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Mag. Eugen PUSCHKARSKI Risk Manager February 08, 2001 Riskmeasurement and Decomposition

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Mag. Eugen PUSCHKARSKI Taxonomy of Risk Market Risk The potential loss in market value on financial assets that results from an adverse movement in market prices or rates Credit Risk The risk that a counterparty will fail to perform on an obligation owed to the firm Liquidity Risk Operational Risk Legal Risk...

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Mag. Eugen PUSCHKARSKI FX - Risk Exposure Value at Risk Interest Rate Risk mod. Duration PVBP Value at Risk Market Risk

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Mag. Eugen PUSCHKARSKI t the portfolio loss which is not exceeded with aa certain probability (e.g. 95 %) over a specific time horizon (e.g. 1 month) Value at Risk (VaR)

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Mag. Eugen PUSCHKARSKI Risk Terminologies Value t n Time t o + 0 Frequency VaR Variance Horizon

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Mag. Eugen PUSCHKARSKI Calculating VaR PositionsPositions - Exposures VolatilitiesVolatilities CorrelationsCorrelations Market value of Portfolio Quantile of the Confidence level

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Mag. Eugen PUSCHKARSKI Positions - Exposures - RiskMetrics Cashflow Mapping 1. The positions are stripped to the individual cashflows. 2. The cashflows of the positions (e.g. Bonds) are mapped to the basic RiskMetrics risk factors.

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Mag. Eugen PUSCHKARSKI Volatilities Written recursively

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Mag. Eugen PUSCHKARSKI Volatilities By varying the „decay factor“ recent observations can be given more weight then older ones The RiskMetrics Research Group has concluded that for short periods (e.g. up to 10 days) a decay factor of 0,94 is optimal and for longer ones ( one month and more) 0,97 is optimal in predicting future volatility Volatility clustering

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Mag. Eugen PUSCHKARSKI Volatilities A higher decay factor corresponds to considering a longer period of historical observations. A decay factor of one is equal to a simple moving average.

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Mag. Eugen PUSCHKARSKI Risk Attribution 8 1 2 3 5 6 4 7 Position (t-1) Position (t) Position changes Pricing Date (t-1) Pricing Date (t) Business Date (t-1) Business Date (t) Market changes Time Decay

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Mag. Eugen PUSCHKARSKI Stress Tests The Problem: VaR does not show how large a possible loss is beyond the confidence level!!! Fat tails

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Mag. Eugen PUSCHKARSKI Stress Tests Solution: Find plausibel Szenarios of Market Stress which result in large losses. Historical Stress Szenarios Hypothetical Stress Szenarios Factor Push Method Extreme Value Theory Monte Carlo Methods

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Mag. Eugen PUSCHKARSKI Stress Tests Simple Stress Test: Stressed Risk Factor has no influence on other Risk Factors Predictive Stress Test: Stressed Risk Factor influence other Risk Factors consistent with observed correlations

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Mag. Eugen PUSCHKARSKI Backtesting Backtesting refers to the testing of VaR models to ensure that VaR estimates are sufficiently accurate Concerned about under- and over-prediction of VaR Under-prediction implies firm riskier than it seems Over-prediction implies firm has excessive risk capital General Issues:

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Mag. Eugen PUSCHKARSKI Backtesting „Clean“ Backtesting: static portfolio holdings corresponding to the VaR assumption holding period: one day in order not to bend the above assumption to much Step 1: calculate VaR (potential P&L) over the next day Step 2: the next day revalue the positions and compare with VaR from the day before Continue with step 1 and 2 Procedure:

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Mag. Eugen PUSCHKARSKI Statistical Tests These are the most popular backtests Usually applied to frequency of excessive losses Based on whether number of losses in excess of VaR is consistent with what we would expect 4 main tests in this class Kupiec’s frequency of failures testKupiec’s frequency of failures test Textbook proportions test Crnkovic-Drachman VaR percentile test Christoffersen’s interval forecast test

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Mag. Eugen PUSCHKARSKI Backtesting If for example 281 observations and 14 exceptions =>4,98% of exceptions versus 5% predicted Teststatistic is the Loglikelyhood Ratio: Kupiec‘s frequency of failures test

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Mag. Eugen PUSCHKARSKI Backtesting Loglikelyhood Ratio is Chi^2(1) distributed Result: We can be 98,907% sure, that 4,98% does not differ from 5% significantly! Kupiec‘s frequency of failures test

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Mag. Eugen PUSCHKARSKI Comparison of methods

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Mag. Eugen PUSCHKARSKI Reference List Value at Risk : A New Benchmark for Measuring Derivatives Risk by Philippe Jorion Hardcover - 332 pages (August 1996) Irwin Professional Pub; ISBN: 0786308486 ; Dimensions (in inches): 1.20 x 9.33 x 6.34 Managing Financial Risk : A Guide to Derivative Products, Financial Engineering and Value Maximization (Irwin Library of Investment & Finance) by Charles W. Smithson, Clifford W. Smith Hardcover - 620 pages 3rd edition (July 1998) McGraw-Hill; ISBN: 007059354X ; Dimensions (in inches): 2.05 x 9.76 x 7.86 Mastering Value at Risk : A Step-By-Step Guide to Understanding and Applying Var by Cormac Butler Paperback - 288 pages (April 1999) Trans-Atlantic Publications, Inc.; ISBN: 0273637525 ; Dimensions (in inches): 0.97 x 9.83 x 6.82

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Mag. Eugen PUSCHKARSKI Internet Resources All About Value-at-Risk http://www.gloriamundi.org/ RiskMetrics Technical Document http://www.riskmetrics.com/research/techdoc/ Risk Waters Group http://www.riskwaters.com/home.htm

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