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Value-at-Risk (VaR)

Value-at-Risk (VaR). Zvi Wiener 02-588-3049 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html. Risk. Business Risk Financial Risk market risk credit risk liquidity risk Operational Risk Legal Risk. How much can we lose?. Everything correct, but useless answer.

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Value-at-Risk (VaR)

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  1. Value-at-Risk (VaR) Zvi Wiener 02-588-3049 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html

  2. Risk • Business Risk • Financial Risk • market risk • credit risk • liquidity risk • Operational Risk • Legal Risk FRM5-VaR

  3. How much can we lose? Everything correct, but useless answer. How much can we lose realistically? FRM5-VaR

  4. duration, convexity volatility delta, gamma, vega rating target zone What is the current Risk? • Bonds • Stocks • Options • Credit • Forex • Total ? FRM5-VaR

  5. Standard Approach FRM5-VaR

  6. Modern Approach Financial Institution FRM5-VaR

  7. Definition VaR is defined as the predicted worst-case loss at a specific confidence level (e.g. 99%) over a certain period of time. FRM5-VaR

  8. VaR1% 1% Profit/Loss VaR FRM5-VaR

  9. VaR 1% Meaning of VaR A portfolio manager has a daily VaR equal $1M at 99% confidence level. This means that there is only one chance in 100 that a daily loss bigger than $1M occurs, under normal market conditions. FRM5-VaR

  10. Main Ideas • A few well known risk factors • Historical data + economic views • Diversification effects • Testability • Easy to communicate FRM5-VaR

  11. History of VaR • 80’s - major US banks - proprietary • 93 G-30 recommendations • 94 - RiskMetrics by J.P.Morgan • 98 - Basel • SEC, FSA, ISDA, pension funds, dealers • Widely used and misused! FRM5-VaR

  12. Current position Market data Risk Mapping Valuation Value-at-Risk Reporting and Risk Management Risk Management Structure FRM5-VaR

  13. Value dollar Interest Rate interest rates and dollar are NOT independent FRM5-VaR

  14. Risk Measuring Programs • CATS, CARMA $400K/yr • Algorithmics, Risk Watch >$1M • Infinity >$1M • J.P. Morgan, FourFifteen $25K/yr • FEA, Outlook $18K • Reuters, Sailfish ? • Theoretics, TARGA $75K • Bankers Trust, RAROC $50K/run • INSSINC, Orchestra $25-75K FRM5-VaR

  15. Why Capital Requirements • Government Protection • Debt financing • In Israel this is not binding! • But it will be!! • Traded assets constitute a small portion • 339-9, 339-10 defines who must use VaR FRM5-VaR

  16. Unifying Approach • One number • Based on Statistics • Portfolio Theory • Verification • Widely Accepted • Easy Comparison FRM5-VaR

  17. Supervision factor, 3  k  4 Capital Requirements Minimal required capital FRM5-VaR

  18. Qualitative Requirements • An independent risk management unit • Board of directors involvement • Internal model as an integral part • Internal controller and risk model • Backtesting • Stress test FRM5-VaR

  19. Quantitative Requirements • 99% confidence interval • 10 business days horizon • At least one year of historic data • Data base revised at least every quarter • All types of risk exposure • Derivatives FRM5-VaR

  20. Types of Assets and Risks • Real projects - cashflow versus financing • Fixed Income • Optionality • Credit exposure • Legal, operational, authorities FRM5-VaR

  21. Risk Factors There are many bonds, stocks and currencies. The idea is to choose a small set of relevant economic factors and to map everything on these factors. • Exchange rates • Interest rates (for each maturity and indexation) • Spreads • Stock indices FRM5-VaR

  22. How to measure VaR • Historical Simulations • Variance-Covariance • Monte Carlo • Analytical Methods • Parametric versus non-parametric approaches FRM5-VaR

  23. Historical Simulations • Fix current portfolio. • Pretend that market changes are similar to those observed in the past. • Calculate P&L (profit-loss). • Find the lowest quantile. FRM5-VaR

  24. Example Assume we have $1 and our main currency is SHEKEL. Today $1=4.30. Historical data: 4.00 4.20 4.20 4.10 4.15 P&L 0.215 0 -0.112 0.052 4.30*4.20/4.00 = 4.515 4.30*4.20/4.20 = 4.30 4.30*4.10/4.20 = 4.198 4.30*4.15/4.10 = 4.352 FRM5-VaR

  25. USD NIS 2000 100 -120 2001 200 100 2002 -300 -20 2003 20 30 today FRM5-VaR

  26. today USD: +1% +1% +1% +1% NIS: +1% 0% -1% -1% Changes in IR FRM5-VaR

  27. 1% of worst cases Returns year FRM5-VaR

  28. VaR1% 1% Profit/Loss VaR FRM5-VaR

  29. Variance Covariance • Means and covariances of market factors • Mean and standard deviation of the portfolio • Delta or Delta-Gamma approximation • VaR1%= P – 2.33 P • Based on the normality assumption! FRM5-VaR

  30. 1% 2.33  Variance-Covariance -2.33 FRM5-VaR

  31. Monte Carlo FRM5-VaR

  32. Monte Carlo • Distribution of market factors • Simulation of a large number of events • P&L for each scenario • Order the results • VaR = lowest quantile FRM5-VaR

  33. Monte Carlo Simulation FRM5-VaR

  34. Weights Since old observations can be less relevant, there is a technique that assigns decreasing weights to older observations. Typically the decrease is exponential. See RiskMetrics Technical Document for details. FRM5-VaR

  35. Stock Portfolio • Single risk factor or multiple factors • Degree of diversification • Tracking error • Rare events FRM5-VaR

  36. Bond Portfolio • Duration • Convexity • Partial duration • Key rate duration • OAS, OAD • Principal component analysis FRM5-VaR

  37. Options and other derivatives • Greeks • Full valuation • Credit and legal aspects • Collateral as a cushion • Hedging strategies • Liquidity aspects FRM5-VaR

  38. Credit Portfolio • rating, scoring • credit derivatives • reinsurance • probability of default • recovery ratio FRM5-VaR

  39. Reporting Division of VaR by business units, areas of activity, counterparty, currency. Performance measurement - RAROC (Risk Adjusted Return On Capital). FRM5-VaR

  40. How VaR is used • Internal Risk Management • Reporting • Regulators FRM5-VaR

  41. Backtesting Verification of Risk Management models. Comparison if the model’s forecast VaR with the actual outcome - P&L. Exception occurs when actual loss exceeds VaR. After exception - explanation and action. FRM5-VaR

  42. Backtesting OK increasing k intervention Green zone - up to 4 exceptions Yellow zone - 5-9 exceptions Red zone - 10 exceptions or more FRM5-VaR

  43. Stress Designed to estimate potential losses in abnormal markets. Extreme events Fat tails Central questions: How much we can lose in a certain scenario? What event could cause a big loss? FRM5-VaR

  44. Risk Management • Risk measurement • Reporting to board • Limits monitoring • Diversification, reinsurance • Vetting • Reporting to regulators • Decision making based on risk FRM5-VaR

  45. Tool, not rule! FRM5-VaR

  46. pluto.mscc.huji.ac.il/~mswiener/ Risk Management resources • Useful Internet sites • Regulators • Insurance Companies • Risk Management in SEC reports FRM5-VaR

  47. How to hedge financial risk? • Static hedge Forwards agreements that fix the price Futures Options static hedge • Dynamic delta or vega hedge, with a variable amount of options held. It is applicable if there is a very liquid market and low transaction costs. FRM5-VaR

  48. RMG • http://www.riskmetrics.com/ • http://www.pictureofrisk.com/ • http://www.riskmetrics.com/rm/splash.html • rmgaccess FRM5-VaR

  49. Who manages risk? Nike Sony Dell Computers Philip Morris Ford Motor AIG General Re Swiss Re Aetna Zurich Citibank Bank of England CIBC J. P. Morgan Bankers Trust FRM5-VaR

  50. Consulting • Oliver, Wyman and Co. • Willis Corroon • Richard Scora • Ernst and Young • Enterprise Advisors • Kamakura FRM5-VaR

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