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• ...

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FX - RiskExposureValue at Risk

Interest Rate Riskmod. DurationPVBPValue at Risk

Market Risk

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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)

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Risk Terminologies

Value

t n

Time

to

+0

Freq

uenc

yVaR Variance

Horizon

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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

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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

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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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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

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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

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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

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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