Forecasting VaR and Risk Mangement under Basel Accords

1

• Forecasting VaR and Risk Mangement under Basel
  Accords
• Michael McAleer
• Erasmus University Rotterdam/ Tinbergen Institute
• The Netherlands / Institute of Economic Research,
  Kyoto University Japan
• Juan-Angel Jimenez-Martin
• Teodosio Perez-Amaral
• Complutense University of Madrid, Spain

2
Paper 1.- Has the Basel II Accord Encouraged Risk
Management During the 2008-09 Financial Crisis?
(January 24, 2010). Available at SSRN
http//ssrn.com/abstract1397239 Paper 2.-
GFC-Robust Risk Management Strategies under the
Basel Accord (October 6, 2010). Available at
SSRN http//ssrn.com/abstract1688385 Paper 3.-
International Evidence on GFC-Robust Forecasts
for Risk Management Under the Basel Accord
(January 16, 2011). Available at SSRN
http//ssrn.com/abstract1741565
3
Motivation

• 1. The Basel II Accord requires that banks and
  other Authorized Deposit-taking Institutions
  (ADIs) communicate their daily risk forecasts to
  the appropriate monetary authorities at the
  beginning of each trading day to determine
  regulatory capital requirements
• 2. There are different types of risk
• Credit Risk
• Operational risk
• Market risk
• Interest rate
• Equity risk
• Exchange rate risk
• 3.- There are several measures of Risk (standard
  deviation, ß, VaR)
• VaR is a measure of risk based on a probability
  of loss and a specific time horizon. Value at
  Risk is an estimate of the worst possible loss an
  investment could realize over a given time
  horizon, under normal market conditions (defined
  by a given level of confidence).
• VaR is denominated in units of a currency or as a
  percentage of portfolio holdings. For e.g., a set
  of portfolio having a current value of say 1
  million- can be described to have a daily value
  at risk of 0.1 million- at a 99 confidence
  level, which means there is a 1/100 chance of
  the loss exceeding 0.1 million, considering no
  great paradigm shifts in the underlying factors.
• Measure of Total Risk rather than Systematic (or
  Non-Diversifiable Risk) measured by Beta.

4
Advantages of VaR

• VaR provides an measure of total risk.
• VaR is an easy number to understand and explain
  to clients.
• VaR translates portfolio volatility into a dollar
  value.

A one day VAR of 0.1 million using a
probability of 5 means that there is a 5 chance
that the portfolio could lose more than 0.1
million the next trading day.

• Additionally
• VaR is useful for monitoring and controlling risk
  within the portfolio.
• VaR can measure the risk of many types of
  financial securities (i.e., stocks, bonds,
  commodities, foreign exchange, off-balance-sheet
  derivatives such as futures, forwards, swaps, and
  options, and etc.)
• It is easy to implement a Back testing procedure

Calculate 1-Day 95 VAR for a (changing)
portfolio each day for some substantial period of
time (e.g., 100 Days) Compare the P/L on the
succeeding trading day with the previous close of
business days VAR Count the number of times the
loss exceeds the VAR
5
Motivation

• Therefore the Basel II Accord requires that
  banks communicate their VaR forecasts to the
  appropriate monetary authorities at the beginning
  of each trading day to determine regulatory
  capital requirements.
• Basel II accord was designed to reward
  institutions with superior risk management
  systems.
• Financial Institutions are permitted to use
  Internal Models to calculate VaR.
• Historical Simulation
• Variance and covariance
• Monte Carlo simulation
• . But the model has to work correctly

6
Motivation

• More than 10 violations in any financial year
  may required to adopt standardized approach.

• When internal models lead to a greater number of
  violations than could reasonably be expected the
  bank is required
• To hold a higher level of capital.
• An the monetary authority can impose a external
  model to forecast VaR .
• These are the reasons why bank managers may
  prefer risk management strategies that are
  passive and conservative rather than active and
  aggressive. But we know that excessive
  Conservatism has a negative impact on the
  profitability

7

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Maximizing Profits, VaR and DCC
A necessary condition to maximize (1) in a given
period of (say) 250 days, is to minimize the
total CRqt (3) for the period. The standard
approach in the literature is to report in the
estimate of VaR obtained from a given model. In
this paper, we propose a robust strategy to
communicate VaR.
8

• Risk management
• Models for Forecasting VaR and Daily Capital
  Charges
• Combining alternative Models to forecast VaR
• Conclusions

Model for Forecasting VaR and Daily Capital
Charges
We assume that daily returns follow
? is the critical value from the distribution of
? to obtain the appropriate confidence level.
It is possible for ? to be replaced by
alternative estimates of the conditional
variance.
The VaR is
GARCH
GJR (Glosten, Jaganathan and Runkle)
Problems with GARCH(p,q) Models -
Non-negativity constraints may still be
violated - GARCH models cannot account for
leverage effects
With both normal and t distribution errors
EGARCH
Exponentially Weighted Moving Average (EWMA) -
RiskmetricsTM (1996)
Daily Capital Charges are
9

• Risk management
• Models for Forecasting VaR and Daily Capital
  Charges
• Combining alternative Model to forecast VaR
• Conclusions

Data
DATA DESCRIPTION Closing daily prices for
Standard and Poors Composite 500 Index. SOURCE
Ecowin Financial Database SAMPLE 3 January 2000
to 12 February 2009
Figure 1. Daily Returns on the SP500 Index, 3
January 2000 12 February 2009
Figure 2. Daily Volatility in SP500 Returns 3
January 2000 12 February 2009
10

• Risk management
• Models for Forecasting VaR and Daily Capital
  Charges
• Combining alternative Models to forecast VaR
• Conclusions

Combining alternative Risk Model to Forecast VaR
Banks need not restrict themselves to using only
one of the available risk models. We propose a
risk management strategy that consists in
choosing from among different combinations of
alternative risk models to forecast VaR. One of
them can can be characterized as an aggressive
strategy and another that can be regarded as a
conservative strategy
Figure 3. VaR for SP500 Returns 2 January 2008
12 February 2009
Note The upper blue line represents daily
returns for the SP500 index. The upper red line
represents the infinum of the VaR forecasts for
the different models described above. The lower
green line corresponds to the supremum of the
forecasts of the VaR for the same models.
11

• Risk management
• Models for Forecasting VaR and Daily Capital
  Charges
• Combining alternative Models to forecast VaR
• Conclusions

Forecasting VaR and Calculating DCC Performance
of the Proposed models
Table 3. Percentage of Days Minimizing Daily
Capital Charges, Mean Daily Capital Charges, and
Number of Violations for Alternative Models of
Volatility
Figure 5. Number of Violations Accumulated Over
260 Days 3 January 2008-12 February 2009
Model of Days Minimizing Daily Capital Charges Mean Daily Capital Charges Number of Violations
Riskmetrics 14.0 0.163 10
GARCH 0.0 0.161 13
GJR 10.0 0.157 7
EGARCH 1.70 0.146 13
GARCH_t 0.00 0.171 3
GJR_t 0.00 0.167 3
EGARCH_t 34.0 0.153 3
Lower bound 0.00 0.177 3
Upper bound 39.6 0.143 16
12

• Risk management
• Models for Forecasting VaR and Daily Capital
  Charges
• Combining alternative Models to forecast VaR
• Conclusions

Forecasting VaR and Calculating DCC Performance
of the Proposed models
Figure 4. VaR and Mean VaR for the Previous 60
Days to Calculate Daily Capital Charges for
SP500 Returns
It can be observed from Figure 4 that daily
capital charges always exceed VaR (in absolute
terms). Moreover, immediately after the financial
crisis had started, a significant amount of
capital was set aside to cover likely financial
losses. This is a positive feature of the Basel
II Accord, since it can have the effect of
shielding banks from possible significant
financial losses.
13

• Risk management
• Models for Forecasting VaR and Daily Capital
  Charges
• Combining alternative Models to forecast VaR
• Conclusions

Forecasting VaR and Calculating DCC Performance
of the Proposed models
Figure 6. Duration of Minimum Daily Capital
Charges for Alternative Models of Volatility
Alternative risk models were found to be optimal
before and during the financial crisis. (1)
Before the global financial crisis from 3 January
2008 to 6 June 2008, the best model for
minimizing daily capital charges is GARCH
(coinciding with the Upperbound). For the period
6 June 2008 to 16 July 2008, GJR was best and,
for only 5 days, EGARCH was the best. This is a
period with relatively low volatility and few
extreme values. (2) Riskmetrics is the best
model from 16 July 2008 to 15 September 2008. The
SP500 reached a peak on 12 August 2008, after
which it started to decrease. In the second half
of September 2008, the volatility on returns
began to increase considerably. (3) During most
of the global financial crisis, from 24 September
2008 to the end of the sample, the best model was
EGARCH_T. This is a period with considerably high
volatility and a large number of extreme values
of returns. EGARCH can capture asymmetric
volatility, thereby providing a more accurate
measure of risk during large financial turbulence.
A Decision Rule to Minimize Daily Capital Charges
in Forecasting Value-at-Risk (February 26, 2009).
Available at SSRN http//ssrn.com/abstract134984
4
14

• Risk management
• Models for Forecasting VaR and Daily Capital
  Charges
• Combining alternative Models to forecast VaR
• Conclusions

Conclusions

• Under the Basel II Accord,
• Banks have to communicate their risk estimates to
  the monetary authorities
• They can use a variety of VaR models to estimate
  risks.
• Banks are subject to a back-test
• Daily capital charges as protection against
  market risk must be set at the higher of the
  previous days VaR or the average VaR over the
  last 60 business days, multiplied by a factor k.
• Banks objective is to maximize profits, so they
  wish to minimize their capital charges while
  restricting the number of violations in a given
  year below the maximum of 10 allowed by the Basel
  II Accord. From this target it follows naturally
  that ADIs have to choose an optimal reporting
  policy that may strategically under-report or
  over-report their forecast of VaR in order to
  minimize the daily capital requirement.
• We define risk management in terms of choosing
  sensibly from a variety of conditional volatility
  (risk) models, considering combining alternatives
  risk models. We propose both a conservative and
  an aggressive strategies.
• We found optimal strategies using different
  combinations or alternatives risk models for
  predicting VaR and minimizing daily capital
  changes.
• In this paper we analyzed the performance of
  existing state-of-the-art, as well as a novel,
  risk management strategies permitted under the
  Basel II framework, as applied to the SP500
  index. Such risk management strategies could well
  have provided adequate coverage against market
  risk during the 2008-09 period, which included
  the global financial crisis.
• The area between the bounds provided by the
  aggressive and the conservative strategy can be
  seen to be fertile area for future research. .

15
Agenda

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• Robust Strategy for Market Risk Disclosures
• Results
• Conclusions

16

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

GFC-Robust Risk Management Strategy
What is a GFC-Robust Risk Management Strategy? A
crisis robust strategy IS an optimal risk
management strategy that remains unchanged
regardless of whether it is used before, during
or after a significant financial crisis.
Parametric methods for forecasting VaR are
typically fitted to historical returns assuming
specific conditional distributions of returns,
such as normality, Student-t, or generalized
normal distribution. The VaR forecast depends on
the parametric model, the conditional
distribution and can be heavily affected by a few
large observations. Some models provide many
violations, but low daily capital charges.
Additionally, these results can change
drastically from tranquil to turbulent periods.
Therefore , regardless of economic turbulence,
is there a model to forecast VaR that provides a
reasonable number of violations and daily capital
charges? Why a GFC-Robust Risk Management
Strategy is Needed?
17

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

GFC-Robust Risk Management Strategy
Duration of Minimum Daily Capital Charges for
Alternative Models of Volatility McAleer,
Jimenez-Martin, Perez-Amaral (2010)
18

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Data
DATA Closing daily prices for Standard and Poors
Composite 500 Index. From Reuters-Ecowin
Financial Database SAMPLE 3 January 2000 to 16
March 2010
Daily Returns on SP500 Index 3 January 2000 16
March 2010
Daily Returns volatitlity on SP500 Index 3
January 2000 16 March 2010
19

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Data
BEFORE CRISIS DURING CRISIS
AFTER CRISIS
20

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

• Proposal use median of the point forecasts of
  the usual VaR models. Or in general, quantiles.
• Associated with robust statistics, turns out to
  be the best in our case.

21

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Data
VaR for SP500 Returns 2 January 2008 16 March
2010
Peak_value Date Trough_value date
SP Returns 1305.323 11/8/2008 676.5302 9/3/2009
22

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Results
Table 3. Comparing Alternative Models of Volatility Table 3. Comparing Alternative Models of Volatility Table 3. Comparing Alternative Models of Volatility Table 3. Comparing Alternative Models of Volatility Table 3. Comparing Alternative Models of Volatility Table 3. Comparing Alternative Models of Volatility Table 3. Comparing Alternative Models of Volatility Table 3. Comparing Alternative Models of Volatility Table 3. Comparing Alternative Models of Volatility Table 3. Comparing Alternative Models of Volatility Table 3. Comparing Alternative Models of Volatility Table 3. Comparing Alternative Models of Volatility Table 3. Comparing Alternative Models of Volatility Table 3. Comparing Alternative Models of Volatility Table 3. Comparing Alternative Models of Volatility Table 3. Comparing Alternative Models of Volatility Table 3. Comparing Alternative Models of Volatility Table 3. Comparing Alternative Models of Volatility
BEFORE CRISIS BEFORE CRISIS BEFORE CRISIS BEFORE CRISIS BEFORE CRISIS BEFORE CRISIS DURING CRISIS DURING CRISIS DURING CRISIS DURING CRISIS DURING CRISIS DURING CRISIS AFTER CRISIS AFTER CRISIS AFTER CRISIS AFTER CRISIS AFTER CRISIS
Model AvDCC NoV FailRa AcLoss AlTick AvDCC NoV FailRa AcLoss AlTick AvDCC NoV FailRa AcLoss AlTick
RSKM 9.03 4 2.5 1.60 6.28 22.51 6 4.0 6.21 16.27 11.19 5 1.9 1.62 10.88
GARCH 9.08 6 3.8 1.89 6.42 21.39 7 4.7 7.40 16.95 10.76 6 2.3 1.74 10.73
GJR 9.00 3 1.9 1.03 5.75 20.11 4 2.7 5.16 15.53 10.71 8 3.0 2.75 11.10
EGARCH 8.87 4 2.5 1.13 5.82 19.92 10 6.7 12.10 20.49 9.92 10 3.8 3.81 11.52
GARCH_t 11.16 1 0.6 0.21 6.03 24.52 2 1.3 2.85 15.51 13.67 1 0.4 0.13 11.52
GJR_t 10.80 1 0.6 0.57 6.26 24.27 2 1.3 2.88 15.57 12.21 3 1.1 0.56 10.47
EGARCH_t 10.75 1 0.6 0.48 6.19 20.95 2 1.3 4.51 15.23 11.14 4 1.5 0.80 9.99
GARCH_g 9.81 2 1.3 0.79 5.90 22.11 5 3.4 4.41 15.35 11.94 2 0.8 0.73 10.75
GJR_g 9.82 1 0.6 0.80 5.96 21.97 3 2.0 3.96 15.37 11.08 4 1.5 1.34 10.39
EGARCH_g 9.75 1 0.6 0.72 5.89 19.58 6 4.0 7.10 16.68 10.20 6 2.3 2.22 10.56
Inf 11.78 1 0.6 0.21 6.42 25.26 2 1.3 2.64 15.78 13.99 1 0.4 0.07 11.56
Sup 8.45 6 3.8 2.06 6.28 20.01 11 7.4 12.28 20.52 9.71 10 3.8 4.31 11.89
Mean 9.77 1 0.6 0.69 5.82 20.73 3 2.0 4.57 15.21 11.11 3 1.1 0.99 10.21
10th Per. 11.43 1 0.6 0.34 6.38 24.56 2 1.3 2.87 15.62 13.34 2 0.8 0.13 11.10
20th Per. 10.81 1 0.6 0.51 6.21 23.21 2 1.3 3.49 15.49 12.39 2 0.8 0.40 10.60
30th Per. 10.37 1 0.6 0.56 6.03 22.07 2 1.3 3.96 15.34 11.85 2 0.8 0.62 10.40
40th Per. 10.06 1 0.6 0.65 5.94 21.23 3 2.0 4.40 15.32 11.38 3 1.1 0.85 10.27
50th Per. (Median) 9.71 1 0.6 0.76 5.86 20.57 3 2.0 4.81 15.37 10.95 4 1.5 1.07 10.14
60th Per. 9.39 2 1.3 0.87 5.80 22.29 5 3.4 5.21 15.41 10.66 5 1.9 1.51 10.29
70th Per. 9.06 3 1.9 1.05 5.80 21.86 7 4.7 6.00 15.84 10.68 8 3.0 2.05 10.53
80th Per. 8.65 4 2.5 1.45 5.95 21.32 8 5.4 7.66 17.04 10.32 9 3.4 2.90 11.06
90th Per. 8.28 4 2.5 1.81 6.11 - 20.97 10 6.7 10.53 19.19 10.01 10 3.8 3.75 11.54
23

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Results
Criteria for Comparing Percentile
Strategies BEFORE CRISIS DURING CRISIS
AFTER CRISIS
24

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Conclusions

• Under the Basel II Accord,
• ADIs have to communicate their risk estimates to
  the monetary authorities
• They can use a variety of VaR models to estimate
  risks.
• ADIs are subject to back-testing
• Daily capital charges as protection against
  market risk must be set at the higher of the
  previous days VaR or the average VaR over the
  last 60 business days, multiplied by a factor k.
• VaR models currently in use can lead to high
  daily capital requirements or an excessive number
  of violations.
• ADIs objective is to maximize profits, so they
  wish to minimize their capital charges while
  restricting the number of violations in a given
  year below the maximum of 10 allowed by the Basel
  II Accord. From this target it follows naturally
  that ADIs have to choose an optimal reporting
  policy that may strategically under-report or
  over-report their forecast of VaR in order to
  minimize the daily capital requirement.

25

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Conclusions II

1. In McAleer et al. (2010), the VaR model
   minimizing DCC before, during and after the GFC
   changed frequently.
2. In this paper we propose robust risk forecasts
   that use combinations of several conditional
   volatility models for forecasting VaR eg the
   median.
3. The median is robust, in that it yields
   reasonable daily capital charges, number of
   violations that do not jeopardize institutions
   that might use it, and more importantly, is
   invariant before, during and after the 2008-09
   GFC.
4. The median is a model that balances daily capital
   charges and violation penalties in minimizing
   DCC.  

26

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Conclusions III

1. Combining forecasting models is within the spirit
   of the Basel II Accord, although its use would
   require approval by the regulatory authorities,
   as for any forecasting model.
2. This approach is not computationally demanding,
   even though several models have to be specified
   and estimated over time.
3. Further research is being carried out using a
   variety of different indexes from different
   countries. Temptative results confirm that the
   median is global financial crisis robust and
   clearly preferred in most cases to single models.

27

• International evidence on GFC-robust forecasts
  for risk management under the Basel Accord
• Michael McAleer
• Erasmus University Rotterdam/ Tinbergen Institute
• The Netherlands / Institute of Economic Research,
  Kyoto University Japan
• Juan-Angel Jimenez-Martin
• Teodosio Perez-Amaral
• Complutense University of Madrid, Spain

28

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Results I
DATA Closing daily prices. From Reuters-Ecowin
Financial Database SAMPLE 3 January 2000 to 14
October 2010
IBEX35 Madrid
CAC 40 Paris
FTSE 100 London
SP500 New York
DAX 30 Frankfurt
NIKKEI TOKYO
Dow Jones100 New York
HSI Hong Kong
SMI Zurich
29

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Results II
Daily Returns 3 January 2000 14 October 2010

30

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Results III
Volatility of Daily Returns 3 January 2000 14
October 2010

31

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Results IV
Daily Returns Correlations 3 January 2008 14
October 2010
Correlations between Daily Returns Volatilities
3 January 2008 14 October 2010
CAC DAX DJI FTSE HSI IBEX NIKKEI SMI SP500
CAC 1
DAX 0.87 1.00
DJI 0.52 0.57 1.00
FTSE 0.89 0.80 0.50 1.00
HSI 0.36 0.32 0.20 0.36 1.00
IBEX 0.88 0.79 0.49 0.81 0.35 1.00
NIKKEI 0.30 0.26 0.12 0.30 0.58 0.28 1.00
SMI 0.83 0.78 0.48 0.81 0.32 0.77 0.30 1.00
SP500 0.54 0.58 0.97 0.51 0.21 0.50 0.12 0.48 1.00
CAC DAX DJI FTSE HSI IBEX NIKKEI SMI SP500
CAC 1
DAX 0.86 1.00
DJI 0.57 0.62 1.00
FTSE 0.90 0.80 0.54 1.00
HSI 0.40 0.44 0.37 0.41 1.00
IBEX 0.85 0.76 0.50 0.78 0.36 1.00
NIKKEI 0.41 0.43 0.54 0.40 0.29 0.40 1.00
SMI 0.81 0.73 0.53 0.81 0.41 0.74 0.43 1.00
SP500 0.57 0.62 0.98 0.54 0.36 0.50 0.54 0.53 1.00

32

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Results V
BEFORE CRISIS DURING CRISIS
AFTER CRISIS
33

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Results VI

• Proposal use median of the point forecasts of
  the usual VaR models. Or in general, quantiles.
• Associated with statistics, turns out to be the
  best in our case.
• Mean of Daily Capital Charges
• Number of Violations
• Accumulated losses
• Tick loss function

34

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Results VII
Daily Capital charges
Table 5 Daily Capital Charges ranking before the GFC Table 5 Daily Capital Charges ranking before the GFC Table 5 Daily Capital Charges ranking before the GFC Table 5 Daily Capital Charges ranking before the GFC Table 5 Daily Capital Charges ranking before the GFC Table 5 Daily Capital Charges ranking before the GFC Table 5 Daily Capital Charges ranking before the GFC Table 5 Daily Capital Charges ranking before the GFC Table 5 Daily Capital Charges ranking before the GFC
Before CAC DAX DJ100 FTSE HSHK IBEX NIKKEI SMI SP500
Before SUP -7.2- (5.55 ) SUP -6.4- (6.9 ) SUP -6.4 - (2.0 ) SUP - 7.3- (6.6 ) EGARCH - 6.6- (5.6 ) EGARCH - 4.8- (6.6 ) SUP - 8.0- (4.6 ) SUP - 8.0- (5.1 ) SUP - 9.6- (2.1 )
Before GARCH -5.8- (5.22 ) EGARCH - 3.2- (4.2 ) GARCH - 6.4- (2.0 ) EGARCH -5.8 - (4.0 ) SUP - 1.7- (0.5 ) SUP -8.0 - (8.2 ) EGARCH - 8.0 (4.5) EGARCH -3.2 - (2.7 ) EGARCH -6.4 - (1.1 )
Before EGARCH -4.3- (4.0 ) GARCH - 4.8- (6.2 ) RSKM -4.8 - (1.7) GJR -5.8 - (4.7 ) GJR - 6.6- (5.5 ) GARCH - 6.4- (6.9 ) GARCH -4.8 - (2.0 ) GJR - 4.8- (3.4 ) GARCH -9.6 - (1.9 )
Before RSKM -2.9- (5.1 ) RSKM - 6.4- (6.5 ) EGARCH - 6.4- (1.0 ) EGARCH_G - 4.4- (3.7 ) GARCH - 6.6- (5.4 ) RSKM - 3.2- (7.0 ) RSKM - 4.8- (2.5 ) GARCH - 8.0- (4.9 ) RSKM -6.4 - (1.6 )
Before GARCH_G - 2.9- (4.8 ) GARCH_G - 4.8- (5.7 ) GJR -6.4 - (1.1 ) GARCH - 7.3- (5.8 ) RSKM - 1.7- (1.3) GJR -3.2 - (5.7 ) GJR - 1.6- (0.7 ) RSKM - 6.4- (4.2 ) GJR - 4.8- (1.0 )
Before GJR - 4.3- (4.1 ) GJR - 3.2- (4.8) GARCH_G - 3.2- (1.1 ) GJR_G - 5.8 - (4.4 ) EGARCH_G -8.3 - (6.8 ) EGARCH_G - 4.8- (5.8 ) EGARCH_G - 1.6- (0.5 ) EGARCH_G -3.2 - (2.2 ) GARCH_G -3.2 - ( 0.8)
Before EGARCH_G - 4.3- (3.6 ) EGARCH_G - 1.6- (4.0 ) MEDIAN - 3.2- (0.7 ) MEDIAN -5.8 - (4.4 ) MEDIAN - 3.3- (1.8 ) GARCH_G -3.2 - (6.4 ) MEDIAN -1.6 - (0.7 ) GARCH_G -6.4- (3.9 ) MEDIAN -1.6- (0.8 )
Before MEDIAN - 2.9- (3.9 ) MEAN - 3.2- (4.5 ) MEAN -3.2- (0.7 ) MEAN - 5.8- (4.3 ) MEAN - 5.0- (3.3 ) MEDIAN -3.2- (5.6 ) MEAN - 1.6- (0.9 ) MEDIAN -3.2- (2.9 ) MEAN - 1.6- ( 0.7)
Before MEAN -2.9 - (3.7 ) MEDIAN -3.2- (4.6 ) GJR_G -1.6- (0.6 ) RSKM -7.3 - (4.9 ) GJR_G - 8.3- (6.4 ) MEAN -3.2- (5.7 ) GARCH_G -1.6 - (1.2 ) GJR_G -3.2- (2.9 ) EGARCH_G - 1.6- (0.7 )
Before GJR_G -2.9 - (3.8 ) GJR_G -3.2- (4.5 ) EGARCH_G -1.6- (0.6 ) GARCH_G -7.3 - (5.2 ) GARCH_G - 8.3- (6.1 ) GJR_G -3.2- (5.3 ) GJR_G - 1.6- (0.3 ) MEAN -3.2- (3.0 ) GJR_G - 1.6- (0.8 )
Before GARCH_T -2.9- (4.5 ) GARCH_T -4.8- (5.2 ) GARCH_T -3.2- (0.4 ) EGARCH_T - 4.4- (2.9 ) EGARCH_T - 8.3- (6.6 ) EGARCH_T -3.2- (4.4 ) EGARCH_T -1.6- (0.0 ) EGARCH_T -3.2- (1.5 ) GJR_T -1.6 - (0.6)
Before GJR_T - 2.9- (3.5 ) EGARCH_T -1.6- (3.9 ) GJR_T -1.6- (0.3 ) GJR_T - 5.8- (3.8 ) GJR_T -6.6 - (4.3 ) GARCH_T -3.2- (5.8 ) GARCH_T - 1.6- (0.6 ) GJR_T -3.2- (2.1 ) EGARCH_T -1.6 - (0.5 )
Before EGARCH_T -1.4 - (1.3 ) GJR_T -3.2- (4.2 ) EGARCH_T -1.6- (0.3 ) GARCH_T -5.8 - (4.3 ) GARCH_T - 8.3- (6.8 ) GJR_T -3.2- (4.6 ) GJR_T - 0.0- (0.0 ) GARCH_T -3.2- (2.9 ) GARCH_T -1.6 - (0.2 )
Before INF - 1.4- (1.3 ) INF -1.6- (3.9 ) INF -1.6- (0.3 ) INF - 4.4- (2.1 ) INF - 5.0- (2.7 ) INF -3.2- (4.4 ) INF - 0.0- (0.0 ) INF -3.2- (1.5 ) INF - 1.6- (0.2 )
Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC
During CAC DAX DJ FTSE HSHK IBEX NIKKEI SMI SP500
During SUP -13.06- (7.3) EGARCH -8.4- (3.9) EGARCH_G -6.7- (6.7) SUP -13.3- (8.0) SUP -4.8- (4.6) SUP -10- (2.5) EGARCH -14.9- (13.0) EGARCH -8.3- (8.0) EGARCH -16.7- (12.2)
During EGARCH -7.5- (4.6) GARCH -8.4- (3.9) EGARCH -11.7- (6.7) EGARCH -13.3- (8.0) EGARCH -4.8- (4.6) EGARCH_G -3- (2.5) SUP -18.2- (13.0) SUP -11.7- (8.0) SUP -18.3- (12.5)
During EGARCH_G -7.5- (5.7) EGARCH_G -8.4- (2.8) GARCH -10. 0- (5.0) EGARCH_G -13.3- (6.6) GJR_N -4.8- (4.2) EGARCH -10- (4.4) RSKM -6.6- (9.8) EGARCH_G -8.3- (4.2) GJR -6.7- (5.2)
During GJR -7.5- (5.1) GJR -8.4- (4.2) GJR -6.7- (3.9) GJR -9.5- (6.5) GARCH -4.8- (5.5) GJR -8.1- (3.5) GARCH -8.3- (8.1) GJR -8.3- (5.1) MEDIAN -5.0- (4.9)
During EGARCH_T -3.7- (3.3) SUP -15.1- (6.5) SUP -15.0- (7.5) EGARCH_T -11.4- (4.3) RSKM -4.8- (5.4) GARCH -8.1- (2.6) EGARCH_G -9.9- (6.7) GARCH -10- (4.8) MEAN -5.0- (4.6)
During GARCH -9.3- (3.9) MEDIAN -6.7- (2.7) MEDIAN -3.3- (3.0) GARCH -7.6- (6.3) EGARCH_G -1.6- (1.0) RSKM -5.0- (2.7) GJR_N -9.9- (5.5) MEDIAN -6.7- (3.7) EGARCH_T -3.3- (4.6)
During MEDIAN -5.6- (3.5) MEAN -6.7- (2.7) MEAN -5.0 - (2.8) MEAN -9.5- (4.9) MEDIAN -4.8- (1.9) MEDIAN -5.0- (1.6) MEDIAN -5.0- (4.8) MEAN -6.7- (3.6) GARCH -11.7- (7.5)
During MEAN -5.6- (3.3) GJR_G -8.4- (3.3) GARCH_G -3.3- (2.5) GJR_G -9.5- (5.6) MEAN -4.8- (1.4) GJR_G -5.0- (1.9) MEAN -5.0- (4.9) GJR_G -8.3- (4.0) EGARCH_G -13.3- (7.2)
During RSKM -1.8- (3.2) GARCH_G -5.0- (2.7) GJR_G -3.3- (2.5) RSKM -9.5- (6.0) GJR_G -3.2- (1.0) MEAN -3.0 - (1.5) GARCH_G -5.0- (6.3) EGARCH_T -6.7- (2.8) GJR_G -5.0- (4.0)
During GJR_G -7.5- (4.4) GJR_T -6.7- (2.5) EGARCH_T -3.3- (2.6) MEDIAN -11.4- (5.4) GARCH_G -4.8- (2.5) GARCH_G -3.0 - (1.3) GJR_G -3.3- (3.8) GARCH_G -8.3- (3.3) GARCH_G -8.3- (4.5)
During GARCH_G -5.6- (2.7) EGARCH_T -3.4 - (1.9) RSKM -10.0- (4.3) GARCH_G -7.6- (5.0) EGARCH_T -0.0- (0.0) EGARCH_T -3.0- (0.6) EGARCH_T -8.3- (3.0) GJR_T -6.7- (2.3) RSKM -10.0- (6.2)
During GJR_T -5.6- (3.3) RSKM -8.4- (3.7) GJR_T -3.3- (1.4) GJR_T -9.5- (4.1) GJR_T -0.0- (0.0) GJR_T -2.0 - (0.2) GJR_T -3.3- (2.8) RSKM -10.0- (5.8) GJR_T -3.3- (3.0)
During GARCH_T -1.9- (1.9) GARCH_T -5.0- (1.7) GARCH_T -3.3- (1.2) GARCH_T -5.7- (3.1) GARCH_T -0.0- (0.0) GARCH_T -2.0 - (0.1) GARCH_T -5.0- (4.3) GARCH_T -1.7- (1.6) GARCH_T -3.3- (2.9)
During INF -1.9- (1.9) INF -3.4- (1.7) INF -3.3- (1.2) INF -5.7- (1.4) INF -0.0- (0.0) INF -0.0 - (0.0) INF -3.3- (2.3) INF -1.7- (0.7) INF -3.3- (2.7)
Increase
35

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Results VIII
Table 5 Daily Capital Charges ranking before the GFC Table 5 Daily Capital Charges ranking before the GFC Table 5 Daily Capital Charges ranking before the GFC Table 5 Daily Capital Charges ranking before the GFC Table 5 Daily Capital Charges ranking before the GFC Table 5 Daily Capital Charges ranking before the GFC Table 5 Daily Capital Charges ranking before the GFC Table 5 Daily Capital Charges ranking before the GFC Table 5 Daily Capital Charges ranking before the GFC
Before CAC DAX DJ100 FTSE HSHK IBEX NIKKEI SMI SP500
Before SUP -7.2- (5.55 ) SUP -6.4- (6.9 ) SUP -6.4 - (2.0 ) SUP - 7.3- (6.6 ) EGARCH - 6.6- (5.6 ) EGARCH - 4.8- (6.6 ) SUP - 8.0- (4.6 ) SUP - 8.0- (5.1 ) SUP - 9.6- (2.1 )
Before GARCH -5.8- (5.22 ) EGARCH - 3.2- (4.2 ) GARCH - 6.4- (2.0 ) EGARCH -5.8 - (4.0 ) SUP - 1.7- (0.5 ) SUP -8.0 - (8.2 ) EGARCH - 8.0 (4.5) EGARCH -3.2 - (2.7 ) EGARCH -6.4 - (1.1 )
Before EGARCH -4.3- (4.0 ) GARCH - 4.8- (6.2 ) RSKM -4.8 - (1.7) GJR -5.8 - (4.7 ) GJR - 6.6- (5.5 ) GARCH - 6.4- (6.9 ) GARCH -4.8 - (2.0 ) GJR - 4.8- (3.4 ) GARCH -9.6 - (1.9 )
Before RSKM -2.9- (5.1 ) RSKM - 6.4- (6.5 ) EGARCH - 6.4- (1.0 ) EGARCH_G - 4.4- (3.7 ) GARCH - 6.6- (5.4 ) RSKM - 3.2- (7.0 ) RSKM - 4.8- (2.5 ) GARCH - 8.0- (4.9 ) RSKM -6.4 - (1.6 )
Before GARCH_G - 2.9- (4.8 ) GARCH_G - 4.8- (5.7 ) GJR -6.4 - (1.1 ) GARCH - 7.3- (5.8 ) RSKM - 1.7- (1.3) GJR -3.2 - (5.7 ) GJR - 1.6- (0.7 ) RSKM - 6.4- (4.2 ) GJR - 4.8- (1.0 )
Before GJR - 4.3- (4.1 ) GJR - 3.2- (4.8) GARCH_G - 3.2- (1.1 ) GJR_G - 5.8 - (4.4 ) EGARCH_G -8.3 - (6.8 ) EGARCH_G - 4.8- (5.8 ) EGARCH_G - 1.6- (0.5 ) EGARCH_G -3.2 - (2.2 ) GARCH_G -3.2 - ( 0.8)
Before EGARCH_G - 4.3- (3.6 ) EGARCH_G - 1.6- (4.0 ) MEDIAN - 3.2- (0.7 ) MEDIAN -5.8 - (4.4 ) MEDIAN - 3.3- (1.8 ) GARCH_G -3.2 - (6.4 ) MEDIAN -1.6 - (0.7 ) GARCH_G -6.4- (3.9 ) MEDIAN -1.6- (0.8 )
Before MEDIAN - 2.9- (3.9 ) MEAN - 3.2- (4.5 ) MEAN -3.2- (0.7 ) MEAN - 5.8- (4.3 ) MEAN - 5.0- (3.3 ) MEDIAN -3.2- (5.6 ) MEAN - 1.6- (0.9 ) MEDIAN -3.2- (2.9 ) MEAN - 1.6- ( 0.7)
Before MEAN -2.9 - (3.7 ) MEDIAN -3.2- (4.6 ) GJR_G -1.6- (0.6 ) RSKM -7.3 - (4.9 ) GJR_G - 8.3- (6.4 ) MEAN -3.2- (5.7 ) GARCH_G -1.6 - (1.2 ) GJR_G -3.2- (2.9 ) EGARCH_G - 1.6- (0.7 )
Before GJR_G -2.9 - (3.8 ) GJR_G -3.2- (4.5 ) EGARCH_G -1.6- (0.6 ) GARCH_G -7.3 - (5.2 ) GARCH_G - 8.3- (6.1 ) GJR_G -3.2- (5.3 ) GJR_G - 1.6- (0.3 ) MEAN -3.2- (3.0 ) GJR_G - 1.6- (0.8 )
Before GARCH_T -2.9- (4.5 ) GARCH_T -4.8- (5.2 ) GARCH_T -3.2- (0.4 ) EGARCH_T - 4.4- (2.9 ) EGARCH_T - 8.3- (6.6 ) EGARCH_T -3.2- (4.4 ) EGARCH_T -1.6- (0.0 ) EGARCH_T -3.2- (1.5 ) GJR_T -1.6 - (0.6)
Before GJR_T - 2.9- (3.5 ) EGARCH_T -1.6- (3.9 ) GJR_T -1.6- (0.3 ) GJR_T - 5.8- (3.8 ) GJR_T -6.6 - (4.3 ) GARCH_T -3.2- (5.8 ) GARCH_T - 1.6- (0.6 ) GJR_T -3.2- (2.1 ) EGARCH_T -1.6 - (0.5 )
Before EGARCH_T -1.4 - (1.3 ) GJR_T -3.2- (4.2 ) EGARCH_T -1.6- (0.3 ) GARCH_T -5.8 - (4.3 ) GARCH_T - 8.3- (6.8 ) GJR_T -3.2- (4.6 ) GJR_T - 0.0- (0.0 ) GARCH_T -3.2- (2.9 ) GARCH_T -1.6 - (0.2 )
Before INF - 1.4- (1.3 ) INF -1.6- (3.9 ) INF -1.6- (0.3 ) INF - 4.4- (2.1 ) INF - 5.0- (2.7 ) INF -3.2- (4.4 ) INF - 0.0- (0.0 ) INF -3.2- (1.5 ) INF - 1.6- (0.2 )
Forecast Model
SUP -7.2- (5.55 )
Number of Violations
Accumulated Losses
36

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Results IX
Daily Capital charges
Table 5 Daily Capital Charges ranking before the GFC Table 5 Daily Capital Charges ranking before the GFC Table 5 Daily Capital Charges ranking before the GFC Table 5 Daily Capital Charges ranking before the GFC Table 5 Daily Capital Charges ranking before the GFC Table 5 Daily Capital Charges ranking before the GFC Table 5 Daily Capital Charges ranking before the GFC Table 5 Daily Capital Charges ranking before the GFC Table 5 Daily Capital Charges ranking before the GFC
Before CAC DAX DJ100 FTSE HSHK IBEX NIKKEI SMI SP500
Before SUP -7.2- (5.55 ) SUP -6.4- (6.9 ) SUP -6.4 - (2.0 ) SUP - 7.3- (6.6 ) EGARCH - 6.6- (5.6 ) EGARCH - 4.8- (6.6 ) SUP - 8.0- (4.6 ) SUP - 8.0- (5.1 ) SUP - 9.6- (2.1 )
Before EGARCH - 3.2- (4.2 ) EGARCH -5.8 - (4.0 ) SUP - 1.7- (0.5 ) SUP -8.0 - (8.2 ) EGARCH - 8.0 (4.5) EGARCH -3.2 - (2.7 ) EGARCH -6.4 - (1.1 )
Before EGARCH -4.3- (4.0 ) RSKM -4.8 - (1.7)
Before RSKM -2.9- (5.1 ) RSKM - 6.4- (6.5 ) EGARCH - 6.4- (1.0 ) RSKM - 3.2- (7.0 ) RSKM - 4.8- (2.5 ) RSKM -6.4 - (1.6 )
Before RSKM - 1.7- (1.3) RSKM - 6.4- (4.2 )
Before )
Before MEDIAN - 3.2- (0.7 ) MEDIAN -5.8 - (4.4 ) MEDIAN - 3.3- (1.8 ) MEDIAN -1.6 - (0.7 ) MEDIAN -1.6- (0.8 )
Before MEDIAN - 2.9- (3.9 ) MEDIAN -3.2- (5.6 ) ) MEDIAN -3.2- (2.9 )
Before MEDIAN -3.2- (4.6 ) RSKM -7.3 - (4.9 )
Before
Before
Before
Before
Before
Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC
During CAC DAX DJ FTSE HSHK IBEX NIKKEI SMI SP500
During SUP -13.06- (7.3) EGARCH -8.4- (3.9) SUP -13.3- (8.0) SUP -4.8- (4.6) SUP -10- (2.5) EGARCH -14.9- (13.0) EGARCH -8.3- (8.0) EGARCH -16.7- (12.2)
During EGARCH -7.5- (4.6) ) EGARCH -11.7- (6.7) EGARCH -13.3- (8.0) EGARCH -4.8- (4.6) SUP -18.2- (13.0) SUP -11.7- (8.0) SUP -18.3- (12.5)
During EGARCH -10- (4.4) RSKM -6.6- (9.8)
During MEDIAN -5.0- (4.9)
During SUP -15.1- (6.5) SUP -15.0- (7.5) RSKM -4.8- (5.4)
During MEDIAN -6.7- (2.7) MEDIAN -3.3- (3.0) RSKM -5.0- (2.7) MEDIAN -6.7- (3.7)
During MEDIAN -5.6- (3.5) MEDIAN -4.8- (1.9) MEDIAN -5.0- (1.6) MEDIAN -5.0- (4.8) MEAN -6.7- (3.6)
During
During RSKM -1.8- (3.2) RSKM -9.5- (6.0)
During MEDIAN -11.4- (5.4)
During RSKM -10.0- (4.3) RSKM -10.0- (6.2)
During RSKM -8.4- (3.7) RSKM -10.0- (5.8)
During
During
Increase
37

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Results X
Daily Capital charges
Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC
During CAC DAX DJ FTSE HSHK IBEX NIKKEI SMI SP500
During SUP -13.06- (7.3) EGARCH -8.4- (3.9) EGARCH_G -6.7- (6.7) SUP -13.3- (8.0) SUP -4.8- (4.6) SUP -10- (2.5) EGARCH -14.9- (13.0) EGARCH -8.3- (8.0) EGARCH -16.7- (12.2)
During EGARCH -7.5- (4.6) GARCH -8.4- (3.9) EGARCH -11.7- (6.7) EGARCH -13.3- (8.0) EGARCH -4.8- (4.6) EGARCH_G -3- (2.5) SUP -18.2- (13.0) SUP -11.7- (8.0) SUP -18.3- (12.5)
During EGARCH_G -7.5- (5.7) EGARCH_G -8.4- (2.8) GARCH -10. 0- (5.0) EGARCH_G -13.3- (6.6) GJR_N -4.8- (4.2) EGARCH -10- (4.4) RSKM -6.6- (9.8) EGARCH_G -8.3- (4.2) GJR -6.7- (5.2)
During GJR -7.5- (5.1) GJR -8.4- (4.2) GJR -6.7- (3.9) GJR -9.5- (6.5) GARCH -4.8- (5.5) GJR -8.1- (3.5) GARCH -8.3- (8.1) GJR -8.3- (5.1) MEDIAN -5.0- (4.9)
During EGARCH_T -3.7- (3.3) SUP -15.1- (6.5) SUP -15.0- (7.5) EGARCH_T -11.4- (4.3) RSKM -4.8- (5.4) GARCH -8.1- (2.6) EGARCH_G -9.9- (6.7) GARCH -10- (4.8) MEAN -5.0- (4.6)
During GARCH -9.3- (3.9) MEDIAN -6.7- (2.7) MEDIAN -3.3- (3.0) GARCH -7.6- (6.3) EGARCH_G -1.6- (1.0) RSKM -5.0- (2.7) GJR_N -9.9- (5.5) MEDIAN -6.7- (3.7) EGARCH_T -3.3- (4.6)
During MEDIAN -5.6- (3.5) MEAN -6.7- (2.7) MEAN -5.0 - (2.8) MEAN -9.5- (4.9) MEDIAN -4.8- (1.9) MEDIAN -5.0- (1.6) MEDIAN -5.0- (4.8) MEAN -6.7- (3.6) GARCH -11.7- (7.5)
During MEAN -5.6- (3.3) GJR_G -8.4- (3.3) GARCH_G -3.3- (2.5) GJR_G -9.5- (5.6) MEAN -4.8- (1.4) GJR_G -5.0- (1.9) MEAN -5.0- (4.9) GJR_G -8.3- (4.0) EGARCH_G -13.3- (7.2)
During RSKM -1.8- (3.2) GARCH_G -5.0- (2.7) GJR_G -3.3- (2.5) RSKM -9.5- (6.0) GJR_G -3.2- (1.0) MEAN -3.0 - (1.5) GARCH_G -5.0- (6.3) EGARCH_T -6.7- (2.8) GJR_G -5.0- (4.0)
During GJR_G -7.5- (4.4) GJR_T -6.7- (2.5) EGARCH_T -3.3- (2.6) MEDIAN -11.4- (5.4) GARCH_G -4.8- (2.5) GARCH_G -3.0 - (1.3) GJR_G -3.3- (3.8) GARCH_G -8.3- (3.3) GARCH_G -8.3- (4.5)
During GARCH_G -5.6- (2.7) EGARCH_T -3.4 - (1.9) RSKM -10.0- (4.3) GARCH_G -7.6- (5.0) EGARCH_T -0.0- (0.0) EGARCH_T -3.0- (0.6) EGARCH_T -8.3- (3.0) GJR_T -6.7- (2.3) RSKM -10.0- (6.2)
During GJR_T -5.6- (3.3) RSKM -8.4- (3.7) GJR_T -3.3- (1.4) GJR_T -9.5- (4.1) GJR_T -0.0- (0.0) GJR_T -2.0 - (0.2) GJR_T -3.3- (2.8) RSKM -10.0- (5.8) GJR_T -3.3- (3.0)
During GARCH_T -1.9- (1.9) GARCH_T -5.0- (1.7) GARCH_T -3.3- (1.2) GARCH_T -5.7- (3.1) GARCH_T -0.0- (0.0) GARCH_T -2.0 - (0.1) GARCH_T -5.0- (4.3) GARCH_T -1.7- (1.6) GARCH_T -3.3- (2.9)
During INF -1.9- (1.9) INF -3.4- (1.7) INF -3.3- (1.2) INF -5.7- (1.4) INF -0.0- (0.0) INF -0.0 - (0.0) INF -3.3- (2.3) INF -1.7- (0.7) INF -3.3- (2.7)
Table 5c Daily Capital Charges ranking after the GFC Table 5c Daily Capital Charges ranking after the GFC Table 5c Daily Capital Charges ranking after the GFC Table 5c Daily Capital Charges ranking after the GFC Table 5c Daily Capital Charges ranking after the GFC Table 5c Daily Capital Charges ranking after the GFC Table 5c Daily Capital Charges ranking after the GFC Table 5c Daily Capital Charges ranking after the GFC Table 5c Daily Capital Charges ranking after the GFC Table 5c Daily Capital Charges ranking after the GFC
CAC DAX DJ FTSE HSHK IBEX NIKEEI SMI SP500
After SUP -7.8- (7.5) SUP -6.6- (7.05) SUP -9.0- (6.52) SUP -9.5- (5.74) SUP -2.4- (2.98) SUP -8.4- (10.6) GARCH -3.6- (2.78) SUP -6.59- (4.01) SUP -10.8- (8.74)
After GJR -4.8- (4.2) EGARCH -4.8- (5.76) EGARCH -9.0- (5.63) MEAN -4.2- (1.94) GJR -1.8- (2.36) EGARCH -7.8- (8.7) SUP -6.6- (4.91) GARCH -4.2- (2.41) EGARCH -10.2- (7.49)
After EGARCH -6.0- (4.9) GARCH -4.2- (3.12) GARCH -5.4- (3.72) EGARCH -7.1- (3.98) EGARCH -1.8- (1.57) GARCH -4.8- (7.0) GJR -4.8- (3.64) GJR -5.4- (2.47) EGARCH_G -6.6- (4.92)
After EGARCH_G -4.2- (3.9) EGARCH_G -4.2- (4.73) GJR -7.2- (4.02) EGARCH_ T -4.2- (2.09) GARCH -2.4- (2.76) MEDIAN -3.6- (4.9) EGARCH -4.8- (3.09) EGARCH -4.8- (1.85) GARCH -7.2- (4.20)
After MEDIAN -3.0- (2.8) MEDIAN -4.2 - (3.58) RSKM -6.0- (4.25) MEDIAN -4.8- (2.37) RSKM -2.4- (2.89) RSKM -4.2- (6.6) RSKM -5.4 - (3.17) GJR_G -3.60- (1.67) MEDIAN -4.8 - (2.73)
After GJR_G -4.2- (3.3) RSKM -4.2- (2.10) EGARCH_G -7.2- (3.38) GARCH -5.3- (2.72) GJR_G -0.6- (1.43) EGARCH_G -6.0- (6.0) MEDIAN -2.4- (1.01) EGARCH_G -3.60- (1.18) GJR -8.4- (5.10)
After MEAN -3.6- (2.4) GJR_N -5.4- (5.50) MEDIAN -4.8- (2.39) GJR_N -6.5- (4.11) MEDIAN -0.6- (1.40) GJR_G -4.8- (4.6) EGARCH_G -2.4- (1.34) RSKM -3.60- (2.51) MEAN -4.8- (2.63)
After EGARCH_T -3.6- (2.9) MEAN -4.2- (2.95) GJR_G -4.8- (2.21) GARCH_G -3.0- (1.82) MEAN -0.6- (1.31) MEAN -3.6- (4.7) MEAN -1.8- (1.00) MEDIAN -3.00- (1.12) RSKM -6.6- (4.19)
After GARCH -5.4- (4.1) GJR_G -4.8- (4.32) MEAN -4.8- (2.20) RSKM -4.2- (2.43) EGARCH_G -0.6- (0.98) GJR_N -7.2- (7.1) GARCH_G -2.4 - (0.97) MEAN -3.00- (1.03) GJR_G -4.8- (2.74)
After RSKM -4.2- (4.3) GJR_T -4.2 - (3.26) EGARCH_T -3.00- (1.59) EGARCH_G -5.9- (3.13) GARCH_G -1.2- (1.51) GARCH_G -3.6- (5.1) GJR_G -3.00- (1.11) GARCH_G -3.00- (1.49) GARCH_G -3.6- (1.93)
After GJR_T -3.0- (2.1) GARCH_G -3.6- (1.51) GARCH_G -4.2- (1.97) GJR_T -3.6- (2.31) GJR_T -0.6- (0.99) GJR_T -3.0- (2.0) GJR_T -1.2- (0.32) EGARCH_T -1.2- (0.54) EGARCH_T -5.4- (2.44)
After GARCH_G -3.6- (2.5) EGARCH_T -4.2- (3.56) GJR_T -3.00- (0.72) GJR_G -6.5- (3.27) EGARCH_T -0.6- (0.46) EGARCH_T -4.2- (2.5) EGARCH_T -1.2- (0.35) GJR_T -1.8- (0.80) GJR_T -3.0- (1.33)
After GARCH_T -1.8- (1.0) GARCH_T -1.8- (0.31) GARCH_T -1.2- (0.69) GARCH_T -1.8- (0.92) GARCH_T -0.6- (0.83) GARCH_T -2.4- (2.9) GARCH_T -0.6- (0.49) GARCH_T -1.2- (0.49) GARCH_T -1.2- (0.59)
After INF -1.2- (1.0) INF -1.8- (0.27) INF -1.2- (0.46) INF -1.2- (0.77) INF -0.6- (0.46) INF -1.8- (1.8) INF -0.0- (0.00) INF -0.6- (0.36) INF -1.2- (0.52)
Increase
38

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Results XI
Daily Capital charges
Table 5c Daily Capital Charges ranking after the GFC Table 5c Daily Capital Charges ranking after the GFC Table 5c Daily Capital Charges ranking after the GFC Table 5c Daily Capital Charges ranking after the GFC Table 5c Daily Capital Charges ranking after the GFC Table 5c Daily Capital Charges ranking after the GFC Table 5c Daily Capital Charges ranking after the GFC Table 5c Daily Capital Charges ranking after the GFC Table 5c Daily Capital Charges ranking after the GFC Table 5c Daily Capital Charges ranking after the GFC
CAC DAX DJ FTSE HSHK IBEX NIKEEI SMI SP500
After SUP -7.8- (7.5) SUP -6.6- (7.05) SUP -9.0- (6.52) SUP -9.5- (5.74) SUP -2.4- (2.98) SUP -8.4- (10.6) SUP -6.59- (4.01) SUP -10.8- (8.74)
After EGARCH -4.8- (5.76) EGARCH -9.0- (5.63) EGARCH -7.8- (8.7) SUP -6.6- (4.91) EGARCH -10.2- (7.49)
After EGARCH -6.0- (4.9) EGARCH -7.1- (3.98) EGARCH -1.8- (1.57)
After MEDIAN -3.6- (4.9) EGARCH -4.8- (3.09) EGARCH -4.8- (1.85)
After MEDIAN -3.0- (2.8) MEDIAN -4.2 - (3.58) RSKM -6.0- (4.25) MEDIAN -4.8- (2.37) RSKM -2.4- (2.89) RSKM -4.2- (6.6) RSKM -5.4 - (3.17) MEDIAN -4.8 - (2.73)
After RSKM -4.2- (2.10) MEDIAN -2.4- (1.01)
After MEDIAN -4.8- (2.39) MEDIAN -0.6- (1.40) RSKM -3.60- (2.51)
After MEDIAN -3.00- (1.12) RSKM -6.6- (4.19)
After RSKM -4.2- (2.43)
After RSKM -4.2- (4.3)
After
After
After
After
Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC Table 5b Daily Capital Charges ranking during the GFC
During CAC DAX DJ FTSE HSHK IBEX NIKKEI SMI SP500
During SUP -13.06- (7.3) EGARCH -8.4- (3.9) SUP -13.3- (8.0) SUP -4.8- (4.6) SUP -10- (2.5) EGARCH -14.9- (13.0) EGARCH -8.3- (8.0) EGARCH -16.7- (12.2)
During EGARCH -7.5- (4.6) ) EGARCH -11.7- (6.7) EGARCH -13.3- (8.0) EGARCH -4.8- (4.6) SUP -18.2- (13.0) SUP -11.7- (8.0) SUP -18.3- (12.5)
During EGARCH -10- (4.4) RSKM -6.6- (9.8)
During MEDIAN -5.0- (4.9)
During SUP -15.1- (6.5) SUP -15.0- (7.5) RSKM -4.8- (5.4)
During MEDIAN -6.7- (2.7) MEDIAN -3.3- (3.0) RSKM -5.0- (2.7) MEDIAN -6.7- (3.7)
During MEDIAN -5.6- (3.5) MEDIAN -4.8- (1.9) MEDIAN -5.0- (1.6) MEDIAN -5.0- (4.8)
During
During RSKM -1.8- (3.2) RSKM -9.5- (6.0)
During MEDIAN -11.4- (5.4)
During RSKM -10.0- (4.3) RSKM -10.0- (6.2)
During RSKM -8.4- (3.7) RSKM -10.0- (5.8)
During
During
Increase
39

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Results XII
Table 6a Model ranking based on asymmetric linear tick loss function, before the GFC Table 6a Model ranking based on asymmetric linear tick loss function, before the GFC Table 6a Model ranking based on asymmetric linear tick loss function, before the GFC Table 6a Model ranking based on asymmetric linear tick loss function, before the GFC Table 6a Model ranking based on asymmetric linear tick loss function, before the GFC Table 6a Model ranking based on asymmetric linear tick loss function, before the GFC Table 6a Model ranking based on asymmetric linear tick loss function, before the GFC Table 6a Model ranking based on asymmetric linear tick loss function, before the GFC
CAC DAX DJ FTSE HSHK IBEX NIKEEI SMI SP500
Before EGARCH_T EGARCH EGARCH INF INF EGARCH_T GJR EGARCH_T GJR
Before INF EGARCH_G EGARCH_G EGARCH_T MEDIAN GJR EGARCH_G EGARCH_G MEAN
Before EGARCH_G EGARCH_T GJR EGARCH_G SUP GJR_G GJR_G EGARCH EGARCH
Before EGARCH MEAN MEDIAN EGARCH MEAN GJR_T MEDIAN INF MEDIAN
Before MEAN GJR_T MEAN GJR_T RSKM MEDIAN EGARCH_T GJR_T EGARCH_G
Before GJR_G GJR_G GJR_G GJR_G GJR_T EGARCH_G MEAN GJR_G GARCH_G
Before GJR MEDIAN EGARCH_T MEAN EGARCH MEAN GJR_T MEDIAN GJR_G
Before MEDIAN GJR GARCH_T MEDIAN GARCH INF INF MEAN GARCH_T
Before GJR_T INF GJR_T GJR GJR EGARCH GARCH_G GJR_N EGARCH_T
Before GARCH_G GARCH_T GARCH_G GARCH_T GARCH_G GARCH GARCH GARCH_T GJR_T
Before SUP GARCH_G SUP RSKM EGARCH_G GARCH_G GARCH_T GARCH_G RSKM
Before GARCH GARCH RSKM GARCH_G EGARCH_T RSKM RSKM RSKM SUP
Before RSKM SUP INF GARCH GJR_G GARCH_T SUP SUP INF
Before GARCH_T RSKM GARCH SUP GARCH_T SUP EGARCH GARCH GARCH
Tick loss Function
Increase
40

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Results XIII
Tick loss Function
Table 6b Model ranking based on asymmetric linear tick loss function, during the GFC Table 6b Model ranking based on asymmetric linear tick loss function, during the GFC Table 6b Model ranking based on asymmetric linear tick loss function, during the GFC Table 6b Model ranking based on asymmetric linear tick loss function, during the GFC Table 6b Model ranking based on asymmetric linear tick loss function, during the GFC Table 6b Model ranking based on asymmetric linear tick loss function, during the GFC Table 6b Model ranking based on asymmetric linear tick loss function, during the GFC Table 6b Model ranking based on asymmetric linear tick loss function, during the GFC Table 6b Model ranking based on asymmetric linear tick loss function, during the GFC Table 6b Model ranking based on asymmetric linear tick loss function, during the GFC
CAC DAX DJ100 FTSE HSHK IBEX NIKEEI SMI SP500
During GARCH_G EGARCH_T GARCH_G INF EGARCH_G EGARCH_T EGARCH_T INF MEAN
During EGARCH_T EGARCH_G MEAN EGARCH_T GJR_G MEDIAN GJR_G EGARCH_T EGARCH_T
During GARCH_T MEDIAN MEDIAN GARCH_T MEAN MEAN GJR_T GARCH_T MEDIAN
During RSKM MEAN GJR_G GJR_T EGARCH_T GARCH_G INF GJR_T GJR_G
During MEAN GARCH_T GARCH_T MEAN MEDIAN GJR_T MEDIAN GARCH_G GARCH_G
During INF GJR_T EGARCH_T MEDIAN EGARCH EGARCH_G GJR MEAN GARCH_T
During MEDIAN EGARCH GJR_T GARCH_G GJR_T GARCH MEAN EGARCH_G GJR
During EGARCH GARCH_G EGARCH_G GJR_G GJR GJR_G EGARCH_G MEDIAN GJR_T
During GARCH GJR_G GJR EGARCH_G GARCH_G GARCH_T GARCH_T GJR_G INF
During GJR_T GARCH INF GARCH SUP INF GARCH_G EGARCH RSKM
During GJR_G INF RSKM RSKM GARCH_T RSKM GARCH GARCH EGARCH_G
During GJR RSKM GARCH GJR INF GJR EGARCH GJR GARCH
During EGARCH_G GJR EGARCH EGARCH GARCH EGARCH RSKM RSKM EGARCH
During SUP SUP SUP SUP RSKM SUP SUP SUP SUP
Increase
41

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Results XIV
Table 6c Model ranking based on asymmetric linear tick loss function, after the GFC Table 6c Model ranking based on asymmetric linear tick loss function, after the GFC Table 6c Model ranking based on asymmetric linear tick loss function, after the GFC Table 6c Model ranking based on asymmetric linear tick loss function, after the GFC Table 6c Model ranking based on asymmetric linear tick loss function, after the GFC Table 6c Model ranking based on asymmetric linear tick loss function, after the GFC Table 6c Model ranking based on asymmetric linear tick loss function, after the GFC Table 6c Model ranking based on asymmetric linear tick loss function, after the GFC Table 6c Model ranking based on asymmetric linear tick loss function, after the GFC Table 6c Model ranking based on asymmetric linear tick loss function, after the GFC
CAC DAX DJ100 FTSE HSHK IBEX NIKKEI SMI SP500
After MEAN RSKM GJR_T MEAN EGARCH EGARCH_T MEDIAN EGARCH_G GJR_T
After MEDIAN GARCH_G GJR_G MEDIAN GJR GJR_T MEAN EGARCH MEDIAN
After GJR_T GARCH_T EGARCH_T EGARCH_T SUP GJR_G GJR_G MEDIAN GJR_G
After GJR_D INF MEAN EGARCH_G GARCH MEAN EGARCH_G MEAN MEAN
After EGARCH_T GARCH MEDIAN GARCH_G RSKM MEDIAN GARCH EGARCH _T EGARCH_T
After EGARCH_D MEAN EGARCH_G RSKM GJR_G EGARCH_G GARCH_G GJR_G GARCH_G
After GJR MEDIAN GARCH_G GARCH EGARCH_G INF EGARCH GJR_T GARCH_T
After GARCH_D GJR_T GJR GJR_T MEDIAN GJR GJR_T GJR GARCH
After GARCH_T EGARCH_T GARCH GARCH_T MEAN GARCH_G RSKM GARCH_G INF
After EGARCH GJR_G GARCH_T GJR_G GARCH_G GARCH_T EGARCH _T GARCH GJR
After INF EGARCH_G INF EGARCH GJR_T GARCH GJR RSKM EGARCH_G
After GARCH GJR RSKM INF EGARCH_T RSKM SUP SUP RSKM
After RSKM EGARCH EGARCH GJR GARCH_T EGARCH GARCH_T GARCH_T EGARCH
After SUP SUP SUP SUP INF SUP INF INF SUP
Tick loss Function
Increase
42

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Conclusions

• Under the Basel II Accord,
• ADIs have to communicate their risk estimates to
  the monetary authorities
• They can use a variety of VaR models to estimate
  risks.
• ADIs are subject to back-testing
• Daily capital charges as protection against
  market risk must be set at the higher of the
  previous days VaR or the average VaR over the
  last 60 business days, multiplied by a factor k.
• VaR models currently in use can lead to high
  daily capital requirements or an excessive number
  of violations.
• ADIs objective is to maximize profits, so they
  wish to minimize their capital charges while
  restricting the number of violations in a given
  year below the maximum of 10 allowed by the Basel
  II Accord. From this target it follows naturally
  that ADIs have to choose an optimal reporting
  policy that may strategically under-report or
  over-report their forecast of VaR in order to
  minimize the daily capital requirement.

43

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Conclusions II

1. In McAleer et al. (2010), the VaR model
   minimizing DCC before, during and after the GFC
   changed frequently.
2. In this paper we propose robust risk forecasts
   that use combinations of several conditional
   volatility models for forecasting VaR, eg the
   median.
3. The median is robust, in that it yields
   reasonable daily capital charges, number of
   violations that do not jeopardize institutions
   that might use it, and more importantly, is
   invariant before, during and after the 2008-09
   GFC.
4. The median is a model that balances daily capital
   charges and violation penalties in minimizing
   DCC.  

44

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Conclusions III

1. Combining forecasting models is within the spirit
   of the Basel II Accord, although its use would
   require approval by the regulatory authorities,
   as for any forecasting model.
2. This approach is not computationally demanding,
   even though several models have to be specified
   and estimated over time.
3. Research is being carried out using a variety of
   different indexes from different countries.
   Results confirm that the median is global
   financial crisis robust and clearly preferred in
   most cases to single models.

45

• Maximizing Profits, VaR and Daily Capital Charges
• Models for Forecasting VaR
• GFC-Robust Risk Management Strategy
• Results
• Conclusions

Conclusions IV

• Before the GFC, the best strategy for minimizing
  DCC and staying below 8 violations is the
  SUPREMUM, in 6 out of 9 indices. The second best
  is the EGARCH in 3 out of 9 indices. RISKMETRICS
  also beats the MEDIAN in 8 out of 9 indices.
  However, the best strategy for staying in the
  green zone (up to 4 violations) is the MEDIAN (8
  out of 9 indices).
• During the GFC, the SUPREMUM violates more than
  8 times in 7 out of 9 indices while RISKMETRICS
  violates more than 8 times in 5 out of 9 indices.
  However, the MEDIAN beats RISKMETRICS in 5
  indices while it keeps you in less than 8
  violations, for 8 out of 9 indices.
• After the GFC, the SUPREMUM is best in 5 out of 9
  indices but violates heavily in the rest. In
  second place, in 2 out of 9 cases, comes EGARCH,
  but it also tends to violate in the other
  indices. The MEDIAN strategy keeps you green or
  with less than 8 violations for all indices,
  while it beats RISKMETRICS in 5 out of 9 indices.