants

12. 11 bUse 99% VaR over reasonable and flexible time-to-close assumption bTake into account dynamic strategies in the form of loss limits Think of an unused loan commitment: One translates this into a Loan Equivalent Exposure, taking into account the probability of being used in the future. Example: Trader A VaRLoss Limit $45 $120 Capital=VaR+VaR Equivalent Unused Commitment Capital=VaR+factor(Loss Limit - VaR) Capital=$45+.5*(120-45)=$82.5 Economic Risk Capital

13. 12 bHow does one allocate while accounting for diversification? Example: VaRVaR-Equivalent Stand-Alone Unused Commitment Capital Trader A$42 $26 $68 Trader B$23 $13 $36 Total$50 ? ? bHow does one allocate while accounting for diversification? Example: VaRVaR-Equivalent Stand-Alone Unused Commitment Capital Trader A$42 $26 $68 Trader B$23 $13 $36 Total$50 ? ? bWe will suppose the total VaR-Equivalent Unused Commitment is reduced similar to the VaR: 50/(42+23)=.77 Total VaR is 77% the sum of the parts Stand-Alone Capital Allocated Capital Trader A $68 $52(=68x.77) Trader B $36 $28(=36x.77) Total $80 Loss Limit Risk is Diversifiable Too

14. 13 Key Point b Unused trading authority necessitates risk capital. VaR calculation alone will miss this. b If a trader doesn’t like this charge, they can have their limits reduced

15. 14 Important Notes b Using VaR and Loss Limits and tying this to a capital charge explicitly incents traders to minimize risk by both lowering their daily VaR and loss limits. b Economic capital different than VaR used in regulatory reporting. It is much more forward looking, in that it takes into account a trader’s discretionary capabilities.

16. 15 Adding Accountability to the Mix Capital charges are an incomplete ex ante incentive. Holding people accountable ex poste is a useful way to minimize operating risk. Capital charges are an incomplete ex ante incentive. Holding people accountable ex poste is a useful way to minimize operating risk. If a trader blows by their loss limit,assuming a truly unforeseeable event did not occur (e.g., October 19, 1987, other 0.1% events), culpability resides in 2 places: If a trader blows by their loss limit,assuming a truly unforeseeable event did not occur (e.g., October 19, 1987, other 0.1% events), culpability resides in 2 places: b Risk Managers b The Trader’s Manager Risk managers should only be held accountable for items they sign off on. they sign off on.

17. 16 Integrating Regulatory and Economic Capital b Case 1 Regulatory Capital = Economic Capital No problem b Case 2 Regulatory Capital < Economic Capital Not clear how to charge for regulatory vs. economic capital, since the fact that regulatory capital can bind tomorrow makes it relevant today b Case 3 Economic Capital < Regulatory Capital Suboptimal, should take more risk

18. 17 Regulatory and Economic Requirements Affect Capital Costs b Credit spreads by rating and issuer type Sovereign Bank Corporate Sovereign Bank Corporate AAA-2bp+2bp+10bp AA 0+5bp+15bp A+5bp+12bp+22bp

19. 18 Return on Equity b Most successful traders generate exceedingly high ROEs. b Nonetheless, ROE is a useful performance measure, especially for new traders (e.g., writing calls on the S&P would have been very profitable over many consecutive months, yet on an ROE basis would have been very weak) b P&L still reigns supreme in performance measurement, and is essential for validation. Risk managers need to know a trader’s P&L and their incentive compensation plan.

20. 19 2 Ways that Bad Traders are Exposed b Blow out. A quiescent market can allow a negative NPV strategy to produce seemingly large returns with low risk for many consecutive months (e.g., Orange County). b Profit drip. A trader might have very low risk, yet have locked in a negative carry (e.g., Joseph Jett at Kidder). Ô In both cases, accurate monthly P&L helps highlight these problems, though the former is usually more painful.

21. 20 What can we Learn from These? First ReportedCompany Estimated loss (millions) 11/92Dell$8 2/93Showa Shell$1,700 7/93Nippon Steel$128 1/94Metallgesellschaft$1,300 1/94Codelco$200 3/94Askin Capital Management$600 3/94Minnetonka Fund/Cargill$100 4/94Mead Corp$7 4/94Procter & Gamble$157 4/94Gibson Greetings$23 5/94Air Products$69 5/94ARCO$22 6/94Dell$35 6/94Virginia Retirement System$66 6/94Florida Treasurer's Office$175 6/94Pain Webber Mutual Fund$33 7/94Glaxo Holdings$100 7/94CS First Boston Inv't Mgt.$40 8/94Piper Jaffray$700 8/94Charles County$2 First ReportedCompanyEstimated loss (millions) 8/94Colonia (Germany)$76 9/94Shoshone Indians$5 9/94Investors Equity Life$90 9/94Odessa College TX$11 10/94Community A Mgmt.$44 10/94Portage County OH$8 10/94Sears$237 11/94Todyo Securities Co.$356 11/943 Farm Credit Banks$23 12/94Orange County CA$1,700 12/94Chemica Bank$70 2/95Barings$1,200 3/95Wisconsin Inv. Board$95 3/95MCN Corp$10 5/95Morgan Stanley clients$28 7/95First Capital Strategists$137 8/95Postipankki (Finland)$110 10/95Daiwa $1,100

22. 21 Asset and Liability VaR b A Balance Sheet Management department has a different risk profile than a trader, as A&L trading horizons are typically 3 months to 1 year in duration b Accounting measures of risk are the industry norm b Deposits will not be marked-to-market anytime soon, making VaR more abstract than accounting risk measures

23. 22 Balance Sheet VaR b Like trading risk, capital should be allocated against the current risk profile, plus a portion of the maximum feasible risk exposure under corporate policy b Often duration limits of 1 or 5 years act as the maximum interest rate risk limit

24. 23 Main Risk Factors b 3 Factors of Yield Curve risk (shift, twist, curvature) b Spread risk b Prepayment risk b Parameter uncertainty

25. 24 Benchmarks for BSM VaR b Call Reports are not very informative b Most banks have a duration between 1 and 5 years b When is a noisy VaR worse than an accounting measure of Risk?

26. 25 Do Banks Have a Comparative Advantage in Riding the Yield Curve? b ROE must be greater than cost of equity capital, or, an agency problem exists b The answer is probably a little of both

27. 26 An Application of BSM VaR b The average return of short funding a long maturity bond is positive, as the yield curve is usually upward sloping b The Sharpe ratio of this risk-return relationship can help one see the relative attractiveness of this strategy b With derivatives one can see how to optimize a common, simply strategy

28. 27 1 5 10 20 4 5 6 7 8 Yield Curve Review MATURITY YIELD (%) RISK PREMIUM EXPECTED YIELD

29. 28 Returns to Riding the Yield Curve

30. 29 1/83-7/98 Performance Return from being long the specific maturity, and short a 6 month security, in basis points 1yr3yr5yr10yr30yr Avg. Return36121209300438 Avg. Volatility73161423601876 Sharpe Ratio.49.75.49.50.50

31. 30 Replicating the 30 Year Risk, using a 3 Year Bond, in a Zero-cost Strategic Alternative

32. 31 Applications are Important b Wholesale replacement of accounting based measures of Balance Sheet risk will not occur soon b Tying Balance Sheet VaR to Capital used in an ROE is an unsolved issue b In the meantime, piecemeal applications of VaR to balance sheet management strategies are quite fruitful

33. 32 Conclusion b Capital allows a VaR manager to take their numbers to a higher degree of relevance b Regulatory capital also is of interest, and to avoid marginalization one should learn these rules b The lack of mark to market accounting makes estimating VaR for the Balance Sheet difficult for both political and statistical reasons. Stick to isolated applications.