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Value at Risk and Market Risk Eric Falkenstein

Value at Risk and Market Risk Eric Falkenstein. VaR: The Big Picture. VaR is the new standard for measuring market risk across a Variety of security types VaR should always be complimented with specific scenario tests

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Value at Risk and Market Risk Eric Falkenstein

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  1. Value at Risk and Market RiskEric Falkenstein

  2. VaR: The Big Picture • VaR is the new standard for measuring market risk across a Variety of security types • VaR should always be complimented with specific scenario tests • VaR is integral in any attempt to allocate capital (for both economic and proposed regulatory charges) Eric Falkenstein 4/14/99

  3. Subtle Benefits of a VAR System • Necessitates the ability to mark a book to market, which by itself is a major preventative against unpleasant surprises • Establishes a clear independent risk monitoring arm • Helps with existing auditing and risk reviews • Securities that are not understood well and therefore have a significant risk are flagged as exceptions more often • If used for capital charge, gives an incentive to economize on risk even when risk limits are not breached Eric Falkenstein 4/14/99

  4. What Can We Learn From These? Eric Falkenstein 4/14/99

  5. VaR is the Best Market Risk Metric • Do not compare VaR to a Platonic ideal, but to feasible alternatives • Most importantly, by measuring VaR more precisely, the right questions get asked which minimizes “operating risk” • While VaR won’t catch the next Baring’s, one can also bet that the next Baring’s won’t have a fully operational VaR risk measurement system in place Eric Falkenstein 4/14/99

  6. What Did We Have Before VaR? Duration • Duration has a practical application in the measurement of a bond’s risk % Change in Price = Duration x Change in Yield • Given a parallel shift in yields, we can know how different securities will react example: • A bond with a duration of 5 years will experience a 0.35% change in price if rates rise 7 basis points (5*.07) Eric Falkenstein 4/14/99

  7. Problems with Duration • Duration measures the risk from parallel shifts in rates; rates do not always move in parallel • Not applicable to FX • Not informative for securities with significant option characteristics (e.g., mortgages, caps/floors, callable bonds) • Does not capture risk from changes in credit spreads Eric Falkenstein 4/14/99

  8. Problem 2: How do you Measure theRisk of This Portfolio? Security Notional Bonds $ 50 Interest Rate Swaps $100 Interest Rate Futures Contracts $150 Caps/Floors $ 45 FX Forwards $130 Total $475 Aggregate Notional is not meaningful in this context Eric Falkenstein 4/14/99

  9. Problem 3: Judgement Expert systems: we should have someone knowledgeable at the helm who can “know” what is happening. Problem: how do you aggregate a bunch of expert opinions? How do you validate them? Eric Falkenstein 4/14/99

  10. VaR Can Give a MeaningfulAggregate Number Security Notional VaR Bonds $100 $ 3 Interest Rate Swaps $100 $ 5 Interest Rate Futures Contracts $100 $ 4 Caps/Floors $100 $ 4 FX Forwards $100 $ 7 Total $11 Eric Falkenstein 4/14/99

  11. So What is VaR? • Assume you had a portfolio that consisted, trivially, of the 30 year Tbond. Your daily P/L would look like this: Eric Falkenstein 4/14/99

  12. So What is VaR? • Converting this information into a histogram, we get: Eric Falkenstein 4/14/99

  13. In Words • VaR is the expected least amount lost 5% of the time or, • VaR is the expected most amount lost 95% of the time • In both of the above examples, you could use a 99% VaR or any other number, and also use different time horizons (e.g., 95% lost over daily observations, or annual observations) • VaR takes into account current estimates of the volatility of various fundamental factors (e.g., on-the-run US Treasury rates) and their covariances (especially important when looking at a hedged portfolios) Eric Falkenstein 4/14/99

  14. VaR: One Factor Example • $1MM 30yr Bond’s DV01=$1400 • Standard Deviation of 30yr bond=4.5 b.p.s Eric Falkenstein 4/14/99

  15. VaR: 2 Factors • Portfolio is $1MM 30yr bond 5yr Key Rate DV01=$100 30yr Key Rate DV01=$1300 Eric Falkenstein 4/14/99

  16. In General • Calculate all portfolio sensitivities to material risk factors at 95% level • Aggregate them taking into account correlations S=an nx1 vector of a portfolio’s change in value to a 95% worst-case scenario change in the n underlying factors =correlation matrix example: • Rate Risk for Bond Option Trading=$86,216 • Volatility Risk for Bond Option Trading=$48,406 • Assume the correlation of those risks is zero Eric Falkenstein 4/14/99

  17. Revaluation Approach forNonlinear Instruments • Replace 1.65 with the calculated  in the value of the derivative for a 1.65 change in the underlying risk factor: Eric Falkenstein 4/14/99

  18. Further Refinements • Which volatilities to use? Examples: moving average, exponential moving average, GARCH, and implied volatilities from options • If a Revaluation approach--Monte Carlo or Historical? • Do you incorporate spread shocks (e.g., Fed Funds-Libor spread)? • Do you incorporate volatility shocks (e.g., cap vols rise)? Always weigh benefits versus costs of implementation Eric Falkenstein 4/14/99

  19. Criticisms of VaR • If refinements are not addressed, VaR could be a poor representation of risk (e.g., using delta-normal VaR for a book with significant spread risk and optionality) • Solutions are within the VaR paradigm • Any good tool needs to be used wisely to add value Eric Falkenstein 4/14/99

  20. Always Compliment with Stress Tests VaR Up 35 bp Down 35 bp Portfolio $6.0M -$26.2M $25.8M • VaR tells you how muchyou lose with a known probability, but with an unknown scenario • Stress tests tell you how muchyou lose in a known scenario, but with an unknown probability Eric Falkenstein 4/14/99

  21. Combine VaR with Stress Tests to get the Complete Picture VaR Gives best estimate of worst-case P&L Robust Risk Measurement Stress Tests 1) User defined scenarios 2) Shows where portfolio loses money 3) Anticipates “non-normal” events Eric Falkenstein 4/14/99

  22. 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: • Intraday trading • Peculiar nonlinearities and spreads • Particular liquidity of the trader portfolio Eric Falkenstein 4/14/99

  23. Validation is Key • Validation is required for use of VaR as a measure of capital • Validation also helps one understand the relative importance of various VaR refinements • 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 Eric Falkenstein 4/14/99

  24. Backtesting • BACKTESTING TYPE 1 • A test of the validity of the simulation method. • A daily comparison of: • EX-ANTE VAR vs. EX-POST HYPOTHETICAL P & L • BACKTESTING TYPE 2 • A test of the “goodness” of VAR as a predictor of worst case P/L loss in trading • A daily comparison of: • EX-ANTE VAR 99% Confidence Level vs. EX-POST ACTUAL P&L • Under BIS rules, • Multiplicative factor (“K”) depends on number of excesses in one year, where excess means that on a given day: • ACTUAL P/L LOSS > VAR 99% C.L. Eric Falkenstein 4/14/99

  25. Regulatory Capital Eric Falkenstein 4/14/99

  26. Regulatory Capital FOR GENERAL MARKET RISK - CAPITAL BIS = K * VAR BIS_GENERAL K DEPENDS ON BACKTESTING factor is the following: Number of exceptions Factor <=4 3 5 3.4 6 3.5 7 3.65 8 3.75 9 3.85 >=10 4 - PARAMETERS FOR VAR BIS • OBSERVATION PERIOD FOR SIMULATION: • AT LEAST ONE YEAR • HOLDING PERIOD • ONE DAY I.e., assume static portfolio • CONFIDENCE LEVEL: • 10-DAY “INSTANTANEOUS” SHOCK IN MARKET RATES • 99% CONFIDENCE LEVEL Eric Falkenstein 4/14/99

  27. Regulatory Capital • FOR GENERAL MARKET RISK AND SPECIFIC MARKET RISK: • IF FULLY CAPTURE SPECIFIC RISK • Correlation Risk • Event Risk • THEN:REGULATORY CAPITAL BIS = K * VAR BIS_TOTAL • K DEPENDS ON BACKTESTING • IF ONLY CAPTURE CORRELATION RISKTHEN:REGULATORY CAPITAL BIS = K * VAR BIS_TOTAL + VAR BIS_SPECIFICK DEPENDS ON BACKTESTING Eric Falkenstein 4/14/99

  28. VaR and Regulatory Capital • The BIS guidelines suggest estimating capital by using 3 or 4 times the VaR plus Specific Risk • Specific risk is either the Standardized amount or that from internal models (not to be less than 50% of the Standardized amount) Eric Falkenstein 4/14/99

  29. The Standardized Regulatory Capital Approach for Specific Risk Capital • 8% against most assets • 1.6% against OECD bank debt • 0% against OECD government debt • 4% against liquid equity portfolio • 2% against equity indexes • apply to both long and short positions Eric Falkenstein 4/14/99

  30. Internal Models Calculation of Specific Risk Capital • If no specific credit risk measurement is operational, 4xMVAR • If a model demonstrably isolates spread, event, and default risk, 3xSVAR • If a model can capture some but not all of specific risk, 4xSVAR Eric Falkenstein 4/14/99

  31. Standardized Vs. Internal Models • For individual security holdings, the standardized regulatory approach allocates less capital for speculative grade bonds and equities • For portfolios, the internal models approach generates lower capital requirements • The BIS has therefore created an employment program for quants Eric Falkenstein 4/14/99

  32. Economic Risk Capital (Not Regulatory) • Use 99% VaR over reasonable and flexible time-to-close assumption • Take into account dynamic strategies in the form of loss limitsThink 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 VaR Loss Limit $45 $120Capital=VaR+VaR Equivalent Unused CommitmentCapital=VaR+factor(Loss Limit - VaR)Capital=$45+.5*(120-45)=$82.5 Eric Falkenstein 4/14/99

  33. Economic Risk Capital A loss limit over the VaR is an unused commitment. Thus, one must translate this into a VaR-equivalent exposureExample: Trader A 99%VaR Loss Limit $45 $120 Capital=VaR+factor(Loss Limit - VaR) Capital=$45+.5*(120-45)=$60 Eric Falkenstein 4/14/99

  34. Loss Limit Risk is Diversifiable Too • How does one allocate while accounting for diversification?Example: VaR VaR-Equivalent Stand-Alone Unused Commitment CapitalTrader A $42 $26 $68Trader B $23 $13 $36Total $50 ? ? • We 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 CapitalTrader A $68 $52(=68x.77)Trader B $36 $28(=36x.77) Total $80 Eric Falkenstein 4/14/99

  35. Important Notes • 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 • Economic capital different than VaR used in regulatory reporting Eric Falkenstein 4/14/99

  36. Integrating Regulatory and Economic Capital • Case 1Regulatory Capital = Economic CapitalNo problem • Case 2Regulatory Capital < Economic CapitalAllocate Economic capital, since economic capital is the binding constraint • Case 3 Regulatory Capital > Economic Capital Not clear Eric Falkenstein 4/14/99

  37. Return on Equity • Most successful traders generate exceedingly high ROEs. • 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) • 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. Eric Falkenstein 4/14/99

  38. 2 Ways that Bad Tradersare Exposed • 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) • Profit drip. A trader might have very low risk, yet have locked in a negative carry through poor pricing • In both cases, accurate monthly P&L helps highlight these problems Eric Falkenstein 4/14/99

  39. Asset and Liability VaR • A Balance Sheet Management department has a different risk profile than a trader, as trading horizons are typically 3 months to 1 year in duration • Accounting measures of risk are the industry norm • Deposits will not be marked-to-market anytime soon, making VaR more abstract than accounting risk measures Eric Falkenstein 4/14/99

  40. Balance Sheet VaR • Like trading risk, capital should be allocated against the current risk profile, plus a portion of the maximum feasible risk exposure under corporate policy • Often duration limits of 1 or 5 years act as the maximum interest rate risk limit Eric Falkenstein 4/14/99

  41. Incorporate Other Risk Factors • 3 Factors of Yield Curve risk (shift, twist, curvature) • Spread risk • Prepayment risk • Parameter uncertainty Eric Falkenstein 4/14/99

  42. Benchmarks for BSM VaR • Call Reports are not very informative • Most banks have duration between 1 and 5 years • When is a noisy VaR worse than an accounting measure of Risk? Eric Falkenstein 4/14/99

  43. Do Banks Have a ComparativeAdvantage in Riding the Yield Curve? • Average duration of 3-5 years • Sharpe ratio of 1.5 • ROE must be greater than cost of equity capital, or, agency problem • The answer is probably a little of both Eric Falkenstein 4/14/99

  44. An Application of BSM VaR • The average return of short funding a long maturity bond is positive, as the yield curve is usually upward sloping • The Sharpe ratio of this risk-return relationship can help one see the relative attractiveness of this strategy • With derivatives one can see how to optimize a common, simply strategy Eric Falkenstein 4/14/99

  45. Yield Curve 8 7 RISK PREMIUM 6 YIELD (%) 5 EXPECTED YIELD 4 1 5 10 20 MATURITY Eric Falkenstein 4/14/99

  46. Returns to Riding the Yield Curve Eric Falkenstein 4/14/99

  47. 1/83-7/98 Performance Return from being long the specific maturity, and short a 6 month security, in basis points 1yr 3yr 5yr 10yr 30yr Avg. Return 36 121 209 300 438 Avg. Volatility 73 161 423 601 876 Sharpe Ratio .49 .75 .49 .50 .50 Eric Falkenstein 4/14/99

  48. Replicate the 5, 10 and 30 Year Strategiesby Replicating the 3 Year Return with aZero-cost Derivative Eric Falkenstein 4/14/99

  49. Applications are Important • Wholesale replacement of accounting based measures of risk will not occur soon • In the meantime, piecemeal applications of VaR to balance sheet management strategies are quite fruitful Eric Falkenstein 4/14/99

  50. Diversification Lowers Risk • Assume portfolio with Sensitivity to 1 Risk Factor, VaR=100 • Add a portfolio with a sensitivity to a new risk factor • See new Portfolio VaR by various Correlation and Relative Size combinations Correlations 0 0.25 0.5 0.75 1.00 10 101 103 105 108 110 size 50 112 122 132 141 150 100 141 158 173 187 200 Eric Falkenstein 4/14/99

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