ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
RESEARCH PROJECT On
Accuracy of Value-at-Risk Model in Commercial Banks
Submitted in partial fulfillment of the requirement for MBA
Degree of Bangalore University
BY
SUGUNA .A Registration Number
05XQCM6098
Under the guidance of
Prof. S.SANTHANAM
M.P.Birla Institute of Management
Associate Bharatiya Vidya Bhavan
Bangalore-560001
2005-2007
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
DECLARATION
I hereby declare that this report titled “Accuracy of Value-at-Risk
Model in Commercial Banks” is a record of independent work carried out by
me, towards the partial fulfillment of requirements for MBA course of Bangalore
University at M.P.Birla Institute of Management. This has not been submitted
in part or full towards any other degree.
PLACE: BANGALORE SUGUNA .A DATE:
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
PRINCIPAL’S CERTIFICATE
This to certify that this report titled “Accuracy of Value-at-Risk Model in Commercial Banks” has been prepared by SUGUNA .A bearing the
registration no.05 XQCM 6098 under the guidance and supervision of PROF. S.SANTHANAM, MPBIM, Bangalore.
Place: Bangalore (Dr.N.S.Malavalli)
Date: Principal
MPBIM, Bangalore
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
GUIDE’S CERTIFICATE
This is to certify that the Research Report entitled “Accuracy of Value-at-Risk Model in Commercial Banks”, done by SUGUNA .A bearing
Registration No.05 XQCM 6098 is a bonafide work done carried under my
guidance during the academic year 2006-07 in a partial fulfillment of the
requirement for the award of MBA degree by Bangalore University. To the best
of my knowledge this report has not formed the basis for the award of any other
degree.
Place: Bangalore PROF. S. SANTHANAM Date:
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
ACKNOWLEDGEMENT
It’s my special privilege to extend words of the thanks to all of them who
have helped me and encouraged me in completing the project successfully.
I would thank Prof. S.SANTHANAM and Dr. T.V.N. Rao for giving me
valuable inputs required for completing this project report successfully. I owe
my sincere gratitude to him for spending his valuable time with me and for his
guidance.
I also wish to express my gratitude to Dr N.S. Malavalli for his valuable
guidance and ideas during the project.
It would be improper if I do not acknowledge the help and
encouragement by my friends and well wishers who always helped me directly
or indirectly.
My gratitude will not be complete without thanking the almighty god and
my loving parents who have been supportive through out the project.
SUGUNA. A.
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
EXECUTIVE SUMMARY
In recent years, the trading accounts at large commercial banks have grown
rapidly and become progressively more complex. To a large extent, this reflects
the sharp growth in the over-the-counter derivatives markets, in which
commercial banks are the principal dealers. To manage market risks, major
trading institutions have developed large scale risk measurement models.
While approaches may differ, all such models measure and aggregate market
risks in current positions at a highly detailed level. The models employ a
standard risk metric, Value-at-Risk (VaR), which is a lower tail percentile for the
distribution of profit and loss (P&L). VaR models have been sanctioned for
determining market risk capital requirements for banks through the 1996 Market
Risk Amendment to the Basle Accord. Spurred by these developments, VaR
has become a standard measure of financial market risk that is increasingly
used by other financial and even non financial firms as well.
In this research paper, we test the performance of bank VaR models. We
analyze the distribution of historical trading P&L and the daily performance of
VaR estimates of seven large banks. P&L and VaR data series are maintained
by the banks to assess compliance with the Basle market risk capital
requirements-they serve as a gauge of the forecast accuracy of the models
used for internal risk management. Regulations stipulate that estimates are to
be calculated for a 99 percent lower critical value of aggregate trading P&L with
a one-day horizon.
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
CONTENTS
CHAPTER TITLE PAGE NO
1 Introduction
1.1 General
1.1.1 Approaches to Managing Risks
1.1.2 The consequences of poor risk management
1.1.3 Advantages of Risk Management
1.2 Value-at-risk Approach
1.2.1 The idea behind VaR
1.2.2 Methods of calculating VaR
1.2.3 Drawbacks of VaR
2 Literature Survey
3 Research Methodology
3.1 Problem Statement
3.2 Objective
3.3 Scope of Study
3.4 Sample size
3.5 Data Required and period of Study
3.6 Sources of Data
3.7 Methodology
4 Data Analysis and Interpretation
5 Conclusion
6 Bibliography
7 Annexure
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
Chapter 1
INTRODUCTION
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
1.1 INTRODUCTION “Risk means being exposed to the possibility of a bad outcome……Risk
management means taking deliberate action to shift the odds in your favour -
increasing the odds of good outcomes and reducing the odds of bad
outcomes."
Risk management is about following a deliberate set of actions designed to
identify, quantify, manage, and then monitor those things, events or actions that
could lead to financial loss. This implies that risk management is an active
process requiring commitment and focus but in many instances there is
insufficient data about a risk to define it precisely. As a result, risk management
involves a large degree of judgement and requires the organization to make
certain assumptions about the future. In order to manage risk effectively it is
necessary to categorize the type of risk that organizations are exposed to and
then manage them accordingly.
1.1.1 APPROACHES TO MANAGING RISK
The basic form of risk management involves four continuous stages:
• Identification. This involves the organization identifying the types of risk it
might be exposed to. Some are more obvious and manageable than
others. The key point is to identify those risks that can be managed.
• Quantification. This involves assessing the severity of the risk which in
its simplest form is the product of its impact (which is usually assessed in
terms of financial loss) and probability or likelihood of occurrence. And
rank the risks when it comes to choosing those it intends to manage
• Managing or responding. This requires the organization to establish a
course of action that will address the risk. Organizations have five
responses- They can transfer the risk by passing it to a third party. They
can avoid the risk by taking a different course of action; they can reduce
the risk by taking action that minimizes its impact or probability. They
can put some contingency in place that allows the organization to cope
with the implications of the risk should it materialize. Finally, they can
accept the risk and its consequences. Ultimately, before this strategy is
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
adopted, it is important to understand the impacts of the risk and how
much it would cost the organization in terms of money and resources to
manage it. Balancing the two will allow an appropriate decision to be
made.
• Monitoring and controlling. Risks are time-based events and as such
their impact and probability will vary with time. This is well known within
banking, but less so in the other areas of risk, such as strategic and
operational risk. Monitoring risk has two strands to it. The first is to
ensure the actions agreed during the response stage are undertaken
and their impact on the risk's impact and probability is tracked. And the
second is to monitor the risk over time, as other events will cause the
risk's probability and impact to increase or decrease.
Risk management in banking is different. According to Joel Bessis, risk
management within the banking community is principally based upon
quantitative measures of risk.
There exist three quantitative indicators that commonly exist:
• Sensitivity - this captures the deviation of earnings from such things as
interest margins or changes in the mark to-market values of financial
instruments (such as derivatives) with a single unit change in a market
parameter such as interest rates, exchange rates, or stock prices.
• Volatility - this captures the variations around the average of a random
parameter or target value both positively (upside) and negatively
(downside). It is a common measure of the dispersion around the
average of a random variable.
• Downside measures of risk such as value at risk that concentrates on
the negative variations only. To allow the effective management of risk,
these are usually classed as worst case values. These tend to be the
most comprehensive measure of risk because they incorporate both
sensitivity and volatility.
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
Financial institutions manage their risks in a variety of different ways.
• Market risk (the loss arising from adverse changes in market rates and
prices) is often dealt with through the use of hedging transactions such
as derivatives.
• Credit risk (the risk that a customer will default on their loan) is usually
managed by setting limits on the amount lent, having credit officers and
credit committees to agree to lend money, and varying the interest rate
and amount of collateral to match the risk rating of the client.
1.1.2 THE CONSEQUENCES OF POOR RISK MANAGEMENT
It is clear that failing to manage risk can result in financial loss of one kind or
another.
At the strategic level, organizations can be seduced into rushing into investing
in speculative bubbles and seeking first mover advantage without thinking
about the downside risks.
At the project and program level, many hundreds of millions of dollar can be
wasted on major change projects and technology programs without any benefit
to the organization.
1.1.3 ADVANTAGES OF RISK MANAGEMENT Actively managing risks has many advantages, including:
• gaining a much better understanding of the risks that are facing the
organization and its activities;
• understanding how risks interact;
• identifying the uncertainties that have to be managed, monitored, and
controlled at all levels;
• providing input into investment decisions;
• understanding the implications of taking different courses of action;
• assessing the financial implications of investments, lending decisions
and the markets;
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
• viewing risks as opportunities, rather than threats; and
• Providing visibility of the risks that the organization wishes to take
deliberately as well as those it needs to guard against and actively avoid.
1.2 VALUE AT RISK APPROACH VaR is the lowest quantile of the potential losses that can occur within a given
portfolio during a specified time period. Value at risk (VaR) has been called the
"new science of risk management".
Value at Risk (VAR) calculates the maximum loss expected (or worst case
scenario) on an investment, over a given time period and given a specified
degree of confidence.
1.2.1 The Idea behind VAR
The most popular and traditional measure of risk is volatility. The main problem
with volatility, however, is that it does not care about the direction of an
investment's movement: a stock can be volatile because it suddenly jumps
higher. Of course, investors are not distressed by gains!
For investors, risk is about the odds of losing money, and VAR is based on that
common-sense fact. By assuming investors care about the odds of a really big
loss, VAR answers the question, "What is my worst-case scenario?" or "How
much could I lose in a really bad month?"
A VAR statistic has three components: a time period, a confidence level and a
loss amount (or loss percentage). For example VAR answers:
• What is the most I can - with a 95% or 99% level of confidence - expect
to lose in dollars over the next month?
• What is the maximum percentage I can - with 95% or 99% confidence -
expect to lose over the next year?
1.2.2 Methods of Calculating VAR
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
There are three methods of calculating VAR: the historical method, the
variance-covariance method and the Monte Carlo simulation.
1. Historical Method (calculates daily VaR) The historical method simply re-organizes actual historical returns, putting them
in order from worst to best. It then assumes that history will repeat itself, from a
risk perspective.
2. The Variance-Covariance Method (calculates daily VaR) This method assumes that stock returns are normally distributed. In other
words, it requires that we estimate only two factors - an expected (or average)
return and a standard deviation - which allow us to plot a normal distribution
curve.
The idea behind the variance-covariance is similar to the ideas behind the
historical method - except that we use the familiar curve (normal curve) instead
of actual data. The advantage of the normal curve is that we automatically
know where the worst case lies on the curve. They are a function of our desired
confidence and the standard deviation ( ):
3. Monte Carlo Simulation (calculates monthly VaR) The third method involves developing a model for future stock price returns and
running multiple hypothetical trials through the model. A Monte Carlo simulation
refers to any method that randomly generates trials, but by itself does not tell us
anything about the underlying methodology.
For most users, a Monte Carlo simulation amounts to a "black box" generator of
random outcomes.
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
In the early 1990s, three events popularized value-at-risk as a practical tool for
use on trading floors:
In 1993, the Group of 30 published a groundbreaking report on derivatives
practices. It was influential and helped shape the emerging field of financial risk
management. It promoted the use of value-at-risk by derivatives dealers and
appears to be the first publication to use the phrase "value-at-risk."
In 1994, JP Morgan launched its free Risk Metrics service. This was
intended to promote the use of value-at-risk among the firm's institutional
clients. The service comprised a technical document describing how to
implement a VaR measure and a covariance matrix for several hundred key
factors updated daily on the internet.
In 1995, the Basel Committee on Banking Supervision implemented market
risk capital requirements for banks. These were based upon a crude VaR
measure, but the committee also approved, as an alternative, the use of banks'
own proprietary VaR measures in certain circumstances. Market risk capital
requirements were set equal to the greater of:
• The previous day’s VaR, or
• The average VaR over the previous sixty business days, multiplied by a
factor of at least 3.
In January 1999, the Basel Committee proposed a new capital accord, which
has come to be known as Basel II. There followed an extensive consultative
period, with the committee releasing additional proposals for consultation in
January 2001 and April 2003. It also conducting three quantitative impact
studies to assess those proposals. The finalized Basel II Accord was released
in June 2004.
Basel II is based on three pillars:
Minimum capital requirements,
Supervisory review, and
Market discipline.
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
Every VaR measure must address this problem. Accordingly, all VaR measures
share certain common components related to solving this problem. All must
specify a portfolio mapping. All must somehow characterize the joint distribution
of . All must somehow combine these two pieces to characterize the
distribution of . Exhibit 5 is a schematic summarizing these three processes
that are common to all practical VaR measures.
Schematic of How VaR Measures Work
All practical VaR measures accept portfolio data and historical market data as
inputs. They process these with three procedures namely, a mapping
procedure, inference procedure, and transformation procedure. Output
comprises the value of a VaR metric. That value is the VaR measurement.
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
Risk has two components:
exposure, and
uncertainty.
By specifying a portfolio mapping, a mapping procedure describes exposure.
By characterizing the joint distribution for , an inference procedure describes
uncertainty. A transformation procedure combines exposure and uncertainty to
describe the distribution of , which it then summarizes with the value of some
VaR metric. In so doing, the transformation procedure describes risk.
1.2.3 DRAWBACKS Unfortunately, VaR is not the panacea of risk measurement methodologies. A
subtle technical problem is that VaR is not sub-additive. That is, it's possible to
construct two portfolios, A and B, in such a way that VaR (A + B) > VaR (A) +
VaR (B). This is unexpected because we'd hope that portfolio diversification
would reduce risk.
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
Chapter 2
LITERATURE SURVEY
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
Review of literature .means examining and analyzing the various literatures
available in any field either for references purposes or for further research.
Further research can be done by identifying the areas which have not been
studied and in turn undertaking research to add value to the existing literature.
For the purpose of literature review various sources of information have been
used.
Sources include books, journals as well as some literature papers.
2.1 Review of Literature
2.1.1 How Accurate Are Value-at-Risk Models at Commercial
Banks? Jeremy Berkowitz; James O'Brien
Objective: How accurate are VaR model in 6 large commercial banks of US?
Abstract: In recent years, the trading accounts at large commercial banks have
grown substantially and become progressively more diverse and complex. This
article provides a descriptive statistics on the trading revenues from such
activities and on the associated Value-at-Risk (VaR) forecasts internally
estimated by banks. For a sample of large bank holding companies, the
performance of banks’ trading risk models is evaluated by examining the
statistical accuracy of the VaR forecasts.
Result: VaR forecasts for six large commercial banks have exceeded nominal
coverage levels over the past two years, and, for some banks, VaRs were
substantially removed from the lower range of trading P&L.
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
2.1.2 Risk Management Techniques and Application in Banking
under Basel II Accord
SN Ghosal
The regulators should develop and prescribe risk management norms and tools
to regulate risk taking activities of banks and financial institutions. Sometimes a
bank takes risk which may affect the whole system. Techniques like VaR
(Value at Risk) used by banks must be approved by the supervisor and these
must be validated by back testing. Banks should be encouraged to align their
business plans and performance budgets with risk management techniques.
The goals set for banks for risk management by the regulatory authorities may
be summed up as follows:
• To impose capital adequacy norms keeping in view the risk banks are
required to take as the competitive market demands.
• To level the competitive field of banks by setting common benchmarks
for all banks.
• To control and monitor `systemic risk' that may arise due to failure of the
whole banking system.
• To develop and prescribe appropriate business and supervisory
practices to sustain risks taken by banks under market commands, and
• To protect the interest of depositors and other stakeholders of banks.
All said and done, implementation of Basel II Accord will not only require
enhancement of capital by all banks but also the up gradation of the skills and
expertise of their executives. Further, it may also need the assistance of
outside expert groups of the field to successfully implement the said Accord. It
is unfortunate that despite the revolution in information technology India is still
far away from having a reliable database to develop dependable risk
assessment technology to assess credit and operational risk that banks
generally face in their day-to-day operations. In fact, banks also lack in
expertise to play with derivatives to mitigate and or reduce the losses that may
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
arise due to risk taken in their day-to-day operations. It is therefore necessary
for Indian banks to not only adhere to the guidelines issued from time to time by
the RBI but also to develop expertise for successful adoption of the Accord. In
this regard, all banks have to adopt a two pronged strategy i.e., to have a
separate nucleus of staff for developing and accessing reliable information in
risk prone activity areas of banking and to continuously develop and train
executives who are actively operating in risk prone activities of banks so that
they are able to successfully gauge risk in their activities and also take suitable
mitigating steps to minimize such risks. This is obviously a continuous process
and needs building of institutions within and outside to accelerate the process
of implementation.
2.1.3 Value at Risk (VaR): A Critique Ch Rajeshwer and Sharath Jutur
Objective: VaR has established itself as a ubiquitous risk management tool for
more than a decade. Yet, it looks far from perfect.
Abstract: The Bank for International Settlements (BIS), the international body
that prescribes prudential measures for banks worldwide, has prescribed VaR
as a risk measurement tool to be used by financial institutions in its Basel II
norms. Since many banks are already using VaR, they have greeted the
change with three cheers. It perhaps will not be an exaggeration to say that the
world of finance today swears by VaR, to minimize the magnitude of losses
they might incur.
After a decade of honeymooning with VaR, finance executives are beginning to
realize VaRs' limitations. If the research studies about the usefulness of VaR
are any indication, one wonders whether the tool which is designed to minimize
risk, is actually increasing it.
The dark side of VaR
The result of a VaR model is simply the dollar amount of VaR or the minimum
loss that may be incurred for holding an asset for n number of days with p%
confidence level. In other words, VaR gives the amount of loss that a portfolio
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
can incur in n days with a probability of 1-p% worst cases, given that the
weightages for various assets in the portfolio do not change. It is argued that
the flaws of the VaR model start emanating from the definition itself.
The VaR model mechanics assume that maturity of assets and weightages of
assets in the portfolio will remain constant during the period of measurement.
VaR assumes that the assets of a portfolio are held for a fixed amount of time
and in the initial weightage size and quantifies the risk number based on those
criteria. Given the volatility and uncertainty of the market, it is next to impossible
to hold a particular asset for the period and weightage specified in the model. In
the course of a trading activity, situations might prompt a trader to dispose the
asset before the time specified considered in the calculation of VaR. These
situations render VaR ineffective.
Another severely constraining aspect of VaR is that it calculates worst case
scenario losses from projected market scenarios, which the model generates
based on past historical trends. But, if the market prices are anything to go by,
they often spring surprises and defy past trends.
The VaR model assumes that the different assets of the portfolio tend to show
the kinds of relationship they have exhibited in the past, in the future too. But
these relationships between the assets are far from stable. Since the assets
tend to diverge from their past levels of correlation they undermine the efficacy
of the VaR results.
Result: It is argued that the flaws of the VaR model start emanating from the
definition itself.
2.1.4 Evaluating the Basle Guidelines for Backtesting Banks'
Internal Risk Management Models André Lucas
The 1996 Amendment to the Basle capital Accord to incorporate market risk
constitutes a breakthrough in the determination of capital requirements. Rather
than dictating these requirements through a uniform supervisory approach,
banks are allowed to use their own internal models for computing the capital
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
required. In order to mitigate moral hazards problem and stimulate banks to use
adequate internal models, the models must be subjected to a backtesting
procedure. If a model produces too many incorrect predictions increase capital
requirements results. This paper provides a evaluation of the correct internal
model approach in conjunction with the proposed backtesting procedure. In
particular, using a stylized representation of the present supervisory framework,
we investigate whether banks are provided with the right incentives to come up
with the correct internal model. We find that, under the current regulatory
framework, banks are prone to under reporting their true market risks. A much
stricter penalty scheme is required in order to align banks incentives with those
of the supervisor. We check the sensitivity of our results to changes in the
length of the planning horizon, portfolio risk, time preferences, risk attitudes and
the distribution of financial returns.
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
Chapter 3
RESEARCH METHODOLGY
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
3.1 Problem Statement
Finding the accuracy of value-at-risk model for commercial banks in India.
3.2 Objective • To study the application of different risk models.
• To ascertain the Performance of Bank VaR models.
3.3 SCOPE OF STUDY The most popular and traditional measure of risk is volatility. The main problem
with volatility, however, is that it does not care about the direction of an
investment's movement: a stock can be volatile because it suddenly jumps
higher. Of course, investors are not distressed by gains!
For investors, risk is about the odds of losing money, and VAR is based on that
common-sense fact. By assuming investors care about the odds of a really big
loss, VAR answers the question, "What is my worst-case scenario?" or "How
much could I lose in a really bad month?"
3.4 SAMPLE SIZE The Sample size considered for the research undertaken has a scope of seven
different banks, three public sector and four private sector banks. These are as
follows:-
1. Bank of India (BOI) was incorporated in 1906 by a group of eminent
businessmen in Bombay. It was under private ownership till 1969, later it
was nationalized along with 13 other major Banks. The bank has grown
rapidly over the year to become one of the leading Indian banks. The
Bank came out with its maiden public issue in 1997. In business volume,
the Bank occupies a premier position among the nationalized banks.
2. HDFC Bank (HDFCBK) was incorporated in Aug. 1994 and promoted by
Housing Development Finance Corporation Limited (HDFC), India's
premier housing finance company which also enjoys an impeccable
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
track record in India as well as in international markets. HDFC was
amongst the first to receive an 'in principle' approval from the Reserve
Bank of India (RBI) to set up a bank in the private sector, as part of the
RBI's liberalization of the Indian Banking Industry. The Bank
commenced operations as a Scheduled Commercial Bank in January
1995.
3. ICICI Bank (ICICIBK) is a commercial bank promoted by ICICI Ltd, an
Indian Financial Institution. It was incorporated in Jan.'94 and received
its banking license from Reserve Bank of India in May.'94. It is the 2nd
largest bank in India. The bank has over 630 branches & extension
counters across India and over 2200 ATMs across the country
4. ING Vysya Bank Ltd incorporated in 1930, as Vysya Bank (VBL) got its
banking license from RBI in 1958 and was granted its status as
scheduled bank in 1974. With successive years of patronage and
constantly setting new standards in banking, the bank has many credits
to its account. Advances, foreign exchange business, deposit mix,
investments and priority sector advances remain the key functional
activities of the bank.
5. Punjab National Bank (PNB) was incorporated in 1894. From its
modest beginning, the bank has grown in size and stature to become a
leading banking institution in India. The number of branches of the Bank
rose from 619 at the time of nationalization in 1969 to touch 4022 as on
March 2004. As many as 7 banks have merged with PNB, the last being
the erstwhile Nedungadi Bank Ltd. PNB Capital services is also
amalgamated with the bank in 2003.
6. State Bank of India's (SBI) origin goes back to in the first decade of the
nineteenth century with the establishment of the Bank of Calcutta in
Calcutta on 2 June 1806. Three years later the bank was re-designed as
the Bank of Bengal on 2 January 1809. It was the first joint-stock bank of
British India sponsored by the Government of Bengal. Two other banks
the Bank of Bombay on 15 April 1840 and the Bank of Madras on 1 April
1843 started its operations. These three banks remained at the apex of
modern banking in India till their amalgamation as the Imperial Bank of
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
India on 27 January 1921. This new bank took on the triple role of a
commercial bank, a banker's bank and a banker to the government.
7. Established in 1929, South Indian Bank (SIB) got its status of
Scheduled Bank in 1946. In 1960, SIB expanded by taking over 15
smaller banks. Presently, it has a network of 391 branches and 50
extension counters, spread over 10 States and 2 Union Territories
3.5 DATA REQUIRED AND PERIOD OF STUDY Daily Stock Returns and the corresponding VaR estimates of the above sample
are considered for a period of two years from April 2005 to April 2007.
3.6 SOURCES OF DATA The data relating to the study is taken from
• Databases
Prowess and
Capital line plus
• NSE Website.
3.7 METHODOLOGY Comparing the returns of equity of the banks with that of the corresponding
estimated value-at-risk forecast of banks. Firstly, the log naturals of the daily
return is taken and then compared with the corresponding day’s VaR to check
for the violation.
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
Chapter 4
DATA ANALYSIS AND INTERPRETATION
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
4.1 STATISTICS OF DAILY RETURNS OF THE SEVEN BANKS
Data is individually interpreted and is as shown
Bank of India
Statistics
Mean 0.1216 Std. Error of Mean 0.12459 Median 0.0315 Mode -11.18 Std. Deviation 2.83843 Variance 8.057 Skewness -0.115 Std. Error of Skewness 0.107 Kurtosis 1.431 Std. Error of Kurtosis 0.214
t - test Skewness -1.07477 Kurtosis 6.686916
Interpretation : The t-test has shown that kurtosis is significant (6.687) but Skewness is
insignificant (1.075). Therefore, we can say that Bank of India exhibits a high
return but less of variations.
HDFC Bank Ltd
Statistics Mean 0.1192 Std. Error of Mean 0.08069 Median 0.0727 Mode -7.56 Std. Deviation 1.83822 Variance 3.379 Skewness 0.09 Std. Error of Skewness 0.107 Kurtosis 1.689 Std. Error of Kurtosis 0.214
t - test Skewness 0.841121 Kurtosis 7.892523
Interpretation : The t-test has shown that kurtosis is significant (7.893) but Skewness is
insignificant (0.841). Therefore, we can say that HDFC Bank Ltd exhibits a high
return but less of variations.
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
ICICI Bank Ltd
Statistics Mean 0.1469 Std. Error of Mean 0.09166 Median 0.2162 Mode -8.75(a) Std. Deviation 2.08805 Variance 4.36 Skewness -0.203 Std. Error of Skewness 0.107 Kurtosis 1.348 Std. Error of Kurtosis 0.214
t - test Skewness -1.8972 Kurtosis 6.299065
Interpretation : The t-test has shown that kurtosis is significant (6.299) but Skewness is
insignificant (1.897). Therefore, we can say that ICICI Bank Ltd exhibits a high
return but less of variations.
ING Vysya Bank Ltd
Statistics
Mean 0.0255 Std. Error of Mean 0.11486 Median -0.0907 Mode -12.18(a)Std. Deviation 2.36512 Variance 5.594 Skewness 0.658 Std. Error of Skewness 0.119 Kurtosis 7.227 Std. Error of Kurtosis 0.237
t - test Skewness 5.529412Kurtosis 30.49367
Interpretation : The t-test has shown that both kurtosis and Skewness are highly significant.
Therefore, we can say that ING Vysya Bank Ltd exhibits a high return and the
returns are highly varying.
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
Punjab National Bank
Statistics Mean 0.0424 Std. Error of Mean 0.0864 Median 0.0749 Mode -9.64 Std. Deviation 1.96827 Variance 3.874 Skewness -0.503 Std. Error of Skewness 0.107 Kurtosis 2.745 Std. Error of Kurtosis 0.214
t - test Skewness -4.70093 Kurtosis 12.8271
Interpretation : The t-test has shown that both kurtosis and Skewness are significant.
Therefore, we can say that Punjab National Bank Ltd exhibits a high return and
the returns are varying.
State Bank of India
Statistics
Mean 0.0956 Std. Error of Mean 0.07729 Median 0.2082 Mode -7.40 Std. Deviation 1.76077 Variance 3.1 Skewness -0.413 Std. Error of Skewness 0.107 Kurtosis 2.035 Std. Error of Kurtosis 0.214 99th Percentiles 4.801
t - test Skewness -3.85981 Kurtosis 9.509346
Interpretation : The t-test has shown that both kurtosis and Skewness are significant.
Therefore, we can say that State Bank of India exhibits a high return and the
returns are varying.
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
South Indian Bank Ltd
Statistics
Mean 0.0891 Std. Error of Mean 0.10319 Median -0.0549 Mode -7.70 Std. Deviation 2.35085 Variance 5.526 Skewness 0.819 Std. Error of Skewness 0.107 Kurtosis 4.643 Std. Error of Kurtosis 0.214 99th Percentiles 8.0081
t - test Skewness 7.654206Kurtosis 21.69626
Interpretation : The t-test has shown that both kurtosis and Skewness are highly significant.
Therefore, we can say that South Indian Bank Ltd exhibits a high return and the
returns are highly varying.
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
4.2 COMPARISION OF Bank Return and VaR Statistics
Daily Return Daily VaR BANK
OBS MEAN STD DEV KURTOSIS SKEW Mean VaR No. Violation
Bank of India 519 0.1216 2.83843 1.431 -0.115 -11.68 1 HDFC Bank Ltd 519 0.1192 1.83822 1.689 0.09 -7.282 1 ICICI Bank Ltd 519 0.1469 2.08805 1.348 -0.203 -7.94 2 ING Vysya Bank Ltd 424 0.0255 2.36512 7.227 0.658 -9.0822 2 Punjab National Bank 519 0.0424 1.96827 2.745 -0.503 -7.9687 4 State Bank of India 519 0.0956 1.76077 2.035 -0.413 -6.9837 1 South Indian Bank Ltd 519 0.0891 2.35085 4.643 0.819 -8.9571 0 To summarize,
• The returns of all the banks in the sample exhibit kurtosis. ING Vysya
Bank Ltd has a high kurtosis value, while ICICI Bank Ltd exhibits low.
• Also returns of banks ING Vysya Bank Ltd, Punjab National Bank, State
Bank of India and South Indian Bank Ltd exhibit Skewness, of which
Punjab National Bank and State Bank of India are negatively and the
other two bank returns are positively skewed.
• When comparing the Daily return with the corresponding days VaR data,
the violation is as shown.
The return of South Indian Bank Ltd has not violated the estimated
VaR in the observed 519 days.
The return of Bank of India, HDFC Bank Ltd and State Bank of
India has violated the estimated VaR once in the observed 519
days.
ICICI Bank Ltd and ING Vysya Bank Ltd have violated the
estimated VaR twice in the observed 519 and 424 days
respectively.
The return of Punjab National Bank has violated the estimated
VaR four times in the observed 519 days.
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
4.3 HISTOGRAMS OF DAILY RETURN OF THE BANKS
Bank of India
HDFC Bank Ltd
ICICI Bank Ltd
ING Vysya Bank Ltd
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
Punjab National Bank
State Bank of India
South Indian Bank Ltd
Interpretation: Histograms of daily returns of Equity stocks for seven banks are presented
above. In all histograms, the daily returns are demeaned and divided by their
standard deviation. The t-test has shown that returns of banks ING Vysya Bank
Ltd, Punjab National Bank, State Bank of India and South Indian Bank Ltd has
significant Skewness, of which Punjab National Bank and State Bank of India
are negatively and the other two bank returns are positively skewed.
Also the histograms clearly show that ING Vysya Bank Ltd has a high kurtosis
value, while ICICI Bank Ltd exhibits low.
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
Bank Daily VaR Models and the corresponding returns
Bank of India
HDFC Bank Ltd
ICICI Bank Ltd
ING Vysya Bank Ltd
Punjab National Bank
State Bank of India
South Indian Bank Ltd
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
Interpretation: In figure ‘ ‘, the Time series of daily returns of the seven banks for April 2005
through April 2007 ( blue line)and the corresponding one-day ahead 99th
percentile VaR forecast (pink line) is plotted. The plots tend to confirm the
conservativeness of the VaR forecasts where violations are relatively few but
large. The plot also shows differences in VaR performance among the banks.
The VaRs of Bank of India, HDFC Bank Ltd, ICICI Bank Ltd, Punjab National
Bank and State Bank of India appear to exhibit same trend. While ING Vysya
Bank Ltd and South Indian Bank Ltd trends are different and trends upward.
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
Chapter 5
CONCLUSION
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
CONCLUSION
After performing t-test we have found that returns of ING Vysya Bank Ltd and
South Indian Bank Ltd are not satisfactory as they are highly varied while
return of all the other Banks are satisfactory.
Comparing the VaR model, we can note that though returns of South Indian
Bank Ltd are highly varying, its VaR model is accurate. It has always
predicted correctly the maximum loss which an individual encounters. Punjab
National Bank’s VaR model has violated the most in our sample, but its return
is consistent.
To conclude we can say that, commercial banks in India follow a better
technique of forecasting value-at-risk..
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
Chapter 6
BIBLIOGRAPHY
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
BIBLIOGRAPHY
BOOKS 1. Risk management by Andrew Holmes
2. Statistics for Management by Richard I Levin and David S. Rubin
WEBSITES 1. www.nseindia.com
2. www.riskglossary.com
3. www.jstor.org
4. www.icfaipress.org
DATABASE 1. Prowess
2. Capital line plus.
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
REFERENCES Jeremy Berkowitz; James O'Brien, “How Accurate Are Value-at-Risk
Models at Commercial Banks?” The Journal of Finance > Vol. 57, No. 3
(Jun., 2002); pp. 1093-1111
Ch Rajeshwer and Sharath Jutur, “Value at Risk (VaR): A Critique “,
ICFAI Journal of Bank Management; 2005.
S. Benninga and Z. Wiener, “Value-at-Risk (VaR)”, Mathematica in
Education and research; Vol. 7 No. 4. 1998; pp. 39-45
SN Ghosal, “Risk Management Techniques and Application in Banking
Under Basel Ii Accord “, ICFAI Journal of Bank Management; 2006.
André Lucas, “Evaluating the Basle Guidelines for Backtesting Banks'
Internal Risk Management Models”, Journal of Money, Credit and
Banking, Vol. 33, No. 3. (Aug., 2001), pp. 826-846.
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
ANNEXURE
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
THE BANKS CALCULATED DAILY RETURN AND THE CORRESPONDING VaR IS SHOWN
DATE BOI ICICI PNB SBI SIB
4-Apr-05 RETURN VaR RETURN VaR RETURN VaR RETURN VaR RETURN VaR 4-Apr-05 2.360682 -13.48 4.584115 -7.57 1.886506 -10.45 0.870993 -8.07 3.966226 -9.23 5-Apr-05 -3.98533 -13.09 0.078629 -7.8 -2.48321 -10.12 -2.34301 -7.84 -1.21851 -9.75 6-Apr-05 -0.84538 -13.06 0.922563 -7.72 -0.78965 -9.91 -0.42702 -8.17 -1.00099 -9.76 7-Apr-05 1.165386 -12.65 -2.27084 -7.46 0.328091 -9.6 1.452864 -7.94 -0.12674 -9.48 8-Apr-05 -2.32769 -12.24 -1.28981 -8.08 -1.71664 -9.3 -1.03961 -7.69 -0.03689 -9.19 11-Apr-05 -0.51786 -11.85 -3.00777 -7.9 0.923021 -9.14 -1.16944 -7.46 -0.65929 -8.89 12-Apr-05 0.944153 -11.53 2.247282 -7.93 1.330906 -9.04 -0.53767 -7.39 0.768216 -8.61 13-Apr-05 0.455853 -11.29 1.262874 -8.29 -0.16886 -8.8 0.789214 -7.19 1.860441 -8.37 15-Apr-05 -4.3015 -10.98 -2.87206 -8.08 -2.62154 -8.54 -2.98732 -6.95 -2.45622 -8.16 18-Apr-05 -2.22371 -11.58 -2.8464 -8.07 -1.86284 -8.65 -1.37756 -7.55 -3.16027 -8.02 19-Apr-05 -0.71158 -11.23 0.300258 -8.68 0.57946 -8.44 0.819028 -7.32 0.895923 -8.43 20-Apr-05 -3.73302 -11.55 -2.19499 -8.44 -0.06753 -8.19 -1.54881 -7.11 -2.21482 -8.16 21-Apr-05 2.498029 -11.2 -1.73675 -8.3 -0.36009 -7.96 1.081001 -6.9 0.219794 -7.94 22-Apr-05 0.838497 -11.24 3.829444 -8.14 0.58477 -7.71 0.487228 -6.79 1.795417 -7.9 25-Apr-05 0.061126 -11 2.983276 -8.46 -0.90869 -7.47 -0.13341 -6.69 0.768968 -7.64 26-Apr-05 0.975504 -10.65 0.578948 -8.61 0.691862 -7.31 0.47774 -6.5 -1.00579 -7.39 27-Apr-05 -0.76906 -10.31 -3.73923 -8.37 -1.53215 -7.14 -0.47393 -6.3 -1.09973 -7.29 28-Apr-05 -6.30048 -9.97 -2.99457 -9.44 -3.7794 -7.09 -2.29355 -6.16 -0.20372 -7.1 29-Apr-05 -5.66094 -12.08 -3.7448 -9.22 -1.51709 -8.08 -3.24457 -6.4 -3.36522 -6.94 2-May-05 -1.57474 -12.37 -0.25664 -10.12 -1.87916 -7.98 -1.13118 -6.85 -5.34019 -6.96 3-May-05 5.351343 -12.01 0.760426 -9.78 1.693949 -7.82 2.089743 -6.66 3.158131 -7.25 4-May-05 3.732588 -11.96 0.319618 -9.5 2.420371 -7.58 1.391766 -6.61 0.733086 -7.04 5-May-05 9.675132 -12.9 3.064793 -9.27 3.033622 -8.41 1.926241 -6.52 14.32145 -7.06 6-May-05 -1.65334 -14.75 0.771245 -9.26 -1.35027 -8.19 -0.55881 -6.43 -3.07373 -15.9 9-May-05 2.654681 -14.29 -0.20632 -8.97 0.32745 -7.95 1.292915 -6.23 0.439677 -15.7910-May-05 0.448218 -13.87 1.922551 -8.74 1.232504 -7.71 0.154505 -6.08 2.353276 -15.2811-May-05 -4.08212 -13.44 0.411369 -8.75 -0.43393 -7.6 -1.37736 -5.94 -0.3089 -14.8 12-May-05 2.182562 -13.22 0.728084 -8.49 1.384974 -7.35 1.00969 -5.77 -4.40903 -14.3613-May-05 -0.42814 -12.85 -0.51868 -8.23 -0.95857 -7.17 -0.33337 -5.6 -4.97061 -14.8916-May-05 1.376007 -12.49 1.435024 -7.97 1.840536 -6.98 1.751234 -5.44 -4.03544 -15.3317-May-05 -1.0843 -12.08 0.407942 -7.83 1.135569 -7.18 0.463179 -5.63 -2.09486 -15.3718-May-05 -1.21691 -11.94 -1.42682 -7.58 -1.07771 -6.99 1.034555 -5.5 -2.11064 -15.1 19-May-05 2.093359 -11.55 2.303115 -7.47 1.336605 -6.77 0.828136 -5.67 1.553633 -14.7120-May-05 -1.32558 -11.31 -1.74212 -7.27 -0.32407 -6.6 0.027561 -5.52 -0.16086 -14.5423-May-05 0.71036 -10.98 1.590812 -7.11 1.050822 -6.41 1.37522 -5.56 0.198951 -14.0824-May-05 2.539569 -10.64 -0.54945 -6.97 0.177093 -6.28 0.836898 -5.37 0.304135 -13.6125-May-05 -0.66458 -10.68 -0.17743 -6.81 -0.57958 -6.08 1.95302 -5.45 -0.31747 -13.2 26-May-05 -0.39219 -10.36 0.059088 -6.6 -0.49812 -6 1.064408 -5.65 -1.15103 -12.7927-May-05 3.204334 -10.05 0.372393 -6.43 0.437699 -5.83 -0.11759 -5.53 -0.02634 -12.4330-May-05 -1.97587 -10.02 -1.86589 -6.23 -1.3581 -5.65 -1.79331 -5.7 -3.21359 -12.0531-May-05 0.452973 -9.96 0.055124 -6.41 0.320771 -5.51 0.396259 -5.6 -1.63302 -12.071-Jun-05 0.50636 -9.84 1.505558 -6.21 0.105951 -5.35 -0.24872 -5.55 0.403107 -11.752-Jun-05 -1.35983 -9.68 -0.3511 -6.24 -1.06528 -5.22 -0.63493 -5.54 0.072528 -11.443-Jun-05 0.426609 -9.42 -0.70226 -6.27 1.700265 -5.19 0.024362 -5.41 3.55232 -11.064-Jun-05 -0.27352 -9.22 1.033763 -6.09 0.62323 -5.99 0.896369 -5.31 -0.45085 -11.016-Jun-05 2.924675 -8.95 0.127065 -5.98 1.633768 -5.82 1.958447 -5.17 1.512576 -10.647-Jun-05 1.515345 -9.28 1.455775 -5.85 1.595573 -5.77 0.263063 -5.49 0.902435 -10.488-Jun-05 4.534664 -9.49 3.010035 -6.23 2.152086 -6.38 1.039312 -5.35 1.74343 -10.249-Jun-05 0.311311 -9.62 -1.07568 -6.8 -1.23093 -6.22 -0.21162 -5.21 -2.31462 -9.93
10-Jun-05 -0.72118 -9.35 0.351041 -6.71 0.006468 -6.09 -0.19627 -5.04 -0.40869 -9.84
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
13-Jun-05 -2.07438 -9.69 1.071448 -6.61 -1.26023 -6.07 -1.17231 -5.03 -0.60535 -9.54 14-Jun-05 2.274342 -9.43 2.946618 -7.2 1.418515 -5.95 0.763925 -4.87 0.916054 -9.23 15-Jun-05 -0.72889 -9.17 0.47673 -7.31 0.074856 -5.81 0.730212 -4.76 -0.91795 -8.94 16-Jun-05 -2.87823 -9.01 -2.5345 -7.1 -1.79759 -5.63 -0.72199 -4.63 -1.09249 -8.71 17-Jun-05 -1.31551 -9.02 -0.27845 -7.71 -1.09195 -5.63 -2.39012 -4.63 -1.54494 -8.45 20-Jun-05 -2.77807 -8.77 -2.18636 -7.46 -2.31866 -5.45 -1.38301 -4.47 -0.65077 -8.4 21-Jun-05 -0.24579 -8.96 0.493729 -7.63 0.30099 -6.16 0.982911 -4.55 2.66632 -8.21 22-Jun-05 -1.98632 -8.68 1.735599 -7.93 -0.21062 -6.01 0.334003 -4.56 -1.72923 -8.93 23-Jun-05 0.37175 -9.22 -1.20856 -7.7 0.693505 -5.86 0.64606 -4.45 -0.65203 -9.18 24-Jun-05 0.587333 -10.2 0.459898 -7.48 0.418384 -6.04 1.404792 -5.18 0.687968 -8.89 27-Jun-05 -0.21943 -10.07 -0.00176 -7.24 -0.41424 -5.88 -0.73297 -5.04 0.038114 -8.83 28-Jun-05 0.858448 -9.74 0.613232 -7.02 -1.18016 -5.74 -0.98846 -4.99 -1.36798 -8.74 29-Jun-05 -0.04564 -9.45 -0.71879 -6.8 -0.28348 -5.68 -0.47685 -5 -0.5517 -8.58 30-Jun-05 1.982282 -9.33 1.477699 -6.59 0.087399 -5.59 2.202216 -5.04 0.531095 -8.32 1-Jul-05 3.782658 -9.64 0.344584 -6.64 1.292609 -5.48 3.002223 -5.04 0.109063 -8.04 4-Jul-05 -0.04215 -9.99 0.320307 -6.51 1.049102 -5.47 1.49007 -5.78 1.244516 -7.79 5-Jul-05 -1.76256 -9.76 1.512841 -6.52 -0.59491 -5.45 -0.33287 -5.66 -0.54982 -7.66 6-Jul-05 1.610745 -9.86 0.364334 -6.33 0.280632 -5.36 0.576295 -5.55 7.272527 -7.44 7-Jul-05 2.08169 -10.26 -1.3215 -6.12 1.19789 -5.23 0.531486 -5.75 0.197853 -11.838-Jul-05 -0.95039 -9.97 -0.93651 -6.3 -0.35552 -5.09 -0.23682 -5.73 0.961948 -12.6411-Jul-05 1.143241 -9.8 5.202996 -6.1 0.266162 -4.94 0.375802 -5.62 1.502103 -13.1712-Jul-05 2.413925 -9.48 3.701818 -8.27 0.184982 -4.8 -0.37645 -5.45 0.368112 -12.8213-Jul-05 3.324305 -9.61 -0.37405 -8.59 1.700164 -4.68 1.541256 -5.31 -0.32448 -12.6114-Jul-05 -2.10728 -9.41 -2.49441 -8.34 -1.10529 -4.68 -1.23003 -5.26 0.070764 -12.2215-Jul-05 2.305748 -9.18 -2.48521 -8.83 -0.2421 -4.82 -0.26868 -5.36 -0.84471 -11.8218-Jul-05 3.593949 -9.48 1.278124 -8.61 0.844999 -4.79 0.262109 -5.25 2.996001 -11.4319-Jul-05 0.981267 -9.79 -0.68739 -8.35 0.545917 -4.7 0.502972 -5.09 2.395534 -11.5720-Jul-05 1.594756 -9.52 0.220161 -8.1 1.331544 -4.55 0.899422 -4.97 -0.37089 -11.2621-Jul-05 -3.68911 -9.38 -0.85767 -7.86 -1.37209 -4.57 -1.6255 -4.85 -1.91166 -10.9322-Jul-05 0.565957 -9.43 2.981518 -7.61 1.799384 -4.63 -0.03672 -5.04 1.648189 -10.7325-Jul-05 4.602566 -9.81 6.286176 -8.07 3.219031 -5.01 2.747835 -5.1 0.448068 -10.9926-Jul-05 4.631983 -9.95 4.509819 -10.82 1.870523 -6.09 1.264146 -5.62 -2.8141 -10.8 27-Jul-05 4.329077 -11.81 2.344599 -10.89 0.254114 -5.91 2.208218 -5.53 -1.18609 -10.5929-Jul-05 4.345396 -11.59 5.022271 -11.06 -0.26923 -5.81 4.619361 -6.03 -0.67011 -10.311-Aug-05 1.003429 -11.79 -1.65423 -10.77 -1.32002 -5.92 -1.10468 -6.49 -0.08578 -10.1 2-Aug-05 0.945222 -11.51 -1.3611 -10.44 1.51217 -5.73 1.297214 -6.4 1.762197 -10 3-Aug-05 -1.38768 -11.23 -0.53361 -10.59 0.630263 -6.14 1.512529 -6.38 -0.91979 -9.67 4-Aug-05 -1.58759 -10.93 -2.0335 -10.27 -0.85381 -6.23 -0.41728 -6.24 0.40946 -9.48 5-Aug-05 1.609272 -10.58 -0.86026 -9.93 0.62432 -6.08 -0.11419 -6.05 0.443111 -9.24 8-Aug-05 -2.52411 -10.23 -3.5823 -9.92 -4.02929 -5.91 -2.39176 -5.87 5.942846 -8.96 9-Aug-05 -1.51916 -10.43 -1.17305 -10.46 -2.72119 -7.28 -1.61248 -6.45 6.742698 -11.42
10-Aug-05 1.092834 -10.09 1.393745 -10.15 2.087878 -7.08 2.210413 -6.27 9.656272 -11.8511-Aug-05 1.560538 -9.98 2.624623 -10.05 1.888507 -7.37 2.670287 -6.98 5.136633 -16.9812-Aug-05 -0.57361 -9.67 2.004743 -10.03 -0.48567 -7.29 -0.41595 -6.86 -7.08546 -16.4516-Aug-05 -1.25462 -9.38 -2.16757 -9.76 -0.72596 -7.27 -0.51134 -6.7 -0.33605 -16.9817-Aug-05 -2.89203 -9.26 -0.16561 -9.56 -0.23413 -7.07 0.394269 -6.49 -2.53879 -16.5318-Aug-05 -2.41746 -9.33 0.657424 -9.26 0.440081 -6.85 0.711098 -6.39 -1.21335 -16.5619-Aug-05 -2.03978 -9.34 -0.95593 -8.99 -0.87356 -6.63 -1.00619 -6.23 -0.69594 -16.0622-Aug-05 -3.80016 -9.25 -1.0743 -8.87 -1.98043 -6.5 -1.46321 -6.07 -2.44161 -15.5123-Aug-05 -2.78454 -9.62 -2.43837 -8.68 -1.45301 -6.48 -1.69874 -6.12 2.944833 -15.2424-Aug-05 -5.08204 -9.73 -1.07682 -8.67 -0.53375 -6.35 -1.35201 -6.09 -4.81054 -14.8 25-Aug-05 2.49632 -10.13 0.578785 -8.5 1.091996 -6.16 0.320339 -5.92 -1.07857 -14.7 26-Aug-05 3.73207 -10.48 0.167399 -8.26 0.525861 -5.99 0.649366 -5.78 2.218429 -14.2629-Aug-05 -1.01038 -11.05 -2.70239 -8.03 -1.58779 -5.81 -1.53873 -5.62 -1.16879 -13.8430-Aug-05 0.975966 -11.1 1.507612 -8.21 0.820502 -5.68 2.00959 -5.58 1.560661 -13.38
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
31-Aug-05 -1.69294 -10.76 0.895283 -8.16 0.16655 -5.53 0.785423 -5.74 2.819299 -12.961-Sep-05 0.571938 -10.48 1.280576 -7.95 0.538666 -5.37 1.22377 -5.66 0.78466 -13.172-Sep-05 1.773663 -10.15 -1.26855 -7.69 0.3437 -5.23 0.240973 -5.48 2.620213 -12.815-Sep-05 0.613762 -10.02 0.796107 -7.47 1.877444 -5.2 1.580995 -5.38 -1.17527 -13.096-Sep-05 -1.30376 -9.71 0.922231 -7.26 0.63233 -5.12 1.633088 -5.36 -2.75611 -12.988-Sep-05 0.654255 -9.42 1.738218 -7.05 1.311208 -5.24 0.949085 -5.54 1.09442 -12.769-Sep-05 0.845079 -9.13 2.120397 -7.53 1.461989 -5.12 1.463658 -5.38 1.108017 -12.55
12-Sep-05 4.146159 -8.93 0.919928 -7.42 1.442711 -5.31 1.862856 -5.6 -1.47213 -12.1813-Sep-05 2.964704 -9.73 0.478277 -7.22 0.701571 -5.31 1.18726 -5.56 -0.30406 -11.7814-Sep-05 -2.00841 -9.54 1.526185 -7 -0.45557 -5.16 2.385261 -5.57 -0.65943 -11.4 15-Sep-05 -0.45222 -9.51 0.990955 -6.93 -1.30054 -5.39 0.568705 -5.64 -0.43852 -11.1216-Sep-05 0.035807 -9.23 1.537609 -6.81 0.085761 -5.22 -0.13094 -5.49 0.2069 -10.7719-Sep-05 -1.26774 -8.93 2.230747 -6.94 2.301249 -5.08 1.008309 -5.33 -0.24699 -10.4220-Sep-05 -1.55323 -8.76 3.231087 -6.9 0.748623 -5.33 0.231499 -5.26 5.17186 -10.0821-Sep-05 -2.23346 -8.52 2.039465 -7.95 -0.99188 -5.22 0.010995 -5.08 -3.8835 -10.8122-Sep-05 -3.86453 -8.48 -1.00543 -7.73 -1.72418 -5.19 -0.2401 -4.97 -4.56282 -11.0323-Sep-05 -3.37196 -10.65 -1.48977 -7.51 -0.85257 -5.92 -2.46147 -5.53 -0.97606 -12.8926-Sep-05 3.486926 -10.31 2.464958 -7.28 2.185327 -5.86 2.163586 -5.37 5.387298 -12.7527-Sep-05 2.588036 -10.52 1.154621 -7.06 0.793016 -5.97 1.9496 -5.73 1.247359 -13.5228-Sep-05 -0.61228 -10.59 1.822744 -7.2 0.711078 -5.8 0.827102 -5.71 -1.80414 -13.1729-Sep-05 -0.90685 -10.33 0.126965 -7.12 -0.07331 -5.82 0.738659 -5.6 3.198374 -12.7630-Sep-05 0.980351 -10.01 -0.15131 -6.91 0.638688 -5.68 -0.90679 -5.45 -4.08252 -12.543-Oct-05 4.657078 -9.91 1.048267 -6.71 2.399039 -5.75 1.604631 -5.3 2.635894 -12.274-Oct-05 1.678567 -9.8 -1.62117 -6.63 0.727383 -5.74 0.733871 -5.19 3.950504 -12 5-Oct-05 1.554499 -10.64 -3.22854 -6.46 -0.65463 -5.55 -0.39488 -5.19 -1.90307 -12.366-Oct-05 -3.83277 -10.67 -6.16329 -7.67 -2.23307 -5.45 -1.78737 -5.16 -1.62482 -12.367-Oct-05 -2.79202 -10.99 -1.49426 -8.72 -2.13845 -5.86 -1.47835 -5.41 -0.66156 -12 10-Oct-05 -1.74093 -10.71 0.899498 -8.48 0.044322 -5.69 -0.92635 -5.32 -0.59364 -11.6611-Oct-05 2.434595 -10.65 -0.95351 -8.23 1.750176 -5.64 0.967575 -5.31 -2.35103 -11.3513-Oct-05 -0.1878 -11.7 1.176473 -8.06 0.885076 -6.45 1.650633 -6.14 0.803494 -10.9914-Oct-05 -4.72487 -12.26 -4.34486 -8.13 -4.35189 -6.85 -2.29618 -6.1 -3.27128 -10.6617-Oct-05 -2.33202 -12.22 -2.58512 -8.57 -0.02278 -6.99 0.257276 -6.03 -5.11381 -10.8418-Oct-05 -0.89269 -11.92 0.572884 -8.37 1.1448 -6.83 0.73471 -5.98 -0.36435 -11.5619-Oct-05 -4.19073 -11.7 -2.4863 -8.15 -2.73116 -6.66 -2.58934 -5.91 -3.22602 -11.1720-Oct-05 -2.63742 -12.29 2.653537 -7.9 -3.30407 -6.86 -2.2754 -6.16 -2.20176 -11.1621-Oct-05 -3.69497 -12.11 -0.83579 -7.64 -3.72969 -7.83 -0.32821 -6.34 -5.71159 -11.5624-Oct-05 2.532257 -11.75 -0.72853 -7.59 0.488285 -7.57 0.060262 -6.43 3.520579 -11.2825-Oct-05 1.741241 -11.36 0.992637 -7.52 0.783483 -7.86 0.408586 -6.64 0.193404 -11.0626-Oct-05 0.527792 -11.23 1.007104 -7.37 0.797496 -8.21 0.473164 -6.78 0.084144 -10.7227-Oct-05 -4.69391 -10.88 -3.57698 -7.23 -1.45265 -7.94 -3.49332 -6.59 -4.54392 -10.4528-Oct-05 -0.70794 -12.19 -1.89151 -9.03 -4.38407 -7.78 -4.19503 -8.53 -1.85252 -10.8931-Oct-05 3.641433 -11.91 2.488399 -8.81 4.224138 -9.2 0.866238 -8.57 -0.83151 -10.6 1-Nov-05 2.634493 -12.35 1.634292 -8.86 3.03843 -11.74 1.943132 -8.88 2.431313 -10.312-Nov-05 -0.32975 -11.99 -0.12275 -8.6 0.046085 -11.37 -1.77786 -8.6 0.358138 -10.067-Nov-05 1.536184 -11.67 0.07471 -8.34 1.617279 -11.19 1.054446 -8.39 3.791349 -9.82 8-Nov-05 3.734284 -11.29 0.689377 -8.08 0.411135 -10.86 0.493096 -8.13 0.859533 -9.92 9-Nov-05 0.236387 -12.13 0.624087 -7.88 -0.2852 -10.49 0.206602 -7.86 3.199726 -9.6
10-Nov-05 -0.50083 -11.83 -0.65448 -7.64 0.725591 -10.18 1.114288 -7.75 1.346233 -9.91 11-Nov-05 1.66066 -11.47 1.47852 -7.39 0.584324 -9.86 1.28084 -7.5 -0.95731 -9.6 14-Nov-05 0.594349 -11.26 2.460228 -7.45 0.836439 -9.74 1.775882 -7.62 0.445474 -9.32 16-Nov-05 3.469658 -10.96 1.552229 -7.49 0.914623 -9.45 1.479767 -7.48 3.741625 -9.04 17-Nov-05 -1.59675 -10.86 1.242292 -7.32 0.695665 -9.15 1.124945 -7.38 -0.628 -9.29 18-Nov-05 -1.27505 -10.64 0.421742 -7.39 1.598341 -9.06 1.607652 -7.3 -0.43893 -9.03 21-Nov-05 -3.2963 -10.54 -2.62799 -7.26 -0.91716 -8.8 -1.59147 -7.06 -0.17617 -8.75 22-Nov-05 -2.06342 -10.55 -0.95675 -7.55 -1.97533 -8.52 -1.52844 -7.06 3.425013 -8.51
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
23-Nov-05 0.698177 -10.28 0.699841 -7.33 -0.31528 -8.85 -0.04358 -7.07 -0.89775 -8.68 24-Nov-05 2.228152 -10.08 1.013853 -7.23 2.005685 -8.72 1.713933 -7.19 -0.37345 -8.46 25-Nov-05 1.535076 -9.81 2.163627 -7.23 0.950135 -8.53 0.137466 -6.96 0.81289 -8.19 26-Nov-05 1.771123 -9.56 -0.45111 -7.05 1.21739 -8.39 0.997553 -6.76 -0.89246 -7.94 28-Nov-05 -0.66375 -9.45 -0.09532 -6.87 1.201815 -8.13 1.386379 -6.56 0.316681 -7.71 29-Nov-05 -2.86058 -9.33 -0.69674 -6.67 -1.19151 -8.04 -0.18983 -6.75 -1.36639 -7.46 30-Nov-05 0.083877 -9.3 1.345605 -6.45 0.325808 -7.83 -1.28042 -6.77 0.08744 -7.38 1-Dec-05 -2.63011 -9.1 -0.71505 -6.27 -2.07258 -7.65 -0.89254 -6.83 -0.31678 -7.2 2-Dec-05 2.437019 -8.83 1.57685 -6.1 0.157118 -7.43 1.868617 -6.83 0.56572 -7.13 5-Dec-05 -0.84427 -8.63 -2.11342 -5.93 -1.44993 -7.41 -2.13156 -6.63 -1.56293 -6.91 6-Dec-05 -1.76889 -8.37 -1.35679 -6.07 -1.3141 -7.17 -1.50753 -6.65 -0.66511 -6.85 7-Dec-05 -0.4085 -8.27 1.131572 -5.89 0.568513 -6.99 -0.13416 -6.57 -1.25439 -6.64 8-Dec-05 0.179749 -8.02 0.728198 -6.06 0.190367 -6.93 -0.31123 -6.4 -0.17164 -6.65 9-Dec-05 0.957488 -7.75 1.162575 -5.88 1.454983 -6.7 1.341166 -6.19 0.246807 -6.45
12-Dec-05 3.429601 -7.54 2.253018 -5.88 0.750871 -6.54 1.348253 -6.13 -0.68166 -6.26 13-Dec-05 5.487505 -8.23 1.018313 -6.02 1.627457 -6.4 1.233534 -6.04 1.647815 -6.09 14-Dec-05 2.573484 -9.94 0.879739 -5.83 4.235219 -6.35 1.423339 -6.07 1.242372 -5.9 15-Dec-05 -1.58753 -9.77 -0.67784 -5.83 -2.62581 -6.92 -2.10556 -5.87 -0.30127 -6.08 16-Dec-05 -1.03076 -11.03 1.698281 -5.83 1.552512 -7.46 -0.39266 -6.51 -1.811 -5.99 19-Dec-05 4.674665 -11.26 0.490563 -6.79 2.631578 -8.24 2.662766 -6.75 -0.05065 -5.8 20-Dec-05 2.163142 -11.88 0.042955 -6.59 -1.2483 -8.13 0.111395 -6.84 -0.95676 -5.7 21-Dec-05 0.145652 -11.62 0.381674 -6.55 -1.00459 -8.04 -1.82362 -6.7 -0.08393 -5.51 22-Dec-05 -1.58937 -11.56 -1.11554 -6.33 -0.71782 -7.93 -0.70873 -6.91 0.190954 -5.33 23-Dec-05 -3.28722 -11.23 0.999127 -6.12 0.144372 -7.77 -1.0971 -6.7 -1.48606 -5.18 26-Dec-05 -5.19274 -11.48 -2.98537 -6.05 -2.04194 -7.61 -2.97015 -6.74 -4.17402 -5.15 27-Dec-05 1.483271 -11.94 1.576898 -6.77 1.324897 -7.54 0.757555 -6.96 0.22086 -5.97 28-Dec-05 1.21465 -12.3 1.424726 -7.19 1.184145 -7.69 1.949378 -7.11 0.554104 -5.84 29-Dec-05 -0.41339 -12.1 -0.65051 -6.96 -0.1779 -7.46 -0.22832 -6.91 0.396263 -5.66 30-Dec-05 3.255239 -11.79 1.239173 -6.74 1.076195 -7.27 0.771301 -6.72 4.268253 -5.63 2-Jan-06 1.840408 -12.27 2.684963 -6.74 1.636008 -7.34 0.665604 -6.71 1.748949 -6.76 3-Jan-06 -0.17493 -11.94 0.465866 -6.76 1.068985 -7.18 0.157733 -6.52 2.741512 -6.61 4-Jan-06 3.345145 -11.57 1.807286 -6.7 1.161131 -6.95 0.855172 -6.37 0.910264 -7.03 5-Jan-06 6.298439 -11.93 -1.35926 -6.57 1.950334 -7.04 1.676036 -6.22 11.52778 -6.8 6-Jan-06 -0.62802 -13.22 -0.46497 -6.51 -0.37663 -7.04 0.687753 -6.42 2.08752 -14.889-Jan-06 -2.20699 -13.17 -1.41219 -6.33 -1.14718 -6.87 -1.02459 -6.23 -5.0717 -14.78
10-Jan-06 1.358368 -12.8 -0.89304 -6.26 -0.73096 -6.83 -1.05071 -6.18 2.538019 -14.4912-Jan-06 -1.52609 -12.38 -1.52006 -6.15 -1.50877 -6.75 0.233911 -6.17 -2.10926 -14.1 13-Jan-06 -0.33895 -12.02 1.190766 -6.08 -0.64939 -6.62 0.517217 -6.34 -1.74976 -13.7216-Jan-06 -2.91964 -11.63 -2.34502 -5.98 -1.79642 -6.44 -0.73914 -6.22 0.738568 -13.3917-Jan-06 -1.64337 -11.49 -0.1235 -6.03 0.051553 -6.35 -0.62129 -6.04 -2.31613 -12.9818-Jan-06 -4.99918 -11.51 -3.02874 -6 -2.39222 -6.16 -2.63447 -5.94 -1.91004 -12.8419-Jan-06 3.154926 -11.38 2.280737 -5.85 0.117843 -6.52 1.489211 -5.94 1.752014 -12.4720-Jan-06 0.537465 -11.4 1.621219 -5.92 0.491652 -6.39 0.489292 -5.94 0.287296 -12.3923-Jan-06 2.788267 -11.05 -0.78188 -5.93 -1.19821 -6.19 -0.45405 -5.76 -0.9936 -12.0124-Jan-06 0.838247 -11.12 0.081866 -5.92 0.932259 -6.06 0.15073 -5.6 -0.20327 -11.6725-Jan-06 -3.8583 -10.78 3.524316 -5.74 -0.24869 -6.02 -1.45116 -5.44 -2.18134 -11.3 27-Jan-06 3.885923 -11.07 2.792733 -6.65 2.450944 -5.92 1.815117 -5.52 2.057681 -11.1930-Jan-06 -1.42307 -12.44 0.410021 -7.25 -0.3895 -6.76 -2.48397 -6.04 1.026507 -11.3131-Jan-06 0.4281 -12.34 -0.46772 -7.06 1.408668 -6.79 -0.2888 -6.55 -1.23954 -10.951-Feb-06 -3.01759 -11.93 -2.09276 -6.89 -2.04731 -6.81 -0.90055 -6.34 -0.39958 -10.682-Feb-06 -2.68619 -12.05 -1.74828 -7.25 -0.78493 -7.07 -1.31492 -6.4 -3.24137 -10.513-Feb-06 -2.40405 -11.88 -2.98382 -7.2 -0.56071 -6.84 -0.10188 -6.21 -0.36352 -10.256-Feb-06 0.018898 -11.93 5.971777 -7.13 -0.63976 -6.66 0.054067 -6.06 3.370127 -9.93 7-Feb-06 5.496321 -11.67 2.942723 -8.99 0.056393 -6.49 1.019005 -5.93 0.420889 -10.038-Feb-06 -0.77032 -12.7 -0.51515 -9.22 -0.52818 -6.3 -0.03028 -5.85 0.650258 -9.71
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
10-Feb-06 3.409944 -12.35 -2.26009 -9.04 0.707952 -6.12 0.921955 -5.66 -0.34356 -9.51 13-Feb-06 2.814958 -12.76 0.686866 -9.04 0.791117 -6.02 0.268376 -5.47 0.018952 -9.22 14-Feb-06 1.56943 -12.39 -1.34388 -8.78 -0.56318 -5.84 -0.97682 -5.31 -1.43766 -8.95 15-Feb-06 -2.96887 -12.07 -0.25935 -8.75 -2.07598 -5.76 -1.04533 -5.38 -0.12267 -8.87 16-Feb-06 3.659868 -12.5 -0.41188 -8.49 -0.17179 -5.72 0.547398 -5.22 0.47329 -8.69 17-Feb-06 -1.36741 -14.07 -1.10333 -8.23 -1.87733 -5.55 -1.0862 -5.08 -0.18122 -8.41 20-Feb-06 -4.66985 -15.01 -1.15966 -8.14 -1.53289 -6.01 -0.12308 -5.05 -1.16273 -8.16 21-Feb-06 1.690362 -14.56 1.73171 -7.93 1.518994 -5.96 0.907598 -4.95 0.680299 -7.98 22-Feb-06 -1.4318 -14.09 -0.56458 -7.68 -0.38661 -5.76 0.113542 -4.81 -0.50146 -7.8 23-Feb-06 -2.34381 -13.75 0.313299 -7.42 -0.87146 -5.59 -1.62714 -4.65 0.422191 -7.65 24-Feb-06 5.523661 -13.37 -0.70199 -7.26 2.557808 -5.45 1.663727 -4.78 -0.66881 -7.5 27-Feb-06 1.970188 -14.32 1.07824 -7.07 3.234762 -6.28 1.770439 -5.23 -0.3912 -7.4 28-Feb-06 -0.88453 -13.86 2.157417 -6.85 -0.86372 -6.52 -0.06321 -5.31 -1.26215 -7.17 1-Mar-06 -0.92301 -13.52 0.716889 -7.18 -1.50801 -6.81 -0.67383 -5.33 -0.51283 -7.04 2-Mar-06 2.942694 -13.07 1.542576 -6.95 2.041461 -6.6 1.870035 -5.16 -0.11907 -6.81 3-Mar-06 2.403247 -12.95 -1.14453 -6.76 -0.34352 -6.65 0.427267 -5.19 -1.35487 -6.59 6-Mar-06 -2.06477 -12.55 -0.14317 -6.67 0.345127 -6.46 0.02026 -5.01 -1.23183 -6.42 7-Mar-06 -2.23182 -12.25 -1.99967 -6.45 -0.52314 -6.31 -0.2366 -4.87 -1.88947 -6.49 8-Mar-06 -1.16881 -11.93 -1.31107 -6.53 0.128701 -6.13 0.593002 -4.78 -1.16877 -6.5 9-Mar-06 -3.46373 -11.83 -0.51424 -6.49 -0.45261 -5.95 -1.13889 -4.87 -2.78328 -6.88 10-Mar-06 2.842111 -11.58 3.234562 -6.48 2.883356 -5.78 3.051563 -5.02 1.846467 -6.75 13-Mar-06 0.962302 -11.46 -0.24881 -6.53 0.151475 -6.2 1.045606 -5.06 1.31137 -7.07 14-Mar-06 0.733672 -11.12 0.211664 -6.48 1.120392 -6.06 2.898464 -4.96 -0.08327 -6.88 16-Mar-06 -1.02156 -10.76 -0.40585 -6.27 -1.4619 -5.93 0.689832 -5.38 0.072862 -6.66 17-Mar-06 -0.18624 -10.42 0.13521 -6.11 1.693 -5.82 0.406135 -5.28 -0.36015 -6.44 20-Mar-06 -1.44372 -10.11 -0.4699 -5.94 0.389839 -6.01 0.035117 -5.12 -0.84317 -6.23 21-Mar-06 0.208125 -10.42 -0.48482 -6.11 0.023063 -5.82 0.899613 -5.28 -0.2294 -6.44 22-Mar-06 -1.11221 -9.53 -1.67823 -5.71 -2.28018 -5.71 -1.9289 -4.87 0.957718 -6.08 23-Mar-06 0.737404 -9.25 0.225161 -5.6 0.092645 -5.64 1.130563 -5.06 -1.28836 -6.01 24-Mar-06 1.224035 -8.97 0.350715 -5.44 0.996212 -5.53 1.58131 -5.47 -1.27703 -5.84 27-Mar-06 2.543212 -8.81 0.697245 -5.34 2.343928 -5.84 0.593051 -5.33 -1.104 -5.72 28-Mar-06 -1.52177 -8.76 -1.00807 -5.19 -0.10129 -5.97 -0.5799 -5.18 -0.996 -5.56 29-Mar-06 -1.07513 -8.73 -0.17179 -5.1 -0.83691 -5.84 -0.16158 -5.03 0.687156 -5.41 30-Mar-06 -0.3929 -8.46 -0.00881 -5.01 0.38456 -5.66 -1.32263 -4.87 -0.53186 -5.27 31-Mar-06 0.23814 -8.29 -0.36547 -5.08 1.531542 -5.59 0.041551 -5.01 1.046273 -5.12 3-Apr-06 -0.34125 -8.18 2.033094 -4.94 -2.14306 -5.56 0.468975 -4.87 1.374312 -4.97 4-Apr-06 0.766477 -7.97 2.443133 -5.29 0.095531 -5.45 2.045691 -4.91 0.497756 -5.13 5-Apr-06 2.825959 -7.72 0.223564 -5.31 0.911995 -5.32 0.73204 -4.91 1.841268 -5.04 7-Apr-06 -3.7089 -8.04 -1.68278 -5.28 -1.20582 -5.15 -0.9231 -4.85 -0.88703 -5.03 10-Apr-06 -1.28381 -8.97 -2.58378 -6.06 -3.17342 -5.4 -3.07286 -5.29 -2.30481 -5.2 12-Apr-06 -1.21136 -8.67 -0.70726 -5.88 -0.67551 -5.3 -1.53811 -5.3 0.271338 -5.13 13-Apr-06 -4.36945 -9.21 -3.60524 -6.12 -1.48597 -5.38 -3.2226 -5.72 -2.20456 -4.97 17-Apr-06 1.51132 -8.97 0.751158 -6.66 -1.56937 -5.46 0.295008 -5.85 -0.01846 -5.16 18-Apr-06 2.198939 -8.76 2.478136 -7 2.288331 -5.29 2.66519 -5.83 0.657759 -5.01 19-Apr-06 -0.81601 -8.5 0.19047 -6.83 -0.68901 -5.27 -0.20611 -5.76 -1.66361 -4.87 20-Apr-06 -0.71705 -8.24 -0.42278 -6.63 -0.43281 -5.27 -0.85301 -5.6 -0.08225 -4.91 21-Apr-06 -1.14371 -7.97 0.512216 -6.41 -0.26266 -5.21 -1.37191 -5.44 -1.03912 -4.8 24-Apr-06 -0.44524 -7.79 -2.20202 -6.21 -0.59592 -5.06 -1.00726 -5.47 -0.1545 -4.72 25-Apr-06 -1.16679 -7.54 -1.85156 -6.95 -2.04762 -4.96 0.122059 -5.33 4.671256 -4.62 26-Apr-06 0.085695 -7.4 0.071358 -6.89 -0.7525 -5.67 -1.16711 -5.33 -1.75719 -5.1 27-Apr-06 -1.18351 -7.24 0.679392 -6.77 -0.12072 -5.53 -0.3722 -5.22 -0.5085 -4.94 28-Apr-06 0.128863 -7.41 -0.95197 -6.55 -1.75908 -5.49 -2.60156 -5.36 1.839992 -4.8 29-Apr-06 1.986722 -7.2 4.28043 -6.55 2.776449 -5.34 3.027385 -5.26 5.080754 -5.66 2-May-06 5.319555 -7.25 4.281045 -6.74 3.547727 -6.02 2.668649 -5.9 4.291622 -6.27 3-May-06 4.894415 -9.97 3.336726 -7.92 4.142061 -6.82 2.51392 -6.2 1.061438 -6.63
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
4-May-06 4.500816 -10.1 2.956532 -8.61 1.390933 -7.67 0.786134 -6.43 -2.47985 -6.49 5-May-06 2.76186 -10.71 -1.34889 -8.47 -1.87156 -7.46 -0.32438 -6.23 0.064078 -6.67 8-May-06 2.020258 -10.95 -1.45691 -8.74 0.288284 -7.34 -0.09729 -6.07 2.964508 -6.62 9-May-06 -0.40135 -10.61 -0.17516 -8.46 1.743953 -7.1 0.793666 -5.87 -0.76022 -6.53 10-May-06 1.717373 -10.27 3.753576 -8.22 3.55342 -7.31 3.295953 -5.96 3.196705 -6.34 11-May-06 0.69492 -10.03 0.566498 -8.53 -1.66238 -7.43 -1.1191 -6.22 1.255739 -6.7 12-May-06 -4.46065 -9.71 -3.07011 -8.27 -2.48572 -7.67 -2.25539 -6.48 -0.86991 -6.52 15-May-06 -5.16083 -10.59 -2.96516 -8.83 0.210823 -7.44 -2.11222 -6.48 -1.92239 -6.39 16-May-06 -3.49808 -11.29 -2.70321 -8.9 -2.82284 -7.2 -3.46787 -7.09 -3.02252 -7.21 17-May-06 4.942233 -10.94 2.9352 -8.63 3.743602 -7.61 5.732963 -6.88 3.229712 -7.11 18-May-06 -3.20108 -11.47 -4.29215 -8.45 -3.48427 -9.4 -2.98864 -9.13 -3.87347 -7.04 19-May-06 -2.75644 -13.77 -4.5414 -9.51 -4.55665 -11.59 -4.92072 -12.02 -3.19799 -7.98 22-May-06 -11.1766 -13.65 -4.94363 -11.09 -4.22063 -12.33 -5.64092 -12.26 -7.70304 -8.84 23-May-06 2.029823 -15 1.800116 -10.72 -2.21159 -12.17 2.560662 -11.93 2.321248 -10.2424-May-06 2.935184 -15.65 5.620211 -11.11 3.944293 -11.8 1.909854 -11.63 5.087812 -10.8725-May-06 -3.81049 -15.83 -4.96295 -10.84 -0.33416 -11.43 -2.92737 -11.25 -0.04276 -10.9626-May-06 2.666184 -15.33 1.539312 -10.62 2.286506 -11.39 2.880188 -10.91 3.567663 -10.7 29-May-06 -0.83236 -15.04 -0.0545 -10.3 -0.93016 -11.02 -0.36441 -10.57 -1.28029 -10.5630-May-06 -1.69858 -14.54 0.386563 -10.01 -2.30753 -10.68 -1.25093 -10.26 -1.40325 -10.5431-May-06 -5.69252 -14.2 -5.66338 -9.71 -3.97369 -10.83 -4.496 -10.19 -4.34805 -10.291-Jun-06 0.801635 -14.63 0.351037 -10.85 -0.92302 -10.73 0.144364 -10.3 1.42423 -9.98 2-Jun-06 -1.69101 -14.15 0.878168 -10.51 0.404849 -10.65 -0.28484 -10.09 -1.3925 -10 5-Jun-06 0.972148 -13.69 -0.26902 -10.59 -0.82037 -10.83 -0.18213 -10.03 0.642657 -10.056-Jun-06 -0.92053 -13.29 -0.60621 -10.53 -2.45469 -11.35 0.69153 -10.09 -3.59258 -10.037-Jun-06 -3.21155 -13.06 -1.46493 -10.22 -1.65592 -10.98 -2.4194 -10.21 -2.33371 -9.96 8-Jun-06 -10.6688 -14.45 -4.12422 -10.02 -3.89718 -11.09 -4.21966 -10.58 -7.13107 -10.019-Jun-06 9.54398 -16.22 -2.77013 -11.5 -2.57936 -11.34 -0.58859 -11.17 3.048249 -10.4
12-Jun-06 -0.5597 -20.03 -3.0551 -11.13 -1.67228 -11 -1.12538 -10.84 -0.10864 -10.1413-Jun-06 -9.14265 -20.78 -6.57888 -11.89 -9.64344 -11.64 -3.4248 -10.93 -2.38355 -9.87 14-Jun-06 1.438267 -20.51 2.222208 -11.87 -1.37436 -13.81 1.811753 -10.58 0.409254 -9.59 15-Jun-06 -0.3171 -20.13 2.987713 -11.6 -0.45951 -13.58 1.534972 -10.29 0.62137 -9.41 16-Jun-06 3.580201 -19.93 6.19741 -12.88 4.334621 -13.37 2.896883 -10.66 1.556412 -9.17 19-Jun-06 -1.50659 -19.26 -1.19668 -13.28 0.014887 -13.5 -4.90981 -10.32 -1.79898 -8.89 20-Jun-06 -0.03877 -18.76 -2.53716 -12.88 -4.05185 -13.09 -0.3646 -10 0.236988 -8.6 21-Jun-06 2.235682 -18.13 1.547857 -12.62 0.484411 -13.82 -0.94816 -9.88 0.24144 -8.34 22-Jun-06 4.75685 -17.76 3.486399 -12.21 3.897674 -13.45 3.175139 -9.57 0.605546 -8.08 23-Jun-06 -2.40249 -17.45 -1.66222 -12.27 -1.48649 -14.46 -0.37264 -10.12 -2.1148 -7.83 25-Jun-06 0.031278 -17.07 0.735728 -11.91 -0.58215 -14.33 -0.61092 -9.87 1.262923 -7.57 26-Jun-06 -2.88955 -16.5 -2.22036 -11.55 -1.72852 -13.9 -1.87553 -9.61 -0.94821 -7.31 27-Jun-06 -3.2064 -16.61 -0.94008 -11.58 -1.47677 -13.83 -1.98632 -9.82 -2.56792 -7.38 28-Jun-06 -2.03561 -16.09 -0.01285 -11.3 -0.02992 -13.41 -1.58572 -9.52 -0.3382 -7.25 29-Jun-06 0.122478 -15.76 -1.44133 -11.09 1.016847 -12.96 -0.17736 -9.43 -0.27341 -7.03 30-Jun-06 3.942798 -15.24 1.760573 -10.92 3.242068 -12.55 1.954531 -9.14 0.443811 -7.06 3-Jul-06 -1.56259 -15.5 -0.87808 -10.7 -0.98372 -12.53 0.929089 -9.18 0.193823 -6.91 4-Jul-06 -0.90211 -15.12 0.418166 -10.34 2.857947 -12.14 2.367857 -9.08 -0.81141 -6.73 5-Jul-06 2.088268 -14.8 0.903776 -10.01 2.588826 -12.32 0.402228 -8.93 -0.21843 -6.53 6-Jul-06 0.160409 -14.41 -1.95757 -9.87 -1.71217 -11.93 -0.94546 -8.63 -0.05488 -6.34 7-Jul-06 -1.78481 -13.96 2.292824 -9.62 -1.47679 -11.57 -1.70091 -8.41 0.784791 -6.15 10-Jul-06 -2.28504 -13.81 -1.37402 -9.63 -1.07247 -11.48 -1.7556 -8.79 8.69603 -6.38 11-Jul-06 0.768643 -13.38 -0.38213 -9.4 1.776122 -11.25 0.742446 -8.58 8.191956 -10.4812-Jul-06 -0.96244 -13.03 -0.91722 -9.16 -1.1929 -10.91 0.22547 -8.3 -2.04585 -12.1913-Jul-06 -0.70713 -12.71 1.642748 -8.85 -0.79095 -10.64 0.377743 -8.1 3.447123 -12.1814-Jul-06 -5.69126 -12.54 -1.31645 -8.67 -2.829 -10.38 -0.88143 -7.85 -2.06416 -12.4 17-Jul-06 -4.48364 -12.71 -1.4489 -8.61 -1.54664 -10.06 -1.02218 -7.64 -0.27972 -12.1918-Jul-06 -6.61925 -13.91 -1.49596 -8.5 -2.16578 -10.36 -3.01755 -8.24 -2.82658 -11.83
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
19-Jul-06 -1.32444 -13.94 -0.2464 -8.28 -0.18172 -10.2 -0.69251 -8.02 -3.79051 -12.1 20-Jul-06 5.584618 -13.73 4.241044 -8.06 4.132588 -9.86 4.017686 -7.91 0.453018 -12.5521-Jul-06 2.277213 -15.22 -1.7181 -9.08 -0.68547 -11.15 -1.35246 -8.93 -2.40124 -12.3924-Jul-06 7.008124 -14.97 5.356063 -8.89 3.796708 -11.01 2.457449 -8.73 2.29069 -12.2125-Jul-06 3.932858 -16.22 4.805947 -10.22 4.632128 -11.42 2.274128 -9 3.010569 -12.1926-Jul-06 4.291705 -15.92 0.697796 -11 0.440419 -11.88 0.343711 -8.76 -2.70382 -11.8227-Jul-06 3.189541 -15.87 0.816224 -10.65 2.799173 -11.52 -0.47955 -8.52 -0.23275 -11.5 28-Jul-06 4.571468 -16.2 -0.19043 -10.32 2.927392 -11.64 5.260766 -8.3 1.110961 -11.1331-Jul-06 1.916201 -15.73 2.905872 -10.01 3.912078 -11.52 3.01767 -8.91 2.458518 -10.911-Aug-06 -3.51895 -15.22 -1.70433 -9.85 -2.66589 -11.44 -0.90264 -8.77 -2.23278 -10.722-Aug-06 5.053056 -14.75 -0.07592 -9.58 1.759121 -11.44 2.010726 -8.49 0.201789 -10.543-Aug-06 3.874765 -14.91 2.104285 -9.26 2.900734 -11.41 1.611561 -8.39 0.684974 -10.2 4-Aug-06 -1.52263 -14.82 -1.08201 -9.1 -3.42741 -11.1 -2.09139 -8.13 3.701908 -9.89 7-Aug-06 -1.23873 -14.53 1.401235 -8.99 -2.29105 -11.46 -1.13367 -8.26 -0.17814 -10.428-Aug-06 2.613436 -14.07 5.094237 -9.35 6.313018 -11.1 2.252426 -8.01 1.002067 -10.119-Aug-06 4.574678 -13.74 1.179455 -10.07 1.706544 -12.8 3.174617 -8.1 0.422646 -9.86
10-Aug-06 3.206569 -14.58 -0.62397 -9.78 3.120456 -12.39 1.152917 -8.6 -0.52238 -9.57 11-Aug-06 0.185235 -14.23 -0.71804 -9.58 1.495889 -12.91 -0.05487 -8.34 0.355539 -9.28 14-Aug-06 0.47088 -13.84 -1.47557 -9.54 -0.09696 -12.64 0.433107 -8.09 0.488615 -9 16-Aug-06 1.03473 -13.47 1.514965 -9.3 2.302449 -12.27 2.795489 -7.92 2.317093 -8.78 17-Aug-06 -1.59091 -13.04 0.671362 -9.26 -0.19999 -12.27 -0.52687 -7.88 1.512906 -8.85 18-Aug-06 -1.69634 -12.68 -0.87444 -8.97 -2.51871 -12.05 -0.83947 -7.67 -0.17716 -8.59 21-Aug-06 5.322304 -12.36 0.507172 -8.68 4.338617 -11.71 0.278586 -7.43 2.607055 -8.31 22-Aug-06 1.037266 -13.99 1.411851 -8.47 2.43195 -12.8 0.704398 -7.22 3.845172 -8.26 23-Aug-06 -2.95266 -13.77 -1.25543 -8.19 -2.53677 -12.41 -1.60673 -7 -0.45114 -9.14 24-Aug-06 0.685423 -13.66 -1.39634 -7.96 1.482376 -12.2 -0.66647 -6.95 -1.77224 -9.43 25-Aug-06 1.924043 -13.71 1.467508 -7.72 3.191348 -12.44 4.527962 -6.84 3.186368 -9.14 28-Aug-06 2.619543 -13.3 -0.81812 -7.46 1.209179 -12.16 0.87305 -7.31 -0.91709 -9.17 29-Aug-06 3.357374 -13.04 1.07217 -7.24 1.77233 -11.81 1.05552 -7.23 -0.89527 -8.98 30-Aug-06 1.64105 -13.22 0.020264 -7.12 0.539704 -11.48 0.22733 -6.99 -1.09912 -8.74 31-Aug-06 -0.9284 -12.82 0.817226 -6.88 1.079247 -11.22 0.804084 -6.82 -1.40715 -8.49 1-Sep-06 0.025208 -12.48 1.324939 -6.68 -0.4835 -10.87 -0.1937 -6.62 -0.78193 -8.31 4-Sep-06 -1.92617 -12.08 1.905225 -6.73 0.32157 -10.53 0.539042 -6.41 0.031388 -8.08 5-Sep-06 0.933129 -11.93 -0.50249 -6.79 0.940205 -10.2 0.912669 -6.2 -2.98621 -7.84 6-Sep-06 0.025953 -11.87 -0.53767 -6.73 -1.1449 -9.93 0.200957 -6.08 0.124167 -8.1 7-Sep-06 -0.59463 -11.52 -1.10634 -6.53 -1.54744 -9.64 -0.78003 -5.91 -0.27348 -7.94 8-Sep-06 -0.0534 -11.18 0.258084 -6.35 0.293323 -9.41 -0.06252 -5.79 0.420827 -7.69
11-Sep-06 -2.59852 -10.86 -1.36832 -6.16 -0.4206 -9.17 -1.13624 -5.64 -1.90886 -7.46 12-Sep-06 -0.5891 -11.43 0.302371 -6.14 2.454259 -8.99 -0.16989 -6.01 0.470059 -7.4 13-Sep-06 7.708783 -11.67 3.443768 -6.06 3.343636 -9.21 3.523055 -5.99 1.880109 -7.25 14-Sep-06 3.046595 -13.07 3.407371 -7.06 0.747936 -9.58 1.473115 -6.78 0.283103 -7.11 15-Sep-06 1.022624 -13.03 0.232931 -7.33 0.416279 -9.28 0.091481 -6.58 -0.59182 -6.88 18-Sep-06 -0.56841 -12.64 -0.09329 -7.11 1.197781 -9.03 1.389244 -6.38 4.821108 -6.67 19-Sep-06 -1.12016 -12.25 0.319925 -6.89 -1.95558 -8.76 -0.34336 -6.27 -0.95857 -7.64 20-Sep-06 -0.40756 -11.89 -0.32527 -6.67 -1.95561 -8.93 -1.25611 -6.2 -3.66796 -8.07 21-Sep-06 0.36448 -11.52 2.364043 -6.51 2.292361 -8.67 1.13955 -6.02 0.412689 -7.87 22-Sep-06 -1.35244 -11.22 -1.03957 -6.52 -0.82068 -8.44 -0.34011 -5.9 2.155519 -7.67 25-Sep-06 -0.32116 -10.88 1.639176 -6.4 0.742396 -8.28 -0.59362 -5.78 -1.7579 -7.76 26-Sep-06 0.14105 -10.57 0.723623 -6.21 1.010955 -8.11 1.396718 -5.63 0.271002 -7.89 27-Sep-06 2.737385 -10.5 3.016649 -6.56 1.819848 -8.03 1.56158 -6.04 0.500055 -7.71 28-Sep-06 5.364628 -10.36 2.262119 -6.5 2.480037 -7.81 1.490629 -5.83 2.772552 -7.47 29-Sep-06 1.208983 -11.6 -0.56334 -6.83 0.845581 -8.34 0.787204 -6.18 -0.35548 -7.64 3-Oct-06 -0.72578 -11.29 -0.038 -6.73 -0.09187 -8.08 0.35387 -5.97 0.926509 -7.39 4-Oct-06 -2.28572 -10.94 -1.0612 -6.52 -0.68837 -7.83 -1.07626 -5.81 -1.70058 -7.18 5-Oct-06 3.450912 -11.1 1.782774 -6.31 2.88634 -7.59 1.734512 -5.83 0.274732 -7.19
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
6-Oct-06 0.588265 -12.35 -0.2064 -6.27 -0.09778 -7.87 -0.27414 -6.04 0.005325 -7 9-Oct-06 1.145058 -12 -0.64134 -6.1 -0.67458 -7.62 -0.23634 -5.86 1.629219 -6.77 10-Oct-06 -0.10828 -11.64 -0.48869 -5.92 -0.39857 -7.41 -0.05329 -5.69 -0.47765 -6.8 11-Oct-06 -1.91257 -11.32 -0.85342 -5.74 -1.58164 -7.21 -1.67086 -5.56 -1.22366 -6.61 12-Oct-06 -0.87794 -11.05 -0.84734 -5.65 0.334701 -7.06 -0.22901 -5.74 -0.00473 -6.51 13-Oct-06 0.073669 -10.73 1.670628 -5.49 1.0661 -6.94 1.335645 -5.96 1.895031 -6.3 16-Oct-06 -1.60979 -10.51 2.105055 -5.36 -0.59067 -6.74 0.000428 -5.79 4.541596 -6.38 17-Oct-06 0.803626 -10.23 1.127423 -6.1 0.204663 -6.52 0.814149 -5.63 5.770334 -8.18 18-Oct-06 0.687561 -10.06 2.482791 -5.95 -0.50096 -6.3 0.952445 -5.51 -2.0192 -8.27 19-Oct-06 -5.69972 -9.8 0.210703 -6.17 -0.86241 -6.12 -0.39227 -5.4 -0.80256 -8.03 20-Oct-06 0.011743 -10.83 0.231439 -5.98 0.176855 -5.97 0.275706 -5.26 -0.11671 -8.03 21-Oct-06 -0.10381 -10.52 0.008236 -5.79 -1.61923 -5.87 -0.14823 -5.09 -0.86609 -7.83 23-Oct-06 -2.03593 -10.19 -1.92389 -5.62 -2.41081 -5.71 -1.19665 -4.94 -0.71924 -7.57 26-Oct-06 1.100406 -10.23 3.058638 -5.9 0.627715 -5.9 1.617979 -4.97 0.027078 -7.32 27-Oct-06 7.255971 -11.05 1.166378 -7.42 3.176482 -5.79 3.401611 -5.98 0.640231 -7.1 30-Oct-06 2.02218 -11.78 2.419703 -7.17 0.917896 -6.5 0.708812 -6.23 2.5755 -6.93 31-Oct-06 3.205938 -11.44 0.697506 -7.75 -0.51955 -6.35 0.746478 -6.05 -1.49154 -6.9 1-Nov-06 2.812176 -11.72 -0.63355 -7.6 -0.09811 -6.15 0.749841 -5.87 -2.34394 -7.17 2-Nov-06 0.562162 -11.46 0.215996 -7.35 0.488927 -5.98 1.440903 -5.87 -1.42835 -7.07 3-Nov-06 -0.37802 -11.1 -0.46598 -7.13 -0.82596 -5.83 0.188438 -5.76 -1.10691 -6.97 6-Nov-06 0.936504 -10.75 -0.80881 -6.96 0.147851 -5.7 -0.67521 -5.58 -1.23402 -6.78 7-Nov-06 -0.81673 -10.43 0.216225 -6.76 -1.06986 -5.55 -1.09928 -5.53 0.626736 -6.68 8-Nov-06 -1.26257 -10.12 0.530062 -6.56 -1.51822 -5.39 0.985248 -5.38 -0.16284 -6.71 9-Nov-06 -0.01096 -9.8 2.935249 -6.58 1.399546 -5.25 1.277696 -5.59 1.736981 -6.66
10-Nov-06 0.575348 -9.49 3.208255 -6.6 0.519798 -5.2 0.566145 -5.4 -1.44041 -6.66 13-Nov-06 0.005611 -9.22 2.046483 -7.24 0.367421 -5.04 -0.00208 -5.23 -0.51583 -6.61 14-Nov-06 -1.17517 -8.93 1.330643 -7.11 0.094319 -4.92 -0.37545 -5.08 -0.7418 -6.43 15-Nov-06 4.59086 -8.73 2.615941 -7.08 3.290343 -4.79 2.24562 -4.99 0.222652 -6.23 16-Nov-06 5.831586 -10.82 3.322706 -7.27 3.680267 -6.87 4.842604 -6.25 0.827741 -6.07 17-Nov-06 -1.33275 -10.86 -2.53201 -7.06 -2.95223 -6.77 0.699265 -6.87 -1.50066 -5.87 20-Nov-06 -2.4958 -10.55 -3.38283 -6.93 -2.03742 -7.35 -1.56823 -6.67 -2.06245 -5.84 21-Nov-06 2.677697 -10.41 2.098786 -6.93 2.209507 -7.17 1.778895 -6.55 3.40333 -5.66 22-Nov-06 2.12642 -10.2 1.320179 -6.87 0.378861 -6.95 1.659121 -6.55 1.760831 -5.71 23-Nov-06 0.819772 -10.06 -0.51443 -6.71 -0.91923 -6.75 0.370024 -6.43 1.546933 -6.34 24-Nov-06 2.193132 -9.89 -0.33233 -6.49 1.667615 -6.55 0.339731 -6.24 0.207522 -6.16 27-Nov-06 0.855567 -9.64 0.702334 -6.31 -0.16336 -6.4 1.116269 -6.05 0.325292 -6 28-Nov-06 -2.05101 -9.37 -1.97695 -6.21 -2.24492 -6.19 0.57919 -6 -1.30974 -5.83 29-Nov-06 1.38575 -9.34 -0.07705 -6.41 1.535102 -6.27 2.551465 -5.96 2.149892 -5.9 30-Nov-06 -0.32241 -9.14 0.51652 -6.23 0.557717 -6.28 0.269408 -5.78 1.136431 -6.31 1-Dec-06 3.432155 -8.86 1.41145 -6.21 1.648665 -6.08 2.745916 -5.73 3.353457 -6.12 4-Dec-06 0.912981 -9.28 -0.67205 -6.04 2.70715 -6.13 0.786524 -6.33 1.376035 -7.65 5-Dec-06 -0.59873 -7.72 -0.71965 -5.31 0.206251 -5.32 -1.09073 -4.91 2.346815 -5.04 6-Dec-06 -1.11884 -8.74 0.272405 -5.77 -1.60391 -6.72 -0.29598 -6.03 -0.436 -7.28 7-Dec-06 0.14996 -8.49 0.612616 -5.6 -1.60447 -6.97 0.232294 -5.83 -1.07887 -7.06 8-Dec-06 0.234302 -8.24 1.034242 -5.55 1.016482 -6.77 1.105182 -5.69 -0.83918 -6.86
11-Dec-06 -10.7369 -7.98 -6.49365 -5.37 -7.91384 -6.55 -6.6888 -5.53 -3.3382 -6.68 12-Dec-06 -6.59921 -12.53 -2.07957 -8.16 -5.96947 -10.23 -5.0965 -9.29 -3.99726 -7.37 13-Dec-06 -0.75638 -16.2 1.237627 -8.12 1.521398 -10.65 0.208228 -10.24 0.376741 -8.14 14-Dec-06 5.150175 -16.37 4.65966 -8.41 1.48195 -10.54 1.547583 -10.48 3.46989 -8.23 15-Dec-06 5.473298 -17.13 1.445456 -9.19 1.674439 -10.21 1.565421 -10.16 1.577583 -8.16 18-Dec-06 0.045622 -17.05 0.251734 -8.89 -0.59616 -9.97 0.183503 -10.27 0.997556 -7.96 19-Dec-06 -0.13556 -16.62 -0.80177 -8.76 -1.2906 -9.65 -0.40722 -9.94 2.505583 -8.12 20-Dec-06 0.050773 -16.25 -0.42058 -8.71 -0.01771 -9.64 -1.0474 -10.06 0.175315 -7.88 21-Dec-06 -0.87788 -15.71 -1.65751 -8.57 -1.3862 -9.34 -1.71742 -9.79 3.423979 -7.65 22-Dec-06 0.423806 -15.2 0.887393 -8.3 0.372756 -9.13 0.213055 -9.49 1.588465 -8.15
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
26-Dec-06 0.205846 -14.69 0.686051 -8.05 1.506852 -8.9 1.721924 -9.19 0.30255 -8.18 27-Dec-06 2.022822 -14.25 3.644833 -7.97 3.068224 -8.87 1.753325 -9.2 -0.13704 -7.94 28-Dec-06 2.227806 -13.9 0.799551 -8.02 -0.94175 -8.72 -0.73087 -8.93 -0.16666 -7.79 29-Dec-06 2.744826 -14.34 -0.39082 -7.8 -0.0321 -8.45 -0.37686 -8.71 0.000582 -7.57 2-Jan-07 2.031924 -10.11 -0.01721 -8.79 -0.92173 -6.96 0.565295 -8.1 1.144526 -7.35 3-Jan-07 -0.25103 -13.91 -0.52172 -7.66 1.508906 -8.28 0.815009 -8.48 3.781762 -7.42 4-Jan-07 1.311417 -13.03 0.400545 -7.21 0.206986 -7.82 -0.21114 -8.01 0.710999 -8.17 5-Jan-07 -1.9809 -12.65 1.360707 -7 -1.32569 -7.61 -1.18641 -7.91 1.152229 -8.08 8-Jan-07 -3.04892 -12.5 -0.63849 -7.05 -0.45827 -7.39 -1.76488 -7.68 1.960118 -8.26 9-Jan-07 -2.32775 -12.26 0.318608 -6.85 -1.08434 -7.17 -2.26026 -7.75 1.014442 -8.15
10-Jan-07 -2.97472 -12.51 -1.84807 -6.65 -2.93775 -7.43 -3.69529 -8.05 -1.47974 -7.94 11-Jan-07 0.383994 -12.31 -0.89484 -7.05 -0.88358 -7.35 -0.56505 -8.36 4.846222 -7.98 12-Jan-07 7.175082 -11.77 7.114776 -6.9 5.551693 -7.15 6.180999 -8.13 3.872411 -10.4415-Jan-07 -0.07488 -13.25 1.741334 -10.3 1.46194 -8.83 0.278155 -9.9 0.334299 -10.1216-Jan-07 -1.1635 -12.91 -0.76641 -10.06 -0.08405 -8.58 -0.33004 -9.6 -4.16046 -10.1317-Jan-07 0.165455 -12.52 1.923554 -9.75 0.621606 -8.31 0.397885 -9.35 1.883871 -9.82 18-Jan-07 1.735871 -12.12 0.423407 -9.78 1.168892 -8.16 1.244052 -9.09 1.326145 -9.61 19-Jan-07 -1.50032 -11.83 -0.3705 -9.6 -1.47732 -7.9 -1.29278 -8.83 -1.67881 -9.39 22-Jan-07 0.171305 -11.48 0.254256 -9.39 0.509454 -7.73 0.114908 -8.58 -0.44749 -9.24 23-Jan-07 -2.43236 -11.1 -1.39103 -9.11 -1.32527 -7.67 -2.8146 -8.31 -0.27247 -8.93 24-Jan-07 -1.34443 -11.34 0.642218 -8.9 -0.32904 -7.7 -2.12347 -8.91 -0.54888 -8.68 25-Jan-07 -0.07457 -10.98 1.169573 -8.69 -0.36623 -7.49 0.576401 -8.63 1.620943 -8.41 29-Jan-07 -0.68013 -10.65 -1.82142 -8.56 -0.92971 -7.24 -0.58184 -8.38 1.088678 -8.66 31-Jan-07 -1.46899 -10.32 -1.21781 -8.94 0.708433 -7.16 -1.00926 -8.27 -1.90817 -8.47 1-Feb-07 1.186629 -10.11 -0.43477 -8.79 2.098951 -6.96 3.281928 -8.1 -0.30787 -8.22 2-Feb-07 0.124086 -10.07 0.335196 -8.59 -0.21879 -7.67 0.241236 -9.25 1.022354 -7.97 5-Feb-07 0.055665 -9.79 -0.61307 -8.37 -0.01467 -7.66 0.066032 -9.12 1.294142 -7.72 6-Feb-07 -0.49709 -9.48 1.809907 -8.12 0.545917 -7.46 0.442836 -8.9 0.787121 -7.96 7-Feb-07 -0.58297 -9.25 1.018282 -7.93 -0.71176 -7.24 -0.48653 -8.63 -1.8652 -7.93 8-Feb-07 -0.05114 -8.97 2.080616 -8.03 -0.31661 -7.03 0.854795 -8.38 0.905798 -7.68 9-Feb-07 -2.10841 -8.67 0.08978 -7.93 -1.99545 -6.81 -0.7581 -8.15 -1.16911 -7.43 12-Feb-07 -4.90528 -8.74 -3.38327 -7.68 -2.84102 -6.86 -0.8658 -7.91 -1.16682 -7.29 13-Feb-07 0.155339 -9.48 1.013416 -7.96 -0.40522 -7.12 -0.02456 -7.74 0.002616 -7.09 14-Feb-07 -7.50745 -9.22 -6.50832 -7.77 -7.25037 -7.04 -7.39696 -7.54 -1.45383 -6.9 15-Feb-07 6.064748 -9.92 3.30516 -8.54 2.295408 -7.69 1.689718 -9.27 2.387565 -6.7 19-Feb-07 1.083267 -9.27 3.323792 -8.95 0.208574 -7.51 1.035955 -9.12 -0.85594 -6.54 20-Feb-07 -0.87968 -10.42 0.009947 -9.14 -0.58731 -7.28 -0.78633 -8.85 2.905377 -6.36 21-Feb-07 -2.54598 -10.16 -0.26061 -8.91 -0.17741 -7.06 -1.4509 -8.79 -0.60638 -6.69 22-Feb-07 -3.67398 -9.96 -1.04736 -8.63 -2.80198 -6.84 -1.74009 -8.52 -1.25837 -6.49 23-Feb-07 -4.15974 -10.75 -5.11795 -8.66 -3.16695 -7.67 -2.31633 -8.58 -0.49061 -6.41 26-Feb-07 0.031493 -11.06 -1.55902 -9.22 1.838823 -7.83 0.600619 -8.47 3.67331 -6.19 27-Feb-07 4.030442 -11.32 -2.20194 -8.93 0.035461 -8.87 1.020166 -8.58 1.031385 -6.65 28-Feb-07 -3.34168 -11.15 -4.44524 -9.11 -3.5422 -8.76 -2.28328 -8.46 -6.13961 -6.45 1-Mar-07 1.375568 -11 0.036815 -10.13 -0.07973 -9.98 -1.57175 -8.52 0.342081 -7.78 2-Mar-07 0.878679 -10.67 0.460179 -10.22 1.066271 -10.5 0.48046 -8.35 -0.79158 -7.53 5-Mar-07 -3.70668 -10.4 -4.04983 -9.98 -6.02656 -10.71 -6.68317 -9.25 -6.44665 -7.5 6-Mar-07 -2.37095 -10.21 4.11563 -9.95 2.974171 -10.87 0.643668 -9.8 1.129172 -9.22 7-Mar-07 -2.00731 -10.71 -0.3603 -10.06 0.052978 -11.01 -0.47572 -9.78 -0.71335 -9.16 8-Mar-07 0.204143 -11.15 0.964465 -9.97 2.52502 -10.68 1.297209 -9.74 -0.89916 -9.83 9-Mar-07 2.670749 -12.77 1.423675 -10.37 -0.41444 -10.62 0.59174 -10 1.928184 -10.2412-Mar-07 -3.9808 -12.7 0.674802 -10.05 -0.61986 -10.37 -1.09911 -9.79 -0.14639 -9.95 13-Mar-07 -1.59815 -12.54 0.461011 -9.8 1.059522 -10.05 -0.8242 -9.52 -1.91325 -9.67 14-Mar-07 -4.36952 -12.12 -4.39657 -9.53 -1.15091 -9.84 -2.46521 -9.24 -1.40573 -9.65 15-Mar-07 -0.88642 -12.95 -0.91203 -10.59 -0.61884 -9.79 -1.32447 -9.48 0.920714 -9.34 16-Mar-07 -4.14854 -12.68 -1.70074 -10.28 -2.18647 -9.6 -3.05739 -9.53 -0.45429 -9.04
ACCURACY OF VALUE-AT-RISK MODEL IN COMMERCIAL BANKS
M P BIRLA INSTITUTE OF MANAGEMENT
19-Mar-07 5.320088 -12.28 -0.10293 -10.09 1.681569 -9.33 0.693519 -9.26 1.186375 -8.76 20-Mar-07 5.52916 -12.37 2.000884 -9.88 1.55656 -9.14 2.752414 -9.06 0.937498 -8.55 21-Mar-07 3.890768 -13.25 2.975415 -9.56 4.1835 -9.19 2.476355 -9.13 0.335587 -8.27 22-Mar-07 9.55252 -13.11 4.676264 -10.55 6.126672 -9.45 4.946258 -9.31 2.436391 -8.12 23-Mar-07 1.082862 -17.07 0.269428 -10.67 0.743626 -11.06 0.925174 -9.95 2.254997 -7.91 26-Mar-07 -0.18505 -16.56 -1.30198 -10.37 0.573634 -10.73 -0.58902 -9.64 2.980055 -8.31 28-Mar-07 -2.00152 -16.09 -3.24692 -10.18 -3.83988 -10.43 -3.22712 -9.4 -1.56522 -8.13 29-Mar-07 -1.51689 -15.56 -0.92719 -10.04 0.714404 -10.31 -1.78476 -9.83 0.81304 -7.87 30-Mar-07 0.547989 -15.35 0.639419 -9.71 0.941323 -10.15 2.426687 -9.59 0.73091 -7.69 2-Apr-07 -8.02784 -14.87 -5.58211 -9.41 -9.44712 -9.82 -6.36989 -9.33 -5.39874 -7.49 3-Apr-07 3.101221 -16.48 -0.47679 -10.64 -0.59871 -13.69 -0.38524 -10.92 -0.69124 -9.57 4-Apr-07 -0.28591 -16.76 2.193782 -10.31 0.488311 -13.26 0.89036 -10.57 1.975645 -9.3 5-Apr-07 0.210079 -16.48 0.520637 -10.08 0.862288 -12.85 0.57676 -10.27 0.556227 -9.21 9-Apr-07 3.757926 -16.11 3.357718 -9.94 4.405716 -12.86 3.948135 -10.01 0.37649 -8.93 10-Apr-07 1.135599 -15.71 -0.67033 -9.86 -0.33941 -12.94 -0.19099 -10.41 -0.68354 -8.63 11-Apr-07 2.27651 -15.75 1.638523 -9.56 -0.42303 -12.59 1.231698 -10.08 0.511037 -8.38 12-Apr-07 -0.7047 -15.4 -1.72772 -9.26 -2.35247 -12.23 -2.48663 -9.79 -1.19012 -8.15 13-Apr-07 5.38474 -15.1 2.306017 -9.03 3.968932 -11.89 3.195698 -9.57 0.20912 -7.9 16-Apr-07 2.578387 -15.16 2.207704 -9.11 1.784191 -11.94 1.283458 -9.67 -0.20661 -7.64 17-Apr-07 0.581479 -14.9 0.30531 -8.95 1.215624 -11.78 0.20899 -9.48 0.567552 -7.39 18-Apr-07 0.881805 -14.46 1.284277 -8.69 1.526501 -11.39 1.09523 -9.19 0.242517 -7.23 19-Apr-07 -0.07166 -14.18 -0.49074 -8.43 -0.02628 -11.1 1.789471 -9.14 -0.24527 -6.99 20-Apr-07 0.822477 -13.73 1.552465 -8.18 1.041273 -10.8 1.910618 -9.01 1.048046 -6.77 23-Apr-07 -0.70613 -13.31 0.051263 -8.02 -0.86917 -10.45 0.053768 -8.92 0.537504 -6.56 24-Apr-07 3.798044 -13.06 3.391908 -7.75 4.863368 -10.21 4.634411 -8.71 2.323621 -6.55 25-Apr-07 2.91314 -14.28 0.95903 -8.14 0.812097 -11.62 2.274744 -10.43 4.306854 -8.45 26-Apr-07 -0.88216 -13.83 2.613977 -7.95 0.960073 -11.25 0.923222 -10.09 -1.81049 -8.59 27-Apr-07 0.654949 -13.38 -4.12989 -7.72 -1.38459 -10.92 -3.03177 -9.79 0.3798 -8.72 30-Apr-07 -3.98777 -13.1 -8.75284 -7.87 -2.54427 -10.72 -2.55132 -10.13 1.830076 -8.65