gunjan shikha

Portfolio Value at Risk

M P Birla Institute of Management

A Research Report on

“Portfolio Value at Risk”

A Dissertation Submitted in partial fulfillment Of the requirements for the award of

M.B.A Degree of Bangalore University

Submitted By GUNJAN SHIKHA

Reg. No: 07XQCM6032

Under the Guidance of Prof. Praveen Bhagawan

(Internal Guide)

M.P.BIRLA INSTITUTE OF MANAGEMENT (Associate Bharathiya Vidya Bhavan)

#43, Race Course Road, BENGALURU-560001 2007-2009



DECLARATION

I hereby declare that the research work embodied in this dissertation

entitle

“Portfolio Value at Risk”, An Analytical Study carried out by me under the

guidance and supervision of Prof. Praveen Bhagawan, M.P.Birla Institute of

Management, Bangalore, (Internal Guide) in partial fulfillment of degree of

Master of Business Administration program is my original work.

I also declare that this dissertation has not been submitted to any

University/Institution for the award of any Degree/Diploma, fellowship or other

similar title or prizes.

Place : Bengaluru Gunjan Shikha

Date : / / 2009 Reg.No.07XQCM6032



GUIDE’S CERTIFICATE

I hereby declare that the research work embodied in this dissertation

entitled, “Portfolio Value at Risk” has been undertaken and completed by

GUNJAN SHIKHA bearing registration No.07XQCM6032 is a bonafide work

done carried under my guidance during the academic year 2007-09 in a

partial fulfillment of the requirement for the award of MBA degree by

Bangalore University.

I also certify that she has fulfilled all the requirements under the covenant

governing the submission of dissertation to the Bangalore University for the

award of MBA degree.

Place: Bengaluru Prof. Praveen Bhagawan

Date : / / 2009 Faculty , MPBIM



PRINCIPAL’S CERTIFICATE

I hereby certify that this dissertation is an offshoot of the research work

undertaken and completed by Miss Gunjan Shikha under the guidance of

Prof. Praveen Bhagawan, MPBIM, Bangalore (Internal Guide).

I also declare that this dissertation has not been submitted to any

University/Institution for the award of any Degree/Diploma, fellowship or other

similar title or prizes. Place: Bangalore Dr. Nagesh S Malavalli

Date : / / 2009 Principal, MPBIM



ACKNOWLEDGEMENT

It is my great pleasure to take this opportunity to thanks all those who

helped me directly or indirectly in the preparation of this research report. I am

happy to express my deep sense of gratitude to my internal guide Prof.

Praveen Bhagawan for his enormous guidance and assistance. He has been

my mentor and guide, his continuous encouragement and valuable suggestions

helped me at every stage of this project.

I would also like to express my thanks to Dr. Nagesh S Malavalli,

Principal, M.P Birla Institute of Management, Bangalore and I am also

thankful to the entire teaching faculty for having given me their valuable

guidance for preparing this research report successfully.

A special thanks to my friends and family for their encouragement and

help in completion of the study successfully.

Finally, I pray to the almighty to bestow upon me success and

progressing in my endeavor.

Gunjan Shikha

Reg. No. 07XQCM6032



CONTENTS

S. No.

Chapters Page No.

1. Theoretical Background 12

1.1 Background 13-15

1.2 Value at Risk (VaR) 16-17

1.3 Mechanics of VaR Estimation 17

1.4 Steps in Constructing VaR 18

1.5 VaR and Confidence Levels 19-20

1.6 Identifying the Important Market Factors 21

1.7 VaR Methods 22

(i) Analytic Method 23-24

(ii) Historical Simulation Method 25-26

(iii) Monte Carlo Simulation Method 27-30

1.8 Review of Literature 31-37

2. Research Design 38

2.1 Statement of Problem 39

2.2 Research Objectives 39

2.3 Hypothesis 40

2.4 Scope of Study 40

2.5 Research Methodology 40-41

2.6 Limitations 41



2.7 Chapter Scheme 41-43

3. Industry Profile 44

3.1 Equity 45-48

3.2 Bonds 49-50

3.3 Currencies 51-53

4. Analysis and Interpretation 54

4.1 ADF Tests for Equities, Bonds and Currencies 55-60

4.2 Historical Simulation 60-73

4.3 Analytic Approach 74-88

4.4 Single Asset Case 89-90

4.5 Two Asset Case 91-92

4.6 Monte Carlo Simulation 92-93

4.7 Value at Risk for Portfolio 94-96

5. Findings and Conclusion 97

5.1 Findings 98

5.2 Conclusion 99-100



5.3 Recommendations 101

Selected Bibliography 102

Annexure 103-128



List of Tables

S. No.

Chart & Tables Page No.

1. Chart 1: Historical Simulation 61

2. Table 1 : Equity ADF Test 47

3. Table 2 : Bonds ADF Test 49

4. Table 3 : Currency ADF Test 51

5. Table 4 : Data for calculation of VaR through Historical Simulation

54-59

6. Table 5 : Calculation of Daily Stock volatility 63-68

7. Table 6 : Simulated Index 77

8. Table 7 78

9. Table 8 79



EXECUTIVE SUMMARY

What is the most I can lose on this investment? This is a question that

almost every investor who has invested or is considering investing in a risky

asset asks at some point in time. Financial institutions and corporate Treasuries

or individuals require a method to become aware of their risk and also require

the mechanism that can be scientifically rigorous. Optimal allocation of a given

capital between different available competing assets is a standard problem

which any fund manager faces. Hence given an IBM and a CISCO stock a fund

manager would have to decide how much money to allocate to each. The

decision would depend on the risk appetite of the person whose money is being

managed by the fund. We are considering Value at Risk, popularly known as

VaR, as a measure of risk. Value at Risk tries to provide an answer, at least

within a reasonable bound. In fact, it is misleading to consider Value at Risk, or

VaR as it is widely known, to be an alternative to risk adjusted value and

probabilistic approaches. After all, it borrows liberally from both. However, the

wide use of VaR as a tool for risk assessment, especially in financial service

firms, and the extensive literature that has developed around it, push us to

dedicate this report to its examination.

We begin with a general description of VaR and the view of risk that

underlies its measurement, and examine the history of its development and

applications. We then consider the various estimation issues and questions that

have come up in the context of measuring VaR and how analysts and

researchers have tried to deal with them, is discussed under Review Literature.

Next, we evaluate about the research design, where we elaborate about the

objectives, data and its source and chapter scheme of the research report. Then

in industry profile, a brief is about the equities, bonds and currencies which is



selected for research report. Next, we calculate VaR using VaR models i.e.

Analytic Method, Historical Simulation and Monte Carlo Simulation and then

constructing portfolio and calculating VaR. In the final section, we focus on

Research findings, conclusion and recommendations on the research report.



CHAPTER 1

THEORITICAL BACKGROUND



1.1 Background

The concept and use of VaR is recent. Value-at-Risk was first used by

major financial firms in the late 1980s to measure the risks of their trading

portfolios. Since that time period, the use of Value-at-Risk has exploded. While

the term “Value at Risk” was not widely used prior to the mid 1990s, the origins

of the measure lie further back in time. The mathematics that underlies VaR

were largely developed in the context of portfolio theory by Harry Markowitz

and others, though their efforts were directed towards a different end – devising

optimal portfolios for equity investors. In particular, the focus on market risks

and the effects of the co movements in these risks are central to how VaR is

computed.

Value-at-Risk (VaR) has become one of the most popular risk measures

since it was recommended and adopted by the Bank of International Settlements

and USA regulatory agencies in 1988. The straightforward interpretation of

VaR makes this risk measure an intuitive criterion for asset management

decisions. The VaR concept has also been extended to the portfolio Value-at-

Risk (PVaR) measure used for managing risks and returns under a multiple-

asset portfolio. Although VaR and PVaR are widely used in practice, recent

criticisms have focused on the financial risks firms face if the VaR or PVaR

estimates are based on poor information. One potentially important source of

estimation error is in the assumptions regarding the probability model of asset

returns.

The impetus for the use of VaR measures, though, came from the crises

that beset financial service firms over time and the regulatory responses to these

crises. The first regulatory capital requirements for banks were enacted in the

aftermath of the Great Depression and the bank failures of the era, when the

Securities Exchange Act established the Securities Exchange Commission

(SEC) and required banks to keep their borrowings below 2000% of their equity



capital. In the decades thereafter, banks devised risk measures and control

devices to ensure that they met these capital requirements. With the increased

risk created by the advent of derivative markets and floating exchange rates in

the early 1970s, capital requirements were refined and expanded in the SEC’s

Uniform Net Capital Rule (UNCR) that was promulgated in 1975, which

categorized the financial assets that banks held into twelve classes, based upon

risk, and required different capital requirements for each, ranging from 0% for

short term treasuries to 30% for equities. Banks were required to report on their

capital calculations in quarterly statements that were titled Financial and

Operating Combined Uniform Single (FOCUS) reports.

The first regulatory measures that evoke Value at Risk, though, were

initiated in 1980, when the SEC tied the capital requirements of financial

service firms to the losses that would be incurred, with 95% confidence over a

thirty-day interval, in different security classes; historical returns were used to

compute these potential losses. Although the measures were described as

haircuts and not as Value or Capital at Risk, it was clear the SEC was requiring

financial service firms to embark on the process of estimating one month 95%

VaRs and hold enough capital to cover the potential losses. At about the same

time, the trading portfolios of investment and commercial banks were becoming

larger and more volatile, creating a need for more sophisticated and timely risk

control measures. Ken Garbade at Banker’s Trust, in internal documents,

presented sophisticated measures of Value at Risk in 1986 for the firm’s fixed

income portfolios, based upon the covariance in yields on bonds of different

maturities. By the early 1990s,

many financial service firms had developed rudimentary measures of Value at

Risk, with wide variations on how it was measured. In the aftermath of

numerous disastrous losses associated with the use of derivatives and leverage

between 1993 and 1995, culminating with the failure of Barings, the British



investment bank, as a result of unauthorized trading in Nikkei futures and

options by Nick Leeson, a young trader in Singapore, firms were ready for more

comprehensive risk measures. In 1995, J.P.Morgan provided public access to

data on the variances of and co-variances across various security and asset

classes, that it had used internally for almost a decade to manage risk, and

allowed software makers to develop software to measure risk. It titled the

service “Risk Metrics” and used the term Value at Risk to describe the risk

measure that emerged from the data. The measure found a ready audience with

commercial and investment banks, and the regulatory authorities overseeing

them, who warmed to its intuitive appeal. In the last decade, VaR has becomes

the established measure of risk exposure in financial service firms and has even

begun to find acceptance in non financial service firms.



1.2 VaR

VaR is generally considered as a probability based measure of loss

potential. This definition is very general however and we need something more

specific. More formally, VaR is the loss that would be exceeded with a given

probability over a specified period of time. This definition has three important

elements. First, we see that VaR is a loss that could be exceeded. Hence, it is a

measure of a minimum loss. Second, we see that VaR is associated with a given

probability. Thus, we would state that there is a certain percent chance that a

particular loss would be exceeded with a given probability. Finally, VaR is

defined for a specific period of time. Therefore, the loss that would be exceeded

with a given probability is a loss that would be expected to occur over a

specified time period. Consider the following example of

VAR for an investment portfolio: The VaR for a portfolio is Rs. 15 million for

one day with a probability of 0.05. Consider what this statement says: There is a

5 percent chance that the portfolio will lose at least Rs. 15 million in a single

day. The emphasis here should be on the fact that the loss is a minimum, not a

maximum. Value at risk is a statistic that summarizes the exposures of

an asset or portfolio to market risks. VaR allows managers to quantify and

express risk. In other words, VaR is a measure of the maximum potential

change in the value of a portfolio of financial instruments with a given

probability over a pre-set horizon.

Thus, the value of VaR depends on: -

The Horizon over which the portfolio's change in value is measured.

The degree of confidence chosen for the measurement.

VaR is often considered a useful summary measure of market risk for

several reasons. One feature of VaR is its consistency as a measure of financial



risk. VaR facilitates direct comparison of risk across different portfolios and

distinct financial products. Also it allows the managers or investors to examine

potential losses over a particular time horizon with which they are concerned.

Another relative advantage of is that it is largely tactical neutral. In other words,

VaR is calculated by examining the market risks of the individual instruments in

a portfolio, not using actual historical performance.

1.3 Mechanics of VaR Estimation

Establishing a VaR measure involves a number of decisions. Two

important ones are the choice of probability and the choice of the time period

over which the VaR will be measured. Once these parameters are chosen, one

can proceed to actually obtain the VaR estimate. The mechanics of VaR

estimation can be described as a 5-step process, which is explained with the

help of an example.



1.4 Steps in Constructing VaR

Assume, for instance, that we need to measure the VaR of Rs.500 cr

equity portfolio over 10 days at the 99 percent confidence level. The following

steps are required to compute VaR: -

Mark-to-market of the current portfolio (e.g., Rs. 100 cr)

Measure the Variability of the risk factors(s) (e.g., 15 % annum)

Set the time horizon, or the holding period (e.g., adjust to 10 business

days)

assuming a normal distribution)

Report the worst loss by processing all the preceding information (e.g., a

Rs. 7 cr VaR)

This is a very simple method of calculating VaR for a given portfolio but

in reality the calculation of VaR for general, parametric and other complex

distribution is more complicated and different methods are used for calculating

VaR which are explained in detail in the subsequent part of the report.



1.5 Value-at-Risk and Confidence levels

A more risk averse manager will want to determine VaR with greater

confidence -

Increasing the confidence level will increase VaR.

Decreasing the confidence level will decrease VaR.



1.6 Identifying the important market factors

In order to compute VaR (or any other quantitative measure of market

risk), we need to identify the basic market rates and prices that affect the value

of the portfolio. These basic market rates and prices are the “market factors”. It

is necessary to identify a limited number of basic market factors simply because

otherwise the complexity of trying to come up with a portfolio level quantitative

measure of market risk explodes. Even if we restrict our attention to simple

instruments such as forward contracts, an almost countless number of different

contracts can exist, because virtually any forward price and delivery date are

possible. The market risk factors are inherent in most other instruments such as

swaps, loans, options, and exotic options of course are ever more complicated.

Thus, expressing the instrument’s values in terms of limited number of basic

market factors is an essential first step in the problem manageable. Typically,

market forces are identified by decomposing the instruments in the portfolio

into simpler instruments more directly related to basic market risk factors, and

then interpreting the actual instruments as portfolios of the simpler instruments.



1.7 VaR Methods

There are three different methods for calculation of VaR namely: -

i. Analytic Method

ii. Historical Method

iii. Monte Carlo Simulation Method

i. Analytic Method

The analytic method follows the variance/ covariance approach, which

uses historic volatility and correlation data to predict the way markets are likely

to move in future. By assuming that underlying market factors follow normal

distribution, the VaR estimate can be calculated analytically for any confidence

interval.

There are essentially two types of analytic method: -

Delta-Normal Method : This method involves linear approximation of

the price changes. It is mainly suitable when the portfolio does not

contain non-linear products and when the movements in the risk factors

are small. This method can accommodate a large number of assets and is

simple to implement.

Delta-Gamma Method : This method improves upon the linear

approximation in the Delta-Normal Method by taking into account the

second order term also. However, inclusion of this term skews the

distribution of changes in portfolio values. Hence the simplicity of the

Delta-Normal approach is lost.

Risk metrics methodology is based on the analytic method. The main

advantage of this method is the simplicity and ease of implementation. This



method is easy to communicate because of standardization. Delta Gamma

method performs well provided the Greeks are stable. Thus, it is not a good

measure of risk for At the money option, Near maturity money options, barrier

options where the price is close to the barrier etc.

Assessment

The strength of the Variance-Covariance approach is that the Value at

Risk is simple to compute, once you have made an assumption about the

distribution of returns and inputted the means, variances and co-variances of

returns. In the estimation process, though, lie the three key weaknesses of the

approach:

Wrong distributional assumption - If conditional returns are not

normally distributed, the computed VaR will understate the true VaR. In

other words, if there are far more outliers in the actual return distribution

than would be expected given the normality assumption, the actual Value

at Risk will be much higher than the computed Value at Risk.

Input error - Even if the standardized return distribution assumption

holds up, the VaR can still be wrong if the variances and co-variances

that are used to estimate it are incorrect. To the extent that these numbers

are estimated using historical data, there is a standard error associated

with each of the estimates. In other words, the variance - covariance

matrix that is input to the VaR measure is a collection of estimates, some

of which have very large error terms.

Non-stationary variables - A related problem occurs when the variances

and co-variances across assets change over time. This non-stationarity in

values is not uncommon because the fundamentals driving these numbers

do change over time.



ii. Historical Simulation Method

The historical method identifies a portfolio's exposure to specific market

factors and calculates (say daily) observed changes in these market factors over

the time horizon (say 100 days) to be used in the VaR calculation. The portfolio

is then revalued as if each change occurred from today's levels, thus creating

100 possible changes to the portfolio's value. From these figures, a VaR number

corresponding to a given confidence level is determined. The method is

relatively simple to implement if historical data is easily available. By relying

on actual prices, the method allows non-linearity and non-normal distributions.

It does not rely on specific assumption about valuation models or the underlying

stochastic structure of the market. It accounts for "fat tails" and since it does not

rely on valuation models, it is not prone to model risk. However, the historical

simulation method uses only one path (i.e. the actual past). It also assumes that

the past represents the immediate future fairly. This method may miss situations

with temporarily elevated volatility. Further, the method puts the same weight

age on all observations in the window, including old data points. Thus, the

measure of risk change significantly after an old observation is dropped from

the window. Historical simulation becomes very cumbersome for large

portfolios with complicated structures.

Assessment

While historical simulations are popular and relatively easy to run, they

do come with baggage. In particular, the underlying assumptions of the model

generate give rise to its weaknesses:

(a) Past is not prologue – While all three approaches to estimating VaR

use historical data, historical simulations are much more reliant on them than

the other two approaches for the simple reason that the Value at Risk is

computed entirely from historical price changes. There is little room to overlay



distributional assumptions (as we do with the Variance-covariance approach) or

to bring in subjective information (as we can with Monte Carlo simulations).

(b) Trends in the data - A related argument can be made about the way

in which we compute Value at Risk, using historical data, where all data points

are weighted equally. In other words, the price changes from trading days in

1992 affect the VaR in exactly the same proportion as price changes from

trading days in 1998. To the extent that there is a trend of increasing volatility

even within the historical time period, we will understate the Value at Risk.

(c) New assets or market risks - While this could be a critique of any of

the three approaches for estimating VaR, the historical simulation approach has

the most difficulty dealing with new risks and assets for an obvious reason:

there is no historic data available to compute the Value at Risk. Assessing the

Value at Risk to a firm from developments in online commerce in the late 1990s

would have been difficult to do, since the online business was in its nascent

stage.

Modifications

As with the other approaches to computing VaR, there have been

modifications suggested to the approach, largely directed at taking into account

some of the criticisms mentioned in the last section.

(a) Weighting the recent past more - A reasonable argument can be

made that returns in the recent past are better predictors of the immediate future

than are returns from the distant past. Boudoukh, Richardson and Whitelaw

present a variant on historical simulations, where recent data is weighted more,

using a decay factor as their time weighting mechanism. In simple terms, each

return, rather than being weighted equally, is assigned a probability weight

based on its recency. In other words, if the decay factor is 0.90, the most recent

observation has the probability weight p, the observation prior to it will be



weighted 0.9p, the one before that is weighted 0.81p and so on. In fact, the

conventional historical simulation approach is a special case of this approach,

where the decay factor is set to 1.

(b) Combining historical simulation with time series models - Cabado

and Moya suggested that better estimates of VaR could be obtained by fitting at

time series model through the historical data and using the parameters of that

model to forecast the Value at Risk.

(c) Volatility Updating - Hull and White suggest a different way of

updating historical data for shifts in volatility. For assets where the recent

volatility is higher than historical volatility, they recommend that the historical

data be adjusted to reflect the change.



iii. Monte – Carlo simulation

The Monte-Carlo simulation methodology has a number of similarities to

historical simulation. The main difference is that rather than carrying out the

simulation using the observed changes in the market factors over the last N

periods to generate N hypothetical portfolio profits and losses, one chooses a

statistical distribution that is believed to adequately capture or approximate the

possible changes in the market forces. Then, a pseudo-random number

generator is used to generate thousands or perhaps tens of thousands of

hypothetical changes in the market factors. These are then used to construct

thousands of hypothetical portfolio profits and losses on the current portfolio,

and the distribution of profits and losses. Finally, the value-at-risk is determined

from this distribution.

General Description

The first two steps in a Monte Carlo simulation mirror the first two steps

in the Variance-covariance method where we identify the markets risks that

affect the asset or assets in a portfolio and convert individual assets into

positions in standardized instruments. It is in the third step that the differences

emerge. Rather than compute the variances and co-variances across the market

risk factors, we take the simulation route, where we specify probability

distributions for each of the market risk factors and specify how these market

risk factors move together. Thus, in the example of the six-month Dollar/Euro

forward contract that we used earlier, the probability distributions for the 6-

month zero coupon $ bond, the 6-month zero coupon euro bond and the

dollar/euro spot rate will have to be specified, as will the correlation across

these instruments. While the estimation of parameters is easier if you assume

normal distributions for all variables, the power of Monte-Carlo simulations



comes from the freedom you have to pick alternate distributions for the

variables. In addition, you can bring in subjective judgments to modify these

distributions. Once the distributions are specified, the simulation process starts.

In each run, the market risk variables take on different outcomes and the value

of the portfolio reflects the outcomes. After a repeated series of runs, numbering

usually in the thousands, you will have a distribution of portfolio values that can

be used to assess Value at Risk. For instance, assume that you run a series of

10,000 simulations and derive corresponding values for the portfolio. These

values can be ranked from highest to lowest, and the 95% percentile Value at

Risk will correspond to the 500th lowest value and the 99th percentile to the

100th lowest value.

Assessment

Much of what was said about the strengths and weaknesses of the

simulation approach in the last chapter apply to its use in computing Value at

Risk. Quickly reviewing the criticism, a simulation is only as good as the

probability distribution for the inputs that are fed into it. While Monte Carlo

simulations are often touted as more sophisticated than historical simulations,

many users directly draw on historical data to make their distributional

assumptions. In addition, as the number of market risk factors increases and

their co-movements become more complex, Monte Carlo simulations become

more difficult to run for two reasons. First, you now have to estimate the

probability distributions for hundreds of market risk variables rather than just

the handful that we talked about in the context of analyzing a single project or

asset. Second, the number of simulations that you need to run to obtain

reasonable estimate of Value at Risk will have to increase substantially (to the

tens of thousands from the thousands). The strengths of Monte Carlo



simulations can be seen when compared to the other two approaches for

computing Value at Risk. Unlike the variance-covariance approach, we do not

have to make unrealistic assumptions about normality in returns. In contrast to

the historical simulation approach, we begin with historical data but are free to

bring in both subjective judgments and other information to improve forecasted

probability distributions. Finally, Monte Carlo simulations can be used to assess

the Value at Risk for any type of portfolio and are flexible enough to cover

options and option-like securities.

Modifications

As with the other approaches, the modifications to the Monte Carlo

simulation are directed at its biggest weakness, which is its computational

bulk. To provide a simple illustration, a yield curve model with 15 key rates and

four possible values for each will require 1,073,741,824 simulations (415) to be

complete. The modified versions narrow the focus, using different techniques,

and reduce the required number of simulations:-

(a) Scenario Simulation - One way to reduce the computation burden of

running Monte-Carlo simulations is to do the analysis over a number of discrete

scenarios. Frye suggests an approach that can be used to develop these scenarios

by applying a small set of pre-specified shocks to the system. Jamshidan and

Zhu (1997) suggest what they called scenario simulations where they use

principal component analysis as a first step to narrow the number of factors.

Rather than allow each risk variable to take on all of the potential values, they

look at likely combinations of these variables to arrive at scenarios. The values

are computed across these scenarios to arrive at the simulation results.



(b) Monte Carlo Simulations with Variance-Covariance method

modification – The strength of the Variance-covariance method is its speed. If

you are willing to make the required distributional assumption about normality

in returns and have the variance-covariance matrix in hand, you can compute

the Value at Risk for any portfolio in minutes. The strength of the Monte Carlo

simulation approach is the flexibility it offers users to make different

distributional assumptions and deal with various types of risk, but it can be

painfully slow to run. Glasserman, Heidelberger and Shahabuddin use

approximations from the variance covariance approach to guide the sampling

process in Monte Carlo simulations and report a substantial savings in time and

resources, without any appreciable loss of precision. The trade off in each of

these modifications is simple. You give some of the power and precision of the

Monte Carlo approach but gain in terms of estimation requirements and

computational time.



1.8 REVIEW LITERATURE

Literature was reviewed with an aim to gain an insight into two major

facets of our problem.

a) VaR Calculation

b) Finding the optimal allocation of VaR calculation methods

VaR is straightforward to estimate and interpret as a measure of risk

exposure, and these advantages often appeal to asset managers (Culp, Mensink,

and Neves 1998). However, most of the current research on Value-at-Risk

(VaR) estimation focuses on the one-dimension (univariate) case. One of the

first attempts to compute PVaR from a model of the joint returns distribution

was reported by Frauendorfer, Moix, and Schmid (1995), but applications of

this method are limited because the PVaR model cannot be stated in closed

form and can only be approximated with complex computational algorithms.

Alternatively, Wang and Wu (2001) use linear combinations of returns

models based on extreme value theory to approximate the tail areas of heavy-

tailed distributions, but this approach may be undesirable because it only

focuses on the lower-tail. The alternative approaches that are currently popular

include the variance-covariance (VC) method, Monte Carlo simulation, delta-

Normal simulation, and historical simulation (HS) (Dowd 1998).

In one of the studies of VaR on the Indian stock market, Varma (1999)

assumes a Generalized Error Distribution (GED) and uses GARCH(GED),

EWMA(GED) and EWMA(RM) models to estimate VaR. The study computes

the nominal coverage, i.e., the ratio of number of exceedences to the total

number of observations, and compares it with the true coverage. The study



preferred the use of GARCH(GED) model over the other two models on the

basis of the results.

In another study of Nifty and S&P 500, Sarma et al. (2003) used four

models (GARCH, EWMA, Risk Metrics-RM, and Historical Simulation-HS)

and their different variations, on the basis of the number of data points used,

under the assumption of normally distributed errors, to find out that GARCH

and RM fare well, with the latter having a slight edge. They used Back Testing

methods for performance assessment of various models by testing for

conditional and unconditional coverage and independence that were perfected

by Christoffersen (1998) as well as loss functions developed by Lopez (1998).

In a study of the indices of the five of the developed countries, Angelidis

et al. (2004) used three variations of GARCH model (naïve, EGARCH,

TGARCH) and various orders of AR processes on normal GED and t-

distributions. They also tested for conditional and unconditional coverage using

Christoffersen's method, but could not point out any model as the `best' model.

They found student's-t distribution to be capturing the risk better than other

distributions.

Bao et al. (2004) checked the performance of VaR models in terms of

empirical coverage taking parametric and nonparametric models. They used

normal, historical simulation, Monte Carlo simulation non parametrically

estimated distribution and the extreme value distribution along with RM as

benchmark. They analyzed the model performance before, during, and after the

Asian financial crisis. In the pre-crisis period, RM was found to be quite a good

model, with normal not being far behind. Historical Simulation(HS), Non-

Parametric (NP) methods and Monte Carlo (MC) simulation were also seen to

be satisfactory. During the Aisan financial crisis, all the models understated the

VaR numbers, however, the EVT-based one did the best job. The post-crisis



period results were found to be similar to the pre-crisis period results. From the

study, it is clear that the conventional models do a good job during the normal

periods.

Nath and Samantha (2003) studied the VaR for the Indian banking

system. They used one day return on the Government of India securities as the

variable. The models used were normal, historical simulation, risk metrics and

Hill's estimator. They found that VaR models under variance-covariance/normal

approach, particularly risk metrics, underestimated VaR numbers. The GARCH

(normal) model performed slightly better than the Risk Metrics model. While

HS provided quite reasonable estimates, Hill's estimator overestimated the VaR

numbers as the number of failures was less than theoretical expectation.

Value at Risk Models in the Indian Stock Market

by

Jayanth R. Varma

IIM A

This paper provides empirical tests of different risk management models

in the Value at Risk (VaR) framework in the Indian stock market. It is found

that the GARCH-GED (Generalised Auto-Regressive Conditional

Heteroscedasticity with Generalised Error Distribution residuals) performs

exceedingly well at all common risk levels (ranging from 0.25% to 10%). The

EWMA (Exponentially Weighted Moving Average) model used in J. P.

Morgan’s RiskMetrics® methodology does well at the 10% and 5% risk levels

but breaks down at the 1% and lower risk levels. The paper then suggests a way

of salvaging the EWMA model by using a larger number of standard deviations

to set the VaR limit. For example, the paper suggests using 3 standard



deviations for a 1% VaR while the normal distribution indicates 2.58 standard

deviations and the GED indicates 2.85 standard deviations. With this

modification the EWMA model is shown to work quite well. Given its greater

simplicity and ease of interpretation, it may be more convenient in practice to

use this model than the more accurate GARCH-GED specification. The paper

also provides evidence suggesting that it may be possible to improve the

performance of the VaR models by taking into account the price movements in

foreign stock markets.

Decomposing Portfolio Value-at-Risk : A General Analysis

Winfried G. Hallerbach

Erasmus University Rotterdam and Tinbergen Institute Graduate School

of Economics

An intensive and still growing body of research focuses on estimating a

portfolio’s Value at Risk. Aside from the total portfolio’s VaR, there is a

growing need for information about (i) the marginal contribution of the

individual portfolio components to the diversified portfolio VaR, (ii) the

proportion of the diversified portfolio VaR that can be attributed to each of the

individual components consituting the portfolio, and (iii) theincremental effect

on VaR of adding a new instrument to the existing portfolio. For many

portfolios, however, the assumption of normally distributed returns is too

stringent. There exist to the best of our knowledge no procedures for estimating

marginal VaR, component VaR and incremental VaR in either a non-normal

analytical setting or a Monte Carlo / historical simulation context. This paper

tries to fill this gap by investigating these VaR concepts in a general

distribution-free setting. We derive a general expression for the marginal

contribution of an instrument to the diversified portfolio VaR whether this



instrument is already included in the portfolio or not. We show how in a most

general way, the total portfolio VaR can be decomposed in partial VaRs that can

be attributed to the individual instruments comprised in the portfolio. These

component VaRs have the appealing property that they aggregate linearly into

the diversified portfolio VaR. We not only show how the standard results under

normality can be generalized to non-normal analytical VaR approaches but also

present an explicit procedure for estimating marginal VaRs in a simulation

framework. Given the marginal VaR estimate, component VaR and incremental

VaR readily follow. The proposed estimation approach pairs intuitive appeal

with computational efficiency. We evaluate various alternative estimation

methods in an application example and conclude that the proposed approach

displays an astounding accuracy and a promising outperformance.

Value-at-Risk for Fixed Income portfolios : A comparison of alternative

models

Gangadhar Darbha

National Stock Exchange, Mumbai, India

December 2001

The paper presents a case for a new method for computing the VaR for a

set of fixed income securities based on extreme value theory that models the tail

probabilities directly without making any assumption about the distribution of

entire return process. It compares the estimates of VaR for a portfolio of fixed

income securities across three methods: Variance-Covariance method,

Historical Simulation method and Extreme Value method and that extreme

value method provides the accurate VaR estimator in terms of correct failure

ratio and the size of VaR.



Portfolio Value at Risk Based On Independent Components : Analysis

Ying Chen, Wolfgang H¨ardle1 and Vladimir Spokoiny

Risk management technology applied to high dimensional portfolios

needs simple and fast methods for calculation of Value-at-Risk (VaR). The

multivariate normal framework provides a simple off-the-shelf methodology but

lacks the heavy tailed distributional properties that are observed in data. A

principle component based method (tied closely to the elliptical structure of the

distribution) is therefore expected to be unsatisfactory. Here we propose and

analyze a technology that is based on Independent Component Analysis (ICA).

We study the proposed ICVaR methodology in an extensive simulation study

and apply it to a high dimensional portfolio situation. Our analysis yields very

accurate VaRs.

Evaluating Portfolio Value-at-Risk using Semi-Parametric GARCH

Models

Jeroen V.K. Rombouts and Marno Verbeek

December 2004

In this paper we examine the usefulness of multivariate semi-parametric

GARCH models for portfolio selection under a Value-at-Risk (VaR) constraint.

First, we specify and estimate several alternative multivariate GARCH models

for daily returns on the S&P 500 and Nasdaq indexes. Examining the within

sample VaRs of a set of given portfolios shows that the semi-parametric model

performs uniformly well, while parametric models in several cases have

unacceptable failure rates. Interestingly, distributional assumptions appear to

have a much larger impact on the performance of the VaR estimates than the

particular parametric specification chosen for the GARCH equations. Finally,



we examine the economic value of the multivariate GARCH models by

determining optimal portfolios based on maximizing expected returns subject to

a VaR constraint, over a period of 500 consecutive days. Again, the superiority

and robustness of the semi-parametric model is confirmed.

Value-at-Risk Based Portfolio Optimization

Working Paper by

Amy v. Puelz

Edwin L. Cox School of Business, Southern Methodist University

The Value at Risk (VaR) metric, a widely reported and accepted measure

of financial risk across industry segments and market participants, is discrete by

nature measuring the probability of worst case portfolio performance. In this

paper I present four model frameworks that apply VaR to ex ante portfolio

decisions. The mean-variance model, Young's (1998) minimax model and Hiller

and Eckstein's (1993) stochastic programming model are extended to

incorporate VaR. A fourth model, that is new, implements stochastic

programming with a return aggregation technique. Performance tests are

conducted on the four models using empirical and simulated data. The new

model most closely matches the discrete nature of VaR exhibiting statistically

superior performance across the series of tests. Robustness tests of the four

model forms provides support for the argument that VaR-based investment

strategies lead to higher risk decision than those where the severity of worst

case performance is also considered.Conclusion



CHAPTER 2

RESEARCH DESIGN



2.1 Statement of Problem

In volatile financial markets, both market participants and market

regulators need models for measuring, managing and containing risks. Market

participants need risk management models to manage the risks involved in their

open positions. Market regulators on the other hand must ensure the financial

integrity of the stock exchanges and the clearing houses by appropriate

margining and risk containment systems.

How inaccurate VaR or PVaR estimates may lead to redundant amount of

risk capital maintained, which will reduce capital management efficiency as

well as increase the financial risk. Therefore an attempt is made in this study to

find out the right tool to measure Portfolio Value at Risk (PVaR).

2.2 Research Objectives

In this paper, my attempt is to propose an integrated method to compute

PVaR, and also,

to use VaR as a measure of risk of Portfolios

to know the application of various Value at-risk (VaR) Models

convenient to measure the risk of portfolios

to compare the results of various model

to give conclusion regarding the best method to be adopted to determine

Value at Risk



2.3 Hypothesis

In order to see the stationarity of data collected, Augmented Dickey-Fuller Unit

Root Test has been incorporated where, Hypothesis is

H0 : Null Hypothesis is accepted as data is non-stationary, and

H1 : Alternate Hypothesis is rejected as data is stationary.

2.4 Scope of the Study

The scope of this study is

To become aware of Value at-risk (VaR) as a measure of risk of

portfolios

It gives simple information to layman investor to guide them in selection

of portfolio for their investment

2.5 Research Methodology

Actual collection of data : Data is the portfolio, consists of 10 elements. Four

Equities :

Reliance Industries Limited, DLF Limited, Bharti Airtel and Infosys

Technologies Limied.

Three AAA Rated Bonds :

Power Finance Corporation Limited, Indian Railway Finance Corporation and

Housing Development Finance Corporation Limited.

Three Currencies :

Dollar, Euro and Pound.



Data Source : For equities closing price is taken for period ranging from July

2007 to March 2009, for bonds weighted average price is taken for period

ranging from December 2008 to March 2009 from nse-india.com and for

currencies exchange rate is taken from oanda.com for period ranging from July

2007 to March 2009.

Data analysis : The data generated would be subjected to rigorous statistical

treatment and inferences would be drawn accordingly. Appropriate statistical

tools would be applied. Excel sheets and appropriate graphs are used as

instruments for preparing the study.

2.6 Limitations

1. The time and resources were the major constrain in conducting the

research.

2. The bond instrument have been chosen on a random basis as AAA rated

trading bonds are very less. Also the ratings have changed over the period

of years.

2. The period of study is restricted only for one year.

2.7 Chapter Scheme

1. Introduction

1.1 Background

1.2 Value at Risk

1.3 Mechanics of VaR estimation



1.4 Steps in Constructing VaR

1.5 VaR and Confidence Levels

1.6 Identifying the important Market Factors

1.7 VaR Methods

1.8 Review of Literature

2. Research Design

Statement of Problem

Research objective

Hypothesis

Scope of study

Research Methodology

Limitations

Chapter Scheme

3. Industry Profile

3.1 Equity

3.2 Bonds

3.3 Currency

4. Data Analysis and Interpretation

4.1 ADF Tests for Equities, Bonds and Currencies

4.2 Historical Simulation



4.3 Analytic Approach

4.4 Single Asset Case

4.5 Two Asset Case

5. Findings, Conclusion and Suggestions

5.1 Comparing Approaches

5.2 Conclusion

5.3 Recommendations

Bibliography

Annexure



CHAPTER 3

INDUSTRY PROFILE



This report was not done in any industry, this research is all about risk

involved in portfolio. Here, I would like to comment on the various assets,

which I have included in the portfolio, and the brief description about the reason

for taking these assets in my portfolio. My portfolio consists of :

four equities,

three AAA rated bonds, and

three currencies.

3.1 EQUITIES

Four equities are from Reliance Industries Ltd., DLF Limited (Real

Estate), Bharti Airtel (Telecom) and Infosys Technologies Ltd.(IT Sector).

Reliance Industries Ltd. (Refineries)

The Reliance Group, founded by Dhirubhai H. Ambani (1932-2002), is

India's largest private sector enterprise, with businesses in the energy and

materials value chain. Group's annual revenues are in excess of US$ 34 billion.

The flagship company, Reliance Industries Limited, is a Fortune Global 500

company and is the largest private sector company in India. Reliance enjoys

global leadership in its businesses, being the largest polyester yarn and fiber

producer in the world and among the top five to ten producers in the world in

major petrochemical products.

Reliance Industries (RIL) is the country's largest private sector company.

The company has a 26% share of the total refining capacity in India and along

with its subsidiary, IPCL, controls over 70% of the country's domestic polymer

capacity. RIL is also a major player in the polyester fiber and yarn with a

combined capacity of 2 million tones. The company has also ventured into the



upstream sector, whereby it has participating interests in existing oil and gas

fields. RIL has a large exploration acreage with 34 domestic exploration blocks

in addition to 1 exploration blocks each in Yemen and Oman. RIL also has

exploration and production rights to 5 coal bed methane (CBM) blocks. The

company also has a presence in the downstream segment and has commissioned

1,218 outlets out of permitted 5,849 outlets (FY06).

DLF Limited (Construction)

The DLF Group was founded in 1946. We developed some of the first

residential colonies in Delhi such as Krishna Nagar in East Delhi, which was

completed in 1949.

DLF is India's largest real estate company in terms of revenues, earnings,

market capitalization and developable area. In line with its current expansion

plans, DLF has over 751 million sq. ft. of development across its businesses,

including developed, on-going and planned projects. This land bank is spread

over 32 cities, mostly in metros and key urban areas across India. Already a

major player in locations across the country, DLF, with over six decades of

experience, is capitalizing on emerging market opportunities to deliver high-end

facilities and projects to its wide base of customers by constantly upgrading its

internal skills and resource capabilities.

All the intensified growth underlines DLF's commitment to quality, trust

and customer sensitivity and, delivering on its promise with agility and financial

prudence. This, in turn, has earned DLF the coveted 'Superbrand' ranking for

three years consecutively, including the current year.



Bharti Airtel (Telecom)

Telecom giant Bharti Airtel is the flagship company of Bharti

Enterprises. The Bharti Group, has a diverse business portfolio and has created

global brands in the telecommunication sector.

Bharti Airtel is one of the topmost companies in the telecom sector in

India and is under the Bharti Enterprises Group. Airtel Bharti has been ranked

as the best performance company in the whole world by the Business Week

magazine in 2007. Airtel comes to you from Bharti Airtel Limited, India’s

largest integrated and the first private telecom services provider with a

footprint in all the 23 telecom circles. Bharti Airtel since its inception has been

at the forefront of technology and has steered the course of the telecom sector

in the country with its world class products and services. The businesses at

Bharti Airtel have been structured into three individual strategic business units

(SBU’s) - Mobile Services, Airtel Telemedia Services & Enterprise Services.

The mobile business provides mobile & fixed wireless services using GSM

technology across 23 telecom circles of India and is the largest mobile service

provider in the country, based on the number of customers, while the Airtel

Telemedia Services business offers broadband & telephone services in 94

cities. The Enterprise services focuses on delivering telecommunications

services as an integrated offering including mobile, broadband & telephone,

national and international long distance and data connectivity services to

corporate, small and medium scale enterprises.

The company has around 50 million customers in 2007 and its market

share of mobile subscribers in India is at 23.4%. The company Bharti Airtel

Limited's total revenue amounted to Rs.12,242 crore in 2006- 2007 and the

net profit stood at Rs.3,126 crore. Bharti's network spans over 364,000 non-

census towns and villages in India. During the period FY05 to FY08, the

company grew its sales and profits at compounded annual rates of 49% and



74% respectively. Bharti Airtel has become a leading company in the telecom

sector in India due to the fact that it has provided the best quality of services to

its customers. And this has been possible for the company has a wide telecom

network that is of the latest technology.

Infosys Technologies Ltd. (IT Software)

Infosys Technologies Ltd, headquartered at Bangalore, India, is a leading

consulting & IT Service Solution Provider. Started in 1991, the company is

adept in technology driven and innovative business transformation initiatives.

The company works with global corporations and new generation technology

companies to deliver end- to-end solutions.

It offers services like software development, maintenance, consulting,

testing and packaging implementation. Infosys offers all these services through

its highly integrated and globally recognized delivery model. The company

achieved the US$ 3 billion revenue mark in FY07.

With a workforce of around 58,000 employees worldwide it has offices in

USA, Canada, Australia, China, UAE and European countries besides India.

Infosys is regarded as a pioneer in strategic offshore outsourcing of

software services. Its expertise is offered in Application Development and

Maintenance, Corporate Performance Management, Enterprise Quality Services,

Infrastructure Services, Packaged Application Services, Product Engineering

and Systems Integration.

Infosys has a global footprint with over 50 offices and development

centers in India, China, Australia, the Czech Republic, Poland, the UK, Canada

and Japan. Infosys has over 103,000 employees.

Infosys takes pride in building strategic long-term client relationships.

Over 97% of our revenues come from existing customers.

http://www.infosys.com/about/who-we-are/locations.asp



3.2 AAA RATED BONDS

Three AAA rated Bonds are from Power Finance Corporation Limited,

Indian Railway Finance Corporation and Housing Development

Finance Corporation Limited.

Power Finance Corporation Limited

Power Finance Corporation Limited is an undertaking of the Government

of India. The Power Finance Corporation Limited is a Financial Institution (FI)

established in the year 1986. The main purpose of the Power Finance

Corporation Limited is to provide financial aid to the Power sector for the

integral development of power based infrastructure. In the year 1990 the Power

Finance Corporation Limited was notified as a Public Financial Institution

under the Companies Act of 1956. The organization is registered by the Reserve

Bank of India as a non banking financial company. The Power Finance

Corporation Limited also provides non-fund based consultancy services to

various clients. The ISIN CODE for bond of this government under taking is

INE134E08BH9 and its rating is AAA.

Indian Railway Finance Corporation

Indian Railway Finance Corporation is a dedicated financing arm of the

Ministry of Railways. Its sole objective is to raise money from the market to

part finance the plan outlay of Indian Railways. The money so made available

is used for acquisition of rolling stock assets and for meeting

other developmental needs of the Indian Railways. The ISIN CODE for bond

of this government under taking is INE053F09FM7 and its rating is AAA.



Housing Development Finance Corporation Limited

Housing Development Finance Corporation

Limited or HDFC (BSE: 500010), founded 1977 by Ravi

Maurya and Hasmukhbhai Parekh, is an Indian NBFC, focusing on

home mortgages. HDFC's distribution network spans 243 outlets that include 49

offices of HDFC's distribution company, HDFC Sales Private Limited. In

addition, HDFC covers over 90 locations through its outreach programmes.

HDFC's marketing efforts continue to be concentrated on developing a stronger

distribution network. Home loans are also Sharcket through HDFC

Sales, HDFC Bank Limited and other third party Direct Selling Agents (DSA).

The Housing Development Finance Corporation Limited (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 in 1994. The ISIN CODE for bond of this

government under taking is INE001A07DT1and its rating is AAA.

http://en.wikipedia.org/wiki/Bombay_Stock_Exchange

http://www.bseindia.com/price_finder/stockreach.asp?scripcd=500010

http://en.wikipedia.org/w/index.php?title=Ravi_Maurya&action=edit&redlink=1

http://en.wikipedia.org/w/index.php?title=Ravi_Maurya&action=edit&redlink=1

http://en.wikipedia.org/wiki/Hasmukhbhai_Parekh

http://en.wikipedia.org/wiki/India

http://en.wikipedia.org/wiki/NBFC

http://en.wikipedia.org/wiki/Mortgages

http://en.wikipedia.org/wiki/HDFC_Bank



3.3 CURRENCIES

The three currencies are Dollar, Euro and Pound.

Dollar (USA)

The United States dollar (sign: $; code: USD) is the unit of currency of

the United States and is defined by the Coinage Act of 1792 to be between 371

and 416 grains (27.0 g) of silver (depending on purity). The U.S. dollar is

normally abbreviated as the dollar sign, $, or as USD or US$ to distinguish it

from other dollar-denominated currencies and from others that use the $

symbol. It is divided into 100 cents (200 half-cents prior to 1857).

Taken over by the Congress of the Confederation of the United States on

July 6, 1785, the U.S. dollar is the currency most used in international

transactions. Although U.S. dollar is a fiat currency, several countries use it as

their official currency, and in many others it is the de facto currency.

The financial market turmoil that begun in August has put serious

pressure on the US dollar: by end-November the dollar had fallen by some 6%

since August against a trade-weighted currency basket tracked by the US

Federal Reserve. Dollar weakness is not a new issue: the currency has lost a

quarter of its value against a broader range of currencies over the past five

years. However, there are fears that, in the current environment, the dollar's

decline could turn into a rout.

Euro (European Union)

The Euro (€) is the official currency of 16 of the 27 member states of

the European Union (EU). The states, known collectively as the Euro zone,

are: Austria, Belgium, Cyprus, Finland, France, Germany, Greece, Ireland, Italy

, Luxembourg, Malta,the Netherlands,Portugal, Slovakia, Slovenia,and Spain.

The currency is also used in a further five European

http://en.wikipedia.org/wiki/Currency_sign

http://en.wikipedia.org/wiki/Dollar_sign

http://en.wikipedia.org/wiki/ISO_4217

http://en.wikipedia.org/wiki/Currency

http://en.wikipedia.org/wiki/United_States

http://en.wikipedia.org/wiki/Coinage_Act_of_1792

http://en.wikipedia.org/wiki/Dollar_sign

http://en.wikipedia.org/wiki/Dollar

http://en.wikipedia.org/wiki/Cent_(currency)

http://en.wikipedia.org/wiki/Half_cent_(United_States_coin)

http://en.wikipedia.org/wiki/Congress_of_the_Confederation

http://en.wikipedia.org/wiki/Fiat_currency

http://en.wikipedia.org/wiki/Dollarization

http://en.wikipedia.org/wiki/Dollarization

http://en.wikipedia.org/wiki/De_facto_currency

http://en.wikipedia.org/wiki/Euro_sign

http://en.wikipedia.org/wiki/Currency

http://en.wikipedia.org/wiki/European_Union_member_state

http://en.wikipedia.org/wiki/European_Union

http://en.wikipedia.org/wiki/Eurozone

http://en.wikipedia.org/wiki/Austria

http://en.wikipedia.org/wiki/Belgium

http://en.wikipedia.org/wiki/Cyprus

http://en.wikipedia.org/wiki/Finland

http://en.wikipedia.org/wiki/France

http://en.wikipedia.org/wiki/Germany

http://en.wikipedia.org/wiki/Greece

http://en.wikipedia.org/wiki/Republic_of_Ireland

http://en.wikipedia.org/wiki/Italy

http://en.wikipedia.org/wiki/Luxembourg

http://en.wikipedia.org/wiki/Malta

http://en.wikipedia.org/wiki/Netherlands

http://en.wikipedia.org/wiki/Portugal

http://en.wikipedia.org/wiki/Slovakia

http://en.wikipedia.org/wiki/Slovenia

http://en.wikipedia.org/wiki/Spain



countries, with and without formal agreements and is consequently used daily

by some 327 million Europeans. Over 175 million people worldwide use

currencies which are pegged to the euro, including more than 150 million

people in Africa.

The euro is the second largest reserve currency and the second most

traded currency in the world after the U.S. dollar. As of November 2008, with

more than €751 billion in circulation, the euro is the currency with the highest

combined value of cash in circulation in the world, having surpassed the U.S.

dollar. Based on IMF estimates of 2008 GDP and purchasing power parity

among the various currencies, the Euro zone is the second largest economy in

the world.

The name euro was officially adopted on 16 December 1995. The euro

was introduced to world financial markets as an accounting currency on 1

January 1999, replacing the former European Currency Unit (ECU) at a ratio of

1:1. Euro coins and banknotes entered circulation on 1 January 2002.

With the dollar seemingly in terminal decline, there is little stopping the

euro from becoming the world's premier reserve currency. the fact that sterling

held the position of reserve currency until the Second World War, but lost it due

to imperial overreach. This, he warns, could happen to the dollar for a variety of

reasons, perhaps including multiple US interventions abroad. This weakness of

the US financial sector will play into the hands of the Europeans, whose

economies are better suited to overcoming the current credit crisis, the author

believes. However, despite gloomy predictions for the dollar, the euro is not in a

position to overtake it at the moment, he argues, pointing out that the euro holds

one-third of global reserves compared to the dollar's two-thirds.

http://en.wikipedia.org/wiki/International_status_and_usage_of_the_euro#With_formal_agreements

http://en.wikipedia.org/wiki/International_status_and_usage_of_the_euro#Without_formal_agreements

http://en.wikipedia.org/wiki/United_States_dollar

http://en.wikipedia.org/wiki/GDP

http://en.wikipedia.org/wiki/Purchasing_power_parity

http://en.wikipedia.org/wiki/European_Currency_Unit

http://en.wikipedia.org/wiki/Coin

http://en.wikipedia.org/wiki/Banknote



Pound (British)

The pound, a unit of currency, originated in England, as the value of

a pound mass of silver. For a long time, £1 worth of silver coins were a troy

pound in mass.

Today, the term may refer to a number of current (primarily British and

related) currencies, and a variety of now-obsolete currencies. Pound

sterling (GBP, represented by the pound sign: "£"), the currency of the United

Kingdom.

The global economic calendar fills out next week; but no other G10

currency can compete with the fundamental authority of the data that populates

the British pound’s docket. Over the past month, its seen that the sterling built

considerable strength against currencies that are considered far better positioned

than itself. This has developed along with the general recovery in risk

sentiment; because there has been no notable improvements in the UK’s

economic checkup recently. This leaves the pound in a precarious position. As

fundamentals continue to deteriorate from under the unit, its advance becomes

more and more dependent on a fragile and altogether volatile driver.

Alternatively, if the need for safety states the appetite for risk, all of the

Kingdom’s economic, interest rate and financial troubles will come rushing

back to the forefront. And, considering the level of event risk in the week ahead,

there is a lot at stake for fundamental traders.

http://en.wikipedia.org/wiki/England

http://en.wikipedia.org/wiki/Pound_(mass)

http://en.wikipedia.org/wiki/Silver

http://en.wikipedia.org/wiki/Troy_pound

http://en.wikipedia.org/wiki/Troy_pound

http://en.wikipedia.org/wiki/United_Kingdom

http://en.wikipedia.org/wiki/Pound_sterling

http://en.wikipedia.org/wiki/Pound_sterling

http://en.wikipedia.org/wiki/Pound_sign





CHAPTER 4

DATA ANALYSIS & INTERPRETATION



4.1 ADF Tests for Equities, Bonds and Currencies

Equity

The closing price of equity for this test is taken from April, 2008 to March, 2009. The data taken are raw rates. The unit root result is as under:

Table No 1: Equity ADF Test

Reliance Equity DLF Equity

Constraints ( log 0)

ADF values

Akaike Info Criterion


ADF values Akaike Info Criterion

Intercept (1st

Difference)

-16.73502 1%(-3.4575521)5%(-2.8733935)10%(-2.573153)

Intercept (2nd

Difference)

-9.9722299 1%(-3.458384) 5%(-2.87375) 10%(-2.57334)

Trend & Intercept

(2nd Difference)

-9.0563009 1%( -3.998132) 5%( -3.429354) 10%( -3.13815)

Trend & Intercept

(1st Difference)

-2741.194 1%( -3.996618) 5%( -3.428622) 10%( -3.13772)

None (1st

difference)

-16.770080 1%( -2.574699) 5%( -1.942163) 10%( -1.61585)

None (2nd

difference)

-9.994969 1%( -2.574991) 5%( -1.942204) 10%( -1.61583)

Bharti Airtel Equity Infosys Equity


ADF values



ADF values


Intercept (1st

Difference)

-2530.684 1%(-3.45709) 5%(-2.87319) 10%(-2.5730)

Intercept (Level)

-2.820407 1%(-1.457552) 5%(-2.803393) 10%(-2.57315)

Trend & Intercept

(1st Difference)

-2509.315 1%(-3.99613) 5%(-3.42890) 10%(-3.1375)

Trend & Intercept(1st Difference)

-16.308672 1%( -3.99678) 5%( -3.42870) 10%( -3.1377)

None (2nd

difference)

-9.635644 1%(-2.57494) 5%(-1.94219) 10%(-1.6158)

None (1st

difference)

-11.45324 1%(-2.574739) 5%(-1.942169) 10%(-1.6158)

(** indicates acceptance of hypothesis) (* indicates rejection of hypothesis) Source:Excel(Add-Ins)



Hypothesis:

H0 = ADF > critical values -- accept null hypothesis i.e., unit root exists.

H1 = ADF < critical values – reject null hypothesis i.e. unit root does not exist.

Interpretation

The above table tells that equities has a unit root problem i.e unit root

does not exists, so they are stationary in their 1st difference and 2nd difference at

various constraints i.e ADF is smaller than critical values at none, intercept and

trend and intercept.. The 1st

difference and 2nd difference level is nothing but the

log natural returns of the raw values. Log natural returns are to make series

mean and variance constant. Thus equity is stationary and null hypothesis is

rejected at 1%, 5% and 10% level of significance.



Bonds

The weighted average price of bonds for this test is taken from April, 2008 to March, 2009. The data taken are raw rates. The unit root result is as under:

Table No 2: Bonds ADF Test

Power Finance Corporation Ltd Indian Railway Finance Corporation


ADF values




Intercept(2nd Difference)

-6.3050974 1%( -3.520355) 5%( -2.90065) 10%( -2.58770)

Intercept (2nd Difference)

-7.725679 1%( -3.592494) 5%( -2.931407) 10%( -2.60396)

Trend & Intercept (Level)

-5.357081 1%( -4.080085) 5%( -3.468479) 10%( -3.16109)

Trend & Intercept (2nd Difference)

-1075.6289 1%( -4.170542) 5%( -3.510728) 10%( -3.18551)

None(Level) 6.3976235 1%( -2.594659) 5%( -1.944965) 10%( -1.61411)

None(2nd difference)

-7.7657838 1%( -2.619939) 5%( -1.948680) 10%( -1.61205)

Housing Development Finance Corporation



Intercept(2nd Difference) -7.725679 1%(-3.592494) 5%(-2.931407) 10%(-2.603966)

Trend & Intercept (2nd Difference)

-7.6579844 1%(-4.1864559) 5%(-3.5180744) 10%(-3.1897344)

None(1st difference) -1301.54327 1%(-2.616296) 5%(-1.948134) 10%(-1.612338)




Hypothesis:



Interpretation

The above table tells that bonds has a unit root problem i.e unit root does

not exists, so they are stationary in their level, 1st difference and 2nd difference at

various constraints i.e ADF is smaller than critical values at none, intercept and

trend and intercept.. The 1st

difference and 2nd difference level is nothing but the

log natural returns of the raw values. Log natural returns are to make series

mean and variance constant. Thus equity is stationary and null hypothesis is

rejected at 1%, 5% and 10% level of significance.



Currencies

The Exchange rate of currencies for this test is taken from April, 2008 to March, 2009. The data taken are raw rates. The unit root result is as under:

Table No 3: Currencies ADF Test

Dollar Euro


ADF values




Intercept(1st Difference)

-11.12287 1%( -3.448307) 5%( -2.869336) 10%( -2.57097)

Intercept (1st

Difference)

-10.652492 1%( -3.448307) 5%( -2.869336) 10%( -2.57097)

Trend & Intercept

(1st Difference)

-11.175576 1%( -3.983691) 5%( -3.422363) 10%( -3.13402)

Trend & Intercept

(1st Difference)

-10.639176 1%( -3.983691) 5%( -3.422363) 10%( -3.13402)

None(2nd Difference)

-11.252048 1%( -2.571587) 5%( -1.941737) 10%( -1.61614)

None(2nd difference)

-11.099348 1%( -2.571587) 5%( -1.941737) 10%( -1.61614)

Pound



Intercept(2nd Difference) -12.546823 1%(-3.4487212) 5%( -2.869518) 10%( -2.571074)

Trend & Intercept (1st Difference)

-11.299146 1%( -3.9836916) 5%( -3.4223637) 10%( -3.1340235)

None(2nd difference) -12.563043 1%( -2.5715877) 5%( -1.9417379) 10%( -1.6161406)




Hypothesis:



Interpretation

The above table tells that currencies has a unit root problem i.e unit root

does not exists, so they are stationary in their level, 1st difference and 2nd

difference at various constraints i.e ADF is smaller than critical values at none,

intercept and trend and intercept.. The 1st

difference and 2nd difference level is

nothing but the log natural returns of the raw values. Log natural returns are to

make series mean and variance constant. Thus equity is stationary and null

hypothesis is rejected at 1%, 5% and 10% level of significance.



4.2 Historical Simulation

The historical simulation methodology is illustrated below. Table 1 shows

observations on market variables affecting the portfolio of “Reliance Industries

Limited” from the period April 1, 2008 to March 31, 2009.

Historical Simulation can be described in the following steps:

(1) The first step is to identify the basic factors, i.e. equity prices in this

case.

(2) The next step is to obtain historical values of the market factors for

the last N periods. For our portfolio, this means collection of equity prices of the

stock for the last 243 trading days. Daily changes in these prices will be used to

construct hypothetical values of the market factors used in the calculation of

hypothetical profits and losses in Step 3 because the daily value at risk number

is a measure of the portfolio loss caused by changes over a one day holding

period, 1 April 2008 to March 31 2009.

(3) This is the key step. We subject the current portfolio to the changes in

market rates and prices experienced on each of the most recent 243 trading

days, calculating the daily profits and losses that would occur if comparable

daily changes in the market factors are experienced and the current portfolio is

marked-to-market.

To calculate the 100 daily profits and losses, we first calculate 243 sets of

hypothetical values of the market forces. The hypothetical market factors are

based upon, but not equal to, the historical values of the market factors over the

243 days. Rather, we calculate daily historical percentage changes in the market

factors, and then combine the historical percentage changes with the current

(March 31, 2009) market factors to compute 243 sets of hypothetical market

factors.



The observations are taken at some particular point in time during the day

(usually the close of trading). We denote the first day for which we have data as

Day 0; the second day as Day 1; and so on. Today is Day 100; tomorrow is Day

101. The values of the market variables tomorrow if their percentage changes

between today and tomorrow are the same as they were between Day (i – 1) and

Day i for 1 ≤ i ≤ 100. The first row shows the values of the market variables

tomorrow assuming their percentage changes between today and tomorrow are

the same as they were between Day 0 and Day 1; second row shows the values

of market variables tomorrow assuming their percentage changes between Day

1 and Day 2 occur; and so on. The 243 rows are the 243 scenario considered.

Reliance Industries Ltd

Table 4 : Data for Calculation of VaR through Historical Simulation

Date Equity price P&L VaR

1-Apr-08 2,345.25 0 0

2-Apr-08 2,343.55 1523.644755 9.450672643

3-Apr-08 2,396.05 1558.907315 -25.81188676

4-Apr-08 2,321.15 1477.086648 56.00878018

7-Apr-08 2,404.90 1579.76489 -46.66946225

8-Apr-08 2,381.75 1510.072482 23.02294578

9-Apr-08 2,418.25 1548.11659 -15.02116169

10-Apr-08 2,468.65 1556.528104 -23.432676

11-Apr-08 2,551.55 1575.952793 -42.85736502

15-Apr-08 2,611.80 1560.754071 -27.65864305

16-Apr-08 2,642.50 1542.672439 -9.577010548

17-Apr-08 2,640.05 1523.336325 9.759103497



21-Apr-08 2,643.60 1526.800288 6.295140127

23-Apr-08 2,577.60 1507.352523 25.74290532

25-Apr-08 2,624.50 1549.457486 -16.36205753

28-Apr-08 2,591.40 1505.519966 27.57546229

29-Apr-08 2,659.95 1565.084033 -31.98860476

30-Apr-08 2,614.50 1498.696921 34.39850701

2-May-08 2,674.75 1559.887192 -26.79176362

5-May-08 2,669.20 1521.586204 11.50922368

6-May-08 2,650.00 1513.782219 19.31320861

7-May-08 2,688.95 1547.160948 -14.06552011

8-May-08 2,667.25 1512.445169 20.65025888

9-May-08 2,528.40 1445.375537 87.7198914

12-May-08 2,553.85 1540.097606 -7.002178194

13-May-08 2,501.10 1493.256152 39.83927552

14-May-08 2,530.75 1542.825582 -9.730153744

15-May-08 2,622.95 1580.299521 -47.20409289

16-May-08 2,635.70 1532.161717 0.933711231

20-May-08 2,602.95 1505.804155 27.29127256

21-May-08 2,667.70 1562.679104 -29.58367648

22-May-08 2,626.05 1500.944536 32.15089245

23-May-08 2,556.20 1484.193351 48.90207677

26-May-08 2,515.60 1500.53247 32.56295793

27-May-08 2,495.10 1512.324585 20.77084341

28-May-08 2,522.50 1541.494078 -8.398650394

29-May-08 2,462.70 1488.6033 44.4921277

30-May-08 2,403.50 1488.097058 44.99836989

2-Jun-08 2,358.80 1496.392885 36.70254262



3-Jun-08 2,406.65 1555.68068 -22.58525179

4-Jun-08 2,307.00 1461.616043 71.47938495

5-Jun-08 2,246.80 1484.962419 48.13300927

6-Jun-08 2,238.50 1519.117356 13.97807221

9-Jun-08 2,162.70 1473.118975 59.97645324

10-Jun-08 2,197.75 1549.461004 -16.36557561

11-Jun-08 2,261.40 1568.908952 -35.81352434

12-Jun-08 2,277.30 1535.470582 -2.375154383

13-Jun-08 2,270.40 1520.130154 12.96527387

16-Jun-08 2,282.35 1532.775353 0.320074538

17-Jun-08 2,332.90 1558.520505 -25.42507718

18-Jun-08 2,287.10 1494.815777 38.2796515

19-Jun-08 2,248.15 1498.783049 34.31237851

23-Jun-08 2,025.70 1471.363412 61.73201575

24-Jun-08 2,062.70 1552.600002 -19.50457447

26-Jun-08 2,239.55 1598.667539 -65.57211062

27-Jun-08 2,182.65 1486.010845 47.08458319

30-Jun-08 2,095.15 1463.624476 69.47095202

1-Jul-08 2,044.15 1487.634638 45.46078967

2-Jul-08 2,144.00 1599.229019 -66.1335914

3-Jul-08 2,070.10 1472.194485 60.90094339

4-Jul-08 2,097.90 1545.22633 -12.13090165

7-Jul-08 2,028.20 1474.092164 59.00326441

8-Jul-08 1,979.45 1488.10097 44.99445793

9-Jul-08 2,079.15 1601.547886 -68.45245778

10-Jul-08 2,046.65 1500.916041 32.17938659

11-Jul-08 2,016.10 1501.990313 31.10511456



14-Jul-08 2,043.45 1545.434446 -12.33901846

15-Jul-08 1,977.40 1475.46583 57.62959815

16-Jul-08 1,943.50 1498.610107 34.48532129

17-Jul-08 2,018.55 1583.629592 -50.53416423

18-Jul-08 2,113.20 1596.245671 -63.1502434

21-Jul-08 2,152.85 1553.358905 -20.26347674

22-Jul-08 2,152.15 1524.254227 8.841201045

23-Jul-08 2,267.30 1606.331192 -73.23576406

24-Jul-08 2,308.05 1552.154209 -19.05878075

25-Jul-08 2,147.10 1418.422792 114.672636

28-Jul-08 2,179.90 1548.04272 -14.94729241

29-Jul-08 2,083.10 1457.042399 76.05302927

30-Jul-08 2,165.50 1585.063667 -51.96823913

31-Jul-08 2,207.50 1554.322616 -21.22718802

1-Aug-08 2,297.60 1586.983284 -53.88785626

4-Aug-08 2,242.40 1488.117775 44.97765293

5-Aug-08 2,276.05 1547.630769 -14.53534149

6-Aug-08 2,298.60 1539.856484 -6.761055821

7-Aug-08 2,272.60 1507.503198 25.5922304

8-Aug-08 2,251.80 1510.794707 22.3007215

11-Aug-08 2,325.25 1574.484829 -41.3894008

12-Aug-08 2,347.25 1539.176191 -6.080762732

13-Aug-08 2,336.85 1517.994265 15.10116344

14-Aug-08 2,276.70 1485.503274 47.59215436

18-Aug-08 2,224.80 1489.991567 43.10386126

20-Aug-08 2,246.35 1543.125862 -10.03043364

21-Aug-08 2,212.65 1501.875526 31.21990215



22-Aug-08 2,244.80 1546.904752 -13.80932422

26-Aug-08 2,179.35 1488.783115 44.31231308

27-Aug-08 2,148.00 1502.816436 30.27899191

28-Aug-08 2,070.85 1469.985353 63.11007535

29-Aug-08 2,136.20 1572.866673 -39.77124511

1-Sep-08 2,141.65 1528.640033 4.455395466

2-Sep-08 2,212.75 1575.369721 -42.27429278

4-Sep-08 2,152.25 1483.060982 50.03444619

5-Sep-08 2,080.90 1474.202474 58.89295385

8-Sep-08 2,133.20 1563.072084 -29.97665619

9-Sep-08 2,142.55 1531.433111 1.662316946

10-Sep-08 2,082.65 1482.122045 50.97338301

11-Sep-08 1,997.40 1462.336758 70.75866954

12-Sep-08 1,932.65 1475.321962 57.7734657

15-Sep-08 1,886.95 1488.695321 44.40010681

16-Sep-08 1,928.05 1557.960856 -24.86542814

17-Sep-08 1,876.65 1484.101599 48.99382923

18-Sep-08 1,938.25 1574.799077 -41.70364881

19-Sep-08 2,055.10 1616.671598 -83.57617009

22-Sep-08 2,039.10 1512.879045 20.21638318

23-Sep-08 2,006.45 1500.335755 32.75967326

24-Sep-08 2,046.10 1554.880996 -21.78556829

25-Sep-08 2,025.70 1509.547957 23.54747091

26-Sep-08 1,963.20 1477.706077 55.38935109

29-Sep-08 1,932.85 1501.178198 31.91723041

30-Sep-08 1,949.35 1537.766207 -4.670778638

1-Oct-08 1,906.70 1491.389861 41.70556728



3-Oct-08 1,761.45 1408.596469 124.498959

6-Oct-08 1,641.60 1421.005195 112.0902334

7-Oct-08 1,674.65 1555.447483 -22.35205464

8-Oct-08 1,648.55 1500.986243 32.10918461

10-Oct-08 1,527.60 1412.882897 120.2125309

13-Oct-08 1,571.40 1568.468284 -35.37285558

14-Oct-08 1,621.05 1572.926045 -39.83061725

15-Oct-08 1,520.20 1429.891089 103.2043389

16-Oct-08 1,391.95 1396.116144 136.9792837

17-Oct-08 1,306.05 1430.654648 102.4407798

21-Oct-08 1,394.95 1610.227884 -77.1324564

22-Oct-08 1,316.80 1439.328148 93.76728004

23-Oct-08 1,217.65 1409.942161 123.1532671

24-Oct-08 1,019.50 1276.625159 256.4702689

28-Oct-08 1,153.00 1632.3461 -99.25067228

29-Oct-08 1,201.75 1589.217964 -56.12253601

31-Oct-08 1,375.45 1745.136166 -212.040738

3-Nov-08 1,441.70 1598.191192 -65.09576397

4-Nov-08 1,451.60 1535.220295 -2.124867484

5-Nov-08 1,269.05 1333.000818 200.0946099

6-Nov-08 1,170.55 1406.403304 126.6921243

7-Nov-08 1,220.75 1590.140158 -57.04473047

10-Nov-08 1,303.10 1627.607393 -94.511965

11-Nov-08 1,207.70 1413.122995 119.9724328

12-Nov-08 1,162.20 1467.305167 65.79026115

14-Nov-08 1,146.75 1504.48035 28.61507823

17-Nov-08 1,141.40 1517.636494 15.45893356



18-Nov-08 1,139.95 1522.813004 10.28242423

19-Nov-08 1,132.45 1514.71831 18.37711799

20-Nov-08 1,056.05 1421.883737 111.2116914

21-Nov-08 1,124.35 1623.363158 -90.26772952

24-Nov-08 1,144.80 1552.48259 -19.38716194

25-Nov-08 1,071.80 1427.521882 105.5735464

26-Nov-08 1,138.90 1620.206918 -87.11149027

28-Nov-08 1,134.45 1518.792376 14.30305158

1-Dec-08 1,109.40 1491.081714 42.01371439

2-Dec-08 1,073.95 1476.027819 57.06760891

3-Dec-08 1,069.10 1517.86417 15.23125835

4-Dec-08 1,159.10 1653.107965 -120.0125366

5-Dec-08 1,117.60 1470.158399 62.93702924

8-Dec-08 1,118.55 1526.046092 7.049335928

10-Dec-08 1,227.20 1672.856108 -139.7606804

11-Dec-08 1,259.00 1564.260308 -31.16488002

12-Dec-08 1,307.10 1583.002959 -49.9075307

15-Dec-08 1,340.55 1563.769882 -30.6744538

16-Dec-08 1,388.50 1579.288632 -46.19320353

17-Dec-08 1,351.40 1484.009471 49.08595735

18-Dec-08 1,361.00 1535.581434 -2.486006068

19-Dec-08 1,351.30 1513.882935 19.21249266

23-Dec-08 1,259.75 1494.14944 38.94598807

24-Dec-08 1,242.00 1503.266124 29.82930377

26-Dec-08 1,210.15 1485.649124 47.4463036

29-Dec-08 1,246.30 1570.297835 -37.20240698

30-Dec-08 1,250.50 1529.88837 3.207058426



1-Jan-09 1,254.65 1551.837426 -18.74199849

2-Jan-09 1,286.40 1563.335113 -30.23968538

5-Jan-09 1,365.85 1618.920855 -85.82542671

6-Jan-09 1,370.90 1530.387506 2.707922051

7-Jan-09 1,200.75 1335.504823 197.5906045

9-Jan-09 1,153.25 1464.433011 68.66241738

12-Jan-09 1,097.90 1451.569933 81.5254952

13-Jan-09 1,077.55 1496.488171 36.6072574

14-Jan-09 1,179.75 1669.364589 -136.2691607

15-Jan-09 1,142.35 1476.412937 56.68249094

16-Jan-09 1,217.35 1624.856141 -91.76071285

19-Jan-09 1,229.90 1540.469072 -7.373644165

20-Jan-09 1,183.65 1467.412259 65.68316887

21-Jan-09 1,119.85 1442.564345 90.53108254

22-Jan-09 1,136.30 1547.147765 -14.05233733

23-Jan-09 1,156.15 1551.385825 -18.29039661

27-Jan-09 1,225.95 1616.80341 -83.70798202

28-Jan-09 1,274.00 1584.511195 -51.4157674

29-Jan-09 1,270.10 1520.082398 13.01303004

30-Jan-09 1,323.60 1588.976537 -55.88110928

2-Feb-09 1,280.00 1474.524025 58.57140261

3-Feb-09 1,306.20 1555.959727 -22.86429856

4-Feb-09 1,307.50 1526.267513 6.827915368

5-Feb-09 1,288.80 1502.942868 30.15255993

6-Feb-09 1,344.85 1591.061482 -57.96605361

9-Feb-09 1,389.70 1575.599565 -42.50413701

10-Feb-09 1,401.95 1538.190446 -5.09501778



11-Feb-09 1,381.25 1502.23684 30.85858824

12-Feb-09 1,351.55 1491.964425 41.13100266

13-Feb-09 1,392.40 1570.834893 -37.73946527

16-Feb-09 1,320.20 1445.687267 87.40816141

17-Feb-09 1,267.30 1463.653746 69.44168236

18-Feb-09 1,295.15 1558.257684 -25.16225566

19-Feb-09 1,293.75 1523.101813 9.993615469

24-Feb-09 1,253.25 1524.567526 8.527901672

25-Feb-09 1,266.55 1540.931269 -7.835840701

26-Feb-09 1,290.80 1553.943626 -20.84819839

27-Feb-09 1,266.05 1495.514206 37.58122169

2-Mar-09 1,225.65 1476.094813 57.00061539

3-Mar-09 1,196.85 1488.921827 44.17360081

5-Mar-09 1,149.80 1447.57456 85.52086768

6-Mar-09 1,169.90 1551.404614 -18.30918585

9-Mar-09 1,153.35 1503.180112 29.91531645

12-Mar-09 1,202.00 1589.066198 -55.97077047

13-Mar-09 1,284.25 1629.085015 -95.98958656

16-Mar-09 1,327.60 1576.218104 -43.12267595

17-Mar-09 1,300.20 1493.281071 39.81435689

18-Mar-09 1,331.40 1561.338371 -28.24294302

19-Mar-09 1,345.70 1541.12669 -8.03126195

20-Mar-09 1,339.20 1517.385153 15.71027529

23-Mar-09 1,438.45 1637.751372 -104.6559441

24-Mar-09 1,452.45 1539.589932 -6.494503871

25-Mar-09 1,532.20 1608.469792 -75.37436442

26-Mar-09 1,565.50 1557.888086 -24.79265776



27-Mar-09 1,548.75 1508.436003 24.65942513

30-Mar-09 1,516.45 1492.950533 40.14489531

31-Mar-09 1,524.75 1533.095428 0

Source : www.nseindia.com

Calculations :

Reliance Industries Ltd(equity)

The 1 day loss (VaR) = 1334.0525

Similarly, loss of 10 day(VaR) = (√10*one day loss) = 4218.6444

Working Notes :

1. P&L = Equity price of nth day*

(Equity price of current day/Equity price of previous day

2. VaR = Value of nth day P&L – Value of current day P&L

Here, for Reliance equity price we have daily VaR, which shows that an

investor has risk of 56.00878 after taking the difference of nth day to current

day i.e. 4 April, 2008. So, for an investor it’s a point where he can calculate

daily risk with respect to nth day P&L to that of current day.

http://www.nseindia.com/



Chart 1. Showing Historical Simulation

Note:

In the above graph, x – axis denotes the scenario number and the y – axis

denotes the Value-at-Risk.

Likewise, worst daily VaR is calculated for all other equities, bonds and Currencies.

DLF Limited(equity)


Bharti Airtel(equity)




Infosys Technologies Ltd(equity)


Power Finance Corporation Limited(bond)


Indian Railway Finance Corporation(bond)


Housing Development Finance Corporation Limited(bond)


Dollar(currency)


Euro(currency)


Pound(currency)




4.3 Analytic Method (Variance-Covariance Approach)

Reliance Industries Ltd.

Table 5 : Calculation of Daily Stock Volatility

Date Equity price Price relative Daily Return

1-Apr-08 2,345.25 0 0

2-Apr-08 2,343.55 0.99927513 -0.00072513

3-Apr-08 2,396.05 1.02240191 0.02215467

4-Apr-08 2,321.15 0.96874022 -0.0317588

7-Apr-08 2,404.90 1.03608125 0.03544557

8-Apr-08 2,381.75 0.99037382 -0.00967281

9-Apr-08 2,418.25 1.01532487 0.01520863

10-Apr-08 2,468.65 1.02084152 0.0206273

11-Apr-08 2,551.55 1.03358111 0.03302958

15-Apr-08 2,611.80 1.0236131 0.02333862

16-Apr-08 2,642.50 1.01175435 0.0116858

17-Apr-08 2,640.05 0.99907285 -0.00092758

21-Apr-08 2,643.60 1.00134467 0.00134377

22-Apr-08 2,607.35 0.98628764 -0.01380724

23-Apr-08 2,577.60 0.98858995 -0.01147565

24-Apr-08 2,582.65 1.00195919 0.00195727

25-Apr-08 2,624.50 1.01620429 0.0160744

28-Apr-08 2,591.40 0.98738807 -0.01269213

29-Apr-08 2,659.95 1.02645288 0.02610906



30-Apr-08 2,614.50 0.98291321 -0.01723445

2-May-08 2,674.75 1.02304456 0.02278304

5-May-08 2,669.20 0.99792504 -0.00207712

6-May-08 2,650.00 0.99280683 -0.00721916

7-May-08 2,688.95 1.01469811 0.01459114

8-May-08 2,667.25 0.99192994 -0.0081028

9-May-08 2,528.40 0.94794264 -0.05346129

12-May-08 2,553.85 1.01006565 0.01001533

13-May-08 2,501.10 0.97934491 -0.02087139

14-May-08 2,530.75 1.01185478 0.01178507

15-May-08 2,622.95 1.03643189 0.03578394

16-May-08 2,635.70 1.00486094 0.00484916

20-May-08 2,602.95 0.98757446 -0.01250338

21-May-08 2,667.70 1.02487562 0.02457126

22-May-08 2,626.05 0.9843873 -0.01573586

23-May-08 2,556.20 0.97340112 -0.02695904

26-May-08 2,515.60 0.98411705 -0.01601044

27-May-08 2,495.10 0.99185085 -0.00818254

28-May-08 2,522.50 1.01098152 0.01092166

29-May-08 2,462.70 0.97629336 -0.02399216

30-May-08 2,403.50 0.97596134 -0.0243323

2-Jun-08 2,358.80 0.98140212 -0.01877299

3-Jun-08 2,406.65 1.02028574 0.02008272

4-Jun-08 2,307.00 0.9585939 -0.04228776

5-Jun-08 2,246.80 0.9739055 -0.026441

6-Jun-08 2,238.50 0.99630586 -0.00370098

9-Jun-08 2,162.70 0.96613804 -0.03444856



10-Jun-08 2,197.75 1.01620659 0.01607667

11-Jun-08 2,261.40 1.02896144 0.02854998

12-Jun-08 2,277.30 1.00703104 0.00700644

13-Jun-08 2,270.40 0.9969701 -0.0030345

16-Jun-08 2,282.35 1.00526339 0.00524959

17-Jun-08 2,332.90 1.02214822 0.02190651

18-Jun-08 2,287.10 0.98036778 -0.01982749

19-Jun-08 2,248.15 0.9829697 -0.01717698

20-Jun-08 2,099.20 0.93374552 -0.06855134

23-Jun-08 2,025.70 0.96498666 -0.035641

24-Jun-08 2,062.70 1.01826529 0.01810048

25-Jun-08 2,136.00 1.03553595 0.03491912

26-Jun-08 2,239.55 1.04847846 0.04734003

27-Jun-08 2,182.65 0.97459311 -0.02573522

30-Jun-08 2,095.15 0.95991112 -0.04091459

1-Jul-08 2,044.15 0.97565807 -0.02464309

2-Jul-08 2,144.00 1.04884671 0.04769119

3-Jul-08 2,070.10 0.96553172 -0.03507633

4-Jul-08 2,097.90 1.0134293 0.01333993

7-Jul-08 2,028.20 0.9667763 -0.03378814

8-Jul-08 1,979.45 0.97596391 -0.02432967

9-Jul-08 2,079.15 1.05036753 0.04914013

10-Jul-08 2,046.65 0.98436861 -0.01575485

11-Jul-08 2,016.10 0.98507317 -0.01503936

14-Jul-08 2,043.45 1.0135658 0.0134746

15-Jul-08 1,977.40 0.96767721 -0.03285671

16-Jul-08 1,943.50 0.98285628 -0.01729238



17-Jul-08 2,018.55 1.0386159 0.03788896

18-Jul-08 2,113.20 1.04689009 0.04582395

21-Jul-08 2,152.85 1.01876301 0.01858916

22-Jul-08 2,152.15 0.99967485 -0.0003252

23-Jul-08 2,267.30 1.05350463 0.05212235

24-Jul-08 2,308.05 1.01797292 0.01781332

25-Jul-08 2,147.10 0.93026581 -0.07228492

28-Jul-08 2,179.90 1.01527642 0.01516091

29-Jul-08 2,083.10 0.95559429 -0.04542184

30-Jul-08 2,165.50 1.03955643 0.03879411

31-Jul-08 2,207.50 1.01939506 0.01920937

1-Aug-08 2,297.60 1.0408154 0.04000445

4-Aug-08 2,242.40 0.97597493 -0.02431838

5-Aug-08 2,276.05 1.01500624 0.01489476

6-Aug-08 2,298.60 1.00990752 0.00985876

7-Aug-08 2,272.60 0.98868877 -0.01137569

8-Aug-08 2,251.80 0.99084749 -0.00919465

11-Aug-08 2,325.25 1.03261835 0.03209766

12-Aug-08 2,347.25 1.00946135 0.00941687

13-Aug-08 2,336.85 0.99556928 -0.00444056

14-Aug-08 2,276.70 0.97426022 -0.02607684

18-Aug-08 2,224.80 0.97720385 -0.02306

19-Aug-08 2,219.60 0.99766271 -0.00234002

20-Aug-08 2,246.35 1.01205172 0.01197968

21-Aug-08 2,212.65 0.98499789 -0.01511578

22-Aug-08 2,244.80 1.01453009 0.01442554

25-Aug-08 2,232.00 0.99429793 -0.00571839



26-Aug-08 2,179.35 0.97641129 -0.02387138

27-Aug-08 2,148.00 0.98561498 -0.01448949

28-Aug-08 2,070.85 0.96408287 -0.03657803

29-Aug-08 2,136.20 1.03155709 0.0310694

1-Sep-08 2,141.65 1.00255126 0.00254801

2-Sep-08 2,212.75 1.0331987 0.03265953

4-Sep-08 2,152.25 0.97265846 -0.02772228

5-Sep-08 2,080.90 0.96684865 -0.03371331

8-Sep-08 2,133.20 1.02513336 0.02482271

9-Sep-08 2,142.55 1.00438309 0.00437351

10-Sep-08 2,082.65 0.97204266 -0.02835559

11-Sep-08 1,997.40 0.95906657 -0.04179479

12-Sep-08 1,932.65 0.96758286 -0.03295422

15-Sep-08 1,886.95 0.97635371 -0.02393035

16-Sep-08 1,928.05 1.02178118 0.02154736

17-Sep-08 1,876.65 0.97334094 -0.02702086

18-Sep-08 1,938.25 1.03282445 0.03229723

19-Sep-08 2,055.10 1.06028634 0.058539

22-Sep-08 2,039.10 0.99221449 -0.00781597

23-Sep-08 2,006.45 0.98398803 -0.01614154

24-Sep-08 2,046.10 1.01976127 0.01956855

25-Sep-08 2,025.70 0.99002981 -0.01002022

26-Sep-08 1,963.20 0.96914647 -0.03133952

29-Sep-08 1,932.85 0.98454055 -0.0155802

30-Sep-08 1,949.35 1.00853662 0.00850039

1-Oct-08 1,906.70 0.97812091 -0.02212198

3-Oct-08 1,761.45 0.92382126 -0.07923667



6-Oct-08 1,641.60 0.93195947 -0.07046596

7-Oct-08 1,674.65 1.0201328 0.01993281

8-Oct-08 1,648.55 0.98441465 -0.01570807

10-Oct-08 1,527.60 0.9266325 -0.07619824

13-Oct-08 1,571.40 1.02867243 0.02826907

14-Oct-08 1,621.05 1.03159603 0.03110715

15-Oct-08 1,520.20 0.93778724 -0.06423218

16-Oct-08 1,391.95 0.9156361 -0.08813626

17-Oct-08 1,306.05 0.93828801 -0.06369833

20-Oct-08 1,320.90 1.01137016 0.01130601

21-Oct-08 1,394.95 1.05606026 0.05454525

22-Oct-08 1,316.80 0.94397649 -0.05765402

23-Oct-08 1,217.65 0.92470383 -0.07828178

24-Oct-08 1,019.50 0.83726851 -0.17761046

27-Oct-08 1,077.00 1.0564002 0.05486709

28-Oct-08 1,153.00 1.07056639 0.06818784

29-Oct-08 1,201.75 1.04228101 0.04141159

31-Oct-08 1,375.45 1.14453921 0.13500212

3-Nov-08 1,441.70 1.04816605 0.04704202

4-Nov-08 1,451.60 1.00686689 0.00684342

5-Nov-08 1,269.05 0.87424222 -0.13439781

6-Nov-08 1,170.55 0.92238288 -0.08079487

7-Nov-08 1,220.75 1.04288582 0.0419917

10-Nov-08 1,303.10 1.06745853 0.06528062

11-Nov-08 1,207.70 0.92678996 -0.07602832

12-Nov-08 1,162.20 0.96232508 -0.03840296

14-Nov-08 1,146.75 0.98670625 -0.01338291



17-Nov-08 1,141.40 0.99533464 -0.00467628

18-Nov-08 1,139.95 0.99872963 -0.00127118

19-Nov-08 1,132.45 0.99342076 -0.00660097

20-Nov-08 1,056.05 0.93253565 -0.06984789

21-Nov-08 1,124.35 1.06467497 0.06266956

24-Nov-08 1,144.80 1.01818829 0.01802486

25-Nov-08 1,071.80 0.9362334 -0.06589047

26-Nov-08 1,138.90 1.06260496 0.06072341

28-Nov-08 1,134.45 0.99609272 -0.00391493

1-Dec-08 1,109.40 0.97791882 -0.02232862

2-Dec-08 1,073.95 0.96804579 -0.03247589

3-Dec-08 1,069.10 0.99548396 -0.00452627

4-Dec-08 1,159.10 1.08418296 0.08082667

5-Dec-08 1,117.60 0.96419636 -0.03646031

8-Dec-08 1,118.55 1.00085004 0.00084967

10-Dec-08 1,227.20 1.09713468 0.09270195

11-Dec-08 1,259.00 1.02591265 0.0255826

12-Dec-08 1,307.10 1.03820492 0.03749319

15-Dec-08 1,340.55 1.025591 0.02526903

16-Dec-08 1,388.50 1.0357689 0.03514405

17-Dec-08 1,351.40 0.97328052 -0.02708294

18-Dec-08 1,361.00 1.00710374 0.00707863

19-Dec-08 1,351.30 0.99287289 -0.00715263

22-Dec-08 1,285.55 0.95134315 -0.04988045

23-Dec-08 1,259.75 0.97993077 -0.02027335

24-Dec-08 1,242.00 0.9859099 -0.01419031

26-Dec-08 1,210.15 0.97435588 -0.02597866



29-Dec-08 1,246.30 1.02987233 0.02943484

30-Dec-08 1,250.50 1.00336998 0.00336431

31-Dec-08 1,232.75 0.98580568 -0.01429603

1-Jan-09 1,254.65 1.01776516 0.0176092

2-Jan-09 1,286.40 1.02530586 0.02499097

5-Jan-09 1,365.85 1.0617615 0.05992933

6-Jan-09 1,370.90 1.00369733 0.00369051

7-Jan-09 1,200.75 0.87588446 -0.1325211

9-Jan-09 1,153.25 0.96044139 -0.04036232

12-Jan-09 1,097.90 0.9520052 -0.04918478

13-Jan-09 1,077.55 0.98146461 -0.01870932

14-Jan-09 1,179.75 1.09484479 0.09061261

15-Jan-09 1,142.35 0.96829837 -0.03221501

16-Jan-09 1,217.35 1.06565413 0.06358882

19-Jan-09 1,229.90 1.01030928 0.0102565

20-Jan-09 1,183.65 0.96239532 -0.03832998

21-Jan-09 1,119.85 0.94609893 -0.05540814

22-Jan-09 1,136.30 1.01468947 0.01458262

23-Jan-09 1,156.15 1.01746898 0.01731815

27-Jan-09 1,225.95 1.06037279 0.05862053

28-Jan-09 1,274.00 1.03919409 0.0384455

29-Jan-09 1,270.10 0.99693878 -0.00306592

30-Jan-09 1,323.60 1.04212267 0.04125966

2-Feb-09 1,280.00 0.96705953 -0.03349522

3-Feb-09 1,306.20 1.02046875 0.02026208

4-Feb-09 1,307.50 1.00099525 0.00099476

5-Feb-09 1,288.80 0.9856979 -0.01440536



6-Feb-09 1,344.85 1.04349007 0.04257093

9-Feb-09 1,389.70 1.03334944 0.03280541

10-Feb-09 1,401.95 1.00881485 0.00877623

11-Feb-09 1,381.25 0.98523485 -0.01487524

12-Feb-09 1,351.55 0.97849774 -0.0217368

13-Feb-09 1,392.40 1.03022456 0.02977679

16-Feb-09 1,320.20 0.94814708 -0.05324564

17-Feb-09 1,267.30 0.95993031 -0.04089459

18-Feb-09 1,295.15 1.02197585 0.02173787

19-Feb-09 1,293.75 0.99891904 -0.00108154

20-Feb-09 1,253.40 0.96881159 -0.03168512

24-Feb-09 1,253.25 0.99988033 -0.00011968

25-Feb-09 1,266.55 1.01061241 0.01055649

26-Feb-09 1,290.80 1.0191465 0.01896551

27-Feb-09 1,266.05 0.98082584 -0.01936036

2-Mar-09 1,225.65 0.96808973 -0.0324305

3-Mar-09 1,196.85 0.97650226 -0.02377821

4-Mar-09 1,211.10 1.01190625 0.01183593

5-Mar-09 1,149.80 0.94938486 -0.05194102

6-Mar-09 1,169.90 1.0174813 0.01733026

9-Mar-09 1,153.35 0.98585349 -0.01424752

12-Mar-09 1,202.00 1.04218147 0.04131608

13-Mar-09 1,284.25 1.06842762 0.06618805

16-Mar-09 1,327.60 1.03375511 0.03319791

17-Mar-09 1,300.20 0.97936125 -0.0208547

18-Mar-09 1,331.40 1.02399631 0.02371292

19-Mar-09 1,345.70 1.01074057 0.0106833



20-Mar-09 1,339.20 0.9951698 -0.0048419

23-Mar-09 1,438.45 1.07411141 0.07149372

24-Mar-09 1,452.45 1.0097327 0.00968564

25-Mar-09 1,532.20 1.05490723 0.05345283

26-Mar-09 1,565.50 1.02173346 0.02150065

27-Mar-09 1,548.75 0.98930054 -0.01075711

30-Mar-09 1,516.45 0.97914447 -0.02107608

31-Mar-09 1,524.75 1.00547331 0.00545839

Source : www.nseindia.com

Reliance Industries Limited (Equity)

Standard deviation of daily return = 0.038926896

Standard deviation of daily return in % = 3.892689561

Assuming that there is 252 trading days in = 252

Square root of 252 = 15.87450787

Volatility of stock per annum (S) = 0.617945311

Standard error of estimate =S/ Sqrt(2n)

SQRT (2n) =22.04540769

Standard error of estimate = 0.028030569

Likewise, the analytic approach is done for all equity, bonds and currencies.

Here are the results of all the equities, bonds and currencies.

http://www.nseindia.com/



DLF (Equity)




Square root of 252 = 15.87450787



SQRT (2n) =22.04540769


Bharti Airtel (Equity)




Square root of 252 = 15.87450787



SQRT (2n) =22.04540769




Infosys Technologies Ltd (Equity)




Square root of 252 = 15.87450787



SQRT (2n) =22.04540769


Power Finance Corporation Limited (Bond)




Square root of 252 = 15.87450787



SQRT (2n) =22.04540769




Indian railway Finance Corporation (Bond)




Square root of 252 = 15.87450787



SQRT (2n) =22.04540769


Housing Development Finance Corporation Limited (Bond)




Square root of 252 = 15.87450787



SQRT (2n) =22.04540769




DOLLAR (Currency)


Standard deviation of daily return in % = 0. 3128319


Square root of 252 = 15.87450787



SQRT (2n) =22.04540769


EURO (Currency)


Standard deviation of daily return in % = 0. 4520986


Square root of 252 = 15.87450787



SQRT (2n) =22.04540769




POUND (Currency)




Square root of 252 = 15.87450787



SQRT (2n) =22.04540769


Working Notes:

(1) Price relative =

Equity price of current period/Equity price of previous period

(2) Daily return = Natural logarithm of Price relative

(3) Standard deviation of daily return = √(Σ Daily return)

(4) Standard deviation in % = Standard deviation * 100

(5) Volatility of stock per annum = Standard deviation of daily return

* √252

(6) Standard error of estimate = Volatility of stock per annum / √2n

where, n = number of trading days = 252



4.4 Single Asset Case

We now consider how VaR is calculated using the analytic approach in a

very simple situation where the portfolio consists of a position in a single stock.

The portfolio we consider is one consisting of Rs.1,25,000 in Reliance

Industries Limited. We suppose that N = 10 and X = 99, so that we are

interested in the loss level over 10 days that we are 99% confident will not be

exceeded. Initially, we consider a one-day time horizon.

We assume that the volatility of 4% per day (corresponding to about 68%

per year). Because the size of the position is Rs.1,25,000, the standard deviation

of daily changes in the value of the position is 4% of

Rs.1,25,000, or Rs.5,000.

It is customary in the model-building approach to assume that the

expected change in a market variable over the time period considered is zero.

This is exactly not true, but it is a reasonable assumption. The expected change

in the price of a market variable over a short time period is generally small

when compared with the standard deviation of the change. Suppose, for

example, that Reliance Industries Limited has an expected return of 20% per

annum. Over a one-day period, the expected return is 0.20/252, or about 0.08%,

whereas the standard deviation of the return is 4%. Over a 10- day period, the

expected return is 0.08 * 10, or about 0.8%, whereas the standard deviation of

the return is 4√10, or about 12.65%. So far, we have established that the change

in the value of the portfolio of Cairn India Limited shares over a one-day period

has a standard deviation of Rs.5,000 and (at least approximately) a mean of

zero. We assume that the change is normally distributed. From the tables of

normal distribution, we find that N (- 2.33) = 0.01. This means that there is a

1% probability that a normally distributed variable will decrease in value by

more than 2.33 standard deviations. Equivalently, it means that we are 99%



certain that a normally distributed variable will not decrease in value by more

than 2.33 standard deviations. Therefore the one-day 99% VaR for our portfolio

consisting of a Rs.1,25,000 position of Reliance Industries Limited is,

= 2.33 * 5,000 = Rs. 11,650

As discussed earlier, the N-day VaR is calculated as √N times the one-day

VaR. The 10-day 99% VaR for Cairn India Limited is therefore,

= 11,650 * √10 = Rs. 36,841

Consider next a portfolio consisting of a Rs. 1,25,000 position in Infosys

Technologies Ltd, and suppose the daily volatility of Infosys is 3%

(approximately 48% per year). A similar calculation to that for Reliance

Industries Limited shows that the standard deviation of the change in the value

of the portfolio in one day is,

= 1,25,000 * 0.03 = Rs. 3,750

Assuming the change is normally distributed, the one-day 99% VaR is,

= 3,750 * 2.33 = Rs. 8,738

and the 10-day VaR is,

= 8,738 * √10 = Rs. 27,632



4.5 Two asset case:

Now consider a portfolio consisting of both Rs 1,25,000 of Reliance

Industries Limited and Rs.1,25,000 of Infosys technologies Ltd. We suppose

that the returns on the two shares have a bi-variate normal distribution with a

correlation of 0.3. A standard result in statistics tells us that, if two variables X

and Y have standard deviations σx and σy, with the coefficient of correlation

between them being equal to ρ, then the standard deviation of X + Y is given

by,

σx+y = √[(σx2 + σy

2 + 2 ρ σxσy]

To apply this result, we set X equal to the change in the value of the position in

Reliance Industries Limited over a one-day period and Y equal to the change in

the value of the position in Infosys Technologies Ltd over a one-day period.

The standard deviation of the change in the value of Reliance position in one

day,

σx = 1,25,000 * 4% = 5,000

The standard deviation of the change in the value of Infosys position in one day,

σy = 1,25,000 * 3% = 3,750

The standard deviation of the change in the portfolio value per day is therefore:

= √[(5,000 * 5,000) + (3,750 * 3,750) + (2 * 0.3 * 5,000 * 3,750)]

= Rs 6,339

The one-day 99% VaR is therefore = Rs 6,339 * 2.33 = Rs 14,770

The 10-day 99% VaR is = √10 * Rs 14,770 = Rs 46,706



The Benefits of Diversification by forming Portfolio

In the example we have just considered –

The 10-day 99% VaR for the portfolio of Reliance is Rs. 36,841.

The 10-day 99% VaR for the portfolio of Infosys is Rs. 27,632.

The 10-day 99% VaR for the portfolio of both Reliance and Infosys is

Rs. 46,706.

The amount i.e. = (36,841+27,632) – 46,706 = Rs. 17,767

represents the benefits of diversification. If Reliance and Infosys were perfectly

correlated, the VaR for the portfolio of both Reliance and Infosys would equal

the VaR for the Reliance the VaR for the Infosys. Less than perfect correlation

leads to some of the risk being “diversified away”.

4.6 Monte Carlo Simulation

The Monte Carlo approach entails simulations of possible portfolio

outcomes derived from random market moves taken from historical data. The

distribution of these simulated portfolio returns reveals the VAR. Like the

historical simulation approach, Monte Carlo analysis expresses the returns as a

histogram. This approach can provide a much greater range of outcomes than

historical simulation, and it is much more flexible than the other approaches.

Any distribution may be simulated, as long as the necessary parameters of the

assumed distribution can be estimated. However, all this makes Monte Carlo

analysis the most expensive and time-consuming method, and tends to make it

unsuitable for large, complex portfolios.



Here, I have taken Reliance equity prices for Monte Carlo simulation

Approach, where I got the result that equity above Rs 1700 is in better position,

its always in winning position.

Table 6. Simulated Index

Index probability

Cumulative

probability

RN

Internal

Random

Number

Below

1700

Above

1700

1100 0.1 0.1 0-999 8417

1300 0.16 0.26 1000-2599 1471 1+1+

1500 0.2 0.46 2600-4599 5660

2000 0.05 0.51 4600-5099 6066

2300 0.15 0.66 5100-6599 1545 1+1+1+

2600 0.34 1 6600-10000 5693 1+

Total 2 4

Above is the table where its shows the relevance of this interpretation.

The anticipated index is 1700.



4.7 Value at Risk for Portfolio

Now, considering the portfolio taken for measuring Value at risk.

Considering Value at Risk first seeing the Equity, Bonds and Currencies

separately.

Table 7

Equity Deviation(3%) 1 day 99% 10 day 99%

Reliance 15000 34950 110521.6042

DLF

Bharti Airtel

Infosys

Investment Rs 500000 for Equities

Bonds Deviation(4%) 1 day 99% 10 day 99%

Power Finance Corporation Ltd 20000 46600 147362.139

Indian Railway Finance Corporation

HDFC

Investment Rs 500000 for Bonds

Currency Deviation(5%) 1 day 99% 10 day 99%

Dollar 25000 58250 184202.6737

Euro

Pound

Investment Rs 500000 for Currency

The Table 7, shows the VaR for 1 day and 10 days separately for equities,

bonds and currencies because here we have invested Rs 5,00,000 individually in

equity, bonds and currencies, assuming deviation to be 3%, 4% and 5%



respectively for equities, bonds and currencies. The daily loss for equities,

bonds and currencies can be seen in the table separately.

Table 8

Constructing Portfolio Coefficient Correlation

of Equity & Bonds

Coefficient Correlation of Equity &

Currency

Coefficient Correlation of

Bonds & Currency

Equity, Bonds and Currencies 0.3 0.35 0.32

Investment Rs 1500000

Coefficient Correlation

(500000*0.03)15000 15000^2=225000000 2*correl• (equity &bond)*15000 180000000

(500000*0.04)20000 20000^2=400000000 2*correl• (equity

&currency)*20000 262500000

(500000*0.05)25000 25000^2=625000000

2*correl• (bond

&currency)*20000 320000000

The standard deviation of the change in the portfolio value per day is

44860.89611

one day 99% 10 day 99%

104525.8879 330539.88

•Correl: coefficient correlation

The Table 8, shows the VaR for 1 day and 10 days for portfolio, which consists

of equities, bonds and currencies where the investment is Rs 15,00,000,

assuming coeffient correlation to be 0.3, 0.35 and 0.32 respectively for equities,

bonds and currencies. The daily loss for equities, bonds and currencies can be

seen in the table separately.



The Benefits of Portfolio :

In this portfolio we have –

The 10-day 99% VaR for Equity is Rs. 1,10,521.

The 10-day 99% VaR for Bonds is Rs. 1,47,362.

The 10-day 99% VaR for Currency is Rs.1,84,202 .

The 10-day 99% VaR for the portfolio of Equity, Bonds and Currency is

Rs. 3,30,539.

The amount i.e. = (1,10,521 + 1,47,362 + 1,84,202 ) – 3,30,539

= Rs. 1,11,546

represents the benefits of portfolio construction. If Equity, Bonds and currency

were perfectly correlated, the VaR for the portfolio of equity, Bonds and

currency would equal the VaR for the portfolio of equity, Bonds and currency.

Less than perfect correlation leads to some of the risk being “diversified away”.



CHAPTER 5

FINDINGS, CONCLUSION

& Recommendations



5.1 Findings

Each of the three approaches for estimating Value at Risk has advantages

and comes with baggage.

In short, the question of which VaR approach is best answered by looking

at the task at hand. If you are assessing the Value at Risk for portfolios,

that do not include options, over very short time periods (a day or a

week), the variance-covariance approach does a reasonably good job.

If the Value at Risk is being computed for a risk source that is stable and

where there is substantial historical data (commodity prices, for instance),

historical simulations provide good estimates.

In the most general case of computing VaR for nonlinear portfolios

(which include options) over longer time periods, where the historical

data is volatile and non-stationary and the normality assumption is

questionable, Monte - Carlo simulations do best.

If Equity, Bonds and currency were taken together then probability of

loss is reduced than all are taken individually. Thus, portfolio leads to

some of the risk being “diversified away”.



5.2 CONCLUSION

Value at Risk has developed as a risk assessment tool at banks and other

financial service firms in the last decade. Its usage in these firms has been

driven by the failure of the risk tracking systems used until the early 1990s to

detect dangerous risk taking on the part of traders and it offered a key benefit: a

measure of capital at risk under extreme conditions in trading portfolios that

could be updated on a regular basis. While the notion of Value at Risk is

simple- the maximum amount that you can lose on an investment over a

particular period with a specified probability – there are three ways in which

Value at Risk can be measured. In the first approach, we run a portfolio through

historical data – a historical simulation – and estimate the probability that the

losses exceed specified values. In the second, we assume that the returns

generated by exposure to multiple market risks are normally distributed. We use

a variance-covariance matrix of all standardized instruments representing

various market risks to estimate the standard deviation in portfolio returns and

compute the Value at Risk from this standard deviation. In the third approach,

we assume return distributions for each of the individual market risks and run

Monte Carlo simulations to arrive at the Value at Risk. Each measure comes

with its own pluses and minuses: the Variance-covariance approach is simple to

implement but the normality assumption can be tough to sustain, historical

simulations assume that the past time periods used are representative of the

future and Monte Carlo simulations are time and computation intensive. All

three yield Value at Risk measures that are estimates and subject to judgment.

We understand why Value at Risk is a popular risk assessment tool in

financial service firms, where assets are primarily marketable securities; there is

limited capital at play and a regulatory overlay that emphasizes short term

exposure to extreme risks. We are hard pressed to see why Value at



Risk is of particular use to non-financial service firms, unless they are highly

levered and risk default if cash flows or value fall below a prespecified level.

Even in those cases, it would seem to us to be more prudent to use all of the

information in the probability distribution rather than a small slice of it.



5.3 Recommendations

Suggestions regarding this study are as follows :

Elements taken for portfolio is based on the personal choice for equities,

for bonds one should take on the basis of the day it is traded and for

currencies one should consider the strong currency compared to home

currency.

For calculating VaR, using the analytic approach it was done separately

for equities, bonds and currencies where its probability of loss for 99%

VaR was found and again, portfolio was constructed taking equities,

bonds and currencies together for 99% VaR, but this time loss was less in

respect of taking equities, bonds and currencies separately where,

investment was equal in each case. Thus, it shows that its always better to

invest in portfolio than individually and using VaR helps us to know the

probability of occurrence of loss.

In this study, measuring portfolio through VaR models i.e. Historical

Simulation , Analytic Approach and Monte Carlo Simulation, found that

if one is assessing the Value at Risk for portfolios, that do not include

options, over very short time periods (a day or a week), the variance-

covariance approach does a reasonably good job but for portfolios of

longer period with volatile and stationary data Monte Carlo Simulations

is best. Thus, for short periods data, go for variance-covariance approach

and for longer period data, go for Monte Carlo Simulation.



Selected Bibliography

Books & Journal

Pramod M Mantravadi, Value at Risk – Concepts and Applications, First

Edition: 2005

Websites

www.nse-india.com

www.jstor.com

www.icfai.org

http://www.nse-india.com/

http://www.jstor.com/

http://www.icfai.org/



Annexure



Date

Equity price of Reliance Date

Equity price of

DLF Date

Equity price of Airtel Date

Equity price of Infosys

1-Apr-08 2,345.25 1-Apr-08 626.95 1-Apr-08 803.1 1-Apr-08 1,423.05

2-Apr-08 2,343.55 2-Apr-08 619.55 2-Apr-08 823.1 2-Apr-08 1,482.80

3-Apr-08 2,396.05 3-Apr-08 623.7 3-Apr-08 819.7 3-Apr-08 1,522.50

4-Apr-08 2,321.15 4-Apr-08 606 4-Apr-08 783.9 4-Apr-08 1,485.45

7-Apr-08 2,404.90 7-Apr-08 617.65 7-Apr-08 818.8 7-Apr-08 1,492.05

8-Apr-08 2,381.75 8-Apr-08 616.25 8-Apr-08 828.45 8-Apr-08 1,466.95

9-Apr-08 2,418.25 9-Apr-08 610.25 9-Apr-08 821.9 9-Apr-08 1,479.95

10-Apr-08 2,468.65 10-Apr-08 600.6 10-Apr-08 798.65 10-Apr-08 1,452.60

11-Apr-08 2,551.55 11-Apr-08 598.05 11-Apr-08 805.1 11-Apr-08 1,421.90

15-Apr-08 2,611.80 15-Apr-08 616.65 15-Apr-08 816.7 15-Apr-08 1,510.40

16-Apr-08 2,642.50 16-Apr-08 624.45 16-Apr-08 807.55 16-Apr-08 1,600.20

17-Apr-08 2,640.05 17-Apr-08 649.85 17-Apr-08 823.4 17-Apr-08 1,659.10

21-Apr-08 2,643.60 21-Apr-08 653.75 21-Apr-08 855.9 21-Apr-08 1,645.80

22-Apr-08 2,607.35 22-Apr-08 676.25 22-Apr-08 856 22-Apr-08 1,598.60

23-Apr-08 2,577.60 23-Apr-08 684.45 23-Apr-08 845.05 23-Apr-08 1,647.95

24-Apr-08 2,582.65 24-Apr-08 676 24-Apr-08 843 24-Apr-08 1,696.05

25-Apr-08 2,624.50 25-Apr-08 667.85 25-Apr-08 922.4 25-Apr-08 1,684.30

28-Apr-08 2,591.40 28-Apr-08 668.5 28-Apr-08 928.05 28-Apr-08 1,663.65

29-Apr-08 2,659.95 29-Apr-08 725.55 29-Apr-08 901.2 29-Apr-08 1,749.55

30-Apr-08 2,614.50 30-Apr-08 705.15 30-Apr-08 898.25 30-Apr-08 1,753.10

2-May-08 2,674.75 2-May-08 721.35 2-May-08 900.25 2-May-08 1,787.45

5-May-08 2,669.20 5-May-08 705.15 5-May-08 893.95 5-May-08 1,785.95

6-May-08 2,650.00 6-May-08 668.2 6-May-08 846.35 6-May-08 1,807.45

7-May-08 2,688.95 7-May-08 650.75 7-May-08 816.15 7-May-08 1,844.15

8-May-08 2,667.25 8-May-08 644.15 8-May-08 829.2 8-May-08 1,784.65

9-May-08 2,528.40 9-May-08 630.65 9-May-08 841.8 9-May-08 1,749.35

12-May-08 2,553.85 12-May-08 621.9 12-May-08 837.95 12-May-08 1,773.40



13-May-08 2,501.10 13-May-08 615.1 13-May-08 820.05 13-May-08 1,748.75

14-May-08 2,530.75 14-May-08 623.35 14-May-08 848.85 14-May-08 1,824.90

15-May-08 2,622.95 15-May-08 644.9 15-May-08 856.2 15-May-08 1,893.10

16-May-08 2,635.70 16-May-08 649.75 16-May-08 852.45 16-May-08 1,871.40

20-May-08 2,602.95 20-May-08 636.75 20-May-08 829.6 20-May-08 1,887.70

21-May-08 2,667.70 21-May-08 631.55 21-May-08 822.45 21-May-08 1,870.65

22-May-08 2,626.05 22-May-08 620.75 22-May-08 817.7 22-May-08 1,863.65

23-May-08 2,556.20 23-May-08 609 23-May-08 837.65 23-May-08 1,828.75

26-May-08 2,515.60 26-May-08 600.8 26-May-08 863.45 26-May-08 1,885.05

27-May-08 2,495.10 27-May-08 596.6 27-May-08 862.75 27-May-08 1,883.10

28-May-08 2,522.50 28-May-08 601.7 28-May-08 884.25 28-May-08 1,911.60

29-May-08 2,462.70 29-May-08 587.85 29-May-08 858.45 29-May-08 1,885.45

30-May-08 2,403.50 30-May-08 586.85 30-May-08 875.95 30-May-08 1,962.80

2-Jun-08 2,358.80 2-Jun-08 567.7 2-Jun-08 877.45 2-Jun-08 1,950.80

3-Jun-08 2,406.65 3-Jun-08 582.65 3-Jun-08 841.4 3-Jun-08 1,922.25

4-Jun-08 2,307.00 4-Jun-08 554.1 4-Jun-08 810.35 4-Jun-08 1,870.70

5-Jun-08 2,246.80 5-Jun-08 538.95 5-Jun-08 822.55 5-Jun-08 1,979.55

6-Jun-08 2,238.50 6-Jun-08 518.4 6-Jun-08 802 6-Jun-08 1,993.55

9-Jun-08 2,162.70 9-Jun-08 480.9 9-Jun-08 781.3 9-Jun-08 1,901.50

10-Jun-08 2,197.75 10-Jun-08 480 10-Jun-08 776.3 10-Jun-08 1,854.05

11-Jun-08 2,261.40 11-Jun-08 512.15 11-Jun-08 806.9 11-Jun-08 1,892.85

12-Jun-08 2,277.30 12-Jun-08 497.45 12-Jun-08 820.05 12-Jun-08 1,874.90

13-Jun-08 2,270.40 13-Jun-08 480.25 13-Jun-08 816.4 13-Jun-08 1,866.65

16-Jun-08 2,282.35 16-Jun-08 492.3 16-Jun-08 840.35 16-Jun-08 1,907.80

17-Jun-08 2,332.90 17-Jun-08 507.65 17-Jun-08 832.55 17-Jun-08 1,911.55

18-Jun-08 2,287.10 18-Jun-08 492.6 18-Jun-08 812.05 18-Jun-08 1,862.45

19-Jun-08 2,248.15 19-Jun-08 477.2 19-Jun-08 805.35 19-Jun-08 1,862.40

20-Jun-08 2,099.20 20-Jun-08 456.8 20-Jun-08 765.7 20-Jun-08 1,827.00

23-Jun-08 2,025.70 23-Jun-08 445.8 23-Jun-08 758.75 23-Jun-08 1,845.80



24-Jun-08 2,062.70 24-Jun-08 439.95 24-Jun-08 750.7 24-Jun-08 1,794.45

25-Jun-08 2,136.00 25-Jun-08 458.85 25-Jun-08 779.9 25-Jun-08 1,746.75

26-Jun-08 2,239.55 26-Jun-08 451.8 26-Jun-08 769.45 26-Jun-08 1,785.10

27-Jun-08 2,182.65 27-Jun-08 425.1 27-Jun-08 747.95 27-Jun-08 1,705.45

30-Jun-08 2,095.15 30-Jun-08 396.4 30-Jun-08 721.25 30-Jun-08 1,736.80

1-Jul-08 2,044.15 1-Jul-08 369.1 1-Jul-08 706.9 1-Jul-08 1,717.00

2-Jul-08 2,144.00 2-Jul-08 423.45 2-Jul-08 742.3 2-Jul-08 1,820.60

3-Jul-08 2,070.10 3-Jul-08 382.85 3-Jul-08 707.75 3-Jul-08 1,743.05

4-Jul-08 2,097.90 4-Jul-08 415.45 4-Jul-08 717.15 4-Jul-08 1,755.80

7-Jul-08 2,028.20 7-Jul-08 425.75 7-Jul-08 727.65 7-Jul-08 1,799.80

8-Jul-08 1,979.45 8-Jul-08 429.6 8-Jul-08 711.05 8-Jul-08 1,736.60

9-Jul-08 2,079.15 9-Jul-08 450.3 9-Jul-08 746.4 9-Jul-08 1,821.90

10-Jul-08 2,046.65 10-Jul-08 459.95 10-Jul-08 741.75 10-Jul-08 1,805.25

11-Jul-08 2,016.10 11-Jul-08 452.7 11-Jul-08 744.9 11-Jul-08 1,676.85

14-Jul-08 2,043.45 14-Jul-08 457 14-Jul-08 735.85 14-Jul-08 1,555.55

15-Jul-08 1,977.40 15-Jul-08 427.35 15-Jul-08 710.05 15-Jul-08 1,544.65

16-Jul-08 1,943.50 16-Jul-08 393.4 16-Jul-08 730.95 16-Jul-08 1,547.60

17-Jul-08 2,018.55 17-Jul-08 430.15 16-Jul-08 710 17-Jul-08 1,582.30

18-Jul-08 2,113.20 18-Jul-08 460.95 17-Jul-08 749.45 18-Jul-08 1,547.40

21-Jul-08 2,152.85 21-Jul-08 463.95 18-Jul-08 803.1 21-Jul-08 1,561.30

22-Jul-08 2,152.15 22-Jul-08 453.95 21-Jul-08 798.55 22-Jul-08 1,578.30

23-Jul-08 2,267.30 23-Jul-08 495.5 22-Jul-08 778.2 23-Jul-08 1,602.25

24-Jul-08 2,308.05 24-Jul-08 507.75 23-Jul-08 816.2 24-Jul-08 1,567.30

25-Jul-08 2,147.10 25-Jul-08 489.5 24-Jul-08 799.65 25-Jul-08 1,550.65

28-Jul-08 2,179.90 28-Jul-08 499.45 25-Jul-08 796.85 28-Jul-08 1,539.45

29-Jul-08 2,083.10 29-Jul-08 472 28-Jul-08 795.15 29-Jul-08 1,540.70

30-Jul-08 2,165.50 30-Jul-08 489.65 29-Jul-08 777.9 30-Jul-08 1,602.05

31-Jul-08 2,207.50 31-Jul-08 511.5 30-Jul-08 809.9 31-Jul-08 1,583.45

1-Aug-08 2,297.60 1-Aug-08 520.15 31-Jul-08 798.7 1-Aug-08 1,639.45



4-Aug-08 2,242.40 4-Aug-08 514.7 1-Aug-08 820.15 4-Aug-08 1,658.85

5-Aug-08 2,276.05 5-Aug-08 552.1 4-Aug-08 816 5-Aug-08 1,678.55

6-Aug-08 2,298.60 6-Aug-08 545.1 5-Aug-08 840.1 6-Aug-08 1,699.35

7-Aug-08 2,272.60 7-Aug-08 557 6-Aug-08 869.4 7-Aug-08 1,726.15

8-Aug-08 2,251.80 8-Aug-08 549.75 7-Aug-08 849.35 8-Aug-08 1,679.60

11-Aug-08 2,325.25 11-Aug-08 568.75 8-Aug-08 840.85 11-Aug-08 1,670.40

12-Aug-08 2,347.25 12-Aug-08 567.1 11-Aug-08 845.55 12-Aug-08 1,603.90

13-Aug-08 2,336.85 13-Aug-08 548.25 12-Aug-08 823.25 13-Aug-08 1,625.95

14-Aug-08 2,276.70 14-Aug-08 500 13-Aug-08 820.85 14-Aug-08 1,693.50

18-Aug-08 2,224.80 18-Aug-08 500.15 14-Aug-08 818.6 18-Aug-08 1,704.35

19-Aug-08 2,219.60 19-Aug-08 500.85 18-Aug-08 809.1 19-Aug-08 1,692.75

20-Aug-08 2,246.35 20-Aug-08 510.5 19-Aug-08 791.9 20-Aug-08 1,699.30

21-Aug-08 2,212.65 21-Aug-08 481.75 20-Aug-08 816 21-Aug-08 1,661.45

22-Aug-08 2,244.80 22-Aug-08 484.9 21-Aug-08 799.25 22-Aug-08 1,696.50

25-Aug-08 2,232.00 25-Aug-08 495.2 22-Aug-08 809.7 25-Aug-08 1,706.45

26-Aug-08 2,179.35 26-Aug-08 498.05 25-Aug-08 816.5 26-Aug-08 1,698.00

27-Aug-08 2,148.00 27-Aug-08 478.85 26-Aug-08 808.8 27-Aug-08 1,708.20

28-Aug-08 2,070.85 28-Aug-08 469.5 27-Aug-08 804.85 28-Aug-08 1,699.40

29-Aug-08 2,136.20 29-Aug-08 493.1 28-Aug-08 804.5 29-Aug-08 1,749.10

1-Sep-08 2,141.65 1-Sep-08 494.05 29-Aug-08 837.5 1-Sep-08 1,723.30

2-Sep-08 2,212.75 2-Sep-08 530.2 1-Sep-08 816.2 2-Sep-08 1,775.25

4-Sep-08 2,152.25 4-Sep-08 523.05 2-Sep-08 834.65 4-Sep-08 1,789.00

5-Sep-08 2,080.90 5-Sep-08 494.15 4-Sep-08 825.8 5-Sep-08 1,712.30

8-Sep-08 2,133.20 8-Sep-08 512.35 5-Sep-08 803.4 8-Sep-08 1,750.05

9-Sep-08 2,142.55 9-Sep-08 502.6 8-Sep-08 819.8 9-Sep-08 1,749.45

10-Sep-08 2,082.65 10-Sep-08 501.75 9-Sep-08 836.9 10-Sep-08 1,759.75

11-Sep-08 1,997.40 11-Sep-08 484.95 10-Sep-08 812 11-Sep-08 1,750.65

12-Sep-08 1,932.65 12-Sep-08 466.45 11-Sep-08 776.95 12-Sep-08 1,644.00

15-Sep-08 1,886.95 15-Sep-08 433.15 12-Sep-08 778.85 15-Sep-08 1,578.15



16-Sep-08 1,928.05 16-Sep-08 422.9 15-Sep-08 766.15 16-Sep-08 1,566.40

17-Sep-08 1,876.65 17-Sep-08 409.2 16-Sep-08 774.1 17-Sep-08 1,579.00

18-Sep-08 1,938.25 18-Sep-08 395.9 17-Sep-08 770.15 18-Sep-08 1,525.40

19-Sep-08 2,055.10 19-Sep-08 426.5 18-Sep-08 761.25 19-Sep-08 1,624.95

22-Sep-08 2,039.10 22-Sep-08 421.25 19-Sep-08 805.85 22-Sep-08 1,629.90

23-Sep-08 2,006.45 23-Sep-08 394.7 22-Sep-08 808.8 23-Sep-08 1,543.95

24-Sep-08 2,046.10 24-Sep-08 400.35 23-Sep-08 792.65 24-Sep-08 1,524.30

25-Sep-08 2,025.70 25-Sep-08 389.25 24-Sep-08 810.55 25-Sep-08 1,506.85

26-Sep-08 1,963.20 26-Sep-08 369.65 25-Sep-08 790.9 26-Sep-08 1,446.90

29-Sep-08 1,932.85 29-Sep-08 350.35 26-Sep-08 776 29-Sep-08 1,393.30

30-Sep-08 1,949.35 30-Sep-08 352.65 29-Sep-08 750.25 30-Sep-08 1,398.05

1-Oct-08 1,906.70 1-Oct-08 345.3 30-Sep-08 784.85 1-Oct-08 1,449.30

3-Oct-08 1,761.45 3-Oct-08 336.35 1-Oct-08 790.7 3-Oct-08 1,391.90

6-Oct-08 1,641.60 6-Oct-08 301.45 3-Oct-08 756.3 6-Oct-08 1,318.65

7-Oct-08 1,674.65 7-Oct-08 303.15 6-Oct-08 727.75 7-Oct-08 1,301.80

8-Oct-08 1,648.55 8-Oct-08 308.85 7-Oct-08 748.25 8-Oct-08 1,254.25

10-Oct-08 1,527.60 10-Oct-08 281.9 8-Oct-08 733.35 10-Oct-08 1,225.20

13-Oct-08 1,571.40 13-Oct-08 302.3 10-Oct-08 692.3 13-Oct-08 1,318.55

14-Oct-08 1,621.05 14-Oct-08 311.15 13-Oct-08 739.85 14-Oct-08 1,397.95

15-Oct-08 1,520.20 15-Oct-08 300.8 14-Oct-08 766.6 15-Oct-08 1,335.40

16-Oct-08 1,391.95 16-Oct-08 324.95 15-Oct-08 714.85 16-Oct-08 1,263.00

17-Oct-08 1,306.05 17-Oct-08 291.9 16-Oct-08 730.65 17-Oct-08 1,202.75

20-Oct-08 1,320.90 20-Oct-08 272.65 17-Oct-08 677.15 20-Oct-08 1,294.55

21-Oct-08 1,394.95 21-Oct-08 286.35 20-Oct-08 708.1 21-Oct-08 1,347.60

22-Oct-08 1,316.80 22-Oct-08 271.9 21-Oct-08 724.35 22-Oct-08 1,299.55

23-Oct-08 1,217.65 23-Oct-08 268.05 22-Oct-08 666.25 23-Oct-08 1,283.25

24-Oct-08 1,019.50 24-Oct-08 204.6 23-Oct-08 615.05 24-Oct-08 1,246.10

27-Oct-08 1,077.00 27-Oct-08 198.1 24-Oct-08 537.1 27-Oct-08 1,251.80

28-Oct-08 1,153.00 28-Oct-08 217.85 27-Oct-08 564.6 28-Oct-08 1,279.35



29-Oct-08 1,201.75 29-Oct-08 202.6 28-Oct-08 610.7 29-Oct-08 1,304.35

31-Oct-08 1,375.45 31-Oct-08 220 29-Oct-08 616.45 31-Oct-08 1,388.95

3-Nov-08 1,441.70 3-Nov-08 253.25 31-Oct-08 653.75 3-Nov-08 1,378.60

4-Nov-08 1,451.60 4-Nov-08 289.75 3-Nov-08 691.5 4-Nov-08 1,331.90

5-Nov-08 1,269.05 5-Nov-08 265.65 4-Nov-08 716.95 5-Nov-08 1,322.00

6-Nov-08 1,170.55 6-Nov-08 272.2 5-Nov-08 685.35 6-Nov-08 1,245.70

7-Nov-08 1,220.75 7-Nov-08 280.6 6-Nov-08 639.4 7-Nov-08 1,262.80

10-Nov-08 1,303.10 10-Nov-08 298.9 7-Nov-08 648.05 10-Nov-08 1,338.50

11-Nov-08 1,207.70 11-Nov-08 268.6 10-Nov-08 711.65 11-Nov-08 1,256.70

12-Nov-08 1,162.20 12-Nov-08 244.9 11-Nov-08 659.45 12-Nov-08 1,259.45

14-Nov-08 1,146.75 14-Nov-08 241.45 12-Nov-08 631.95 14-Nov-08 1,213.20

17-Nov-08 1,141.40 17-Nov-08 232.5 14-Nov-08 647.5 17-Nov-08 1,232.40

18-Nov-08 1,139.95 18-Nov-08 224.3 17-Nov-08 664.4 18-Nov-08 1,180.50

19-Nov-08 1,132.45 19-Nov-08 225.45 18-Nov-08 622.9 19-Nov-08 1,172.70

20-Nov-08 1,056.05 20-Nov-08 205.25 19-Nov-08 612.35 20-Nov-08 1,121.85

21-Nov-08 1,124.35 21-Nov-08 198.25 20-Nov-08 592 21-Nov-08 1,184.65

24-Nov-08 1,144.80 24-Nov-08 190.95 21-Nov-08 618.85 24-Nov-08 1,196.20

25-Nov-08 1,071.80 25-Nov-08 188.2 24-Nov-08 637.8 25-Nov-08 1,181.95

26-Nov-08 1,138.90 26-Nov-08 198.5 25-Nov-08 627.8 26-Nov-08 1,187.10

28-Nov-08 1,134.45 28-Nov-08 198.4 26-Nov-08 653 28-Nov-08 1,243.85

1-Dec-08 1,109.40 1-Dec-08 178.7 28-Nov-08 671.05 1-Dec-08 1,231.20

2-Dec-08 1,073.95 2-Dec-08 181.95 1-Dec-08 650.7 2-Dec-08 1,208.35

3-Dec-08 1,069.10 3-Dec-08 191.95 2-Dec-08 670.85 3-Dec-08 1,156.55

4-Dec-08 1,159.10 4-Dec-08 213.45 3-Dec-08 664 4-Dec-08 1,192.40

5-Dec-08 1,117.60 5-Dec-08 203.45 4-Dec-08 685.7 5-Dec-08 1,134.50

8-Dec-08 1,118.55 8-Dec-08 221.55 5-Dec-08 664.8 8-Dec-08 1,157.75

10-Dec-08 1,227.20 10-Dec-08 262.9 8-Dec-08 701.25 10-Dec-08 1,173.75

11-Dec-08 1,259.00 11-Dec-08 255.35 10-Dec-08 735.8 11-Dec-08 1,134.90

12-Dec-08 1,307.10 12-Dec-08 277.15 11-Dec-08 742.4 12-Dec-08 1,104.85



15-Dec-08 1,340.55 15-Dec-08 280.85 12-Dec-08 723.5 15-Dec-08 1,102.30

16-Dec-08 1,388.50 16-Dec-08 276.2 15-Dec-08 737.4 16-Dec-08 1,124.80

17-Dec-08 1,351.40 17-Dec-08 253.5 16-Dec-08 744.8 17-Dec-08 1,141.55

18-Dec-08 1,361.00 18-Dec-08 277.4 17-Dec-08 709.25 18-Dec-08 1,177.05

19-Dec-08 1,351.30 19-Dec-08 307.9 18-Dec-08 710.15 19-Dec-08 1,191.30

22-Dec-08 1,285.55 22-Dec-08 316.55 19-Dec-08 721.7 22-Dec-08 1,186.80

23-Dec-08 1,259.75 23-Dec-08 301.8 22-Dec-08 722.1 23-Dec-08 1,176.05

24-Dec-08 1,242.00 24-Dec-08 294.9 23-Dec-08 710.85 24-Dec-08 1,174.00

26-Dec-08 1,210.15 26-Dec-08 275.45 24-Dec-08 689.4 26-Dec-08 1,109.25

29-Dec-08 1,246.30 29-Dec-08 276.35 26-Dec-08 686.4 29-Dec-08 1,113.75

30-Dec-08 1,250.50 30-Dec-08 285.3 29-Dec-08 712.05 30-Dec-08 1,127.90

31-Dec-08 1,232.75 31-Dec-08 282.15 30-Dec-08 722.6 31-Dec-08 1,115.45

1-Jan-09 1,254.65 1-Jan-09 291.75 31-Dec-08 715.5 1-Jan-09 1,148.15

2-Jan-09 1,286.40 2-Jan-09 300.55 1-Jan-09 719.95 2-Jan-09 1,132.10

5-Jan-09 1,365.85 5-Jan-09 295.95 2-Jan-09 704.9 5-Jan-09 1,172.80

6-Jan-09 1,370.90 6-Jan-09 278.5 5-Jan-09 685.65 6-Jan-09 1,168.55

7-Jan-09 1,200.75 7-Jan-09 233.85 6-Jan-09 657 7-Jan-09 1,187.55

9-Jan-09 1,153.25 9-Jan-09 216.35 7-Jan-09 650 9-Jan-09 1,203.40

12-Jan-09 1,097.90 12-Jan-09 204.75 9-Jan-09 638.9 12-Jan-09 1,159.70

13-Jan-09 1,077.55 13-Jan-09 205.45 12-Jan-09 623.85 13-Jan-09 1,228.15

14-Jan-09 1,179.75 14-Jan-09 212.4 13-Jan-09 607.05 14-Jan-09 1,303.60

15-Jan-09 1,142.35 15-Jan-09 202.2 14-Jan-09 622.75 15-Jan-09 1,251.70

16-Jan-09 1,217.35 16-Jan-09 195.55 15-Jan-09 603.65 16-Jan-09 1,267.40

19-Jan-09 1,229.90 19-Jan-09 195.15 15-Jan-09 600.5 19-Jan-09 1,262.05

20-Jan-09 1,183.65 20-Jan-09 188.7 16-Jan-09 634.75 20-Jan-09 1,251.75

21-Jan-09 1,119.85 21-Jan-09 181.35 19-Jan-09 646.85 21-Jan-09 1,223.85

22-Jan-09 1,136.30 22-Jan-09 164.15 20-Jan-09 616.35 22-Jan-09 1,230.90

23-Jan-09 1,156.15 23-Jan-09 161.3 21-Jan-09 583.05 23-Jan-09 1,204.65

27-Jan-09 1,225.95 27-Jan-09 166.5 22-Jan-09 619.2 27-Jan-09 1,252.10



28-Jan-09 1,274.00 28-Jan-09 177.45 23-Jan-09 613.15 28-Jan-09 1,286.70

29-Jan-09 1,270.10 29-Jan-09 164.05 27-Jan-09 647.4 29-Jan-09 1,310.15

30-Jan-09 1,323.60 30-Jan-09 177.65 28-Jan-09 652.15 30-Jan-09 1,306.65

2-Feb-09 1,280.00 2-Feb-09 153 29-Jan-09 627.4 2-Feb-09 1,279.65

3-Feb-09 1,306.20 3-Feb-09 132.85 30-Jan-09 633.95 3-Feb-09 1,282.50

4-Feb-09 1,307.50 4-Feb-09 139.45 2-Feb-09 615.8 4-Feb-09 1,281.65

5-Feb-09 1,288.80 5-Feb-09 140 3-Feb-09 625 5-Feb-09 1,255.85

6-Feb-09 1,344.85 6-Feb-09 137.95 4-Feb-09 634.3 6-Feb-09 1,288.90

9-Feb-09 1,389.70 9-Feb-09 139.95 5-Feb-09 628.65 9-Feb-09 1,312.10

10-Feb-09 1,401.95 10-Feb-09 152.6 6-Feb-09 647.05 10-Feb-09 1,308.40

12-Feb-09 1,351.55 12-Feb-09 156.6 10-Feb-09 663.55 12-Feb-09 1,254.55

13-Feb-09 1,392.40 13-Feb-09 160.55 11-Feb-09 673.45 13-Feb-09 1,251.65

16-Feb-09 1,320.20 16-Feb-09 156.65 12-Feb-09 650.85 16-Feb-09 1,221.45

17-Feb-09 1,267.30 17-Feb-09 148.25 13-Feb-09 651.75 17-Feb-09 1,173.95

18-Feb-09 1,295.15 18-Feb-09 158.75 16-Feb-09 637.75 18-Feb-09 1,178.80

19-Feb-09 1,293.75 19-Feb-09 156 17-Feb-09 632.65 19-Feb-09 1,208.85

20-Feb-09 1,253.40 20-Feb-09 154.85 18-Feb-09 640.85 20-Feb-09 1,177.15

24-Feb-09 1,253.25 24-Feb-09 158.15 19-Feb-09 648.45 24-Feb-09 1,185.55

25-Feb-09 1,266.55 25-Feb-09 154.8 20-Feb-09 642.7 25-Feb-09 1,217.45

26-Feb-09 1,290.80 26-Feb-09 156.2 24-Feb-09 636.65 26-Feb-09 1,236.00

27-Feb-09 1,266.05 27-Feb-09 152 25-Feb-09 640.75 27-Feb-09 1,231.25

3-Mar-09 1,196.85 3-Mar-09 148.35 27-Feb-09 638.5 3-Mar-09 1,197.60

4-Mar-09 1,211.10 4-Mar-09 147.65 2-Mar-09 616.8 4-Mar-09 1,199.20

5-Mar-09 1,149.80 5-Mar-09 146.85 3-Mar-09 601.15 5-Mar-09 1,181.95

6-Mar-09 1,169.90 6-Mar-09 145.8 4-Mar-09 600.65 6-Mar-09 1,219.35

9-Mar-09 1,153.35 9-Mar-09 138.75 5-Mar-09 589.75 9-Mar-09 1,202.05

12-Mar-09 1,202.00 12-Mar-09 136.65 5-Mar-09 601 12-Mar-09 1,227.80

13-Mar-09 1,284.25 13-Mar-09 152.65 6-Mar-09 602.25 13-Mar-09 1,297.05

16-Mar-09 1,327.60 16-Mar-09 161.95 9-Mar-09 587.75 16-Mar-09 1,287.80



17-Mar-09 1,300.20 17-Mar-09 159 12-Mar-09 548.45 17-Mar-09 1,265.50

18-Mar-09 1,331.40 18-Mar-09 172.3 13-Mar-09 557.65 18-Mar-09 1,278.05

19-Mar-09 1,345.70 19-Mar-09 174 16-Mar-09 571.3 19-Mar-09 1,297.20

20-Mar-09 1,339.20 20-Mar-09 171.5 17-Mar-09 571.55 20-Mar-09 1,296.20

23-Mar-09 1,438.45 23-Mar-09 166.65 18-Mar-09 569.75 23-Mar-09 1,331.30

24-Mar-09 1,452.45 24-Mar-09 166.3 19-Mar-09 570.7 24-Mar-09 1,320.75

25-Mar-09 1,532.20 25-Mar-09 176.65 20-Mar-09 569.4 25-Mar-09 1,338.95

26-Mar-09 1,565.50 26-Mar-09 176.35 23-Mar-09 593.2 26-Mar-09 1,379.15

27-Mar-09 1,548.75 27-Mar-09 182.8 24-Mar-09 603.7 27-Mar-09 1,344.90

30-Mar-09 1,516.45 30-Mar-09 165.5 25-Mar-09 591 30-Mar-09 1,301.30

31-Mar-09 1,524.75 31-Mar-09 167.3 26-Mar-09 621.85 31-Mar-09 1,323.90

27-Mar-09 621.85

30-Mar-09 609.65

31-Mar-09 625.75

Date

Weighted Average Price (Rs.) of PFCL Date

Weighted Average Price (Rs.) of IRFC Date

Weighted Average Price (Rs.) of HDFC

4-Dec-08 106.1302 16-Apr-08 97.9005 2-Apr-08 100.6671

5-Dec-08 105.7138 24-Apr-08 97.6224 3-Apr-08 100.6995

8-Dec-08 108.5793 25-Apr-08 97.6242 17-Apr-08 100.4636

10-Dec-08 109.8788 2-May-08 98.4558 28-Apr-08 100.4503

11-Dec-08 110.2972 8-May-08 98.2629 29-Apr-08 100.5818

12-Dec-08 113.5564 9-May-08 98.2994 30-Apr-08 100.6651

15-Dec-08 113.2589 12-May-08 98.1833 2-May-08 100.7385

16-Dec-08 113.3345 3-Jun-08 97.4791 5-May-08 100.7956

17-Dec-08 115.3004 4-Jun-08 97.3769 7-May-08 100.8008



18-Dec-08 116.324 5-Jun-08 97.3386 13-May-08 100.762

19-Dec-08 116.6233 6-Jun-08 97.3092 27-May-08 100.534

22-Dec-08 115.6992 20-Jun-08 95.4794 5-Jun-08 100.3139

23-Dec-08 115.1241 23-Jun-08 95.4856 9-Jun-08 100.2774

24-Dec-08 115.5771 25-Jun-08 94.5031 10-Jun-08 100.1821

26-Dec-08 115.5641 2-Jul-08 93.7075 13-Jun-08 99.9128

29-Dec-08 115.7616 3-Jul-08 93.8755 16-Jun-08 99.9195

30-Dec-08 116.4699 24-Jul-08 94.0921 18-Jun-08 99.9881

31-Dec-08 116.9221 25-Jul-08 94.2608 19-Jun-08 99.9102

1-Jan-09 116.8284 31-Jul-08 93.9185 20-Jun-08 99.9102

2-Jan-09 116.7426 8-Sep-08 96.4773 24-Jun-08 99.546

5-Jan-09 119.531 9-Sep-08 96.4595 9-Jul-08 98.71

6-Jan-09 119.15 10-Sep-08 96.4816 16-Jul-08 98.3655

7-Jan-09 115.3182 31-Oct-08 91.8076 18-Jul-08 98.36

9-Jan-09 114.1236 28-Nov-08 93.5805 28-Jul-08 98.4496

12-Jan-09 115.6353 5-Dec-08 96.7837 4-Aug-08 98.2534

13-Jan-09 116.2045 8-Dec-08 97.7193 6-Aug-08 98.2577

14-Jan-09 115.7981 10-Dec-08 97.8765 1-Sep-08 98.076

15-Jan-09 116.3177 11-Dec-08 99.7823 3-Oct-08 96.7154

16-Jan-09 116.4797 16-Dec-08 99.9854 7-Oct-08 96.7266

19-Jan-09 115.7576 18-Dec-08 100.6647 14-Nov-08 97.2949

20-Jan-09 115.6321 23-Dec-08 101.0713 3-Dec-08 98.0464

21-Jan-09 114.6265 24-Dec-08 101.0057 4-Dec-08 98.0464

22-Jan-09 114.1985 29-Dec-08 101.132 18-Dec-08 100.0802

23-Jan-09 114.8757 30-Dec-08 101.2493 19-Dec-08 100.2504

27-Jan-09 114.4195 1-Jan-09 101.4469 13-Jan-09 101.4442

28-Jan-09 113.9598 13-Jan-09 100.8325 14-Jan-09 101.5511

29-Jan-09 113.5184 28-Jan-09 100.4136 15-Jan-09 101.7126

30-Jan-09 113.198 30-Jan-09 100.4433 13-Feb-09 101.3687



3-Feb-09 113.1854 10-Feb-09 99.8498 27-Feb-09 101.9291

4-Feb-09 112.5258 27-Feb-09 101.3307 3-Mar-09 101.9135

5-Feb-09 112.6236 2-Mar-09 101.6278 6-Mar-09 101.7805

9-Feb-09 113.5627 4-Mar-09 101.689 18-Mar-09 101.7511

11-Feb-09 112.4814 5-Mar-09 101.8062 19-Mar-09 101.6574

12-Feb-09 112.82 20-Mar-09 101.2521 23-Mar-09 101.7252

13-Feb-09 112.9919 23-Mar-09 101.4268 31-Mar-09 102.1553

17-Feb-09 112.0221 2-Apr-09 102.0395 6-Apr-09 102.5982

18-Feb-09 111.9203 16-Apr-09 104.4128 24-Apr-09 103.5354

19-Feb-09 112.5648 17-Apr-09 105.049 27-Apr-09 103.458

24-Feb-09 112.3776 20-Apr-09 105.049

25-Feb-09 112.0372 24-Apr-09 104.9622

26-Feb-09 112.5568 28-Apr-09 105.0211

27-Feb-09 113.2551

2-Mar-09 113.5717

3-Mar-09 113.7237

6-Mar-09 112.0355

9-Mar-09 113.72

12-Mar-09 109.9913

13-Mar-09 110.0535

16-Mar-09 112.193

17-Mar-09 111.3056

18-Mar-09 110.9029

19-Mar-09 111.2793

20-Mar-09 111.905

23-Mar-09 112.2412

24-Mar-09 112.5665

25-Mar-09 112.3017



26-Mar-09 112.2243

31-Mar-09 112.6018

2-Apr-09 113.9368

6-Apr-09 113.8556

8-Apr-09 115.0941

9-Apr-09 115.0598

13-Apr-09 116.0479

15-Apr-09 116.0628

16-Apr-09 116.6922

17-Apr-09 117.1333

20-Apr-09 117.3871

21-Apr-09 117.9761

22-Apr-09 119.931

23-Apr-09 118.7522

24-Apr-09 118.6424

27-Apr-09 118.4951

28-Apr-09 118.1423

29-Apr-09 118.1216

Date Exchange

Rate of Dollar Date Exchange

Rate of Euro Date Exchange

Rate of Pound

4/1/2008 40.0611 4/1/2008 63.3022 4/1/2008 79.7261

4/2/2008 40.15 4/2/2008 63.0198 4/2/2008 79.5199

4/3/2008 39.9926 4/3/2008 62.4644 4/3/2008 79.2149

4/4/2008 40.0158 4/4/2008 62.5687 4/4/2008 79.5382

4/5/2008 39.9698 4/5/2008 62.8169 4/5/2008 79.7895

4/6/2008 39.9698 4/6/2008 62.9216 4/6/2008 79.6925

4/7/2008 39.955 4/7/2008 62.8988 4/7/2008 79.6639



4/8/2008 39.97 4/8/2008 62.7809 4/8/2008 79.4684

4/9/2008 40.0184 4/9/2008 62.9569 4/9/2008 79.2168

4/10/2008 40.0151 4/10/2008 62.9801 4/10/2008 78.8361

4/11/2008 39.9629 4/11/2008 63.2393 4/11/2008 78.9987

4/12/2008 39.9509 4/12/2008 63.0972 4/12/2008 78.8211

4/13/2008 39.9509 4/13/2008 63.1735 4/13/2008 78.6909

4/14/2008 39.9509 4/14/2008 63.1448 4/14/2008 78.6861

4/15/2008 39.96 4/15/2008 63.0209 4/15/2008 78.9102

4/16/2008 39.9704 4/16/2008 63.236 4/16/2008 78.7334

4/17/2008 39.9674 4/17/2008 63.425 4/17/2008 78.6922

4/18/2008 39.9306 4/18/2008 63.6027 4/18/2008 78.9796

4/19/2008 39.925 4/19/2008 63.2923 4/19/2008 79.5749

4/20/2008 39.925 4/20/2008 63.1685 4/20/2008 79.7881

4/21/2008 39.925 4/21/2008 63.1693 4/21/2008 79.7901

4/22/2008 39.93 4/22/2008 63.3226 4/22/2008 79.513

4/23/2008 39.9558 4/23/2008 63.6532 4/23/2008 79.3474

4/24/2008 40.0198 4/24/2008 63.8384 4/24/2008 79.6222

4/25/2008 40.185 4/25/2008 63.4389 4/25/2008 79.4144

4/26/2008 40.1626 4/26/2008 62.8379 4/26/2008 79.4472

4/27/2008 40.145 4/27/2008 62.7643 4/27/2008 79.7396

4/28/2008 40.145 4/28/2008 62.7527 4/28/2008 79.7404

4/29/2008 40.1699 4/29/2008 62.8193 4/29/2008 79.8036

4/30/2008 40.3823 4/30/2008 63.0308 4/30/2008 80.0374

5/1/2008 40.4968 5/1/2008 63.0547 5/1/2008 79.8535

5/2/2008 40.51 5/2/2008 63.017 5/2/2008 80.3475

5/3/2008 40.665 5/3/2008 62.8331 5/3/2008 80.4342

5/4/2008 40.665 5/4/2008 62.7424 5/4/2008 80.2024

5/5/2008 40.665 5/5/2008 62.742 5/5/2008 80.2011

5/6/2008 40.5968 5/6/2008 62.7919 5/6/2008 80.0834



5/7/2008 40.8724 5/7/2008 63.4343 5/7/2008 80.6318

5/8/2008 41.2755 5/8/2008 63.8275 5/8/2008 81.0055

5/9/2008 41.7216 5/9/2008 64.1043 5/9/2008 81.5427

5/10/2008 41.5908 5/10/2008 64.205 5/10/2008 81.2156

5/11/2008 41.5908 5/11/2008 64.415 5/11/2008 81.2838

5/12/2008 41.5908 5/12/2008 64.4125 5/12/2008 81.283

5/13/2008 41.9668 5/13/2008 64.8936 5/13/2008 82.0114

5/14/2008 42.0853 5/14/2008 65.2604 5/14/2008 82.1084

5/15/2008 42.427 5/15/2008 65.5751 5/15/2008 82.4814

5/16/2008 42.6065 5/16/2008 65.9523 5/16/2008 82.9016

5/17/2008 42.6413 5/17/2008 66.0897 5/17/2008 83.1517

5/18/2008 42.6413 5/18/2008 66.4449 5/18/2008 83.4681

5/19/2008 42.6413 5/19/2008 66.444 5/19/2008 83.4677

5/20/2008 42.6413 5/20/2008 66.3754 5/20/2008 83.3466

5/21/2008 42.6385 5/21/2008 66.479 5/21/2008 83.5267

5/22/2008 42.7858 5/22/2008 67.2101 5/22/2008 84.1648

5/23/2008 43.0374 5/23/2008 67.8209 5/23/2008 85.0474

5/24/2008 42.756 5/24/2008 67.3503 5/24/2008 84.6788

5/25/2008 42.756 5/25/2008 67.4147 5/25/2008 84.6646

5/26/2008 42.756 5/26/2008 67.4142 5/26/2008 84.6654

5/27/2008 42.6917 5/27/2008 67.3166 5/27/2008 84.5649

5/28/2008 42.9379 5/28/2008 67.6633 5/28/2008 84.9604

5/29/2008 42.7785 5/29/2008 67.063 5/29/2008 84.5902

5/30/2008 42.7958 5/30/2008 66.7036 5/30/2008 84.5965

5/31/2008 42.533 5/31/2008 66.0378 5/31/2008 84.0523

6/1/2008 42.533 6/1/2008 66.1766 6/1/2008 84.3339

6/2/2008 42.533 6/2/2008 66.1775 6/2/2008 84.3254

6/3/2008 42.3248 6/3/2008 65.7846 6/3/2008 83.3232

6/4/2008 42.612 6/4/2008 66.1714 6/4/2008 83.7463



6/5/2008 42.7228 6/5/2008 66.0097 6/5/2008 83.679

6/6/2008 42.9022 6/6/2008 66.3203 6/6/2008 83.7823

6/7/2008 42.7086 6/7/2008 66.8953 6/7/2008 83.8197

6/8/2008 42.7086 6/8/2008 67.2016 6/8/2008 84.1268

6/9/2008 42.7086 6/9/2008 67.407 6/9/2008 84.186

6/10/2008 42.8898 6/10/2008 67.5944 6/10/2008 84.6049

6/11/2008 42.944 6/11/2008 66.7894 6/11/2008 84.3204

6/12/2008 42.8786 6/12/2008 66.464 6/12/2008 83.9375

6/13/2008 42.844 6/13/2008 66.2548 6/13/2008 83.7052

6/14/2008 42.9217 6/14/2008 65.9867 6/14/2008 83.5443

6/15/2008 42.9217 6/15/2008 66.0376 6/15/2008 83.6051

6/16/2008 42.9217 6/16/2008 66.0492 6/16/2008 83.6081

6/17/2008 42.9393 6/17/2008 66.2626 6/17/2008 84.0141

6/18/2008 42.9104 6/18/2008 66.5253 6/18/2008 84.1018

6/19/2008 42.897 6/19/2008 66.5093 6/19/2008 83.8671

6/20/2008 42.962 6/20/2008 66.7016 6/20/2008 84.4445

6/21/2008 42.9537 6/21/2008 66.9833 6/21/2008 84.825

6/22/2008 42.9537 6/22/2008 67.0602 6/22/2008 84.8997

6/23/2008 42.9537 6/23/2008 67.0597 6/23/2008 84.8975

6/24/2008 42.9713 6/24/2008 66.8651 6/24/2008 84.5856

6/25/2008 42.9631 6/25/2008 66.8055 6/25/2008 84.5037

6/26/2008 42.7891 6/26/2008 66.6732 6/26/2008 84.3185

6/27/2008 42.7028 6/27/2008 67.0302 6/27/2008 84.5341

6/28/2008 42.8494 6/28/2008 67.4938 6/28/2008 85.2134

6/29/2008 42.8494 6/29/2008 67.6982 6/29/2008 85.503

6/30/2008 42.8494 6/30/2008 67.6969 6/30/2008 85.5026

7/1/2008 43.04 7/1/2008 67.9188 7/1/2008 85.8007

7/2/2008 43.3311 7/2/2008 68.3236 7/2/2008 86.4035

7/3/2008 43.2225 7/3/2008 68.3945 7/3/2008 86.1291



7/4/2008 43.2825 7/4/2008 68.5093 7/4/2008 86.053

7/5/2008 43.1674 7/5/2008 67.7737 7/5/2008 85.6053

7/6/2008 43.1674 7/6/2008 67.8341 7/6/2008 85.5928

7/7/2008 43.1674 7/7/2008 67.8345 7/7/2008 85.5928

7/8/2008 43.2476 7/8/2008 67.762 7/8/2008 85.4256

7/9/2008 43.3061 7/9/2008 67.9793 7/9/2008 85.4741

7/10/2008 43.1687 7/10/2008 67.7623 7/10/2008 85.1821

7/11/2008 43.2 7/11/2008 67.986 7/11/2008 85.4721

7/12/2008 43.2 7/12/2008 68.3567 7/12/2008 85.593

7/13/2008 43.2 7/13/2008 68.8699 7/13/2008 85.9369

7/14/2008 43.2 7/14/2008 68.8725 7/14/2008 85.9395

7/15/2008 42.8957 7/15/2008 68.2011 7/15/2008 85.2886

7/16/2008 42.8957 7/16/2008 68.3731 7/16/2008 85.8715

7/17/2008 42.8957 7/17/2008 68.1732 7/17/2008 85.9131

7/18/2008 42.8957 7/18/2008 67.9733 7/18/2008 85.8243

7/19/2008 42.8341 7/19/2008 67.8857 7/19/2008 85.5402

7/20/2008 42.69 7/20/2008 67.6747 7/20/2008 85.351

7/21/2008 42.69 7/21/2008 67.6739 7/21/2008 85.351

7/22/2008 42.7258 7/22/2008 67.787 7/22/2008 85.2674

7/23/2008 42.7382 7/23/2008 67.9084 7/23/2008 85.493

7/24/2008 42.3095 7/24/2008 66.6505 7/24/2008 84.4247

7/25/2008 42.0889 7/25/2008 65.9928 7/25/2008 83.8128

7/26/2008 42.2112 7/26/2008 66.3 7/26/2008 84.0208

7/27/2008 42.205 7/27/2008 66.3214 7/27/2008 84.0774

7/28/2008 42.205 7/28/2008 66.3226 7/28/2008 84.0774

7/29/2008 42.3752 7/29/2008 66.6383 7/29/2008 84.3325

7/30/2008 42.5858 7/30/2008 66.8568 7/30/2008 84.7287

7/31/2008 42.47 7/31/2008 66.1797 7/31/2008 84.1101

8/1/2008 42.5239 8/1/2008 66.3385 8/1/2008 84.2747



8/2/2008 42.28 8/2/2008 65.7116 8/2/2008 83.4438

8/3/2008 42.45 8/3/2008 66.0879 8/3/2008 83.8642

8/4/2008 42.45 8/4/2008 66.0896 8/4/2008 83.8651

8/5/2008 42.4088 8/5/2008 66.0831 8/5/2008 83.5559

8/6/2008 42.2735 8/6/2008 65.5873 8/6/2008 82.7588

8/7/2008 42.089 8/7/2008 65.0751 8/7/2008 82.2264

8/8/2008 42.0547 8/8/2008 64.8303 8/8/2008 81.9163

8/9/2008 42.2122 8/9/2008 64.0212 8/9/2008 81.4383

8/10/2008 42.18 8/10/2008 63.3156 8/10/2008 81.048

8/11/2008 42.1806 8/11/2008 63.3151 8/11/2008 81.0487

8/12/2008 42.1515 8/12/2008 63.1353 8/12/2008 80.8255

8/13/2008 42.3936 8/13/2008 63.161 8/13/2008 80.7323

8/14/2008 42.6474 8/14/2008 63.6068 8/14/2008 80.4632

8/15/2008 42.9413 8/15/2008 63.9255 8/15/2008 80.2852

8/16/2008 43.2526 8/16/2008 63.7596 8/16/2008 80.5922

8/17/2008 43.38 8/17/2008 63.73 8/17/2008 80.9631

8/18/2008 43.38 8/18/2008 63.7313 8/18/2008 80.9662

8/19/2008 43.3873 8/19/2008 63.8688 8/19/2008 81.0107

8/20/2008 43.684 8/20/2008 64.2037 8/20/2008 81.3663

8/21/2008 43.7931 8/21/2008 64.5878 8/21/2008 81.5795

8/22/2008 43.6431 8/22/2008 64.6023 8/22/2008 81.5084

8/23/2008 43.4617 8/23/2008 64.5358 8/23/2008 81.1091

8/24/2008 43.34 8/24/2008 64.1029 8/24/2008 80.353

8/25/2008 43.465 8/25/2008 64.3182 8/25/2008 80.5576

8/26/2008 43.6472 8/26/2008 64.4202 8/26/2008 80.7115

8/27/2008 43.9423 8/27/2008 64.4792 8/27/2008 80.9773

8/28/2008 43.8583 8/28/2008 64.4827 8/28/2008 80.7515

8/29/2008 43.8441 8/29/2008 64.6745 8/29/2008 80.4268

8/30/2008 43.9187 8/30/2008 64.6289 8/30/2008 80.2772



8/31/2008 44.095 8/31/2008 64.7248 8/31/2008 80.319

9/1/2008 44.095 9/1/2008 64.7297 9/1/2008 80.3111

9/2/2008 44.1851 9/2/2008 64.6874 9/2/2008 79.762

9/3/2008 44.3856 9/3/2008 64.5509 9/3/2008 79.3673

9/4/2008 44.5723 9/4/2008 64.4926 9/4/2008 79.2046

9/5/2008 44.5075 9/5/2008 64.3765 9/5/2008 79.0595

9/6/2008 44.655 9/6/2008 63.7173 9/6/2008 78.7009

9/7/2008 44.7 9/7/2008 63.7949 9/7/2008 78.963

9/8/2008 44.7003 9/8/2008 63.8074 9/8/2008 78.9805

9/9/2008 44.6106 9/9/2008 63.6973 9/9/2008 79.1241

9/10/2008 44.865 9/10/2008 63.4086 9/10/2008 78.966

9/11/2008 45.1367 9/11/2008 63.6915 9/11/2008 79.4496

9/12/2008 45.578 9/12/2008 63.5767 9/12/2008 79.8303

9/13/2008 45.7102 9/13/2008 64.3385 9/13/2008 80.8806

9/14/2008 45.7291 9/14/2008 65.0871 9/14/2008 82.0658

9/15/2008 45.73 9/15/2008 65.1012 9/15/2008 82.0716

9/16/2008 45.887 9/16/2008 65.5152 9/16/2008 82.465

9/17/2008 46.5038 9/17/2008 66.1084 9/17/2008 83.2622

9/18/2008 46.5564 9/18/2008 66.0896 9/18/2008 83.3531

9/19/2008 46.6639 9/19/2008 67.0938 9/19/2008 84.89

9/20/2008 46.6639 9/20/2008 66.7915 9/20/2008 84.7171

9/21/2008 45.37 9/21/2008 65.659 9/21/2008 83.1206

9/22/2008 45.3713 9/22/2008 65.6659 9/22/2008 83.1257

9/23/2008 45.3919 9/23/2008 66.1877 9/23/2008 83.5451

9/24/2008 45.8024 9/24/2008 67.5846 9/24/2008 84.9937

9/25/2008 46.2718 9/25/2008 67.9081 9/25/2008 85.8069

9/26/2008 46.6197 9/26/2008 68.4107 9/26/2008 86.3127

9/27/2008 46.54 9/27/2008 68.021 9/27/2008 85.6428

9/28/2008 47.095 9/28/2008 68.8392 9/28/2008 86.8874



9/29/2008 47.095 9/29/2008 68.8402 9/29/2008 86.8874

9/30/2008 47.3476 9/30/2008 68.4112 9/30/2008 86.0519

10/1/2008 47.9547 10/1/2008 68.5489 10/1/2008 86.2701

10/2/2008 47.3634 10/2/2008 66.7422 10/2/2008 84.2823

10/3/2008 47.3678 10/3/2008 65.908 10/3/2008 83.6846

10/4/2008 47.6787 10/4/2008 65.9349 10/4/2008 84.357

10/5/2008 46.9992 10/5/2008 64.7659 10/5/2008 83.2953

10/6/2008 47.0107 10/6/2008 64.7436 10/6/2008 83.2898

10/7/2008 47.9792 10/7/2008 65.2109 10/7/2008 84.2553

10/8/2008 48.4806 10/8/2008 65.8085 10/8/2008 84.7857

10/9/2008 48.9225 10/9/2008 66.6931 10/9/2008 85.381

10/10/2008 49.0448 10/10/2008 67.0413 10/10/2008 84.7038

10/11/2008 49.0448 10/11/2008 66.4082 10/11/2008 83.3659

10/12/2008 50.63 10/12/2008 67.8817 10/12/2008 86.349

10/13/2008 50.63 10/13/2008 67.9338 10/13/2008 86.3778

10/14/2008 49.8905 10/14/2008 67.7543 10/14/2008 85.8361

10/15/2008 49.156 10/15/2008 67.1712 10/15/2008 85.9832

10/16/2008 49.9261 10/16/2008 67.8346 10/16/2008 87.0936

10/17/2008 50.1418 10/17/2008 67.4362 10/17/2008 86.4946

10/18/2008 49.878 10/18/2008 67.1228 10/18/2008 86.3762

10/19/2008 50.3544 10/19/2008 67.5675 10/19/2008 87.102

10/20/2008 50.355 10/20/2008 67.5724 10/20/2008 87.1091

10/21/2008 50.303 10/21/2008 67.4966 10/21/2008 87.1058

10/22/2008 50.4755 10/22/2008 66.8694 10/22/2008 86.1444

10/23/2008 51.2318 10/23/2008 66.1818 10/23/2008 84.1237

10/24/2008 52.1082 10/24/2008 66.8047 10/24/2008 84.4908

10/25/2008 52.1082 10/25/2008 65.9489 10/25/2008 82.2297

10/26/2008 52.1082 10/26/2008 66.1926 10/26/2008 82.9299

10/27/2008 53.7639 10/27/2008 67.8963 10/27/2008 85.5701



10/28/2008 53.7322 10/28/2008 67.2614 10/28/2008 83.8814

10/29/2008 53.3624 10/29/2008 66.6534 10/29/2008 83.3084

10/30/2008 53.0901 10/30/2008 67.8778 10/30/2008 85.5318

10/31/2008 52.3572 10/31/2008 68.3528 10/31/2008 86.2835

11/1/2008 52.3572 11/1/2008 66.7114 11/1/2008 84.7189

11/2/2008 50.7156 11/2/2008 64.5721 11/2/2008 81.5907

11/3/2008 50.715 11/3/2008 64.5856 11/3/2008 81.602

11/4/2008 50.1156 11/4/2008 64.0973 11/4/2008 80.7833

11/5/2008 49.0971 11/5/2008 62.4922 11/5/2008 77.761

11/6/2008 48.0973 11/6/2008 62.223 11/6/2008 76.7089

11/7/2008 48.6559 11/7/2008 62.5554 11/7/2008 77.2115

11/8/2008 48.813 11/8/2008 62.2409 11/8/2008 76.6246

11/9/2008 48.9943 11/9/2008 62.336 11/9/2008 76.6894

11/10/2008 49.005 11/10/2008 62.3633 11/10/2008 76.7276

11/11/2008 48.4696 11/11/2008 62.2471 11/11/2008 76.4007

11/12/2008 48.5775 11/12/2008 61.6939 11/12/2008 75.6692

11/13/2008 49.7131 11/13/2008 62.3721 11/13/2008 76.0601

11/14/2008 50.4523 11/14/2008 63.0447 11/14/2008 75.0413

11/15/2008 50.2804 11/15/2008 63.9994 11/15/2008 74.5331

11/16/2008 49.876 11/16/2008 62.9271 11/16/2008 73.5916

11/17/2008 49.88 11/17/2008 62.8842 11/17/2008 73.5481

11/18/2008 49.9824 11/18/2008 63.0683 11/18/2008 74.1618

11/19/2008 49.9824 11/19/2008 63.1307 11/19/2008 74.9631

11/20/2008 50.7945 11/20/2008 64.1464 11/20/2008 76.2268

11/21/2008 51.4512 11/21/2008 64.4108 11/21/2008 76.6598

11/22/2008 51.2877 11/22/2008 64.2116 11/22/2008 76.1114

11/23/2008 51.2212 11/23/2008 64.4896 11/23/2008 76.4508

11/24/2008 51.23 11/24/2008 64.5119 11/24/2008 76.4874

11/25/2008 50.8706 11/25/2008 64.5573 11/25/2008 76.2026



11/26/2008 50.5224 11/26/2008 65.2351 11/26/2008 76.7047

11/27/2008 50.0581 11/27/2008 64.9318 11/27/2008 76.9187

11/28/2008 50.3776 11/28/2008 65.0148 11/28/2008 77.5417

11/29/2008 50.4807 11/29/2008 64.8051 11/29/2008 77.661

11/30/2008 51.0888 11/30/2008 64.8659 11/30/2008 78.5603

12/1/2008 51.105 12/1/2008 64.8916 12/1/2008 78.576

12/2/2008 50.8859 12/2/2008 64.4373 12/2/2008 77.167

12/3/2008 50.9114 12/3/2008 64.4126 12/3/2008 75.8854

12/4/2008 50.3924 12/4/2008 63.887 12/4/2008 74.7178

12/5/2008 50.1842 12/5/2008 63.7009 12/5/2008 73.801

12/6/2008 49.9567 12/6/2008 63.6104 12/6/2008 73.2436

12/7/2008 50.1627 12/7/2008 63.8215 12/7/2008 73.7632

12/8/2008 50.3633 12/8/2008 64.0833 12/8/2008 74.0512

12/9/2008 50.3355 12/9/2008 64.5845 12/9/2008 74.6033

12/10/2008 50.7878 12/10/2008 65.4746 12/10/2008 75.266

12/11/2008 50.3189 12/11/2008 65.2103 12/11/2008 74.4373

12/12/2008 49.7178 12/12/2008 65.3406 12/12/2008 74.1108

12/13/2008 48.4496 12/13/2008 64.6417 12/13/2008 72.4101

12/14/2008 48.2393 12/14/2008 64.5929 12/14/2008 71.7804

12/15/2008 48.4496 12/15/2008 64.8589 12/15/2008 72.2708

12/16/2008 49.5213 12/16/2008 66.8651 12/16/2008 74.6637

12/17/2008 49.3497 12/17/2008 67.7191 12/17/2008 75.5203

12/18/2008 48.9631 12/18/2008 69.2299 12/18/2008 76.0427

12/19/2008 48.4778 12/19/2008 69.9967 12/19/2008 74.6757

12/20/2008 48.5052 12/20/2008 68.4927 12/20/2008 72.8853

12/21/2008 48.7186 12/21/2008 67.8008 12/21/2008 72.7657

12/22/2008 48.725 12/22/2008 67.8145 12/22/2008 72.7986

12/23/2008 49.1347 12/23/2008 68.7045 12/23/2008 73.1252

12/24/2008 50.0344 12/24/2008 69.927 12/24/2008 74.0949



12/25/2008 50.3209 12/25/2008 70.3154 12/25/2008 74.2228

12/26/2008 50.4475 12/26/2008 70.7053 12/26/2008 74.3783

12/27/2008 49.4729 12/27/2008 69.5193 12/27/2008 72.9309

12/28/2008 49.205 12/28/2008 69.0686 12/28/2008 71.7281

12/29/2008 49.205 12/29/2008 69.0681 12/29/2008 71.7242

12/30/2008 49.6782 12/30/2008 70.4919 12/30/2008 72.8049

12/31/2008 49.7178 12/31/2008 70.0891 12/31/2008 71.9874

1/1/2009 49.9002 1/1/2009 70.0738 1/1/2009 72.3597

1/2/2009 50.095 1/2/2009 70.0238 1/2/2009 73.2975

1/3/2009 49.8918 1/3/2009 69.4753 1/3/2009 72.7512

1/4/2009 49.655 1/4/2009 69.1426 1/4/2009 72.2793

1/5/2009 49.655 1/5/2009 69.1337 1/5/2009 72.2714

1/6/2009 49.52 1/6/2009 68.1183 1/6/2009 72.0189

1/7/2009 49.6709 1/7/2009 67.0423 1/7/2009 72.9775

1/8/2009 49.7595 1/8/2009 67.5664 1/8/2009 74.5766

1/9/2009 50.255 1/9/2009 68.5569 1/9/2009 76.0299

1/10/2009 49.7903 1/10/2009 67.8279 1/10/2009 75.7381

1/11/2009 49.555 1/11/2009 66.7982 1/11/2009 75.168

1/12/2009 49.5555 1/12/2009 66.7999 1/12/2009 75.1574

1/13/2009 49.7973 1/13/2009 66.7338 1/13/2009 74.6775

1/14/2009 50.0963 1/14/2009 66.5143 1/14/2009 73.5013

1/15/2009 49.9717 1/15/2009 66.0296 1/15/2009 72.7938

1/16/2009 50.0063 1/16/2009 65.7747 1/16/2009 73.0401

1/17/2009 49.5689 1/17/2009 65.5852 1/17/2009 73.3467

1/18/2009 49.505 1/18/2009 65.707 1/18/2009 72.959

1/19/2009 49.505 1/19/2009 65.7436 1/19/2009 73.007

1/20/2009 49.4202 1/20/2009 65.5435 1/20/2009 72.6531

1/21/2009 49.8541 1/21/2009 64.7121 1/21/2009 70.4174

1/22/2009 49.9315 1/22/2009 64.5005 1/22/2009 69.1342



1/23/2009 49.6635 1/23/2009 64.5645 1/23/2009 68.8853

1/24/2009 49.7772 1/24/2009 64.2729 1/24/2009 68.3651

1/25/2009 49.685 1/25/2009 64.5552 1/25/2009 68.6249

1/26/2009 49.685 1/26/2009 64.5557 1/26/2009 68.6205

1/27/2009 49.7264 1/27/2009 64.6254 1/27/2009 68.4494

1/28/2009 49.5385 1/28/2009 65.4037 1/28/2009 69.7785

1/29/2009 49.3836 1/29/2009 65.3606 1/29/2009 70.3918

1/30/2009 49.4441 1/30/2009 64.7066 1/30/2009 70.3654

1/31/2009 49.432 1/31/2009 63.6358 1/31/2009 70.7234

2/1/2009 49.7295 2/1/2009 63.7383 2/1/2009 72.3276

2/2/2009 49.73 2/2/2009 63.728 2/2/2009 72.3084

2/3/2009 49.5849 2/3/2009 63.3214 2/3/2009 70.8905

2/4/2009 49.2849 2/4/2009 63.5115 2/4/2009 70.3429

2/5/2009 48.9808 2/5/2009 63.4017 2/5/2009 70.6945

2/6/2009 49.1162 2/6/2009 63.0588 2/6/2009 71.3187

2/7/2009 48.9725 2/7/2009 62.8082 2/7/2009 71.8975

2/8/2009 49.28 2/8/2009 63.793 2/8/2009 72.8999

2/9/2009 49.28 2/9/2009 63.7969 2/9/2009 72.895

2/10/2009 48.974 2/10/2009 63.5438 2/10/2009 72.6936

2/11/2009 49.04 2/11/2009 63.392 2/11/2009 72.4468

2/12/2009 49.0957 2/12/2009 63.3851 2/12/2009 70.8928

2/13/2009 49.0802 2/13/2009 63.122 2/13/2009 70.1537

2/14/2009 49.0117 2/14/2009 63.18 2/14/2009 70.5725

2/15/2009 49.255 2/15/2009 63.3794 2/15/2009 70.7376

2/16/2009 49.255 2/16/2009 63.3626 2/16/2009 70.6726

2/17/2009 49.0957 2/17/2009 62.7164 2/17/2009 69.9349

2/18/2009 49.7212 2/18/2009 62.9117 2/18/2009 70.7891

2/19/2009 50.2348 2/19/2009 63.2145 2/19/2009 71.4766

2/20/2009 50.1322 2/20/2009 63.328 2/20/2009 71.7407



2/21/2009 50.1789 2/21/2009 63.5014 2/21/2009 71.7067

2/22/2009 50.685 2/22/2009 65.038 2/22/2009 73.178

2/23/2009 50.685 2/23/2009 65.0136 2/23/2009 73.1547

2/24/2009 50.1541 2/24/2009 64.3603 2/24/2009 72.7355

2/25/2009 50.167 2/25/2009 63.9674 2/25/2009 72.7506

2/26/2009 50.1797 2/26/2009 64.2953 2/26/2009 72.4259

3/1/2009 51.975 3/1/2009 65.8752 3/1/2009 74.4246

3/2/2009 51.975 3/2/2009 65.8643 3/2/2009 74.4173

3/3/2009 52.1604 3/3/2009 65.6814 3/3/2009 73.8868

3/5/2009 51.93 3/5/2009 65.1415 3/5/2009 73.0935

3/6/2009 51.8575 3/6/2009 65.2669 3/6/2009 73.3437

3/7/2009 51.6796 3/7/2009 65.2873 3/7/2009 73.2698

3/8/2009 52.325 3/8/2009 66.2382 3/8/2009 73.7652

3/9/2009 52.325 3/9/2009 66.2403 3/9/2009 73.7662

3/10/2009 52.3981 3/10/2009 66.2679 3/10/2009 73.2971

3/11/2009 51.8655 3/11/2009 65.7996 3/11/2009 71.6625

3/12/2009 52.3691 3/12/2009 66.6088 3/12/2009 72.1054

3/13/2009 52.7869 3/13/2009 67.6384 3/13/2009 73.0512

3/14/2009 51.5464 3/14/2009 66.5402 3/14/2009 71.967

3/15/2009 52.9405 3/15/2009 68.4743 3/15/2009 74.1538

3/16/2009 52.94 3/16/2009 68.4705 3/16/2009 74.1578

3/17/2009 52.5265 3/17/2009 68.0401 3/17/2009 73.89

3/18/2009 52.473 3/18/2009 68.1457 3/18/2009 73.7734

3/19/2009 52.4997 3/19/2009 68.6748 3/19/2009 73.5961

3/20/2009 51.8076 3/20/2009 70.1532 3/20/2009 74.3621

3/21/2009 51.5785 3/21/2009 70.2886 3/21/2009 74.6831

3/22/2009 52.195 3/22/2009 70.9132 3/22/2009 75.5215

3/23/2009 52.195 3/23/2009 70.9147 3/23/2009 75.5199

3/24/2009 51.8337 3/24/2009 70.6613 3/24/2009 75.3118



3/25/2009 51.6914 3/25/2009 70.277 3/25/2009 75.8498

3/26/2009 51.8867 3/26/2009 70.0418 3/26/2009 75.932

3/27/2009 51.6635 3/27/2009 70.1275 3/27/2009 75.2008

3/28/2009 51.6458 3/28/2009 69.4847 3/28/2009 74.3642

3/29/2009 51.72 3/29/2009 68.7602 3/29/2009 74.0899

3/30/2009 51.72 3/30/2009 68.7509 3/30/2009 74.0558

3/31/2009 52.1743 3/31/2009 68.9097 3/31/2009 74.1579

gunjan shikha

Documents

gunjan shikha reg

financial service firms

monte carlo simulation

monte carlo simulations

perfect correlation leads

basic market rates

research work embodied

reliance industries limited