Transcript Management of Financial Risk

Financial Risk Management
Zvi Wiener
Following
P. Jorion, Financial Risk Manager Handbook
http://pluto.huji.ac.il/~mswiener/zvi.html
FRM
972-2-588-3049
Chapter 11
Introduction to Market Risk Management
Following P. Jorion 2001
Financial Risk Manager Handbook
http://pluto.huji.ac.il/~mswiener/zvi.html
FRM
972-2-588-3049
Old ways to measure risk
• notional amounts
• sensitivity measures (duration, Greeks)
• scenarios
• ALM, DFA
assume linearity
do not describe probability
Ch. 11, Handbook
Zvi Wiener
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1938
1952
1963
1966
1973
1983
1986
1988
1993
1994
1997
Ch. 11, Handbook
Bonds duration
Markowitz mean-variance
Sharpe’s CAPM
Multiple risk-factors
Black-Scholes option pricing
RAROC, risk adjusted return
Limits on exposure by duration
Risk-weighted assets for banks;
exposure limits by Greeks
VaR endorsed by G-30
Risk Metrics
CreditMetrics, CreditRisk+
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How much can we lose?
Everything
correct, but useless answer.
How much can we lose realistically?
Ch. 11, Handbook
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What is the current Risk?
• Bonds
• Stocks
• Options
• Credit
• Forex
• Total
Ch. 11, Handbook
duration, convexity
volatility
delta, gamma, vega
rating
target zone
?
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Standard Approach
Ch. 11, Handbook
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Modern Approach
Financial Institution
Ch. 11, Handbook
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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.
Ch. 11, Handbook
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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.
Ch. 11, Handbook
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VaR
1
0.8
0.6
0.4
VaR1%
1%
0.2
Profit/Loss
-3
Ch. 11, Handbook
-2
-1
1
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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%
Ch. 11, Handbook
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Returns
year
1% of worst cases
Ch. 11, Handbook
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Main Ideas
• A few well known risk factors
• Historical data + economic views
• Diversification effects
• Testability
• Easy to communicate
Ch. 11, Handbook
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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!
Ch. 11, Handbook
Zvi Wiener
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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
Ch. 11, Handbook
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slide 16
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
Ch. 11, Handbook
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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 entire distribution
• 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
Ch. 11, Handbook
-2
-1
1
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2
3
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Properties of Risk Measure
• Monotonicity (X<Y, R(X)>R(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!
Ch. 11, Handbook
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No subadditivity of VaR
Bond has a face value of $100,000, during the
target period there is a probability of 0.75%
that there will be a default (loss of $100,000).
Note that VaR99% = 0 in this case.
What is VaR99% of a position consisting of 2
independent bonds?
Ch. 11, Handbook
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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
Ch. 11, Handbook
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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
Ch. 11, Handbook
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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(1day) T
This formula is valid (in particular) for iid
normally distributed returns.
Ch. 11, Handbook
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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
Ch. 11, Handbook
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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
Ch. 11, Handbook
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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.
60
k


MRCt  Max VaRt i ,VaRt 1   SRCt
 60 i 1

VaRt  VaRt (1d , 99%)  10
Ch. 11, Handbook
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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
Ch. 11, Handbook
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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
Ch. 11, Handbook
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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
Ch. 11, Handbook
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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
No limits!
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
Ch. 11, Handbook
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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.
Ch. 11, Handbook
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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.
Ch. 11, Handbook
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