Riskmeasurement and Decomposition

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Riskmeasurement and Decomposition
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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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Market Risk

• FX - Risk
• Exposure
• Value at Risk
• Interest Rate Risk
• mod. Duration
• PVBP
• Value at Risk

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Value at Risk (VaR)

• the portfolio loss which is not exceeded with
• a certain probability (e.g. 95 )
• over a specific time horizon (e.g. 1 month)

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Risk Terminologies

Time
0
Value
t
o
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Calculating VaR

• Positions - Exposures
• Volatilities
• Correlations

Quantile of the Confidence level ?
Market value of Portfolio
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Positions - Exposures - RiskMetrics Cashflow
Mapping

• 1. The positions are stripped to the individual
  cashflows.

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Volatilities
Written recursively
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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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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
Business Date (t)
Business Date (t-1)
Pricing Date (t)
Pricing Date (t-1)
Position (t-1)
Position (t)
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Stress Tests
The Problem VaR does not show how large a
possible loss is beyond the confidence level!!!
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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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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
General Issues

• 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

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Backtesting
Procedure

• 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 PL) 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

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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
• Kupiecs frequency of failures test
• Textbook proportions test
• Crnkovic-Drachman VaR percentile test
• Christoffersens interval forecast test

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Backtesting
Kupiecs frequency of failures test

• If for example 281 observations
• and 14 exceptions
• gt4,98 of exceptions versus 5 predicted
• Teststatistic is the Loglikelyhood Ratio

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Backtesting
Kupiecs frequency of failures test

• Loglikelyhood Ratio is Chi2(1) distributed
• Result We can be 98,907 sure, that 4,98 does
  not differ from 5 significantly!

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Comparison of methods
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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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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