Mag. Eugen PUSCHKARSKIRisk ManagerFebruary 08, 2001
Riskmeasurement and Decomposition
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 RiskThe risk that a counterparty will fail to perform on an obligation owed to the firm
• Liquidity Risk• Operational Risk• Legal Risk• ...
Mag. Eugen PUSCHKARSKI
FX - RiskExposureValue at Risk
Interest Rate Riskmod. DurationPVBPValue at Risk
Market Risk
Mag. Eugen PUSCHKARSKI
the portfolio loss which is not exceeded witha certain probability (e.g. 95 %) over a specific time horizon (e.g. 1 month)
Value at Risk (VaR)
Mag. Eugen PUSCHKARSKI
Risk Terminologies
Value
t n
Time
to
+0
Freq
uenc
yVaR Variance
Horizon
Mag. Eugen PUSCHKARSKI
Calculating VaR
•Positions - ExposuresPositions - Exposures•VolatilitiesVolatilities•CorrelationsCorrelations
)(** QPVaR P
2,122
22
21
21
22
22
21
21
2 *****2** wwwwP
21 ,ww22
21 ,
2,1
Market value of Portfolio
Quantile of the
Confidence level
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.
Mag. Eugen PUSCHKARSKI
Volatilities
Written recursively
Mag. Eugen PUSCHKARSKI
VolatilitiesBy 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
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.
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
Mag. Eugen PUSCHKARSKI
Stress TestsThe Problem:
VaR does not show how large a possible loss is beyond the confidence level!!!
Fat tails
Fat tails
Mag. Eugen PUSCHKARSKI
Stress TestsSolution:
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
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
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:
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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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
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
ExceptionsofNumberXnsObservatioofNumberN
obabilityobservedpobabilityectedpppppLR
NX
XNX
XNX
__...__...
Pr_......~Pr_exp...
)~1(~)1(ln2
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
00,10,20,30,40,50,60,70,80,9
1
0 2 4 6 8 10
Mag. Eugen PUSCHKARSKI
Comparison of methods
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
Mag. Eugen PUSCHKARSKI
Internet Resources
All About Value-at-RiskAll About Value-at-Risk
http://www.gloriamundi.org/
RiskMetrics Technical DocumentRiskMetrics Technical Document
http://www.riskmetrics.com/research/techdoc/
Risk Waters GroupRisk Waters Group
http://www.riskwaters.com/home.htm