Master of Science in Finance : Advance Risk 1Comparing VaR model and BacktestingMaster of Science in Finance : Advance Risk2Agenda Objective Literature Review Value at Risk (VaR) Backtesting Empirical study ConclusionMaster of Science in Finance : Advance Risk 3ObjectiveMaster of Science in Finance : Advance Risk4Objective To compare VaR estimate from different VaR approaches as a market risk measurement Variance-Covariance method Historical simulation Monte Carlo simulation To figure out the quality of VaR estimate by Backtesting Kupeic-POF Basel Committee traffic light The mixed Kupeic-testMaster of Science in Finance : Advance Risk 5Literature ReviewMaster of Science in Finance : Advance Risk6Literature Review Olli Nieppola, Backtesting Value at Risk models, department of economic, Helsinki school of economy The objectives are : To examine the accuracy of a VaR model from software for the companys investment To figure out reliable and suitable backtests for model validationMaster of Science in Finance : Advance Risk7Literature Review Methodology Select three different portfolios (equities, bonds and equity options) Perform daily VaR estimates for one yearValidate backtesting process. Result Some indication of potential problems within the software system Underestimation, especially Equity and Equity Options. High volatility during 2008 due to the turbulent marketMaster of Science in Finance : Advance Risk 8Value at Risk (VaR)Master of Science in Finance : Advance Risk9Overview VaR VaR does not give a consistent method for measuring risk VaR cannot measure risk such as liquidity risk, political risk VaR does not reliable in time of great volatility Parameter need Time horizon Confidence levelMaster of Science in Finance : Advance Risk10VaR approaches Variance Covariance matrix combine linear position with covariance Historical Simulation replicates current portfolio over historical data Monte Carlo Simulation create simulations of financial variableMaster of Science in Finance : Advance Risk11Steps in computing VaR Mark to market the current portfolio Measure the variability of the risk factor Set the time horizon, or holding period Set the confidence level Report the worst potential loss by VaRMaster of Science in Finance : Advance Risk12Variance Covariance matrix Assumptions Returns are normally distributed Payoff are linear in the risk factors Method Standardize the instrument Calculate VaR by using estimated variance covariance and the weights on the standardized positionsMaster of Science in Finance : Advance Risk13Variance Covariance matrix Advantage Simple method Fast computation Can be extended to time vary risk Easy to explain DisadvantageFat tails in distribution of returns Applicable to linear portfolio Relies on normal approximation Master of Science in Finance : Advance Risk14Historical-Simulation Assumption Recent historical data relevant Full valuation Method Simulate hypothetical return Compile distribution of portfolio changesMaster of Science in Finance : Advance Risk15Historical-Simulation Advantage Accounts for non-normal data Full valuation method Easy to explain Disadvantage Only on sample path Assumption that future and past are alikeMaster of Science in Finance : Advance Risk16Monte Carlo Assumption Define joint stochastic model for risk factor Full valuation Method Use numerical simulations for risk factors to horizon Value portfolioMaster of Science in Finance : Advance Risk17Monte Carlo Advantage Most flexible method Appropriate for complex instruments Allows fat tail and time-variation in risk Disadvantage Computational cost Most difficult to implement Subject to model riskMaster of Science in Finance : Advance Risk18Comparing VaR methodsVariance CovarainceHistorical SimulationMonte Carlo SimulationNonlinear instrumentlimit to linear instrumentBoth linear and nonlinearBoth linear and nonlinearImplementation and explanationEasy Easy DifficultFlexibility in assumptionFlexible Rely on historical returnFlexibleReliability of resultTend to underestimate under high confidence levelGood under high confidence levelGoodMaster of Science in Finance : Advance Risk 19BacktestingMaster of Science in Finance : Advance Risk20Backtesting Techniques for verifying VaR model Statistical framework comparing the historical VaR with portfolio return Two types of backtesting Unconditional coverage Conditional coverageMaster of Science in Finance : Advance Risk21Unconditional Coverage Examine whether the frequency of exception is in line with the selected confidence level Ignore when the exception occurs Number of exception < selected confidence level, system is over-estimated risk otherwise under-estimated riskMaster of Science in Finance : Advance Risk22Kupiec-POF test Failure rate = number of exception/ nubmer of observation Find out whether the failure rate is different from the failure rate suggested by the confidence level or notMaster of Science in Finance : Advance Risk23Basel Committees traffic light Classify outcome into3 categories Green zone: model is accurate as the probability of accepting in accurate model is quite low Yellow zone: both accurate and inaccurate model depending on the reasons Basic integrity of the model Model accuracy could be improved Intra-day trading Bad luck Red zone: model has a problemMaster of Science in Finance : Advance Risk24Conditional Coverage Bad model produce a sequence of consecutive exceptions. Deal with the problem of clustering of exceptions. Testing both number of exceptions and time when they occurMaster of Science in Finance : Advance Risk25The Mixed Kupeic-test Measure time between exception instead of observing only whether and exception today depends on the outcome of the previous dayMaster of Science in Finance : Advance Risk 26Empirical Study : SET50 PortolioMaster of Science in Finance : Advance Risk27Calculation and Testing ProcessData Select currently trading day (t = 28/8/2552). Select 25 largest Market Cap Stock from SET50 Closing price (350 days), and (100 Days) of each stock Average Market Return and (100 Days)Calculation Compute actual daily Profit & Loss from 27 Mar - 28 Aug 2009 total 100 Compute daily VaR on the same period (Delta-Normal , Historical , Mote Carlo) Confidence Level 95% , 99% Backtesting Process Basel Traffic Light Approach. Kupiecs POF Tests.Compare Compare betweenDaily trading outcome (Profit & Loss) andEstimated VaR for the same period , total 100 observations. Collect number of Exception from VaR.Master of Science in Finance : Advance Risk28Result:VaR estimatesConfidence level99% 95%Variance Covariance6,294,914 4,453,922Historical6,784,861 4,083,551Monte Carlo Simulation6,904,898 4,742,282Master of Science in Finance : Advance Risk29Result:Basel traffic light testApproach Confidence NumberObs. Number Test OutcomeLevel of Obs. ofExceptionsVariance covariance99.0% 250 7Yellow Zone95.0% 250 14Green ZoneHistorical 99.0% 250 6Yellow Zone95.0% 250 22Yellow ZoneMonte Carlo Simulation99.0% 250 6Yellow Zone95.0% 250 14Green ZoneCut off Table for 250 Obs. Green Yellow Red99.0% 0-4 5-9 10 or more95.0% 0-17 18-26 27 or more*Master of Science in Finance : Advance Risk30Result:Kupiecs POF-TestApproach Confidence Test Stat. Critical Value Test OutcomeLevel LRPOFX2(1)Variance covariance99.0% 5.50 3.84Reject95.0% 0.18 3.84AcceptHistorical 99.0% 3.56 3.84Accept95.0% 6.26 3.84RejectMonte Carlo Simulation99.0% 3.56 3.84Accept95.0% 0.18 3.84AcceptLRPOF=-2ln (1-p)T-xpx[1- (x/T)]T-x(x/T)xT = Total Obs.x= Number of ExceptionP =Prob. of loss exceeding VaR(1-Confidence Level)Master of Science in Finance : Advance Risk31Result:Mixed Kupiec-TestApproach Confidence Test Stat. Critical Value Test OutcomeLevel LRINDX2Variance covariance99.0% 27.95 14.07Reject95.0% 27.21 23.68RejectHistorical 99.0% 22.48 12.59Reject95.0% 35.15 33.92RejectMonte Carlo Simulation99.0% 22.48 12.59Reject95.0% 22.11 23.68Accept ) )48 . 221 111ln 21 111ln 211211