- 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

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

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.

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

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

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

- 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.

- 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

- 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

- 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.

- 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

- 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.

- 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

- 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. .

Agenda

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

- 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?

- 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)

- 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

- 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

- 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.

- 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

- 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

- 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

- 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.

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

Conclusions II

- In McAleer et al. (2010), the VaR model

minimizing DCC before, during and after the GFC

changed frequently. - In this paper we propose robust risk forecasts

that use combinations of several conditional

volatility models for forecasting VaR eg the

median. - 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. - The median is a model that balances daily capital

charges and violation penalties in minimizing

DCC.

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

Conclusions III

- 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. - This approach is not computationally demanding,

even though several models have to be specified

and estimated over time. - 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.

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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.

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

Conclusions II

- In McAleer et al. (2010), the VaR model

minimizing DCC before, during and after the GFC

changed frequently. - In this paper we propose robust risk forecasts

that use combinations of several conditional

volatility models for forecasting VaR, eg the

median. - 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. - The median is a model that balances daily capital

charges and violation penalties in minimizing

DCC.

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

Conclusions III

- 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. - This approach is not computationally demanding,

even though several models have to be specified

and estimated over time. - 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.

- 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.