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RISK MANAGEMENT

RISK MANAGEMENT . GOALS AND TOOLS. ROLE OF RISK MANAGER. MONITOR RISK OF A FIRM, OR OTHER ENTITY IDENTIFY RISKS MEASURE RISKS REPORT RISKS MANAGE -or CONTROL RISKS. COMMON TYPES OF RISK. MARKET RISK CREDIT RISK LIQUIDITY RISK OPERATIONAL RISK SYSTEMIC RISK. COMMON TOOLS.

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RISK MANAGEMENT

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  1. RISK MANAGEMENT GOALS AND TOOLS

  2. ROLE OF RISK MANAGER • MONITOR RISK OF A FIRM, OR OTHER ENTITY • IDENTIFY RISKS • MEASURE RISKS • REPORT RISKS • MANAGE -or CONTROL RISKS

  3. COMMON TYPES OF RISK • MARKET RISK • CREDIT RISK • LIQUIDITY RISK • OPERATIONAL RISK • SYSTEMIC RISK

  4. COMMON TOOLS • SCENARIO ANALYSIS • ASSESS IMPLICATIONS OF PARTICULAR COMBINATIONS OF EVENTS • NO PROBABILITY STATEMENT • STATISTICAL ANALYSIS • FIND PROBABILITY OF LOSSES • HOW TO ASSESS EVENTS WHICH HAVE NEVER OCCURRED?

  5. STATISTICAL ANALYSIS OF MARKET RISK • PORTFOLIO STANDARD DEVIATION • DOWNSIDE RISK SUCH AS SEMI-VARIANCE • VALUE AT RISK

  6. Value at Riskis a single measure of market risk of a firm, portfolio, trading desk, or other economic entity. It is defined by a confidence level and a horizon. For convenience consider 95% and 1 day.A ny loss tomorrow will be less than the Value at Risk with 95% certainty

  7. HISTOGRAM OF TOMORROW’S VALUE - BASED ON PAST RETURNS

  8. CUMULATIVE DISTRIBUTION

  9. Weakness of this measure • The amount we exceed VaR is important • There is no utility function associated with this measure • The measure assumes assets can be sold at their market price - no consideration for liquidity • But it is simple to understand and very widely used.

  10. THE PROBLEM • FORECAST QUANTILE OF FUTURE RETURNS • MUST ACCOMMODATE TIME VARYING DISTRIBUTIONS • MUST HAVE METHOD FOR EVALUATION • MUST HAVE METHOD FOR PICKING UNKNOWN PARAMETERS

  11. TWO GENERAL APPROACHES • FACTOR MODELS--- AS IN RISKMETRICS • PORTFOLIO MODELS--- AS IN ROLLING HISTORICAL QUANTILES

  12. FACTOR MODELS • Volatilities and correlations between factors are estimated • These volatilities and correlations are updated daily • Portfolio standard deviations are calculated from portfolio weights and covariance matrix • Value at Risk computed assuming normality

  13. FACTOR MODEL: EXAMPLE • If each asset is a factor, then an nxn covariance matrix, Ht ,is needed. • LET wtbe the portfolio weights on day t • Then standard deviation is • And assuming normality, VaRt=-1.64 st • Quality of VaR depends upon H and normality assumption.

  14. PORTFOLIO MODELS • Historical performance of fixed weight portfolio is calculated from data bank • Model for quantile is estimated • VaR is forecast

  15. COMPLICATIONS • Some assets didn’t trade in the past- approximate by deltas or betas • Some assets were traded at different times of the day - asynchronous prices-synchronize these • Derivatives may require special assumptions - volatility models and greeks.

  16. PORTFOLIO MODELS - EXAMPLES • Rolling Historical : e.g. find the 5% point of the last 250 days • GARCH : e.g. build a GARCH model to forecast volatility and use standardized residuals to find 5% point • Hybrid model: use rolling historical but weight most recent data more heavily with exponentially declining weights.

  17. GARCH EXAMPLE • Choose a GARCH model for portfolio • Forecast volatility one day in advance • Calculate Value at Risk • Assuming Normality, multiply standard deviation by 1.64 for 5% VaR • Otherwise (and better) calculate 5% quantile of standardized residuals as factor • Multi-day forecasts: what distribution to use?

  18. DIAGNOSTIC CHECKS • Define hit= I(return<-VaR)-.05 • Percentage of positive hits should not be significantly different from theoretical value • Timing should be unpredictable • VaR itself should have no value in predicting hits • TESTS?

  19. Tests • Cowles and Jones (1937) • Runs - Mood (1940) • Ljung Box on hits (1979) • Dynamic Quantile Test

  20. Dynamic Quantile Test To test that hits have the same distribution regardless of past observables Regress hit on • constant • lagged hits • Value at Risk • lagged returns • other variables such as year dummies

  21. Distribution Theory • If out of sample test , or • If all parameters are known • Then TR02 will be asymptotically Chi Squared and F version is also available • But the distribution is slightly different otherwise

  22. Dynamic Quantile Test -SP Dependent Variable: SAV_HIT Sample: 5 2892 Included observations: 2888 Variable Coefficient Std. Error t-Statistic Prob. C 0.0051 0.0096 0.5277 0.5977 SAV_HIT(-1) 0.0397 0.0187 2.1277 0.0334 SAV_HIT(-2) 0.0244 0.0187 1.3051 0.1920 SAV_HIT(-3) 0.0252 0.0187 1.3468 0.1781 SAV_HIT(-4) -0.0044 0.0187 -0.2370 0.8127 SAV_VAR -0.0034 0.0066 -0.5241 0.6002 R-squared 0.0029 Mean dependent var 0.0006 Adjusted R-squared 0.0012 S.D. dependent var 0.2191 S.E. of regression 0.2190 Akaike info criterion -0.1975 Sum squared resid 138.2105 Schwarz criterion -0.1851 Log likelihood 291.2040 F-statistic 1.7043 Durbin-Watson stat 1.9999 Prob(F-statistic) 0.1301

  23. Some Extensions • Are there economic variables which can predict tail shapes? • Would option market variables have predictability for the tails? • Would variables such as credit spreads prove predictive? • Can we estimate the expected value of the tail?

  24. THE CAViaR STRATEGY • Define a quantile model with some unknown parameters • Construct the quantile criterion function • Optimize this criterion over the historical period • Formulate diagnostic checks for model adequacy • Read Engle and Manganelli

  25. SPECIFICATIONS FOR VaR • VaR is a function of observables in t-1 • VaR=f(VaR(t-1), y(t-1), parameters) • For example - the Adaptive Model

  26. How to compute VaR If beta is known, then VaR can be calculated for the adaptive model from a starting value.

  27. CAViaR News Impact Curve

  28. More Specifications • Proportional Symmetric Adaptive • Symmetric Absolute Value: • Asymmetric Absolute Value:

  29. Asymmetric Slope • Indirect GARCH

  30. REMAINING PROBLEMS • Other Risks, I.e. credit and liquidity risk • Derivatives are not easy in either approach • Approximate by delta and ignore volatility risk? • Simulate and reprice using BS? • Use simulation of simulations • Longstaff&Schwarz clever idea • one simulation plus a regression.

  31. RISK MANAGEMENT • IN MEAN VARIANCE WORLD, RISK MANAGEMENT DOES NOT EXIST AS A SEPARATE PROBLEM, MERELY COORDINATION. • COULD MAXIMIZE UTILITY s.t. VaR CONSTRAINT. • RISK REDUCTION CAN BE A MEAN VARIANCE PROBLEM ITSELF.

  32. Value at Risk: A Case Study • $1Million Portfolio at a point in time- March 23,2000 • Find 1% VaR • Construct historical portfolio • 50% Nasdaq, 30%DowJones,20% LongBonds • Build GARCH • Compute VaR - Gaussian, Semiparametric • Estimate CAViaR

  33. PORTFOLIO COMPONENTS

  34. STATISTICS NQ DJ RATE Mean 0.000928 0.000542 0.000137 Median 0.001167 0.000281 0.000000 Maximum 0.058479 0.048605 0.028884 Minimum -0.089536 -0.074549 -0.042677 Std. Dev. 0.011484 0.009001 0.007302 Skewness -0.530669 -0.359182 -0.202732 Kurtosis 7.490848 8.325619 4.956270

  35. CORRELATIONS NQ DJ RATE NQ 1.000000 0.695927 0.145502 DJ 0.695927 1.000000 0.236221 RATE 0.145502 0.236221 1.000000

  36. HISTORICAL QUANTILE • DECADE OF HISTORICAL DATA: • VaR=$22600 • ONE YEAR OF HISTORICAL DATA: • VaR=$24800 • WORST LOSS OVER YEAR: $36300

  37. Value at Risk by GARCH(1,1) C 1.40E-06 4.48E-07 3.121004 ARCH(1) 0.077209 0.017936 4.304603 GARCH(1) 0.904608 0.019603 46.14744

  38. CALCULATE VaR • ASSUMING NORMALITY • VaR=2.326348* 0.014605*1000000 • $33,977 • ASSUMING I.I.D. DISTURBANCES • VaR=2.8437*0.014605*1000000 • $39,996

  39. CAViaR MODEL • MAXIMIZE QUANTILE CRITERION BY GRID SEARCH: • var=c(1)+c(2)*var(-1)+c(3)*abs(y) c(1) =0.002441 c(2) =0.796289 c(3) =0.346875

  40. VaR over TIME

  41. CAViaR ESTIMATE • 1% VaR is $38,228 • This is very plausible - it is worse than the rolling quantiles as volatility was rising • It lies just below the semi-parametric GARCH.

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