Financial Risk Management
Introduction to Market Risk Management Following P. Jorion, Financial Risk Management Chapter 11
Daniel HERLEMONT
Old ways to measure risk notional amounts sensitivity measures (duration, Greeks) scenarios ALM, DFA assume linearity do not describe probability
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1938
Bonds duration
1952
Markowitz mean-variance
1963
Sharpe’s CAPM
1966
Multiple risk-factors
1973
Black-Scholes option pricing
1983
RAROC, risk adjusted return
1986
Limits on exposure by duration
1988
Risk-weighted assets for banks; exposure limits by Greeks
1993
VaR endorsed by G-30
1994
Risk Metrics
1997
CreditMetrics, CreditRisk+
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How much can we lose?
Everything correct, but useless answer.
How much can we lose realistically?
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What is the current Risk?
Bonds
duration, convexity
Stocks
volatility
Options
delta, gamma, vega
Credit
rating
Forex
target zone
Total
?
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Standard Approach
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Modern Approach
Financial Institution
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Definition VaR is defined as the predicted worst-case loss at a specific confidence level (e.g. 99%) over a certain period of time.
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Definition (Jorion) VaR is the maximum loss over a target horizon such that there is a low, prespecified probability that the actual loss will be larger.
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VaR 1 0.8 0.6 0.4
VaR1%
1%
0.2
Profit/Loss -3
-2
-1
1
2
3
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Meaning of VaR A portfolio manager has a daily VaR equal $1M at 99% confidence level. This means that there is only one chance in 100 that a daily loss bigger than $1M occurs,
under normal market conditions.
VaR 1%
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Returns
year
1% of worst cases Daniel HERLEMONT
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Main Ideas
A few well known risk factors Historical data + economic views Diversification effects Testability Easy to communicate
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History of VaR
80’s - major US banks - proprietary 93 G-30 recommendations 94 - RiskMetrics by J.P.Morgan 98 - Basel SEC, FSA, ISDA, pension funds, dealers Widely used and misused!
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FRM-99, Question 89
What is the correct interpretation of a $3 overnight VaR figure with 99% confidence level? A. expect to lose at most $3 in 1 out of next 100 days B. expect to lose at least $3 in 95 out of next 100 days C. expect to lose at least $3 in 1 out of next 100 days D. expect to lose at most $6 in 2 out of next 100 days
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VaR caveats VaR does not describe the worst loss VaR does not describe losses in the left tail VaR is measured with some error
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Other Measures of Risk The expected left tail loss
The standard deviation
The semi-standard deviation
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Risk Measures 1 0.8 0.6 0.4 0.2
Profit/Loss -3
-2
-1
1
2
3
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Properties of Risk Measure Monotonicity (XR(Y)) Translation invariance R(X+k) = R(X)-k Homogeneity R(aX) = a R(X) (liquidity??) Subadditivity R(X+Y) ≤ R(X) + R(Y) the last property is violated by VaR!
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No subadditivity of VaR
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FRM-98, Question 22 Consider arbitrary portfolios A and B and their combined portfolio C. Which of the following relationships always holds for VaRs of A, B, and C? A. VaRA+ VaRB = VaRC B. VaRA+ VaRB ≥ VaRC C. VaRA+ VaRB ≤ VaRC D. None of the above
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Confidence level low confidence leads to an imprecise result. For example 99.99% and 10 business days will require history of 100*100*10 = 100,000 days in order to have only 1 point.
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Time horizon long time horizon can lead to an imprecise result. 1% - 10 days means that we will see such a loss approximately once in 100*10 = 3 years. 5% and 1 day horizon means once in a month. Various subportfolios may require various horizons.
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Time horizon When the distribution is stable one can translate VaR over different time periods.
VaR (T days ) = VaR (1 day ) T This formula is valid (in particular) for iid normally distributed returns.
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FRM-97, Question 7 To convert VaR from a one day holding period to a ten day holding period the VaR number is generally multiplied by: A. 2.33 B. 3.16 C. 7.25 D. 10
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Basel Rules horizon of 10 business days 99% confidence interval an observation period of at least a year of historical data, updated once a quarter
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Basel Rules MRC Market Risk Charge = MRC SRC - specific risk charge, k ≥3.
k 60 MRCt = Max ∑ VaRt −i , VaRt −1 + SRCt 60 i =1 VaRt = VaRt (1d , 99%) × 10 Daniel HERLEMONT
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FRM-97, Question 16 Which of the following quantitative standards is NOT required by the Amendment to the Capital Accord to Incorporate Market Risk? A. Minimum holding period of 10 days B. 99% one-tailed confidence interval C. Minimum historical observations of two years D. Update the data sets at least quarterly
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VaR system
Risk factors
Portfolio
Historical data
positions
Model
Mapping
Distribution of risk factors
VaR method
Exposures
VaR
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FRM-97, Question 23 The standard VaR calculation for extension to multiple periods also assumes that positions are fixed. If risk management enforces loss limits, the true VaR will be: A. the same B. greater than calculated C. less then calculated D. unable to determine
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FRM-97, Question 9 A trading desk has limits only in outright foreign exchange and outright interest rate risk. Which of the following products can not be traded within the current structure? A. Vanilla IR swaps, bonds and IR futures B. IR futures, vanilla and callable IR swaps C. Repos and bonds D. FX swaps, back-to-back exotic FX options
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Stress-testing scenario analysis stressing models, volatilities and correlations developing policy responses
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Scenario Analysis Moving key variables one at a time Using historical scenarios Creating prospective scenarios The goal is to identify areas of potential vulnerability.
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FRM-97, Question 4 The use of scenario analysis allows one to: A. assess the behavior of portfolios under large moves B. research market shocks which occurred in the past C. analyze the distribution of historical P&L D. perform effective back-testing
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FRM-98, Question 20 VaR measure should be supplemented by portfolio stress-testing because: A. VaR measures indicate that the minimum is VaR, they do not indicate the actual loss B. stress testing provides a precise maximum loss level C. VaR measures are correct only 95% of time D. stress testing scenarios incorporate reasonably probable events.
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FRM-00, Question 105 VaR analysis should be complemented by stress-testing because stress-testing: A. Provides a maximum loss in dollars. B. Summarizes the expected loss over a target horizon within a minimum confidence interval. C. Assesses the behavior of portfolio at a 99% confidence level. D. Identifies losses that go beyond the normal losses measured by VaR.
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