# Value At Risk And Other Risk Measurement Techniques Finance Essay

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Value at Risk (VaR) methods , which are Historical simulation, Monte Carlo simulation and Parametric method (aka, variance-covariance VaR), are widely used to measure and determine the risk position of firms or portfolio in the field of investment management. Furthermore, Stress testing stress tests is an exercise in order to shows the probable losses or profits of the portfolio and has been growing its important and the area of usage.

This study develops two historical stress test scenarios of crisis to create an integrated market risk modelling and analyses the effects of Brazilian crisis and Terrorist Attack in USA, September 11th on the degree of risk of created portfolio by using variance-covariance VaR and Historical Simulation. Moreover, Portfolio is comprise of five widespread DJIA ( the Dow Jones Industrial Average, USA ) stocks.

## Introduction

The risk measurement techniques which means magnitude of the risk management has been ascending rapidly in financial institutions ,particularly the investment department of commercial banks since the 1990s. The bankruptcy of Barings Banks in 1995 and massive amount of assets losses in banks (for instance, the catastrophe of the Sumitomo Corporation and Allied Irish Banks ) stressed the significance of the risk management to authorises, managers and all manner of bank clients. The Financial institutions particularly investment banks and the investment section of commercial banks constitute the risk management unit to measure and manage risk. Furthermore, risk management simultaneously provides to scrutinise the fundamental concept of portfolio's loss and earning , and raise returns on banks' assets without managing risk. Then, all sorts of financial institutions accepted to necessity and importance of risk management as a part of their organisation, measurement tools and techniques has growing expeditiously. One of the major and the crucial tools is Value at Risk (VaR), which measures the degree of risk exposure on financial institutions and portfolios.

Basically, the VaR measures the risk of portfolio or market with the ways of quantitative in order to determine loses or profits of the specific portfolios in a specific time period . The VaR is discovered by JP Morgan and it is employed by Basel Committee in setting assets needs for financial institutions. With globalisation, the countries have interacted each other . Risk or volatility of market, which appeared in a country, rapidly and acrimoniously affects other country, as a matter of fact it has caused large scale financial crisis . Therefore, employing the VaR measure have increased rapidly and the importance of its penetrability have came into prominence since its existed. Research by Choudhry (2006)suggest that the basis of statistical methods due to based on quantitative makes VaR sophisticated . On this basis it may be inferred that The VaR might seem to be an inscrutable puzzle for public or non academic people. However, it has became more comprehensible concept from public in course of time.

Value at Risk has a number of limitations which are unnecessary reliance on history and to focus on systemic risk. Whilst the VaR has demonstrated themselves to be effective and functional risk measurement method, Financial crises and the triggers of economic rigour which have arose last decade all over the world point out the VaR's limitations. The stress test is the free response to these problems for financial institutions. Thus, firms have needed the stress tests as a complement the outcomes of VaR analysis. Aragones and Blanco (1999) has drawn attention to the fact that the stress tests evaluate the losses which appear under improbable but reasonable conditions or scenarios, and the significance of stress tests has been escalating since last decade and financial crisis such as the Asia and Latin America Crisis, 2002. Therefore, a lot of financial institutions and risk managers recently behold the stress tests as well as the methods of VaR for determining firms' specific risk.

Whilst the VaR methods deal with market risk ( systemic risk ) and neglects firms' risk ( unsystematic risk ) , Stress tests do not leave out the existence of firm's risks. Moreover, the VaR models exclusively concentrate on the usual market hazards rather than the uncertain circumstances in related to extraordinary or uncommon events. In a article by Jorion ( 1999 ), the extreme scenarios for financial markets qualified by great volatility ranks and he defined this case as Event Risk. Given this evidence, it can be seen that strategic planning, hedging and other major assessments ,which are determined by financial institutions, are provided substantial information such as knowledge of market, firm's position in the market by Event Risk. Therefore, stress tests provides risk managers to take effective and fruitful decisions. Many influential people point out the significance of stress testing such as William J. McDonough (Dominguez and Alfonso, 2004 , p. 62) , the Chief Executive Officer of the Federal Reserve Bank of New York,

"One of the most important functions of Stress-testing is to identify hidden vulnerabilities, often the result of hidden assumptions, and make clear to trading managers and senior management the consequences of being wrong in their assumptions".

However, stress tests also have a number of issues that connected with reliance and interpretation of stress tests. Aragones, Blanco and Dowd (2001) rightly point out that there was the associated issue that managers and authorises often didn't identify whether to rely on their stress test outcomes. In the other word, risk managers suspect and misinterpret the results of stress tests. Risk managers encountered the same problem while they evaluated the value at risk outcomes. Many researches by Aragones, Blanco and Dowd (2001), Huang, Zhou and Zhu (2009), Akkaya et all ( 2008), Kupiec (1998) suggest that the key solution to this problem is to incorporate stress testing into fair risk modelling by allocating likelihoods to each stress test's scenarios, so that the results of risk modelling include both the estimations the value at risk and the results of stress testing. The indications are therefore that formal risk modelling which integrates the stress tests and the value at risk can provide risk managers to better and clearer interpretations and taking a truer decisions.

The aim of this paper is to assess the response of the value at risk methods to the stress tests based on scenarios. Thus, risk modelling will determine the market risk, firm's risk and portfolio risk and will provide decision makers to comprehensive information with incorporating the stress tests into model.

## Theoretical Framework

## Value at Risk

Whilst the value at risk as a term was not extensively used beginning of the 1990's, essentially the origins of this method is base before the 1990's. The value at risk is the part of the portfolio theory produced by Harry Markowitz. His effort is devised the optimal portfolios to investors by diversifying portfolio . One of the main concern of portfolio theory, which is the measurement of the market risk and the impacts of co movements, constitute core of the computation of Value at risk. As specified in introduction, Value at Risk has proved its importance after experienced financial crisis and it has rapidly became the leader risk management tool.

Value at risk developed by JP Morgan is a risk measurement tool and to estimate the losses in a certain time horizon by setting confidence intervals . In other words , Choudry (2006, p. 30) defined VaR as follows :

"VaR is a measure of 'market risk'. It is the maximum loss which can occur with X% confidence over a holding period of t days."

Damadoran (no date, p. 1) basically exemplifies VaR to understand the concept of it better as follows :

"... if the VaR on an asset is $ 100 million at a one-week, 95% confidence level, there is a only a 5% chance that the value of the asset will drop more than $ 100 million over any given week."

According to example and definition, there are 4 steps to compute Value at Risk :

Decide the time period (horizon) to predict probable losses - Time horizons are determined and specified by decision maker. Generally ,the time horizons are from 1 day to 1 year.

Select the confidence point to apply to the estimation of VaR - Typically, the convenient confidence intervals have been chosen as fitting for purposes or requirements ( i.e., 99% or 95% confidence interval).

Produce a likelihood distribution of probable profits for the assets or portfolio - if we distribute prospective returns as a historical, it seems to be the curve related to the normal distribution.

Last step is that compute Value at Risk

Basically, VaR is based on quantitative methods and included statistical calculations. For computing VaR, there are 3 different methodologies, which are Variance - Covariance -also known as parametric method- , Historical Simulation and Monte Carlo Simulation -also known as un parametric method-. Each method differently compute the values of VaR by using complex statistical methods and applications. Apart from this, The weaker point of the calculations of the VaR is that the results don't show the worst case. In section of methodology, this paper broadly presents and discusses the methods of them. Suppose to state is that the complex methods of VaR might intimidate non academic people, but the benefits of VaR is greater than the costs of it. Therefore, non academic people and regulators have paid more attention and effort to understand the estimations of VaR.

VaR is not only a risk management tools. Besides this, it uses to determine the allocation of sources in firm and to measure the performance of firms. Moreover, the methods of Var estimate the total impacts of ' market risks ' such as stock prices, interest rates, exchange rates, inflation rates. Thus, VaR express to estimate comprehensively the total effects of market risks on the assets or portfolio in a certain confidence interval and time period. However, there is a great limitation for risk assessment models. VaR neglects the risk position of financial institution in the market. In other words, VaR is lower importance given to firms' specific risks than market risks. If we expect comprehensive and perfect market risk modelling , we need to incorporate the complementary methods of VaR instead of using only Value at risk in market risk modelling. Question is that How can we integrate Firms' specific risk which is the limitation of the VaR method into market risk modelling? The answer is Stress Testing which estimates the firms' specific risk (un systematic risk).

## Stress Testing

Basically, stress tests is an exercise in order to manifesting probable losses or profits which is anticipated in the light of the creation of scenarios. There are three different ways to create the Stress test exercise. Dowd ( 1998) has expressed three main approaches:

Historical Scenarios of Crisis: This type of scenarios are created by taking account previous period disasters and crises. Well known examples in related to this approach are the attack of 9/11, the Asia crisis of 1997, the 1987 US market stock crisis, the Argentina (aka The Latin America Crises) Crisis of 2001, the Russian crisis and most recently the Sub Prime crisis of 2007 and its outcomes.

Stylized Scenarios: this approach which is useful in practice is constituted by using impacts of some market parameters or variables in order to simulating effects of these variables on the portfolio. These parameters are risk factors, that affect the portfolio, such as the indexes of stock prices , interest rates, exchange rates, the rates of gross domestic product. As the Derivates Policy Groups (1995) implies:

Stock index shifts of Y%

Currency changes of X%

Yield curve shifts in plus or minus Z basis points

Volatility changes of Q%

Hypothetical Events( aka Mechanical Search ) : In the case of changes in certain risk factor or the outcomes of definite hypothetical circumstances, these scenarios evaluate the losses or profits on the portfolio under these risk factors. The examples of particular hypothetical circumstances and risk factors are an internal war , an earthquake, a flood and a country ruptures relationships with other countries or neighbour countries.

## Figure 1

## Types of Scenario Analysis

As above mentioned, there are different sorts of stress tests intended for different goals. However , stress tests have a number of limitations. The most important issue of the stress test exercises is that the outcomes of tests depend on risk managers or decision makers selected or created scenarios. This means stress tests are unavoidably subjective. To create inconvenient scenarios to purpose is avoided to obtain the expected utility of stress tests. As a consequence, subjectivity increases the subjectivity of the stress tests' results.

Another problem in related to stress tests is the interpretation the tests 's outcomes. The existence of incomplete information whilst to create scenarios for stress tests is led to misinterpret the outcomes of tests by regulators. Suppose for example that Aragones, Blanco and Dowd (2001) exemplifies that our firms will go bankrupt according to a specific scenario. We can't act on this information. Because we don't have enough information whether our firms will fail. For this reason, acting on this information cause us to end up awful results. As Berkowitz ( 1999) suggests the solution to this limitation is that the probability theory should be incorporated into the risk modelling constitute by using stress test. Thus, it manifest the probabilities of scenarios of stress test to evaluate concretely the results.

There is an another limitation is that stress tests can difficulty apply back testing which is . It is the view of Schachter (1998) that back testing can't apply to stress tests because of the scenarios can't be approved based on actual market events. However back testing procedures easily apply to the value at risk methods due to it is based on statistical data which means quantitative. But the work of Aragones and Blanco (1999) asserts that back testing is not good approach to discriminate which one is good or bad VaR method or the scenario of stress tests. Apart from this, according to Kupeic (1998) the methodology of stress-testing exercises is the stage of beginning, that is to say infancy and approaches prone the questioning.

According to literature review and above mentioned problems motivate that how we can combine a stochastic risk predicts such as the Value at Risk with the damage estimates created by stress testing? Researchers (Aragones, Blanco and Dowd (2001), Kupeic (1999)) have tried to find a answer , but they couldn't find it. Nevertheless they think that the best solution to this problem is to work with these estimates independently from one to the other and these two sets of estimates is used to narrow the gaps of each other. In other words, the one of these methods check for the other methods' probable losses which are unnoticed and underrated. In this sense, stress testing and Value at Risk are supplementary of each other. Suppose to recall again that stress testing concentrates on un systemic risk ( Firms' risk exposure) whilst the Value at Risk focuses on more systemic risk ( Market risk ) rather than un systemic risk. The risk modelling produced by both stress testing and value at risk provides the integrated risk estimation.

## Combining or integrating Stress Test exercises with Market Risk Modelling

Integrating Stress tests in to risk modelling which means to unite the Value at risk estimates and stress tests is possible If we can add probabilities to scenarios , which produced for a portfolio or a financial institute, in considering the circumstances. Before all else, scenarios as depending the structure of probabilities are produced, then these scenarios is determined with respect to occurring the probabilities of them. At this stage, it is very significance to assign accurate probabilities to scenarios.

Aragones, Blanco and Dowd (2001) decently elucidates this process which is to assign possibilities to stress tests. We have z unit scenarios. The probability of r scenarios will be ß. After that we can assume our returns that originate in combined distribution which will be Æ‘stress,1 (.) and Æ‘stress,2 (.) with probabilities ß1 and ß2 respectively, and Æ‘(.) with probability 1 - Æ‘stress,1 (.) is the probability of r scenario, and Æ‘(.) is the probability of none scenario occurring.

## Methodology

Demonstrating the utility of this market risk modelling which is the integrated stress tests- VaR , this paper will calculate VaR to a common stocks portfolio, and then will evaluate computed the same parameters with respect to scenarios. To reach more productive results, this paper will explain and discuss the VaR's methodologies. But firstly we will generate scenarios after creating portfolio and will determine time horizon according to scenarios. Next stage is that the approved methodologies will calculate the VaR of created portfolio.

## Scenarios

Above mentioned, first step is to generate stress testing exercise in order to create an integrated risk modelling. whilst we generated two scenarios , we take into account stress test approaches. Under consideration of experienced Global Financial crisis(2008), the historical scenarios of crises is well matched in terms of being more realistic associated with situations which affects present day world. Therefore , two scenarios are built up within the framework of this paper' purposes and the historical scenarios. Improved scenarios illustrated in figure 2.

Table 2

## Scenarios

## Description

## Scenario 1

11 September 2001 Terrorist Attack in USA

## Scenario 2

South America Crisis ( Brazilian Crisis ( July 2002))

We have assigned these scenarios to the same weight for plainness and straightforwardness. Because of this, each scenarios have the probability of scenario occurring by approximately %33,33. To distribute probabilities is a pivotal step. Since, it is the view of Berkowitz (2000) that financial institutions protect themselves to attempt to obtain the greatest estimations of catastrophic scenarios occurring. Given this evidence, it can be seen that respectively assigning probabilities to scenarios gives an opportunity to conserve their institutions from encountering probable scenarios in the future. Table 3 illustrates the probabilities of scenarios.

Table 3

## Scenarios

## Description

## Probability

## Scenario 1

11 September 2001 Terrorist Attack in USA

%33.33

## Scenario 2

South America Crisis ( Brazilian Crisis ( July 2002))

%33.33

In addition , the probability of %33.33 (1 - 0.6666) without two scenarios demonstrates the continued normal condition which means the probability of none scenario occurring.

## Portfolio

The chosen portfolio is consist of the five widespread DJIA ( the Dow Jones Industrial Average, USA ) stocks, which are Bank Of America Corporation Common ( BAC) , General Electric Company Common ( GE ), Intel Corporation ( INTC ), Hewlett Packard Company Common ( HPQ ), Wal Mart Stores, Inc. Common St ( WMT ). These stocks are the blue chips of DJIA stock market and moreover, they stand for approximately % 50 of Dow Jones Stock Market (DJI).

If we consider that the beginning date of portfolio has been arranged on September 3st , 2002, It is very significant to explain the initial values of selected portfolio's stocks and the weights of stocks in portfolio. We will invest to 100,000 $ which distributed equally among share certificates. To arrange the same weights for each share seems to be simplicity, however this paper's main point is not diversification of portfolio or decreasing the risk of portfolio by arranging the weights of shares in portfolio. The fundamental point is to evaluate the global position (Dominguez and Alfonso, 2004). Because of this, we have assigned the even weight among share certificate by 20 %. Table 1 shows the details of portfolio dated September 3st ,2002.

Table 4

## 03/09/2002

## BAC

## GE

## HPQ

## INTC

## WMT

## TOTAL

## Closing Price

67,13 $

28,46 $

12,55 $

15,86 $

51,87 $

## Value

20,000 $

20,000 $

20,000 $

20,000 $

20,000 $

100,000 $

## Weight

20%

20%

20%

20%

20%

100%

The date intervals (time horizon) are essential for calculating VaR and the accuracy of risk modelling. In the light of scenarios, we considered time horizon which starts from 31 January 2000 and 3 September 2002. It contains 650 days of trading in DJI. For this period, we convert daily Stock's prices to continuously compounded return which uses for benchmarking, predicting value and modelling. It formulates as followings:

Rt = ln ( Rt / Rt-1)

After computed rate of continuously compounded return, the observations of portfolio date decreased from 650 to 649 unit which means that sample data is consists of 649 historical daily returns. After this process , the next step is a calculation of the historical volatility of periodic return series. Historical volatility measures the movements of an asset's price in a certain time as following formula demonstrates;

To be more precise, the historical volatility is an the real price movement and standard deviation of periodic return figures 2 illustrates that the periodic daily volatility of each stock in portfolio. Besides, figure 3 shows the daily volatility of the Dow Jones Industrial stock market ( DJI ). Both figures demonstrate the market movements after Terrorist attacks (9, 11 ) and Brazilian crisis.

Figure 2

Figure 3

## Stress testing on VaR methodologies and parameters

Briefly, Value at Risk (VaR) measures the loss of portfolio or the risk of market in a certain period of time with a determined level of confidence. That is to say that VaR as an quantitative method requires :

The time horizon should be one day or the certain period of time. For instance if we will estimate the historical simulation of portfolio, we need time intervals associated with scenarios.

The level of confidence has been set by %95.

The Dollar will be used to explain the results of VaR.

FÄ°GURE VarCUNCEOP

Note : Graph taken from the article of Dominguez and Alfonso (2004, p. 65)

After determining VaR parameters, this paper used the historical simulation and the parametric method to estimate loses on created portfolio and will discuss the calculation of these two methods in the next section.

## Variance - Covariance ( Parametric ) VaR

this approach determines the parameters which effect the values of portfolio and calculates the profit- loss of portfolio based on parameters' volatilities in a certain level of probability. The basis of variance - covariance method is based on a specific variance assumption. Therefore, financial firms generally carry out variance - covariance method because of distribution assumption and they assume that returns distribute to their account as normal. By referring the hypothesis of normal distribution, it is possible to calculate the VaR's value of portfolio returns and the standard deviations of each assets returns in portfolio as linear ( Bozkus , 2005 ). Advantage of this method is that it is very easy to apply rather than other methods. However, parametric methods have number of limitations. It is the view of Rogachev ( 2007 ) sums up the most important problem of method that variance - covariance method is criticised because of method assumes that returns distribute as normal and so that the variance - covariance value of returns is a constant. Within the framework of variance - covariance method, the Var of portfolio is calculated as following:

Where

- simple risk vector

initial position vector

volatility vector

Therefore simple risk vector =

To take account of the effect of portfolio, the following formula is used to calculate the VaR of portfolio.

Where

the correlation vector between variables

the transposed vector of V and it is calculated as :

After explained parametric method, we should apply the attributes of scenarios to method. Stress test exercises is very simple to apply to variance - covariance method and we have to calculate the parametric VaR for each our scenarios ,which are S-11 Terrorist Attack , Latin America Crisis, on 1 September 2002. We can specify the formula of variance - covariance method with respect to scenarios as following:

Where

initial value of the position in stock ( 20,000 $ )

daily volatility of each stock relevant to the stressed scenarios

the level of confidence is at %95 which equals to 1.6449 .

The generated matrixes ( daily volatility matrix, the correlation matrix and - simple risk vector or covariance matrix ) to find out the portfolio and individual of VaR illustrate in Appendix as an matrix formation.

## Historical Simulation Method:

A different and simple approach for VaR calculation is called Historical Simulation. This approach does not make any assumptions about financial assets and the distribution of portfolio returns and accepts that the history will repeat. Goorbergh and Vlaar (1999) point out "This technique is nonparametric and does not require any distributional assumptions. This is because HS uses essentially only the empirical distribution of the portfolio returns." In other words, by using historical changes in market prices, historical simulation approach builds up a distribution , which exhibits the future potential profit or loss of portfolio, by using historical changes in market prices and rates and then calculates VaR by using the comprised distribution. The prospective profit or loss distribution of portfolio is obtained by means of applying the changes of market factor occurred by previous N period to actual portfolio. In simple terms, this technique revaluate portfolio with historical prices of assets which are comprise of portfolio. To revaluate portfolio builds up a profit or loss distribution to compute VaR at selected confidence interval. Table X illustrates the limitations and advantages of Historical Simulations.

## Table X - the advantages and disadvantages of Historical Simulation

## Advantages

## Disadvantages

Apply easily for non linear positions.

Don't make any assumption about distributions.

Rely on volatility and correlation deriving from time series.

Reasonable scenarios easily describe unbalanced and non distribution markets.

The calculation of method requires intense operation because of accurate assessing.

Method don't take account of future events or changes in market. It considers only past changes. This is the most controversial issue.

Unconscious scenarios bears analyst to wrong interpretations.

The stages of calculation of Historical Simulation Method are aligned as follow :

Determine the risk factors of portfolio and calculate the positions of risk exposures with the market price of assets.

Prove past historical data to stressed risk factors

Obtained presumptive values from past historical data compare with their recent values in portfolio and it leads to determine profit or loss.

Obtained daily profit or loss juxtapose from the worst to the best .

Assign loss of portfolio corresponding selected confidence interval.

Stressed tests on parametric simulation included more mathematical process which is derived from the volatility and correlation, if comparing with historical simulation. However, correlation cannot be carried out on historical simulation. Since, used data is included historical prices series. Thus , implementation of our scenarios on historical simulation are aligned as the following stages:

There are two historical periods associated with both scenarios. For the first scenario, we have used the last 20 days from 11 September 2001. the last 20 days from 9 August 2002 applied for the second scenario.

Calculating the returns of historical stocks for the each time period.

the next step produces historical simulated values as follow :

Pi Pt i = 1,2,3...18,19

Where Pi is the simulated values of the scenarioi , Pt is the recent values of the stock and Ri is is the historical return.

Another VaR method is the Monte Carlo Simulation. It is based on pricing portfolio process which follows a certain model. Basically, it is almost the same with the historical simulation , which is the other un parametric method, except couple differences. The Monte Carlo simulation lets more flexible analysis on its results rather than the Historical Simulation. However, the programming(spreadsheet) of Monte Carlo simulation is the hardest one among VaR methods. Moreover, the historical simulation has easier explanation in terms of its link with managers than the the Monte Carlo simulation. Therefore, we selected the Historical Simulation among un parametric methods in this study. The variance-covariance method as parametric is more different than un parametric methods. Apart from the other methods, the parametric method is able to analyse and handle the individual instruments in portfolio. However, pricing model is not required and it is not easy to understand its explanation by managers. The implementation of variance-covariance method is easier than the Monte Carlo simulation. We selected the parametric method because of evaluating the individual instruments in portfolio in this paper.

## Empirical Results

The computation of historical and parametric VaR is used Microsoft Excel 2007 software . The Table Y shows the individual and portfolio VaR according to the parametric VaR. The table X illustrates the outcomes of VaR portfolio with respect to the historical simulation.

Table Y

Individual VaR for Scenario 1

## Scenario 1

## BAC

## GE

## HPQ

## INTC

## WMT

## Initial Value

20,000 $

20,000 $

20,000 $

20,000 $

20,000 $

## Daily volatility

2,31 %

2,71 %

5,61 %

4,19 %

2,00%

## Z (%95)

1,6449

1,6449

1,6449

1,6449

1,6449

## VaR individual

759.95 $

891.53 $

1845.57 $

1378.42 $

657.96 $

Individual VaR for Scenario 2

## Scenario 2

## BAC

## GE

## HPQ

## INTC

## WMT

## Initial Value

20,000 $

20,000 $

20,000 $

20,000 $

20,000 $

## Daily volatility

2,47 %

3,21 %

4,99 %

5,17 %

3,07 %

## Z (%95)

1,6449

1,6449

1,6449

1,6449

1,6449

## VaR individual

812.58 $

1056.02 $

1641.61 $

1700.82 $

1009.96 $

Portfolio VaR according to Scenarios

## Parametric

## Normal

## Scenario 1

## Scenario 2

## VaR

3489.54 $

5160.07 $

5442.09 $

## Ratio VaR

3,49 %

5,16 %

5,45 %

Table X

Portfolio VaR (Historical Simulation) with respect to scenarios

## Historical Simulation

## Normal

## Scenario 1

## Scenario 2

## VaR

3061.3 $

4813.23 $

4183 $

## Ratio VaR

3,07 %

4,82 %

4,19 %

## Critical Z ( % 95 )

1,6449

1,6449

1,6449

In the table Y, it can be seen the each individual stocks of VaR and the portfolio VaR with respect to variance-covariance analysis. Analysing the individual stocks of VaR means that if the portfolio build up only single stocks, it tries to find the portfolio of VaR. According to scenario 1 (Terrosist Atack in NY, September 11th ), the losses of each individual stocks are less than 759.95 $, 891.53 $, 1845.57 $, 1378.42 $, 657.96 $ respectively ,at the probability of % 99. At the same probability, according to Scenario 2 ( Brazilian Crisis), the each individual stocks of VaR are less than 812.58 $, 1056.02 $, 1641.61 $, 1700.82 $, 1009.96 $ , respectively. Apart from these, the loss of portfolio is 5230.07 $ for Scenario 1, whilst it is 6222.09 $ at the probability of 99%. The probability of more excessive losses of portfolio and individual stocks is at 1%. This case indicates that the economic basis of Brazilian crisis has more impacts on the losses than the uneconomic crisis of September 11.

According to Historical simulation , the VaR of portfolio connected with scenarios is calculated as 4813.23 $ and 4183 $ , respectively. In this sense, the losses of created portfolio are less than these values, at the 95 percent probability. In the same way, the probability of more excessive losses of portfolio stocks is at 1%. Historical simulation denotes that scenario 2 has the less impacts on the losses of portfolio than Brazilian Crisis. The main reason of this difference ,which is associated with the impacts of scenarios on the losses, between two methods is holding periods and the normal distributions assumption of parametric VaR. However, if we look at the volatility of individual stocks figure ( Figure 2), the volatility of scenarios 1 fluctuates more than scenario 2. Therefore, historical simulation might be outperformed vis-a-vis parametric VaR method. In addition, the biggest disadvantage of the parametric VaR method is that it assumes data sets to normally distribute (Basu , 2009) .

## Conclusion

When using VaR methods alone, its results cannot be apprised about the risk position of financial institutions or portfolios. Stress test is seen as filing the gap of VaR by academicians and decision makers. Therefore, we applied stress tests on VaR methods by creating portfolio in this paper.

We selected two scenario for stress test exercise which are 11 September 2001 Terrrorist attack in USA and Brazilian Crisis. the main reason of selected these scenarios is that the stress test exercises denoted a greater degree of risk measured in the light of VaR and selected time period for portfolio. With assigning probabilities to scenarios, the integrated risk model relating to portfolio has constituted. Then, the VaR values of created portfolio has analysed by using the variance covariance and the historical simulation methods.

The outcomes of parametric method was greater than the historical method. But impacts of scenarios on the losses of portfolio were different with respect to two VaR methodologies. Nevertheless, as general result , the response of Value at Risk methods to the stress test scenarios is not identical. For both exercises , variance covariance method is more reactive whilst the simulation method is more realistic.

As a result, VaR models is significant to measures the losses of portfolio under certain conditions and specific time period. stress tests and the similar techniques is crucial in order to removing the issues created by VaR.

## Appendix

## Scenario 1

## Covariance Matrix

## BAC

## GE

## HPQ

## INTC

## WMT

## BAC

0,230

0,185

0,100

0,222

0,113

## GE

0,185

0,460

0,333

0,362

0,158

## HPQ

0,100

0,333

0,399

0,402

0,104

## INTC

0,222

0,362

0,402

0,630

0,157

## WMT

0,113

0,158

0,104

0,157

0,133

## Volatility Matrix

## BAC

## GE

## HPQ

## INTC

## WMT

## BAC

0,480

0,00

0,00

0,00

0,00

## GE

0,386

0,558

0,00

0,00

0,00

## HPQ

0,208

0,453

0,387

0,00

0,00

## INTC

0,463

0,329

0,406

0,378

0,00

## WMT

0,235

0,120

0,003

0,019

0,250

## Correlation Matrix

## BAC

## GE

## HPQ

## INTC

## WMT

## BAC

1,000

0,568

0,329

0,584

0,645

## GE

0,568

1,000

0,777

0,673

0,638

## HPQ

0,329

0,777

1,000

0,803

0,454

## INTC

0,584

0,673

0,803

1,000

0,543

## WMT

0,645

0,638

0,454

0,543

1,000

## Appendix

## Scenario 2

## Covariance Matrix

## BAC

## GE

## HPQ

## INTC

## WMT

## BAC

0,185

0,198

0,225

0,213

0,146

## GE

0,198

0,447

0,350

0,330

0,227

## HPQ

0,225

0,350

0,578

0,375

0,258

## INTC

0,213

0,330

0,375

0,515

0,243

## WMT

0,146

0,227

0,258

0,243

0,243

## Volatility Matrix

## BAC

## GE

## HPQ

## INTC

## WMT

## BAC

0,431

0,00

0,00

0,00

0,00

## GE

0,460

0,485

0,00

0,00

0,00

## HPQ

0,523

0,225

0,503

0,00

0,00

## INTC

0,494

0,212

0,138

0,455

0,00

## WMT

0,339

0,146

0,095

0,070

0,304

## Correlation Matrix

## BAC

## GE

## HPQ

## INTC

## WMT

## BAC

1,000

0,688

0,688

0,688

0,688

## GE

0,688

1,000

0,688

0,688

0,688

## HPQ

0,688

0,688

1,000

0,688

0,688

## INTC

0,688

0,688

0,688

1,000

0,688

## WMT

0,688

0,688

0,688

0,688

1,000