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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 May-2000

  3. How much can we lose? Everything correct, but useless answer. How much can we lose realistically? May-2000

  4. Derivatives 1993-1995 ($ million) • Shova Shell, Japan 1,580 • Kashima Oil, Japan 1,450 • Metallgesellschaft 1,340 • Barings, U.K. 1,330 • Codelco, Chile 200 • Procter & Gamble, US 157 May-2000

  5. Barings • February 26, 1995 • 233 year old bank • 28 year old Nick Leeson • $1,300,000,000 loss • bought by ING for $1.5 May-2000

  6. Public Funds ($ million) • Orange County 1,640 • San Diego 357 • West Virginia 279 • Florida State Treasury 200 • Cuyahoga County 137 • Texas State 55 May-2000

  7. Orange County • Bob Citron, the county treasures • $7.5B portfolio (schools, cities) • borrowed $12.5B, invested in 5yr. notes • interest rates increased • reported at cost - big mistake! • realized loss of $1.64B May-2000

  8. Financial Losses • Barings $1.3B • Bank Negara, Malaysia 92 $3B • Banesto, Spain $4.7B • Credit Lyonnais $10B • S&L, U.S.A. $150B • Japan $500B May-2000

  9. Metallgesellshaft • 14th largest industrial group • 58,000 employees • offered long term oil contracts • hedge by long-term forward contracts • short term contracts were used (rolling hedge) • 1993 price fell from $20 to $15 • $1B margin call in cash May-2000

  10. May-2000

  11. duration, convexity volatility delta, gamma, vega rating target zone What is the current Risk? • Bonds • Stocks • Options • Credit • Forex • Total ? May-2000

  12. Standard Approach May-2000

  13. Modern Approach Financial Institution May-2000

  14. Risk Management • Risk measurement • Reporting to board • Limits monitoring • Diversification, reinsurance • Vetting • Reporting to regulators • Decision making based on risk May-2000

  15. 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 May-2000

  16. Regulators • BIS • FSA • SEC • ISDA • FASB • Bank of Israel • Galai’s committee May-2000

  17. Basic Steps in RM process • Identify risks • Data base (market + position) • Risk measurement • Regulators • Risk Management • Reporting • Strategic decisions May-2000

  18. Building a RM system • Initial study of risks • Decision, Risk Manager • Risk measurement system • Responsibilities and structure • Testing • ActiveRisk Management • Staff training and maintenance May-2000

  19. Risk Management andRisk Measurement May-2000

  20. Can NOT Risk Management System • Predict future • Identify business opportunities • Be always right! Risk Management System Can • Predict loss, given event • Identify most dangerous scenarios • Recommend how to change risk profile May-2000

  21. Tool, not rule! May-2000

  22. Definition VaR is defined as the predicted worst-case loss at a specific confidence level (e.g. 99%) over a certain period of time. May-2000

  23. VaR1% 1% Profit/Loss VaR May-2000

  24. 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. May-2000

  25. 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! May-2000

  26. Current position Market data Risk Mapping Valuation Value-at-Risk Reporting and Risk Management Risk Management Structure May-2000

  27. Value dollar Interest Rate interest rates and dollar are NOT independent May-2000

  28. Risk Measuring Software • CATS, CARMA • Algorithmics, Risk Watch • Infinity • J.P. Morgan, FourFifteen • FEA, Outlook • Reuters, Sailfish • Kamacura • Bankers Trust, RAROC • INSSINC, Orchestra May-2000

  29. 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 May-2000

  30. 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 May-2000

  31. Types of Assets and Risks • Real projects - cashflow versus financing • Fixed Income • Optionality • Credit exposure • Legal, operational, authorities May-2000

  32. 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 May-2000

  33. How to measure VaR • Historical Simulations • Variance-Covariance • Monte Carlo • Analytical Methods May-2000

  34. 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. May-2000

  35. 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 4.10*4.10/4.20 = 4.198 4.15*4.15/4.10 = 4.352 May-2000

  36. USD NIS 2000 100 -120 2001 200 100 2002 -300 -20 2003 20 30 today May-2000

  37. today USD: +1% +1% +1% +1% NIS: +1% 0% -1% -1% Changes in IR May-2000

  38. 1% of worst cases Returns year May-2000

  39. VaR1% 1% Profit/Loss VaR May-2000

  40. 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. May-2000

  41. 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! May-2000

  42. 1% 2.33  Variance-Covariance -2.33 May-2000

  43. Monte Carlo May-2000

  44. Monte Carlo • Distribution of market factors • Simulation of a large number of events • P&L for each scenario • Order the results • VaR = lowest quantile May-2000

  45. Monte Carlo Simulation May-2000

  46. Real Projects Most daily returns are invisible. Proper financing should be based on risk exposure of each specific project. Note that accounting standards not always reflect financial risk properly. May-2000

  47. Example • You are going to invest in Japan. • Take a loan in Yen. • Financial statements will reflect your investment according to the exchange rate at the day of investment and your liability will be linked to yen. • Actually there is no currency risk. May-2000

  48. Airline company • fuel - oil prices and $ • purchasing airplanes - $ and Euro • salaries - NIS, some $ • tickets $ • marketing - different currencies • payments to airports for services May-2000

  49. Airline company • loans • equity • callable bonds May-2000

  50. Airline company Base currency - by major stockholder. Time horizon - by time of possible price change. Earnings at risk, not value at risk, since there is too much optionality in setting prices. One can create a one year cashflow forecast and measure its sensitivity to different market events. May-2000

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