Thesis for the Degree of Master of...?

INCORPORATING LIQUIDITY RISK INTO VAR MODEL
TO IMPROVE RISK MANAGEMENT
AND APPLYING THE LIQUIDITY ADJUSTED VALUE AT RISK MODEL
ON VIETNAMESE STOCK MARKET

Student:
Ten truong:
Ten khoa hoc:

September, 2012

INCORPORATING LIQUIDITY RISK INTO VAR MODEL
TO IMPROVE RISK MANAGEMENT
AND APPLYING THE LIQUIDITY ADJUSTED VALUE AT RISK MODEL
ON VIETNAMESE STOCK MARKET

by student Avised by
Ten giao su
Submitted to Ten khoa of Ten truong in the partial fulfilment of the requirements for the degree of
Master of ...?
Dissertation Committee
...Ten thanh vien hoi dong

ABSTRACT
In this paper, based on Bangia et. al (1999) Liquidity Adjusted Value at Risk, an explanation and demonstration for the importance of integrate liquidity risk component into Value at Risk Model are presented. The component is considered to be resulted from the exogenous liquidity risk, indeed, the bid-ask spread of a stock or a portfolio.
This research is conducted from the analysis of an estimation of Value at Risk (VaR) and Liquidity adjusted Value at Risk for two portfolios containing stocks that are currently trading on Vietnamese Stock Market. After applying the Bangia Model to calculate, the backtesting will be executed to check the accuracy level of the results. The difference between the results of two portfolios, according to separate approaches will be the evidence to reach the conclusion of the research.

Table of Contents List of tables v List of figures vi Chapter 1 – Introduction 1 1.1 BACKGROUND TO THE RESEARCH 1 1.2 REASONS FOR CHOOSING THE TOPIC 3 1.3 RESEARCH PURPOSES AND KEY RESEARCH QUESTIONS 3 1.4 STRUCTURE OF DISSERTATION 4 Chapter 2 - Literature review 6 2.1 RISK MANAGEMENT 6 2.2 LIQUIDITY RISK MANAGEMENT 7 2.2.1 Why manage Liquidity Risk? 7 2.2.2 Liquidity Risk Measurement 11 2.3 VALUE AT RISK 11 2.3.1 VaR description 11 2.3.2 VaR Approach 12 2.4 INTEGRATION OF LIQUDITY RISK INTO VAR MODEL 15 2.4.1. Liquidity Adjusted Value-at-Risk 15 2.4.2. Bid-ask spread 17 2.5 BACKTESTING 18 Chapter 3 - Methodology 21 3.1. RESEARCH PHILOSOPHY AND RESEARCH APPROACH 21 3.2 RESEARCH METHOD 22 3.2.1 Literature review 22 3.2.2 Secondary information 23 3.2.3 Data analysis 24 3.2.4 Possible limitations 25 Chapter 4 - Empirical Findings and Data Analyses 26 4.1 DATA DESCRIPTIONS 26 4.2 MAIN PRODUCT OF STUDY 27 4.1.1 VaR 27 4.1.2 LVaR 35 4.3 BACKTESTING 39 4.4 ANALYSIS 43 4.4.1 The importance of the integration of Liquidity Risk into VaR 43 4.4.2 Historical Data and Variance-Covariance Method, which is better approach? 44 Chapter 5 – Conclusion and recommendation 47 5.1 MAIN EVIDENCE AND GENERAL CONCLUSION 47 5.2 RECOMMENDATIONS 49 5.3 SUGGESTION FOR FURTHER STUDY 50 Bibliography 53 Appendix 1: The daily share price of equities in one year period 59 Appendix 2: The bid-ask price of two portfolios in one year period 66 Appendix 3: The histograms of daily normal return (VND) 73

List of tables Table 1: The Variance-Covariance matrix of liquid portfolio's returns 44 Table 2: The Variance-Covariance matrix of less liquid portfolio's return 44 Table 3: The Standard Deviation of each equity 45 Table 4: : Average value and standard deviation of spreads of two portfolios 47 Table 5: LR Test Statistic for liquid portfolio 51 Table 6: LR Test Statistic for less liquid portfolio 51 Table 7: Liquidity Adjusted Value at Risk results 53

List of figures Figure 1: Histogram of liquid portfolio's gains and losses 38 Figure 2: Histogram of less liquid portfolio's gains and losses 38 Figure 3: Normal Distribution of ACB's daily log return 40 Figure 4: Normal Distribution of SSI’s daily log return 40 Figure 5: Normal Distribution of KLS’s daily log return 41 Figure 6: Normal Distribution of DTC’s daily log return 41 Figure 7: Normal Distribution of HAI’s daily log return 42 Figure 8: Normal Distribution of BPC’s daily log return 42 Figure 9: Bid-ask spread distribution of liquid portfolio 47 Figure 10: Bid-ask spread distribution of less liquid portfolio 47 Figure 11: Backtesting result for liquid portfolio 49 Figure 12: Backtesting results for less liquid portfolio 49 Figure 13: Histogram of daily normal return of ACB 77 Figure 14: Histogram of daily normal return of SSI 77 Figure 15: Histogram of daily normal return of KLS 78 Figure 16: Histogram of daily normal return of DTC 78 Figure 17: Histogram of daily normal return of HAI 79 Figure 18: Histogram of daily normal return of BPC 79

1. INTRODUCTION
1.1 Background to the research
“What makes Value at Risk (VaR) so appealing is that its complex formulae distil the range of potential daily profits or losses into a single dollar figure” (The Economists, 2010). The calculation of this value has been the study subject for many researchers. There are many benefits of VaR but its essential task is a tool for investors to measure the market risk, which is resulted from the changes in financial market prices and rates reducing the value of the investment (Crouhy, 2006). However, almost the traditional VaR calculation methods contain a serious drawback, which is ignoring totally the impact of liquidity risk. In fact, the growing number of failures in the recent year occurs due to this shortage, such as the near-collapse of Long-Term Capital Management (LTCM), a hedge fund in the United States in late 1990s. A reality of market and investors’ behaviour is needed to explain for such of this debacle. The equity is often marked at the middle price of the bid-ask spread in the market and then, the investor who could be a bank, a hedge fund uses mid-prices for calculating their possible worst loss for a time period by calculating VaR. This thing obviously causes a problem because the realistic value of the stock/portfolio is not always maintained at the middle price. In case of LTCM failure, Dunban (2000) demonstrates the Russian financial crises in August 1998 led to an illiquidity market, in which only the bid price existed as the realistic value for the portfolio. The hedge fund LTCM therefore received the huge losses as an uncertainty of market. A support idea from Lawrence (1996) affirms that the market risk will be underestimated if excluding the liquidity market risk component and the underestimated amount can rise up to 30 percent. The liquidity risk has been neglected when calculating VaR. It may lead to the inaccuracy in estimation of market risk, and then the wrong regulators for managing market risk. This is one of reason causing the financial crisis that began in 2007. The negative impact of neglecting liquidity risk is realized not only to the investors, but also to the overall economy.
Many of articles talking about the recent financial crisis are considered to clarify the importance to do a research about adjusting liquidity component to VaR. The financial crisis 2007 with the origins and spreading, which is furnished by Furceri and Mourougane (2009) happened due to “a sudden evaporation of liquidity” (The Economists, 2010). Financial Crisis, often called a Credit Crunch, which is defined “a severe shortage of credit”, according to Concise Oxford English Dictionary. Simply, it is a crisis caused by banks being too nervous to lend money to us or each other (Times, 2008). Before the crisis happened, a large capital inflow of foreign funds from fast-growing economies in Asia and some oil-producing countries had streamed into the US, as a result of high consumption and low saving rates in the US. Combining with low interest rates and easy credit conditions, these factors created housing and credit bubbles. In these bubbles, there is a potential risk of various subprime loans hiding behind mortgage-backed securities. In July 2007, when a lot of investors lost their confidence in the value of securitized mortgages in the United States, in other words, the housing prices went down and the house market lost its liquid. Obviously, the securities backed with subprime mortgages promptly fell in value. Then, a liquidity crisis exploded. As a result, on the day the world changed, the European Central Bank and the US Federal Reserve injected 90 billion dollars into fidgety financial markets (The Guardian, 2008). In spite of the attempt to recover the economy, the financial crisis deepened in 2008. The financial market suddenly became illiquidity, resulted to the growing number losses of mass financial corporations in the US and worldwide such as Lehman Brothers, Morgan Stanley or HBOS.
Since the Credit Crunch, a raising number of opinions that encourages integrating the liquidity risk component into VaR, named as Liquidity Adjusted Value at Risk (LVaR) model is admitted, as a solution for improving Risk Management performance within the financial institutions. As the market liquidity risk consists of exogenous liquidity risk and endogenous liquidity risk, the component of liquidity risk can be incorporated both of these kinds. While the exogenous component concerns the bid-ask spreads of the equity’s price, the other endogenous risk is reflected by the particular position of the trader. Though the integration of liquidity risk into VaR Models is suggested, the importance of this work still has to be examined.

1.2 Reasons for choosing the topic
It is reasonable to make a research on Liquidity Adjusted Value at Risk, due to a number of factors:
Firstly, at present, the risk management is an essential concern for almost financial institutions. This is because of the impact of the Credit Crunch. As mentioned in the background section, the ignorance of market liquidity risk has been seen as one of main causes. Although the impact of the crisis on Vietnamese stock market was not terrible in comparison with the American or Western stock markets, it is necessary to learn from their lessons to improve the technique in risk management.
The other reason for deciding to investigate this topic is basically personality. My bachelor background at the university is Finance and Banking, therefore choosing a topic in this subject is the best, as I have chance to display and apply my knowledge and skills of managing risk, similarly to supplement the knowledge. Furthermore, the dissertation is absolutely helpful for my future’s job on Investment and Banking Sector when I come back my country.
1.3 Research purpose and key research questions
The study aims to apply LVaR Model on two portfolios of equities that are trading on Vietnamese Stock Market, in order to assess the significance of incorporating liquidity component to estimate the worst possible losses due to the total market risk. Because the LVaR Model is mainly based on the VaR Model, this paper will follow different methods of VaR calculation to make use of the advantage of each method and bring an adequate outcome.
In addition, the two main purposes and key questions of the research are presented as below: A. At first, the VaR and LVaR of two portfolios with the different liquid level will be estimated and then compared to each other to define the difference between the values.
Two key research questions are: 1. How many percentage of liquidity component contributed to LVaR, estimated for two portfolios? 2. Is integrating the liquidity component for less liquid portfolio more significant than for liquid fortfolio? B. Secondly, a backtesting is conducted to check the accuracy of different approaches to calculate VaR and LVaR.
Two key research questions: 3. What is the better approach to calculate VaR and LVaR? 4. Whether or not integrating the liquidity risk into estimation of possible worst loss improves the accuracy of model?
1.4 Structure of thesis
This paper will be organized in as follows:
Chapter 1 is the introduction that provides the general background of theory about the VaR model and integration of liquidity risk into this model to evaluate overall market risk. It sets the stages for what will contain in later chapters.
Chapter 2 is the literature review, in which there will be a reference to the past authors research linking to the objects of the paper. The chapter contains four separate parts, thus, part one will analyse and evaluate published books and articles closely related to Liquidity Risk Management. Part two is the description of VaR concept as a popular method to estimate market risk. Part three will explain the motivation of incorporating Liquidity Risk into VaR Models and, discuss the common methods to estimate LVaR, in which one of these methods will be used in the later empirical analysis. Part four is a review of several ways to conduct a backtesting.
Chapter 3 presents and illustrate the appropriate research philosophy and methodology for the research after a discussion of pros and cons of these methods.
Chapter 4 is an analysis of dissertation’s issue. It displays all the main Findings of the data and analysis. They will be formed and shown regarding to tables, graphs and charts, additionally to the discussion upon these estimations. In its first section, research will show the outcomes from using the quantitative methods on the collected data. In the second section, an analysis on the outcomes will be conducted, in order to answer the key research questions.
Chapter 5 is a conclusion and recommendation. By reviewing all arguments and analysis of the research above, it will draw the significance of incorporation of Liquidity in VaR, as well as suggest the better method to estimate LVaR. Finally, it will give recommendations for the investors in generally and for the banks in particularly to strengthen the risk management.

2. LITERATURE REVIEW
This chapter will start with a looking into the existing theories which are valuable on Liquid Risk Management (LRM) section. This part will be followed by reviewing two methods to calculate Value at Risk, a popular measure of market risk. In the third part, the motivation to integrate Liquidity Risk component into Value at Risk is explained, as well as an evaluation the available model to estimate Liquidity Adjusted Value at Risk. After that, a review on existing backtesting models will be established.
2.1 Risk management In life, we often speak of the “risk damage”, the “risk bearer” or “risk of audit”. During this period, people talk about “risk management” as an important part of plan to limit the negative effect from recent crisis. In these examples, the word “risk” is used “in the sense of an undesirable outcome”, suggests Lewin (2001); in a supplemental manner, Roughley and his colleagues (1984) proclaims that “risk is inevitable, by the nature or probability, that bodily injury, property damage or financial loss will occur sooner or later”. Financial risk, a measure of the whole range of outcomes from the investment, concluding both the upside and downside outcomes (Lewin, 2000) will be the main concept in this research. Since 1916, people first knew the risk management concept under the name of “security”, one of six basic activities of a corporation (Gallati, 2003). “Security” was described by Fayol (1916) as below: “The purpose of this function is to safeguard property and persons against theft, fire and flood, to ward off strikes and felonies and broadly al social disturbances liable to endanger the progress and even the life of the business. It is the master’s eye, the watchdog of the one man business, the police of the army n the case of the state. It is general speaking all measures conferring security upon the undertaking and requisite peace of mind upon the personnel”. Till now, there is much of the recent work introducing Risk management. Being a special business skill, risk management is described as a system comprising tools and technique, as well as a top-down a and bottom-up process (Besis, 1998) of managing uncertainty that arises in the normal course of activities, including those related to business ventures (Banks, 2002). Furthermore, Waring and Glendon (1998) inside a broad and fresh perspective to the subject of risk depicts that all activities of risk management as seeking to eliminate, reduce and generally control pure risks and to enhance the benefits and avoid detriment from speculative risks. They also acknowledge that in these times, dividing risk cannot be effective when the risk is increasing among investors. However, the work of Waring and Glendon generally is almost theoretical and does not supply plan of action to manage risks. In addition, a variety of methods have been suggested, though all of them are direct to the same goal as managing financial risks. Lore and Borodovsky (2000) introduce authorization, control and limit setting as a set of different ways to supervise uncertainties. They consider the limit setting to be the most common and advanced technique with a revolving five-step process, from setting up the maximum loss, dividing the loss to categories, limiting loss for each category, making a comparison between the real exposure and limits, dealing with the fluctuation situation and calculating actual loss. This can be a useful guidance for Financial Risk Management. Siems (2010) with up-to-date evidences synthesizes three methods to manage financial risks, depending on the risk’s complexity and insurability. Purchasing insurance is chosen as the first method to deal with risks that are predictable by normally using portfolio theory. Besides, in order to reach the corporation’s goals and reduce risk exposure, Siems applying portfolio immunization gives the second approach as the necessity of considerable balance and combination between the assets and liabilities. Because of this approach mainly focuses on on-balance sheet assets and liabilities, similarly to forget the off-balance sheet ones, other approach is provided, named hedging. The guideline of Siems after carefully reviewing the risk is the key for managers to be at liberty to control risk taking.
2.2 Liquidity risk management
2.2.1 Why manage Liquidity Risk? It is required to discuss on the basic knowledge of Liquidity Risk to explore the concept of LRM. This kind of risk can be defined as “the recent or prospective risk arising from an institution’s inability to meet its liabilities/ obligations as they fall due without incurring unacceptable losses” (The Basel Committee in the Principles of Sound Liquidity Risk, 2009). According to this explanation and several similar description of Bessis (1998) Liquidity Risk simply is the potential for running short of resources and other funds, or “an obverse of credit risk” (Cade, 1997). Though there are also different explanations for the existence of Liquidity Risk, this kind of risk is often distinguished into two groups: funding liquidity risk and market liquidity risk, presented by Bessis (1998) and Culp (2001). While funding liquidity risk rises from the insufficiency of cash inflows and current balance to cover cash outflow requirements, the initiate of market liquidity risk is from the cost of liquidating a position. There are a lot of works have discussed about funding liquidity risk. However, the market liquidity risk had not been a serious concern before the recent financial crisis although the illiquidity obviously is a potential risk with all the markets, as well as a big source of risk to investors (Economists, 1999). The market liquidity risk, which is Dowd (2002) suggests to divide into two groups. The first group comprises all the “normal liquidity risk” initiating from the exchanges on markets with the little liquid. The second one is more complicated, which attaches to the liquidity level of the stock market. When a crisis occurs, the market will become not liquid and the investors will face the risk of losses in investments. According to Kroszner (2008), the result from a search through LexisNexis presented that only in six months of 2008, there are around 2,000 financial articles linking the word “liquidity” to talk about the market. The result implies the care and caution of people with Liquidity, as well as LRM when the Credit Crunch occurs. Many of articles talking about the Credit Crunch are considered to comprehend the road its impact developing in Banks and other financial structures. The financial crisis 2007 with the origins and spreading, which is furnished by Furceri and Durand (2009), the impacts on the international financial markets, which is demonstrated by Ross (2009), is the factor causing losses. Bruner and Carr (2007) recognize the influence of the interaction and possible of market forces to crisis by relating the recent crisis to the one in 1907. Martin (2009) summarized five lessons from the liquidity crisis for the Deutsche bank where he has worked. Among these lessons, the failure in LRM and stress testing appliance, the poor instruction and management of funding and balance sheet, the inaccurate measurement of liquidity market risk are noticeable. The Basel Committee agrees with this idea when commenting on the “LRM and Supervisory Challenges”, published in February 2008, that the reality of LRM integration inside almost financial institution was not in fine condition and this thing was the main reason of recent Financial Crisis (2009). Indeed, many financial institutions has gotten troubles to build an adequate framework to measure and control liquidity risks, as well as to decide the exact amount of liquidity for satisfying their obligation. Tirole (2008) finds out the core of the subprime crisis as a liquidity risk, named asset bubbles. Indeed, when the price of an asset exceeds its fundamental value, it is often visible for a bubble. A potentiality that this bubble will burst in case of a recession, results to a shortage of liquidity and a crisis. Schwartz (2010) additionally points out the serious problem in risk management strategies of the bank deepening the turmoil of the financial market.
As a section of Risk Management, LRM not only helps to reduce the liquidity uncertainties but also creates benefits. Rawls and Smithson (1990) demonstrate the positive outcomes of applying RM as reducing transaction costs, decreasing taxes and developing investment decisions. Schröck and Steiner (2002) affirm the nature of financial institutions in the risk business. They also provided evidence, which showed that implement risk management as equipment could enhance value of corporations. Gallati (2003) agrees with this idea by recognizing risk management for financial institutions as tool of raising shareholder value, as well as clarifying the perspective and performance of managers to reduce and absorb the risk. A remarkable illustration of risk management’s significant role in management of all institutions is provided by Lam (2003). His idea has a high value because it bases on not only theory, but also on his twenty-year experience working as one of the world’s top risk management experts (Euromoney, 2005). There are four reasons given. Firstly, Lam insists the responsibility of institutions’ managers on risk management and arranges risk management into one of the manager’s jobs. The second benefit of risk management in reducing earning volatility was noticed. Indeed, the financial institutions, whose exposure to interest rates, foreign exchange rates and many other market variables is huge, controlling swing of earnings is more difficult. Obviously, they need to apply an efficient Risk Management Framework. In the discussion of the third benefit, Lam develops further the Gallati’s argument, in which also implies the capability of Risk Management on maximizing shareholder value. When creation of value for shareholder is the most paramount goal of corporate management (Hitchner, 2003), the major object of almost joint stock companies are also maximizing the return in long-term period on the capital invested by their owners (Maharaj, 2005). When the public and sometimes private shareholders hold almost the stocks of these institutions, the importance of Risk Management is worth concerned (Johnson & Johnson, 1989). The last benefit of Risk Management is the increase of job and financial security. There is no debate on this obvious influence of Risk Management to society.
As can be seen, the role of RM with the financial firms’ operation is absolute acceptable but the value of LRM still needs to be discussed. According to Holmstrom (2000), two main advantages are dealt with as taxes and managerial stimulus. Stultz (1996) does not highly value LRM benefit to taxes, due to taxes’ local and time characteristic. On the other hand, Stultz and some other financiers as Fite-Pfleidere (1995) assert the benefit of managing Liquidity Risk on encouragement activity of management. A debate about the value of LRM was raised. However, no one can deny the significant role of LRM in the financial companies nowadays. For instance, with the banks which are a main group of financial system, one of two functions of banks in the economy is liquidity providers, in accordance with Kroszner (2008). Thus, an effective LRM is especially important, furthermore, challenging. It assures the liquidity for the bank, indeed, the bank is able to quickly sell and purchase huge amount of quantities with low cost and a stable price (Pastor and Stambaugh, 2003). The role of LRM is more clarify as with the bank and all business people who use their personal assets under collateral type, being liquid is actually vital and essential (Rosalind, 2009). An exploration of Fox (2009) implies that maintaining the positive degree of liquidity via managing this king of risk could safeguard the financial stability and rescue the worldwide financial system, which was got critical impact from the crisis.
2.2.2 Liquidity Risk Measurement
The process of LRM often makes use of several steps. Jorion (2009) presents three steps in the LRM guideline are identifying and measuring liquidity risk, tactical management and integrating strategy. He affirms that the first step, which aims to measure liquidity risk, is one of the most important segments through the process and also suggests a combination between different metrics to measure liquidity risk. There are several other ways to value liquidity risk. Liquidity risk can be defined in the relationship with the expected return (Fowler, 2000). Additionally, Value-at-Risk (VaR) is considered to be one of the most popular measures integrated to formalize and estimate Liquidity Risk (Berkowits, 2000 and Jarrow, 2005) because of the ease of quantifying variance (possible losses) and distribution (probability of occurrence) of portfolio risk (Kyle, 1985).
2.3 Value at risk
2.3.1 VaR description Regarding to all investors, risk is similarly to the loss money. Thus, VaR is built as a single, summary, statistical measure of possible portfolio losses, due to “normal” market movements (Linsmeier, 1996). It is a measure for investors and reveals how much the cash value of a risky asset or portfolio could decrease over the time-horizon at pre-specified confidence interval. Till now, after being developed by J.P. Morgan, VaR is widely used as the best known of RiskMetrics (Dowd 2002). A number of works have analysed this mathematical risk measurement advantages. VaR is known to bring an effective way to evaluate the loss in market value over a given time period, from one day to two weeks (Duffie, 1997). It allows the financial institutions to put an estimated value on their worst case scenario, then prepare the plan and set the suitable regulation. Within a typical work of this type, Butler (1999) through an objective points out the strength and weakness of risk measurement methods and expresses that VaR may not be the perfect risk metrics but it signposts the way that risks develop. Other usages of VaR is applying into risk management in a categories of sections besides quantifying market risk, such as assessing the performance of risk takers, guiding the regulatory decisions (Manganelli and Engle (2001), helping banks or investment institutions to meet capital requirements (BIS, 1996). As one of popular study of this type, the book “An introduction to market risk measurement” written by Dowd in 2002 provides a quite useful way to estimate different types of VaR in Excel. His work is a clear guide to use software to measure risks, as well as a correct perception of the software’s importance in learning risks. Overall, this book is valuable in practice, indeed brings a collection of models, mathematical formulae and statistics to calculate and utilize Value at Risk (VaR).
2.3.2 VaR Approach
2.3.2.1 Historical Data Method This is the simplest way to calculate VaR for any assets or portfolios. To conduct this method, the analyst does not have to assume the shape of the distribution of returns. The volatilities and correlations are decided to represent inside the historical data, thus it is not necessary to draw the distribution. The VaR for the portfolio is achieved by predicting the possible gains or losses in the portfolio via the actual historical data within a hypothesis of time series. Urbani (2005) provides more detailed guidance for approach with this method. At first, the analyst has to compute the empirical returns of the portfolio and then arrange them in order from smallest to largest. The returns can be estimate through the changes which would have occurred in each period in the share price. The continuous step is defining the change of portfolio value, according to the confidence level. The result is known as VaR. In particular, for the 99% confidence level, the VaR will be the third worst losses when at 95% confidence level, the thirteenth largest value will be picked as VaR. Although Historical data method is actually easy to implement, it contains several serious of disadvantages. It basically depends on the assumption that the history usually repeats itself. In other words, it equals the market risk factor through different periods. It is easy to realize that this assumption is impossible because of the present of high volatility period and low volatility period in reality. The moves in historical market may not depict the market risk posed in the future. Moreover, the result of VaR highly depends on the choice of examined data length. Therefore, with such a portfolio, the VaR can change suddenly if we vary the time, for example from short period to long period. Hendricks (1996) demonstrates that the longer period will give the more stable VaR estimation; furthermore, it is hard to reach a correct VaR for data collected in short period. This problem results to accuracy limit in the calculation process.
2.3.2.2 Variance-Covariance Method This is the approach that is most closely related to modern portfolio theory and not too complicated to understand. A main assumption of this method is that stock log-returns are frequently distributed; otherwise, the method aims to compute the probability distribution of the portfolio’s value through the changes in risk factors, resulted from the sensitivities of portfolio’s value to returns of risk factors. There are two factors required for the estimation process. The first is the average expected return of the portfolio, which can be approximated by variance (Eftekari, 2000), as

Where x is the portfolio return, i=1nxiis the portfolio return on the ith time period, n is the number of observations. As a result, standard deviation can be figured out using: SD (x)=Variancex When the Variance and standard deviation are calculated, they will be used for the following formulation: Value-at-Risk VaR= ∝xTx, where α is the confidence level, xT is the vector of sensitivities of absolute changes in portfolio value to returns of risk factors, x is the variance-covariance matrix of returns over a given holding period. In spite of the advantage that are simplicity and estimation speed, the Variance-Covariance Method seems to have some drawbacks. At first, the most important issue is the consequence of the assumption about normal distribution. In fact, the distribution of equities’ returns can have fat tail, noticed by Mandelbrot (2004) and Taleb (2005). In case of the log returns distribute in a fat tail position, the Variance Method may underestimate the VaR that are far different from its accurate value. Moreover, it can be used to incorporate multiple time horizons, as well as a limit in the reliability of the estimated result if the portfolio composes options and other “non-linear” instruments.
2.3.3. Disadvantages of VaR
Practically, VaR is useful to estimate risks; therefore, it becomes the most popular risk measuring tool in banks, insurance companies and other financial institutions. However, there are remarkable limitations when using it as a Risk measure in case it is just a probabilistic statement. One of them that drove many financial institutions to losses from the financial crisis is known as no information of Tail losses. Dowd (2002) agrees with Butler (1999) that VaR is not the best to measure the risk, due to a number of alternatives to VaR. He defends his opinion by giving the expected tail loss (ETL), which is defined as the loss we can expect to make if we get a loss in excess of VaR. In addition, he expresses that: “VaR only tells us the most we can lose if a tail event does not occur”. The same idea came from Stulz (2008) indicates that: “VaR is an estimate of the minimum worst loss expected, as opposed to the expected worst loss”. For instance, If a VaR is estimated by a bank at one million pounds with a 99% confidence, it only provides us we has a 1% chance of making a loss in excess of one million pound but nothing about the exact amount we may lose. Sometimes, the amount will be small but if unfortunately, the bank will be exposed to the danger of a very large loss. In fact, in the 2006 annual report, UBS confirmed that it never had a loss that is higher than its daily VaR. But the exception happened in 2007 when the loss exceeded its daily VaR 29 times, counted as CHF 4,384 million. As can be seen, the risk capacity was not effectively calculated. In contrast, its risk exposure was gained by the certain complicated and volatile economy conditions. The definition of volatility is given by Butler (1999) as the statistical measure of the price variation of an instrument. The gap between the risk capacity and exposure contributed to the fail of risk appetite.
Miller (2000) also suggests several serious problem of extremely relying upon VAR method for RM due to the fact that VaR is estimated under assumptions. The assumption is worthy to notice is that assets are traded in a liquid market. Toggins (2008) gives supplement ideas as in VaR calculation, markets are perfect and the investors can buy or sell any amount of stock without influencing the changes in price. It is easy to realize that the factual stock markets are not frictionless. Furthermore, the market even can turn to illiquidity as an uncertainty over investors’ expectation. For instance, the bankruptcy of Long-Term Capital Management can be an evidence for such of market risk occurred in reality. A suggestion to integrate the liquidity factor to VaR Model is initiated to improve the accuracy and reliability of the calculation result.
2.4 Integration of liquidity risk into VAR model
2.4.1. Liquidity Adjusted Value-at-Risk
The research focuses on the incorporation of market liquidity risk to estimate the worst possible return, which often called as LVaR. Lawrence and Robinson (1995) realized the shortage of liquidity risk on the traditional VaR Model and suggested to add the liquidity cost into the total market risk effects. However the method to calculate had not been discovered. The concept of LVaR was then first formed from the idea of Almgren and Chriss (1998), and extended by Hisata (2000) to become a model. This model almost interested in the endogenous liquidity risk resulted from the investor’s own dealing. In the same year, Haberle detailed another approach to calculate LVaR basing on an assumption that the liquidity could not cause changes in price.
Among these methods, LVaR model which was provided by Bangia and his colleagues in 1999 is chosen to apply for this research because of its noticeable positive points. The initiation of Bangia’s model was from a comment that the more market exposures to the liquidity risk, the larger the size of losses for the stocks is recorded. Bangia also distinguished the endogenous component and the exogenous one of liquidity risk. When the endogenous liquidity risk especially depends on the investor’s position and does not influent the total market, the exogenous segment relies on the market conditions and plays an important role for the computation of LVaR. The solution for the LVaR is given by adjusting the liquidity term (L1):
LVaR = VaR + L1
The detailed formula is also supplied as to calculate the percentage of the worst expected returns, due to the return market risk and liquidity market risk on the current value of an equity or a portfolio:
LVaR=VaR+12(Spread+ α.σt,spread),
Where VaR is the return market risk component;
Spread is the average of the difference between the bid and ask price α is the quantile of spread’s distribution; σt,spread is the standard deviation of the bid-ask spread.
As can be seen, there are two separate components contributing to the market risk: the market return uncertainty and the market liquidity uncertainty. The idea to calculate LVaR by estimating each risk component in turn is flashed here. Although till now, there are many other modern Models that have been proposed to estimate LVaR, the appliance of Bangia Method is still popular and spacious due to main pros of this model, known as the simplicity and relative accuracy.
Beside Bangia et al, some researches has been taken in order to estimate LVaR. Almgren and Chriss, in 1999 – 2000 introduced asolution, which was based on how to construct an optimal trading strategy. With the assumption of externally setting a sale completion period, the optimum is where transaction cost variance takes the minimum with any given expected transaction cost. At this point, with normal distribution, LVaR is understood as the p-th percentile possible loss that a trading position can encounter when liquidity effects are incorporated into the risk measure computation. After that, Almgren developed his research using the theory of continuous time approximation. Then, a non-linear and stochastic temporary market impact function had been introduced.
Alternatively, Jarrow and Subramanian (1997 and 2001) suggested another approach known as liquidity discount model. One requirement is that sale completion period should be recognized as an exogenous factor. The model, as a result, derives an optimal trading strategy by maximizing investor’s expected utility of consumption.
However, two models mentioned above have the same limitation that both require externally setting a fixed horizon for liquidation. In order to prevail over this restriction, in 2000, Hisata and Yamai presented an approach, which is also extended Almgren and Chriss’s model. They used continuous approximation and assumed that sale would grow at a constant rate. In this setting, the sale completion becomes an endogenous variable and an optimal holding period is constructed.
2.4.2. Bid-ask spread
The LVaR will not be estimated if the calculation process lacks a treatment of Liquidity term. The Liquidity term appears within the illiquidity market where the investors do not get the mid-price for trading. This is because of the influence of bid-ask spread on the price of portfolio, thus Bangia considers estimating Liquidity term as the half of worst value of spread at a specific confidence level.
There are two main categories of price of assets that market makers need to consider: bid price and ask price, according to Fragniere (2009). Bid price is the highest price that investor is willing to pay for an asset in a given period of time whereas ask price is the lowest price that investor is willing to sell it. The difference between two prices is the bid-ask spread. The size of the spread depends on transaction costs, the volatility and size of accumulated order flows, or even the degree of information between market makers and initiators of transactions in case of insider trading of the asset. Moreover, the spread is used to measure the liquidity in a given period of time. However, the quote spread, the difference between best bid price and best ask price, does not reflect transaction cost since certain transactions can be traded at prices located within or even outside this spread. In brief, the spread and its variability should be taken into consideration in terms of risk measurement and management.
From the series of spreads in percentage, the worst loss of portfolio spread (Spread+ α.σt,spread). The σt,spread can be estimated through the standard deviation of the bid-ask spread, while the spread is the average of difference between bid and ask price at a time period. The relative α parameter is corresponded to the scaling factor in order to correct the bid-ask spread distribution. It is necessary to know about this factor but actually, it is complex for a direct calculation. The distribution of spread is not normal distribution; therefore applying the Variance-Covariance approach in this case is not realizable. A suggestion to calculate the scaling factor is using Historical Data Method to measure the worst possible relative spread. After that, the scaling α factor will be computed.
2.5 Backtesting
The backtesting framework is summed up with the aim for deciding market risk capital requirements (Basle Committee on Banking Supervision, 1996). The definition of backtesting is also introduced as “the internal model-based approach to market risk measurement routinely compare daily profit and losses with model-generated risk measures to gauge the quality and accuracy of risk measurement systems”. In fact, every firm has a wide range of models to choose from in their estimation of VaR, as well as many ways of implementing each of these models. Inevitably, some models will work much better than others. The significance of assessing that a risk model results to accurate or inaccurate outcome is patent. As can be seen, in case of applying a model which systematically understates the true VaR of a firm’s portfolio, the firm will not hold sufficient capital to cover unexpected losses. The insufficiency capital providing against uncertainties may cause a trouble, sometimes failure or even a bankruptcy for the firm.
Currently, there are different kinds of backtestings performed by different companies. The standards for these companies to investigate the results of the backtesting are distinguished. However, the approach to conduct backtestings is basically similar in the comparison of actual returns with the risk measures that are generated in the model. When the gap between figures in the fact and the model are quite far, the companies should discuss and correct the way they estimate VaR, or LVaR in particularly.
The most common backtesting framework that is implementing within a number of banks is developed by the Basle Committee. It applies the internal market risk measurement models to capture the market risk capital requirement. Indeed, the forecasts of a VaR model are compared with actual gains or losses for a period. Then the number of the returns that exceeds the estimated VaR will be counted and summed up. If the percentage of exceptions’ number on total observations is counted over the confidence level, the model may be inaccurate. Additionally, the Committee describe a method to interpret the results of backtesting, named three-zone approach. The method bases on the fact that the responses of backtesting can fall in three zones and each zone implies a level of model’s accuracy. Firsly, the safe green zone is considered for a strong and correct model. Secondly, the yellow zone can be presented for a accurate or inaccurate model and the judgement for the model is needed to be more investigated. Thirdly, if the responses of backtesting fall into red zone, it will be the same meaning as the model does not cover the entire risk component and a problem exists within the model. The disadvantage of such kind of test is that it mainly depends on the historical data. With the small data size or a high confidence level, the test is not able to direct to a reliable result.
Being an extension of Basle Committee’s framework, the Kupiec test uses a ratio to interpret the responses of back tests. Also beginning with calculating the number of tail losses which exceeds the model’s VaR, the Kupiec test will continue by comparing the real number with the expected number of tail losses at the confidence level. A likelihood ratio (LR) is then computed, following below formula:
LR=2ln⁡[1-NT1-pT-N(NTp)N
Where N is the observed number of tail losses exceeding VaR;
T is the total number of observations or sample size; p is the nominal significance level.
The computed LR is compared with the critical values to reach a conclusion that the model is passed or rejected. Shen (2006) proposes the way to obtain critical values for the LR statistics in Excel. He explains that under the null hypothesis of correct unconditional coverage, the LR statistic has a chi-squared distribution with on degree of freedom. Therefore, the supervisor is able to use the CHIINV function to estimate the critical values. With the test of Kupeic, the unconditional coverage of a VaR model is checked to be equal or not to the nominal confidence level. In addition, the independence property of VaR model is able to be judged.

3. METHODOLOGY
Research is defined as the study and/or investigation into a phenomenon or phenomena for many purposes, such as to discover new facts, to confirm current existing facts or to create a new perspective on existing facts (Clark et al. 1998). It is also known as one way to find answers for the questions and because the questions can be raised in almost professions, the research is diversified (Kumar, 2005). Veal (1997), Irving and Smith (1998) and O’Leary (2004) suggests the necessary of implementing methodical processes, logic, reason and systemic examination of evidence to draw logical and unbiased conclusions. Bernard (2006) describes the process of a research, which concludes a set of techniques that are relevant to the topic of research with aims to gather and handle data. This chapter hence is basically an explanation of how the data and techniques were chosen and then how they will be applied to analyse.
3.1. Research philosophy and research approach
Saunders et al (2003) views the research philosophy containing enormous weight in the process of doing research. Generally, the research process can be viewed in two types, known as positivism and interpritivism, basing on assumptions about how to perceive the world and what is the best way for us to know it.
At first, positivism is one kind of philosophy and basically depending on experience collecting from actual sense. Collis and Hussey (2003) explains that in positivism, people believe the singular and objective form of social reality, besides, the reality is not influenced by the act of investigating it. As a result, the researcher is able to do their work independently to make generalizations (Lee and Lings, 2008). Secondly, interpritivism is different from the positivism in the main point, which is the assumption of a subjective social reality and a belief that all the object of the reality is in our mind, in accordance with Collis and Hussey (2003). People following positivism think that the social reality can get impact from the act of exploring it, resulted from the research.
In terms of the subject matter of the research, which is to examine the VaR and LVaR Models in case of Vietnamese Stock Market by quantifying extent of these variation, then to find out the importance of integration of Liquidity into the calculation of Market Risk, the paper seems to be empirical and logical. It is suitable for the study to use positivism with quantitative method with data analysis due to the method’s reliability and objectivity (Kumar, 2005). Moreover, the literature and theory has already been studied and researched in variety works and this study only applies the model in a particular case study. Veal (1992) and O’Leary (2004) pointed out two methods of knowledge flow are inductive and deductive. If there is little or even no source of theory or data to support the research, inductive structure is guided to follow. On the other hand, deductive will base on existing theory and test it with empirical observation. Therefore, a deductive approach is suggested here. The paper thus starts with a discussion of existing literature in Liquidity Risk Management and Liquidity Adjusted Value at Risk. Then it will test the models in a case study of stock market in Vietnam.
3.2 Research method
According to O’Leary (2004), the research method composes from the strategy and collection of procedures with the purpose to collect, gather and analyse the data. In particulars, Ethridge (2004) shows that the methodology in economics contains many types of analysis, such as regression analysis, mathematical analysis. Since this research intends to examine a financial model on a case study of Vietnamese stock market, it will be composed principally by secondary research, for example literature review, secondary information and data analysis.
3.2.1 Literature review It is essential to produce the review of related literature for almost academic research at all levels in the social sciences. Likewise, a good quality literature review is one of first condition to make the success of research or to narrow down and focus the topic (Hart 1998). Relying on the selection of existing documents linking to the topic of dissertation, the hypothesis base and knowledge background are built in and they became the foundation for later analysis. Kumar (2005) insists that the literature review is one of the essential preliminary tasks, furthermore, expresses the importance of integration of the research with existing theories, especially when conducting a research study at high academic level. The functions of literature review are variety. Besides giving the background of theory to the research, it makes the methodology become better, and extends the researcher’s knowledge on the topic of research. For this research, the literature review is precious because there is a huge source of previous works linking to the research’s main subject, thus the researcher is able to choose and implement the effective and high quality method. The attempt to adjusting liquidity factor to VaR model is recognized among a lot of studies and they depends on the quantitative methods on the data from stock market, the same approach is suggested for using do complete the research.
3.2.2 Secondary information The combination of sources of data and other information collected by others and saved in several forms composes secondary information (Stewart, 1993). The variety of sources and forms of secondary data is recognized, for example, it can easily be found in a company reports, internet data resource or books and journal. There are a number of benefits from this kind of information. Kamins (1993) thinks that it is fast, inexpensive and efficient to use secondary data for research, due to its large availability. Veal (1992) agrees with this idea by supplying more evidences, for example, the researcher only needs a few months to collect high quality secondary data without distance obstacle while it will take a year or more to obtain primary data. Furthermore, the term “secondary” does not imply the importance of the data, compared with primary information. It only links to the existing information that can help the researcher quickly gain the basic knowledge to do their work instead of repeat the investigation on an old topic. Due to the dissertation objective and condition, the dissertation is extremely conducted by using the secondary data sources with careful consideration and evaluation. Data is mainly chosen as the closing price, which indices the daily returns of six companies’ equities and grouped into two portfolios. The statistics were accurately downloaded from the Viet stock database (www.vietstock.com.vn) under the website permission. Besides, as the time and data size are important factors within the assessing information process and sometimes they can affect the outcomes of research (Stewart, 1993). In order to make certain that the collected information is “up-to-date enough for current decision” (Kotler, 2008), the calendar year of the dissertation is considered as one year period, from 02/01/2009 to 06/01/2010. In addition, with the purpose to gain the initial insight into the research subject matter, this study consults a growing literature on Liquidity Risk Management and Value at Risk estimation. A wide range of books and journal articles are investigated in Chapter two to explain why carrying out the research and which models are useful to apply for findings and analysis. Text books are one of the most reliable sources offering the good starting point for the researcher in obtaining the basic knowledge. However, the books tend to be less up-to-date and helpful than the journal because they are often used for reading and teaching, furthermore, authors need longer time to publish their books than journal articles. Thus, a number of financial journals and e-journals will presented as the main source of data to cite and reference for this study.
3.2.3 Data analysis After collecting the data, the next step of research project is analyzing them, in other words, the data will be ordered and structured to answer key research questions (Sharp et al. 2002). With such a dissertation in finance with risk management, the quantitative analysis basing on sets of variables and substantial samples will be involved. According to Blaikie (2003), there are four types of quantitative data analysis, depending on the purpose of research: univariate descriptive analysis, bivariate descriptive analysis, explanatory analysis and inferential analysis. As the study’s intention is presenting the VaR and LVaR of two portfolios in Vietnam Stock Market, then evaluate the importance of integrating liquidity component to market risk estimation, the research will apply the bivariate descriptive analysis. Using this type of analysis, it authorizes the researcher to establish similarities or differences between the VaR and LVaR estimated for two portfolios, as well as to clarify the connection between them. The process of quantitative analysis on the secondary information is assisted by Microsoft Office Excel software spreadsheets and trial @Risk 6.0 tool for Excel. These programs will help to calculate the VaR and LVaR of two portfolios, following two different approaches as Historical Data Method and Variance-Covariance Method. The outcomes of calculation process are the base to make a judgement about the significance of adjusting Liquidity into Value at Risk to measure market risk. After the analysis, a recommendation for a better measure of Risk to improve Risk Management within financial institutions will be given.
3.2.4 Possible limitations
Firstly, the limited time due to submission deadline is one of obstacle for the author to completely estimate and analyse the VaR and LVaR following all popular approaches. Although the study wanted to calculate as many of approaches as possible, there are only two methods conducted as Historical Simulation and Variance-Covariance. It is suggested that more time should be spent to apply at least one more approach like Monte Carlo Simulation for more variable outcomes.
Secondly, because of fully analysing on secondary data, the paper seems to have some shortcomings of these data. Although the data is gotten from viet stock database, one of the most reliable sources for investors in Vietnam, its accuracy still has to be checked. The sample size, which is packed in 252 daily share prices for each stock, is quite small, resulting to a limitation in research’s reality. Moreover, because the information on Vietnamese stock market is not easily to access and collect, it takes time to choose the suitable source, as well as find the high value data. The obstacle of language is also considered to be one limitation of this research, because it is written in the language which is not the mother language of the author. During the research period, the findings and analysis is still affected by language mistakes. Though of these limitations, the study has made an effort to explore the new knowledge and the outcome will be presented in the next chapter.

4. EMPIRICAL FINDINGS AND ANALYSIS In this section, all research findings will be presented by an application of the Liquidity adjusted Value at Risk model provided by Bangia et al. (1999) on the Vietnamese Stock Market. As the objectives of this study contains two issues. At first, the chapter calculates two kinds of traditional VAR and LVaR of two portfolios and then compares the results to highlight the significance of incorporating liquidity into VaR Method. Furthermore, the components of market risk and liquidity risk in the LVaR will be computed to support the above idea. In the next step, basing on the backtesting’s outcomes, the research wants to find out which kind of approach between Historical Data and Variance-Covariance is more suitable and accurate in compute VaR and LVaR.
4.1 Data descriptions
As mentioned in the Methodology chapter, two portfolios of stocks that are currently trading on Vietnamese Stock Market are used for the research. Establishing from 1998, the Vietnamese Stock Market includes two stock exchange, known as Hochiminh city Stock Echange (HoSE) and Hanoi Stock Exchange (HNX). The difference between two Stock Exchanges is the size for trading. In fact, the HNX is quite small in comparison with the HoSE. For the first portfolio, from the HoSE, three chosen stocks are Asia Commercial Bank Equity (ACB), Saigon Securities Inc. Equity (SSI) and Kim Long Securities Corporation Equity (KLS) with a proportion 40%, 30%, and 30% respectively. Otherwise, three stocks composing the second portfolio are Viglacera DongTrieu Join-stock Company Equity (DTC), HAI Agrochem Join-stock Company Equity (HAI) and Bim Son Cement Company (BPC), which are also invested with proportion 40%, 30% and 30% respectively and trading on HNX. Due to the aim of research is test the importance of integrating liquidity into value the market risk, the way to categorize three different stocks into two portfolios bases on the liquidity level of each Equity, resulting to the different liquidity of portfolios. Moreover, the liquidity of Equities can be recognized via such factors as bid-ask spreads, trading volume or turnover value (Breen, 2002). Thus it is simple and evident to examine one of these factors as the foundation to divide which Portfolio is more liquid and which is less liquid. In fact, on December 30, 2011, the turnover of equities in the first portfolio as ACB, SSI and KLS reached 32,801 million of VND, 18,915 million of VND and 25,263 million of VND respectively. On the same day, the volume of turnover recorded for three Equities of the second portfolio in comparison was quite small. While DTC turnover was 100 million of VND and HAI turnover was 598 million of VND, the amount for BPC was only 129 million of VND. As can be seen, the first portfolio is highly more liquid than the second one. Thanks to the development of technology and internet in particular, the research used the Vietstock Data Resources (vietstock.vn) to collect the share prices (See appendix 1), trading volumes, turnovers value and the bid, ask price (See appendix 2) of equities composing two portfolios in one year period, from the beginning of 2011 to the beginning of 2012. The data, which represents 252 trading days, is opted to estimate the VaR and LVaR in a one day time horizon, following Historical Data Method and Variance-Covariance Method.
4.2 Estimation results
4.1.1 VaR According to Bangia et al. (1999), the first stage requires estimating Value at Risk from the return. The gains and losses of each equity and portfolio are in two kinds: normal daily return or log-normal daily return. The decision of applying which kind is made basing on the assumption and requirement for different methods. The outcomes and explanation after using two methods: Historical simulation and Variance-Covariance are shown below, will help to reach VaR results and bring about the necessary conditions for the next step of the research.
4.1.1.1 Historical Simulation Method By the approach Historical Simulation, the VaR will be estimate by one of the simplest method. The process begins with calculating the actual daily normal returns of every security. The estimation is presented in six histograms (see the Appendix 3): In terms of ACB: Figure 13. In term of SSI: Figure 14. In term of KLS: Figure 15. In term of BPC: Figure 16. In term of HAI: Figure 17. In term of DTC: Figure 18. From the calculation, the daily returns of two portfolios are computed and re-arranged in order from the worst value to the best value. Two sets of 251 observations then are plotted in two different histograms (See Figure 1 and Figure 2). It is worthy to clarify that each points of the histogram are respective to the frequency of the amount of losses/gains every single days. Indeed, the highest point of the histogram of liquid portfolio recorded no more than 39 days in which the daily returns was approximately from 0 to 10,000 VND. Similarly, at the highest point of the less liquid portfolio, there were 57 days in history when the daily returns stayed from 0 to 10,000 VND. Because the returns continuously grow from the left to the right of the x-axis, the biggest losses obviously are on the left tail of the histograms. Moreover, there are 251 observations, resulting to each returns contributed to 1/251 of total portfolio’s gains/losses. With 95% confidence, it is expected that the worst 5% losses or the VaR respectively is the thirteenth lowest returns, which locates on the left tail. As can be seen, both of VaR calculating for the liquid portfolio and less liquid portfolio is around losses of 30,000 VND to 40,000 VND. However, the accurate VaR for each portfolio is dissimilar. The liquid portfolio gets the value of -39,208 VND, accounted to 3.9% while the less liquid portfolio gets the value of -31,292 VND, accounted to 3.1%. It means that the investor, who is holding the liquid portfolio, can be 95% confident that his current portfolio will not lose exceed 3.9% in each trading day. The other investor, who owns the less liquid portfolio, expects the worst daily loss may be less than 3.1%, with the same 95% confidence. Nevertheless, there is still 5% chance that the worse loss will happen for both of these investors with their investments.

Figure [ 1 ]: Histogram of liquid portfolio's gains and losses

Figure [ 2 ]: Histogram of less liquid portfolio's gains and losses
4.1.1.2 Variance – Covariance Method The VaR calculation process with the Variance-covariance approach bases on the main assumption of normal distribution of log-returns. The normal distribution of return of each stock is displayed in the graph below: In regards to ACB: Figure 3. In regards to SSI: Figure 4. In regards to KLS: Figure 5. In regards to BPC: Figure 6. In regards to HAI: Figure 7. In regards to DTC: Figure 8. With the effort to calculate the worst losses that could occur, the main output of estimation is Value-at-Risk VaR= ∝xTx, regarding to two portfolios. Within the formula, at the confidence level 95%, α = -1.645, xT = (4/10, 3/10, 3/10), x is the variance-covariance matrix of daily log returns.

Figure 3: Normal Distribution of ACB's daily log return

Figure 4: Normal Distribution of SSI’s daily log return Figure 5: Normal Distribution of KLS’s daily log return Figure 6: Normal Distribution of DTC’s daily log return Figure 7: Normal Distribution of HAI’s daily log return Figure 8: Normal Distribution of BPC’s daily log return

From the returns of two portfolios in one year period, the matrix of Variance and Covariance of liquid and less liquid portfolio’s returns are presented in Table 1 and Table 2. The covariance is known as a measure of how much two variables change together while the variance is a special state of the covariance. It can run from -1 to +1 and cover a wide range of numbers. Therefore it is able to explain that the matrix of Variance and Covariance in table 1 and table 2 implies the dependence level of each pairs of equities inside two portfolios. For simplification, an example from table 1 can be taken. The covariance between ACB and SSI at -0.001% suggests that the higher than average returns of ACB’s log returns tends to be paired with lower than average returns of SSI’s log returns. In contrast, the positive covariance between KLS and ACB indicates that the log returns of KLS and ACB tend to move following one direction, for instances, they can move up or down together. By the same way, when the statistic of 0.013%, which is laying on the cross road of BPC returns and DTC returns in table 2, we can predict that if the returns of BPC go up, the DTC’s returns will go down in the same time period and vice versa.
Table 1: The Variance-Covariance matrix of liquid portfolio's returns Matrix | ACB | SSI | KLS | ACB | 0.087% | -0.001% | 0.077% | SSI | -0.001% | 0.213% | 0.004% | KLS | 0.077% | 0.004% | 0.193% |
Table 2: The Variance-Covariance matrix of less liquid portfolio's return Matrix | DTC | HAI | BPC | DTC | 0.155% | 0.003% | 0.013% | HAI | 0.003% | 0.097% | 0.017% | BPC | 0.013% | 0.017% | 0.107% | In addition, the standard deviations of securities’ returns are reported in Table 3. As a quantitative measure of the variation of specific returns to the mean of returns, the statistics of six equities run from 0.02 to 0.07. As can be seen, the standard deviation of ACB is the smallest; this indicates that the ACB log returns in one year period from 2009 to 2010 are quite clustered around the mean at 0.114%. In comparison, the returns of HAI seem to be quite spread far apart from the average returns at 0.545%, resulted from the largest standard deviation.
Table 3: The Standard Deviation of each equity | Minimum | Maximum | Mean | Standard Deviation | ACB | -7.18% | 6.76% | 0.114% | 0.0295 | SSI | -43.19% | 19.91% | 0.447% | 0.0462 | KLS | -23.42% | 6.75% | 0.355% | 0.0439 | DTC | -11.29% | 7.06% | 0.312% | 0.0397 | HAI | -40.88% | 74.79% | 0.545% | 0.0705 | BPC | -7.70% | 7.30% | 0.353% | 0.0328 | These data are used to calculate VAR. The results show that with the liquid Portfolio, the daily VaR is 4.34% and with less liquid portfolio the outcome is 3.67%. Consequently, the expected largest loss at 95% confidence on the liquid portfolio, (equally 43,400 VND) is considerable smaller than the one on the less liquid portfolio (equalled 36,700 VND).
4.1.2 LVaR
The second value that is needed for calculating LVaR is the illiquidity component, which is known as Liquidity term (½ (Spread+ α.σt,spread)), according to Bangia et. al, 1999. At first, the daily spread of ask and bid prices of each stocks are computed basing on the weighted data from the source of vietstock (See Appendix 2). To assist the LVaR calculation process, these spreads are accounted in percentage format by dividing the bid-ask spread by the midpoint of the bid and ask prices: Spread %=ask -bidmid. Then the spreads are relatively combined to make a series of daily spread for each portfolio.
Table 4 reports the estimates of Spread term contributed to the Liquidity Adjusted Value at Risk for both the liquid and less liquid portfolio in the sample chosen on Vietnamese Stock Market. The third row represents the average bid-ask spread for different equities which composes two portfolios. The fourth row shows the estimation of the average spread of two portfolios in one year period. As can be seen, the spread of almost stocks’ bid-ask prices runs from 3% to 4%, for example, 3.13% spread calculated for SSI, 3.62% for ACB. The spread of DTC and BPC are little higher but the statistic are under 4%. HAI reports the spread at 4.51%, when the biggest number belongs to KLS’s spread at 4.84%. On the fifth row, the small standard deviation of bid-ask spread suggests that the amount by which the ask price exceeds the bid price are relatively tightly bunched together. In particular, the standard deviation of spread is accounted as 0.02 for Liquid portfolio and 0.03 for the Less Liquid Portfolio.

Table 4: Average value and standard deviation of spreads of two portfolios | Liquid Portfolio | Less Liquid Portfolio | | ACB | SSI | KLS | DTC | HAI | BPC | Spread | 3.62% | 3.13% | 4.84% | 3.92% | 4.51% | 3.85% | | 3.84% | 4.06% | σt,spread | 0.02 | 0.03 |
Basing on the series of historical data, the worst possible spreads of two portfolios are estimated. Similarly to the case of VaR, the worst movement of spread is calculated via 252 historical data and a histogram of distribution for bid-ask spread of two portfolios are created (see Figure 9 and Figure 10). As can be seen, the distribution of spread is far distinctive to the normal distribution.

Figure [ 9 ]: Bid-ask spread distribution of liquid portfolio

Figure [ 10 ]: Bid-ask spread distribution of less liquid portfolio
With 95% confidence, the worst movement bid-ask spread for portfolio is decided as the sixth lowest spread of bid-ask price. The liquid portfolio containing SSI, KLS and ACB gets the result at 0.72% when the less liquid portfolio of DTC, HAI and PCB obtains the worst spread value at 1.24%. By regressing from the formula, the scaling factor α respectively is -1.84 and -0.87. The liquidity component in LVaR is then estimated by dividing the worst possible spread by two. Applying the Bangia formula, this portion is added to the Value at Risk, to calculate LVaR: LVAR=VaR+ L1
The integration of liquidity risk increases the worst returns at 95%, which was estimated in the previous VaR calculation section and creates a new value, LVaR. The previous process gave two different results of VaR for each portfolio, following two separate methods. Thus, the LVaR will receive the same number of results. With the Historical Method, the overall Liquidity Adjusted Value at Risk of liquid portfolio, given a 95% confidence is 4.28% when the same measure of less liquid portfolio is smaller, at 3.75%. With the Variance-Covariance Method, the LVaR of Liquid portfolio is 4.70%, in comparison with 4.29% of Less Liquid portfolio.
4.3 Backtesting
In the previous section, there are two different approaches to estimate VaR and each methods directs to different values. The accuracy of VAR value should be tested in order to decide which approach gave more reality and adequate results. The first chosen test is the simplest, named the unconditional coverage test. This test is conducted on Exel worksheet, following these steps. Firstly, the actual daily log-return on one year period is calculated. Secondly, it will be compared with the estimated VaR and LVaR that are obtained from the above section. The number of exceptions is calculated, as well as the percentage of exceptions. The results of the amount of returns that exceeds the Var and LVaR are shown on the Figure below, respectively to Liquid portfolio and Less Liquid portfolio.

Figure [ 11 ]: Backtesting result for liquid portfolio

Figure [ 12 ]: Backtesting results for less liquid portfolio
In order to test whether the unconditional coverage of these VaR and LVaR Model is equal to the nominal confidence level, the Likelihood Ratio (LR) test, introduced by Kupiec (1995) is applied. The LR is written as:
LR=2ln⁡[1-NT1-pT-N(NTp)N
Table and table are concerned regarding the rejection of the VaR and LVaR at the 5% significance. These tables point out the LR Test Statistics and compare them with critical values at 95% confidence level in order to extend the backtesting process. The Excel function helps to estimate the critical value at 3.84.
Table 5: LR Test Statistic for liquid portfolio | Number violations | % exceptions | LR Statistic | In comparisonwith critical value | VaR(Historical Method) | 15 | 5.95% | 0.45 | < 3.84 | LVaR(Historical Method) | 12 | 4.76% | 0.03 | < 3.84 | VaR (Variance-Covariance Method) | 12 | 4.76% | 0.03 | < 3.84 | LVaR (Variance – Covariance Method) | 10 | 3.97% | 0.61 | < 3.84 |

Table 6: LR Test Statistic for less liquid portfolio | Number violations | % exceptions | LR Statistic | In comparisonwith critical value | VaR(Historical Method) | 14 | 5.56% | 0.16 | < 3.84 | LVaR(Historical Method) | 11 | 4357% | 0.22 | < 3.84 | VaR (Variance-Covariance Method) | 10 | 3.97% | 0.61 | < 3.84 | LVaR (Variance – Covariance Method) | 7 | 2.78% | 3.1 | < 3.84 |

4.4 Analysis
4.4.1 The importance of the integration of Liquidity Risk into VaR
The foundation of Bangia, Diebold, Schuermann and Stroughair Model (1999) is the distinction of the market risk into two segments: market return risk and market liquidity risk. From long time ago, people use the VaR to evaluate market return risk and often pretend not to know the market liquidity risk. Basing on the theory suggested by Bangia et. Al, an attempt to measure the VaR and LVaR of two portfolios with different level of liquidity was carried out through the Findings chapter. An expectation is also implied that the findings could be the evidence showing the significance of adjusting liquidity component into VaR for both liquid portfolio and less liquid portfolio.
Table 7: Liquidity Adjusted Value at Risk results | Liquid portfolio | | Less liquid portfolio | | | Historical Method | Variance-Covariance | Historical Method | Variance-Covariance | VaR | 3.92% | 4.34% | 3.13% | 3.67% | Worst spread | 0.72% | 0.72% | 1.24% | 1.24% | Liquidity term | 0.36% | 0.36% | 0.62% | 0.62% | LVaR | 4.28% | 4.70% | 3.75% | 4.29% |
In table 7, the final outcomes for both portfolios are demonstrated. Obviously, the data in the table are quite clear, let’s see what they show. Before integrating liquidity component, the Historical Data approach results to the higher possible daily worst loss due to the market risk for the liquid portfolio at 3.92%, in comparison with 3.13% of the less liquid portfolio. After adjusting the liquidity term, the daily worst loss which caused by average return risk and exogenous liquidity risk calculated for liquid portfolio is still bigger than for illiquid portfolio, though the gap between two possible worst losses is narrowed. The main reason is that the liquidity component is much larger for less liquid portfolio. Indeed, the liquidity term represents 8.45% of total risk in the LVaR of liquid portfolio while the liquidity term represents 16.51% of total risk in the LVaR of less liquid portfolio. In accordance with the Historical Data approach, the investor holds the liquid portfolio can 95% certain that he will not lose more than 4.28% in one day. At the same time, if he invests to the less liquid portfolio, the worst loss at the same percentage of confidence is smaller, accounted to 3.75%.
Tthe Variance-covariance method also calculates the higher Value at Risk for the liquid portfolio at 4.34% in comparison with 3.67% of less liquid portfolio. This thing is similarly occurred on the Liquidity Adjusted Value at Risk results. The integration of Liquidity component raised the total worst loss for the liquid portfolio to 4.70% and for the less liquid portfolio to 4.29%. As can be seen, in case of less liquid portfolio, the component from the liquidity risk equalled 14.42% of total LVaR is more significant than in case of liquid portfolio. The percentage of the liquidity component of portfolio, which includes SSI, KLS and ACB Equities, is estimated at only 7.69% of LVaR.
In spite of the different outcomes, both of these approaches have reached to a common trend. Whether the Historical Data or Variance-Covariance Method is applied, the VaR and LVaR of liquid portfolio are not too much dissimilar. Otherwise, the LVaR of the portfolio, which higher exposures to liquidity risk, is further different from its VaR. In other words, it is significant to integrate the liquidity risk component into the VaR calculation model to get a more accurate of possible worst losses for the investment. Especially with the illiquid portfolio, the significance of estimating LVaR is more evident. With both of portfolios of equities that are trading on Viet Nam Stock Market, the liquidity component presents around 10% of total LVaR estimation.
4.4.2 Historical Data and Variance-Covariance Method, which is better approach?
There are many factors that make the difference between two VaR calculation methods. One can be explained that while the Historical Data method uses the daily normal return, the Variance-covariance computation is depending on the log return. In particular, although the log return is often used in quantitative finance because of its benefits, such as time additive, mathematically convenient, it still has some drawbacks. Other reason is that because of the disadvantage of each method due to their assumptions, the accuracy of estimated value should be checked and judged through the back testing.
For interpreting the backtesting results, the framework of Basel Committee (1996) is useful to apply. As can be seen, the biggest number of returns that exceeds estimated VaR of two portfolios is resulted from the Historical Simulation. In particular, the outcomes from this method almost fall into the red zone, which is defined by having over ten exceptions. A prediction is suggested that there are not enough multiplication factors applying to the calculation model and it leads to an inaccurate estimation. After integrating the liquidity component, the result of violations has some changes, however, these changes do not much affect the accuracy of the Historical Data method. Both of two portfolio’s exceptions decrease, though they are remained within the red zone. However, the exceptions of less liquid portfolio nearly reach the yellow zone (from five to nine exceptions). The yellow zone is believed to be better than the red zone, similarly to present a more accurate model. This thing is valuable because once again, the importance to adjust illiquidity factor to calculate market risk with the less liquid portfolio is evident.
On the other hand, the backtesting shows that the Variance-Covariance Method is preferable to the Historical Simulation Method. With the more liquid portfolio, the difference between two methods is not worth to be considered, as the results are still unable to shift into the yellow zones in spite of a small decrease. It is noticed that the number of violations using the Variance-Covariance is significantly reduced with the less liquid portfolio. The Variance-Covariance leads 11 exceptions with VaR while a yellow zone is absolutely achieved with LVaR. The integration of liquidity component to Value at Risk for less liquid portfolio in both methods actually improves the accuracy of the model, for instance, with Variance-Covariance, the results moves from red to yellow zone. Though the yellow zone may depict an accurate or less accurate model, the Variance-Covariance, which gives the most adequate outcome, seems to be the better method and it should be applied for both portfolios.
The independence of all methods is also needed to comment. Both methods have no problem with the LR statistics test with the exception of VaR and LVaR result of less liquid portfolio. They passed this test because all of its LR statistics for both portfolios are smaller than the critical value (equalled 3.84).

5. Conclusion and recommendation
5.1 Main evidence and general conclusion
In this paper, based on the review of the related literature on the Value at Risk and integration Liquidity risk into the VaR model together with the findings and analysis of the results from the secondary research, the main judgement and recommendations from the research process will be summed up as follows.
In order to assess the importance of applying LVaR instead of VaR Model for risk management, the first step of this research is inspecting the existing literature that deals with the VaR, LVaR and risk management, as well as choose the framework to estimate LVaR from a number of available methods for applying in the analysis step. It is demonstrated that the range of works that explains the motivation to incorporate liquidity market risk into the most traditional market risk measure – VaR is quite wide; however, they can be divided into three kinds in general. The first one is incorporation of endogenous liquidity risk while the second one is calculating exogenous liquidity risk component and then adjusting to traditional Value at Risk. The other type is the combination of the first and the second one and it requires the complex calculation process. As the research focuses on the integration of exogenous liquidity risk rising from the bid-ask spread volatility of stocks in the market, a Model provided by Bangia et. al (1999) is chosen as the base approach to apply and follow throughout the LVaR estimation.
The data using in the research is the share price and bid-ask price of two portfolios. Each of portfolios has three equities from two Stock Exchange of Viet Nam’s market and they are distinguished by the liquidity level. The analysis collected the data in one year period and generated the main findings about the integration of liquidity risk into VaR Model.
First and foremost, the research reaches a conclusion that though of the usage which kind of calculation methods between Historical Simulation and Variance-Covariance, the component of liquidity risk presenting on the LVaR results is averagely around 10%. This percentage estimation implies the difference between the expected maximum losses, with one is calculated through the traditional VaR Model and one is calculated via the LVaR Model. As can be seen, when adjusting liquidity component, the possible worst return rises to a higher number (in percentage format) and it will require the investors and the financial institutions planning more capital providing against the loss. Being supported by the backtesting results, the accuracy of estimation respects the LVaR Model more than the VaR Model. Indeed, the number of exceptions getting from the unconditional backtesting within LVaR Model is smaller than the one of VaR estimation. The movement of the zone of exceptions also indicates that the LVaR method with the integration of Liquidity market risk component increases the accuracy of risk measure, in comparison with the traditional VaR method.
Secondly, the worst possible returns for both liquid and less liquid portfolio of Vietnamese stocks run in the range from 3% to 5%. It is an estimation of market risk that affects the returns of portfolio. Indeed, the worst possible loss is acknowledged in the case of more liquid portfolio and counted to 4.70%.
Thirdly, the important level for estimating expected worst loss for the investment is higher towards the less liquid portfolio. The analysis shows that in case of the less liquid portfolio, the VaR estimation is quite different with the LVaR estimation. In other words, the liquidity component of the portfolio high exposure to liquidity risk makes up more than 14% of the possible worst loss, for instances, the percentage of liquidity component calculating by the Historical Simulation Method is over 16.51% and by the Variance-covariance Method is over 14%. Otherwise, the LVaR does not really refine the market risk measure for the liquid portfolio as the liquidity component is quite small.
Last but not least, the backtesting interpretation indicates the more accuracy and independence of the calculation through the Variance-Covariance Method when comparing with the Historical Simulation Method. Two tests were carried out: the unconditional coverage test and test of independence. The unconditional coverage test shows that the Variance-Covariance Method reduces the number of violations in case of VaR and LVaR. For example, while the number of exceptions of VaR and LVaR calculated with Variance-Covariance approach almost fall into the yellow, all of the violations in Historical Data approach belong to red zones. Though both of methods are independent as no LR ratio in Variance-Covariance Method is larger than the critical value at 5% confidence level (approximately 3.84%).
Thus, we can conclude that market liquidity risk is an angle of total market risk, which has been neglected by traditional value at risk model. The negligence obviously leads to the extension of Model to combine liquidity component into the VaR estimation. Basing on the Bangia et. al LVaR Model, the exogenous liquidity component resulting from the influence of bid-ask spread is affirmed to significantly adjusted into the traditional VaR Model to improve the accuracy and independence of the calculation of the worst possible loss for an equity or a portfolio. This thing is especially meaningful with the portfolio that has the low liquidity level. The inaccuracy of a VaR and LVaR estimation may lead to the failure in arranging market risk capital requirements, thus, threaten the safety of the financial institution.
5.2 Recommendations
The recommendations are given as to helping the investors and financial institutions to improve the adequacy and accuracy of the worst possible return estimation due to the overall market risk. * Using more than or at least two methods to estimate VaR and LVaR.
The suggestions come from the knowledge that there are a number of available methods to calculate VaR and the more number of methods, the more adequate and accurate measure that the investors can achieve. The study has been executed and it demonstrates that the numbers of VaR and LVaR estimations are variable. Regarding to one portfolio, the worst possible returns at a constant confidence level are different, depending on which approach is applied. As there is no agreement about the most perfect approach to measure risk by VaR, it is necessary to carry out several methods to be more adequate. Besides the Historical Simulation approach and Variance-Covariance approach, one of the other popular and important methods which can be used is Monte-Carlo. Because of the limitation in the research time, as well as the difficulties in collecting data, there were two approaches applied. * The larger collected data
The estimation of LVaR providing by Bangia et. al (1999) following Historical Simulation and Variance-Covariance was completed basing on 252 days data in one year period. The analyses of historical data have both advantages and disadvantages. From the historical daily returns of equity, the Variance-Covariance finds the average returns and also the statistic drawing that how the daily data is clustered around this average number within a set of data. As can be seen, the average returns and the standard deviation, two important factors of this method are much influenced by the size of collected data and by trend of the period. The same comment is made with the Historical Simulation; however, with the Historical Simulation method, the dependency of result on the data size is bigger. The main reason is given as the Historical Data approach principally computes the possible future loss by what happened over a specific historical window. It requires data on all risk factors during a long historical period with the aim to give an accurate representation of what might happen in the future. Such of a short time period that is only one year may not underestimate or upper estimate the VaR and LVaR measures. * Applying the LVaR instead of tradition VaR model
In the conclusion, the significance of incorporating Liquidity component into the VaR calculation is generated. Many of financial institutions including commercial banks, investment banks, financial funds or others has neglected counting this part of market risk. It resulted to a fast growing number of failure and bankruptcy, especially the huge damage to the global economy during the recent financial crisis. By applying the suitable model, the relative high level of accuracy of the worst possible loss due to the overall market risk in the future is ensured. The estimation for the capital market risk requirements is therefore correct and the safety of the financial position of institutions is also more guaranteed. Besides the exogenous liquidity risk, the endogenous liquidity risk component is recommended to be adjusted by combination the Bangia model with other endogenous liquidity risk estimation models or usage of other generated models for two kinds of liquidity risk component.
5.3 Suggestion for further study While finalizing the research, the author became aware of that the researched topic can be extended or analysed from a different points of view to reach a broader perspective of adjusting Liquidity Risk into Value-at-Risk Model. There are two flashed ideas which rise from the base knowledge of Liquidity risk management of the author. The methodology to conduct the other study has still needed to be discussed. These two suggestions below are only limited as the initiation for another researches on a wide topic like VaR and Liquidity risk management. Otherwise, the idea contributing to the suggestion is hopefully useful for the related and further study research. The first suggestion for extending the research is due to a fact that the liquidity risk contains both of exogenous and endogenous aspects. As this research has calculated the percentage of exogenous component within the total LVaR for two portfolios on Vietnamese Stock Market, it will be natural and logical to continue adjust the rest of liquidity risk aspect in order to generally compute the worst possible returns for the portfolio. In addition, it may be helpful to affirm the significance of integration of Liquidity Risk into Value at Risk Model as the increase of total liquidity component within the LVaR estimation. The second suggestion is also come from the above reality; however, the research should be retaken from the beginning as in this case, only the endogenous liquidity risk component is wanted for representing the liquidity component in LVaR. Starting with the same review of the literature related to the Liquidity Risk management and VaR Method and integrating Liquidity risk aspect, the research can continue by explain and present the knowledge about endogenous liquidity risk component. Besides, the motivation to adjust this risk component in total market risk, the introduction and explanation for the Model to apply are necessary and determined clarified. The findings basing on the required data of the Model for two portfolios with different liquidity risk level, and also following different approaches will be presented and analysed. At the last step, the conclusion is expected as the significance of incorporating endogenous liquidity risk into the VaR Model and the supposed highest loss will be used for the capital market risk requirement estimation.

References
Bangia, A., Diebold, F., Schuermann, T. and Stroughair, J., 1999. Liquidity on the outside, Risk (12 June 1999) paper 68-73
Banks, E., 2002. The simple rules of risk. England: John Wiley & Son
Basle Committee on Banking Supervision, 1996. Supervisory Framework for the use of “backtesting” in conjunction with the internal models approach to market risk capital requirements. Available from: http://www.bis.org/publ/bcbs22.pdf
Bessis, J., 1998. Risk management in banking:. John Wiley & Son
Blaikie, N.W.H., 2003. Analyzing quantitative data: from description to explanation. SAGE
Breen, W.J., Hodrick, L.S. and Korajczyk, R.A., 2002. Predicting Equity Liquidity. Management Science, Volume 48, No.4, paper 470-483. Available from: http://www.jstor.org/pss/822546
Burner, R. F and Carr, S. D. (2007) “Lessons from the Financial Crisis of 1907”, Journal of Applied Corporate Finance, Vol. 19, No. 4, pp. 115-124
Collis, J., and Hussey,R.,2003. Business research: a practical guide for undergraduate and postgraduate Students.2nd ed. Basingstoke:Palgrave Macmillan.
Corwin, S.A., and Schultz, P.J., 2010. A simple way to estimate bid-ask spreads from daily high and low prices. Available from: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1106193
Culp, C.L., 2001. The risk management process: business strategy and tactics. Volume 81 of Wiley Finance John Wiley and Sons.
Culp, C.L., Miller, M.H. and Neves, A.M.P., 1998. Value at Risk: Uses and Abuses. Journal of Applied Coporate Finance Volume 10 Issue 4, pp. 26-38 Available from: http://www3.interscience.wiley.com/journal/119133221/abstract?CRETRY=1&SRETRY=0
David, J., 2009. Risk and reward.BRW Volume 31 issue 19 (2009-05-14) ISSN: 0727-758X. Available from: http://linksource.ebsco.com/ls.48579438-CB85-4BD2-B500C0D055272560.true/linking.aspx?sid=webfeat&genre=article&issn=0727758X&date=20090514&spage=53&volume=31&issue=19&title=BRW&atitle=RISK%20AND%20REWARD.&aulast=James,%20David
Dermine, J., Bissada, Y.F., 2002. Asset and Liability Management. 2nd edition, Financial Times
Duffie, D., 1997. An overview of Value at Risk. Journal of Derivatives, Vol. 4, No. 3, pp. 7-49. Available from: http://www.iijournals.com/doi/abs/10.3905/jod.1997.407971
Eftekhari, B., Pedersen, C.S. and Satchell, S.E., 2000. On the volatility of measures of financial risk an investigation using returns from European markers. The European Journal of Finance, Volume 6, pp. 18-38 Available from: http://web.ebscohost.com/
Ernst, C.M., Stange, S., and Kaserer, C., 2009. Accounting for Non-Normality in Liquidity Risk. CEFS Working Paper No. 2008-14. Available from: http://ssrn.com/abstract=1316769
Fox, R., 2009. Control system. Available from: http://wf2dnvr16.webfeat.org/yTBoN14412/url=http://content.ebscohost.com/pdf23_24/pdf/2009/DYX/22Oct09/45104424.pdf?T=P&P=AN&K=45104424&S=R&D=bth&EbscoContent=dGJyMNHr7ESeprU4y9fwOLCmr0iep7ZSsay4S7KWxWXS&ContentCustomer=dGJyMPGts0y1ra5QuePfgeyx44Hy7fEA, accessed 20 January, 2010
Frenkel, M., Hommel, U., Dufey,G. and Rudolf, M., 2005. Risk management: challenge and opportunity. 2nd edition, Springer
Friedlob, G.T., Welton, R.E., 2001. Keys to reading an annual report. 3rd edition, Barron's Educational Seriesa
Furceri, D., Durand, A.Z., 2009. The real effect of financial crises in the European Transition Economies. Available from: http://ideas.repec.org/p/hal/journl/halshs-00431044_v1.html, accessed 16 January, 2010
Gallati, R.R., 2003. Risk management and capital adequacy. McGraw-Hill Professional
Goldberg, L.R., MIller, M., Weinstein, J., 2007. Beyond Value at Risk: Forecasting Portfolio Loss at Multiple Horizons Available from: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=102344
Greuning, H.V., Bratanovic, S.B., 2009. Analyzing banking risk: a framework for assessing corporate governance and risk management. 3rd edition, World Bank Publications
Hart, C., 1998. Doing a literature review: releasing the social science research imagination. SAGE
Hitchner, J.R., 2003. Financial valuation: application and Models, volume 132 of Wiley Finance. John Willey and Sons
Holmstrom, B., Tirole, J., 2000. Liquidity and Risk Management. Journal of Money, Credit and Banking, Vol. 32, No. 3, Part 1 (Aug., 2000), pp. 295-319 Available from: http://www.jstor.org/stable/2601167?origin=JSTOR-pdf
Kumar, R., 2005. Research methodology: a step-by-step guide for beginners. 2nd edition SAGE
Kroszner, R.S., 2008. Liquidity-Risk Management in the Business of Banking. Available from: http://linksource.ebsco.com/ls.48579438-CB85-4BD2-B500-C0D055272560.true/linking.aspx?sid=webfeat&genre=article&issn=0890927X&date=2008-10-24&spage=1&volume=2008&issue=33&title=FRBSF%20Economic%20Letter&atitle=What%20Is%20Liquidity%20Risk%3F&aulast=Lopez,%20Jose%20A
Lam, J., 2003. Enterprise Risk Management: from incentives to controls, Volume 181 of Wiley Finance, John Wiley and Sons
Lee,N and Lings,I.,2008.Doing Busines Research:A guide to theory and practice.1st ed.London:SAGE
Lore, M., Borodovsky, L., 2000. The professional’s handbook of financial risk management. Butterworth-Heinemann
Maharaj, A., 2005. Megabank Consolidations in the United States: The Enigma Continues.iUniverse.
Manganelli, S. and Engle, R.F., 2001, Value at Risk models in finance. Available from: http://www.exinfm.com/training.pdfiles/variskbiz.pdf
Matz, L.M., Neu, P., 2007. Liquidity risk measurement and management: a practitioner's guide to global best pratices. Volume 408 of Wiley finance series. John Wiley and Sons.
Martin, A., 2009. Designing a strong LRM Framework. Available from: www.garp.com/events/apc2009/andrewmartin.pdf
Pastor, L., Stambaugh, R.F., 2003. Liquidity Risk and Expected Stock Returns. The Journal of Political Economy, Vol. 111, No. 3 (Jun., 2003), pp. 642-685. The Univeristy of Chicago Press. Available from: http://www.jstor.org/stable/3555255
Rawls,S.W., III, Smithson, C.W., 1990. Strategic Risk Management. Volume 2, Issue 4, Pages 6-18, Journal of Applied Corporate Finance, Morgan Stanley
Rosalind, R., 2009. The importance of being liquid. Available from: http://wf2dnvr16.webfeat.org/yTBoN14215/url=http://content.ebscohost.com/pdf23_24/pdf/2009/ENT/01Nov09/44903338.pdf?T=P&P=AN&K=44903338&S=R&D=bth&EbscoContent=dGJyMNHr7ESeprU4y9fwOLCmr0iep7ZSsKi4Sq%2BWxWXS&ContentCustomer=dGJyMPGts0y1ra5QuePfgeyx44Hy7fEA
Roughley, R., Dyton, R.E., Loscombe, J.E., Souyave, K.G and Symes, C.T., 1987. Risk management practical Techniques to Minimise Exposure to Accidental Losses. England: Kogan Page
Schröck, G., Steiner, M., 2002. Risk Management and Value Creation in Financial Institutions. John Wiley & Sons
Schwartz, E., 2010. Liquidity Risk still on regulatory data. American Banker Volume 175, issue 22. Available from: http://web.ebscohost.com/ehost/detail?vid=2&hid=9&sid=b99808a7-fe2b-403e-b9e7098ec643452b@sessionmgr14&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#db=bth&AN=48066174
Siems, Thomas F. Risk analysis. The Blackwell Encyclopedia of Management. Cooper, Cary L. Blackwell Publishing, Blackwell Reference Online. Available from: http://www.blackwellreference.com
Stange, S., Kaserer, C., 2009. Market Liquidity Risk - An Overview (March 18, 2009). CEFS Working Paper Series 2009 No. 4. Available from: SSRN: http://ssrn.com/abstract=1362537
Stange, Sebastian and Kaserer, Christoph, 2009. Why and How to Integrate Liquidity Risk into a VaR-Framework (February 13, 2009). CEFS Working Paper No. 2008-10. Available from: SSRN: http://ssrn.com/abstract=1292289
Stange, S., Kaserer, C., 2009. Why and How to Integrate Liquidity Risk into a VaR-Framework (February 13, 2009). CEFS Working Paper No. 2008-10. Available from SSRN: http://ssrn.com/abstract=1292289
Stewart, D.W., Kamins, M.A., 1993. Secondary research: information sources and methods. Volume 4 of Applied social research methods series. 2nd edition SAGE
Toggins, W.N., 2008. New Econometric Modelling Research. Nova Publishers.
Waring, A., Glendon, A.I., 1998. Managing risk. Cengage Learning EMEA

Appendix 1: The daily share price of equities in one year period The daily share price | ACB | SSI | KLS | DTC | HAI | BPC | 04/01/2011 | 27.90 | 27.50 | 12.50 | 41.00 | 21.50 | 10.00 | 05/01/2011 | 27.90 | 26.70 | 13.00 | 44.00 | 21.90 | 9.90 | 06/01/2011 | 28.40 | 26.70 | 12.10 | 43.00 | 21.50 | 10.00 | 07/01/2011 | 29.20 | 26.70 | 11.60 | 44.60 | 21.80 | 10.10 | 10/01/2011 | 28.60 | 26.50 | 12.40 | 41.90 | 22.00 | 10.00 | 11/01/2011 | 28.60 | 25.70 | 12.40 | 42.60 | 21.90 | 9.70 | 12/01/2011 | 28.50 | 24.50 | 12.50 | 42.60 | 22.00 | 9.80 | 13/01/2011 | 28.30 | 24.50 | 12.20 | 42.60 | 21.60 | 9.90 | 14/01/2011 | 28.30 | 23.50 | 12.00 | 42.60 | 21.90 | 9.70 | 17/01/2011 | 28.00 | 22.40 | 12.20 | 40.00 | 22.00 | 9.70 | 18/01/2011 | 28.10 | 21.30 | 11.90 | 40.00 | 21.50 | 9.70 | 19/01/2011 | 28.10 | 22.30 | 12.00 | 40.50 | 21.80 | 9.40 | 20/01/2011 | 28.00 | 21.20 | 11.80 | 40.50 | 21.90 | 9.30 | 21/01/2011 | 28.00 | 21.40 | 11.50 | 40.70 | 22.00 | 9.60 | 24/01/2011 | 28.10 | 21.60 | 11.30 | 40.20 | 22.00 | 9.70 | 25/01/2011 | 28.20 | 20.60 | 11.60 | 40.50 | 21.40 | 9.70 | 26/01/2011 | 28.00 | 20.90 | 11.90 | 40.00 | 21.00 | 9.90 | 27/01/2011 | 27.20 | 21.40 | 11.60 | 41.70 | 20.80 | 9.70 | 28/01/2011 | 27.00 | 21.10 | 11.10 | 44.60 | 20.10 | 9.80 | 08/02/2011 | 26.20 | 20.90 | 11.30 | 44.00 | 20.00 | 9.80 | 09/02/2011 | 26.00 | 21.20 | 10.70 | 44.00 | 20.00 | 9.70 | 10/02/2011 | 26.90 | 22.20 | 10.90 | 42.50 | 20.30 | 9.80 | 11/02/2011 | 26.60 | 21.50 | 11.30 | 41.30 | 20.30 | 9.80 | 14/02/2011 | 26.10 | 21.80 | 11.00 | 43.00 | 20.20 | 9.80 | 15/02/2011 | 26.20 | 22.30 | 10.70 | 43.00 | 20.30 | 10.00 | 16/02/2011 | 26.00 | 23.40 | 10.70 | 42.50 | 19.90 | 10.10 | 17/02/2011 | 25.80 | 24.50 | 10.70 | 41.70 | 20.20 | 10.00 | 18/02/2011 | 25.20 | 24.50 | 10.60 | 44.60 | 19.80 | 9.90 | 21/02/2011 | 24.20 | 25.20 | 10.10 | 47.60 | 19.30 | 9.70 | 22/02/2011 | 24.50 | 24.00 | 9.70 | 45.70 | 19.40 | 9.80 | 23/02/2011 | 24.30 | 25.20 | 9.80 | 42.60 | 18.90 | 10.00 | 24/02/2011 | 23.50 | 26.40 | 9.70 | 42.60 | 18.50 | 10.20 | 25/02/2011 | 22.70 | 27.70 | 9.20 | 40.60 | 18.30 | 9.60 | 28/02/2011 | 24.00 | 28.00 | 8.70 | 40.80 | 19.30 | 10.00 | 01/03/2011 | 24.50 | 28.00 | 9.30 | 40.80 | 19.30 | 9.90 | 02/03/2011 | 25.00 | 27.50 | 9.00 | 40.80 | 19.00 | 9.90 | 03/03/2011 | 24.10 | 28.80 | 9.10 | 40.80 | 18.80 | 9.80 | 04/03/2011 | 24.20 | 30.20 | 9.10 | 41.00 | 18.90 | 9.80 | 07/03/2011 | 25.20 | 31.70 | 8.90 | 42.50 | 19.40 | 9.90 | 08/03/2011 | 25.10 | 33.20 | 9.00 | 40.50 | 19.50 | 9.90 | 09/03/2011 | 24.20 | 34.80 | 9.30 | 41.00 | 19.90 | 9.80 | 10/03/2011 | 25.20 | 36.50 | 9.20 | 42.10 | 19.60 | 9.90 | 11/03/2011 | 25.10 | 38.30 | 9.30 | 42.00 | 19.50 | 10.10 | 14/03/2011 | 25.80 | 40.20 | 9.70 | 41.80 | 19.80 | 10.20 | 15/03/2011 | 26.30 | 42.20 | 10.30 | 41.40 | 19.60 | 10.40 | 16/03/2011 | 27.70 | 44.30 | 10.30 | 41.00 | 19.60 | 10.00 | 17/03/2011 | 27.00 | 46.50 | 10.60 | 40.40 | 19.30 | 10.00 | 18/03/2011 | 27.30 | 44.20 | 10.70 | 41.00 | 20.20 | 10.20 | 21/03/2011 | 27.40 | 42.00 | 11.30 | 40.30 | 20.70 | 10.40 | 22/03/2011 | 27.80 | 39.90 | 12.00 | 40.80 | 20.40 | 10.80 | 23/03/2011 | 29.60 | 38.00 | 12.70 | 42.20 | 19.70 | 10.20 | 24/03/2011 | 28.70 | 36.30 | 12.80 | 40.40 | 19.90 | 10.00 | 25/03/2011 | 28.00 | 34.50 | 12.20 | 40.90 | 20.10 | 10.50 | 28/03/2011 | 29.80 | 22.40 | 13.00 | 41.20 | 20.20 | 10.40 | 29/03/2011 | 29.90 | 21.30 | 13.30 | 41.60 | 19.80 | 9.80 | 30/03/2011 | 30.40 | 22.30 | 13.70 | 43.40 | 19.60 | 10.00 | 31/03/2011 | 30.20 | 21.20 | 13.50 | 44.30 | 19.60 | 9.80 | 01/04/2011 | 28.90 | 21.40 | 12.80 | 43.70 | 19.60 | 10.00 | 04/04/2011 | 28.60 | 21.60 | 12.50 | 41.60 | 20.20 | 10.40 | 05/04/2011 | 29.80 | 20.60 | 13.30 | 41.50 | 20.00 | 10.20 | 06/04/2011 | 30.50 | 20.90 | 14.10 | 43.00 | 20.70 | 10.30 | 07/04/2011 | 32.20 | 21.40 | 15.00 | 43.00 | 20.80 | 10.40 | 08/04/2011 | 33.80 | 21.10 | 16.00 | 45.40 | 20.60 | 10.50 | 13/04/2011 | 33.90 | 20.90 | 16.50 | 48.40 | 20.80 | 10.40 | 14/04/2011 | 34.30 | 21.20 | 17.20 | 45.30 | 21.10 | 10.60 | 15/04/2011 | 36.70 | 22.20 | 18.40 | 43.20 | 22.30 | 11.00 | 18/04/2011 | 39.20 | 21.50 | 19.60 | 46.10 | 22.20 | 11.60 | 19/04/2011 | 41.70 | 21.80 | 20.90 | 49.30 | 21.20 | 11.40 | 20/04/2011 | 41.60 | 22.30 | 21.90 | 52.50 | 21.40 | 10.80 | 21/04/2011 | 42.40 | 23.40 | 23.40 | 49.80 | 21.00 | 10.80 | 22/04/2011 | 40.40 | 24.50 | 22.90 | 48.00 | 20.10 | 10.00 | 25/04/2011 | 37.60 | 24.50 | 21.30 | 51.30 | 19.60 | 10.40 | 26/04/2011 | 35.00 | 25.20 | 19.90 | 52.80 | 19.60 | 10.90 | 27/04/2011 | 37.00 | 24.00 | 18.60 | 51.20 | 20.20 | 10.80 | 28/04/2011 | 36.80 | 25.20 | 17.30 | 53.30 | 20.10 | 10.50 | 29/04/2011 | 35.40 | 26.40 | 16.10 | 51.80 | 20.00 | 10.30 | 04/05/2011 | 35.60 | 27.70 | 15.10 | 50.80 | 20.00 | 10.40 | 05/05/2011 | 35.80 | 28.00 | 15.90 | 46.00 | 21.00 | 10.20 | 06/05/2011 | 36.70 | 28.00 | 17.00 | 43.70 | 22.40 | 10.80 | 09/05/2011 | 39.20 | 27.50 | 18.10 | 46.40 | 23.90 | 11.30 | 10/05/2011 | 41.90 | 28.80 | 19.30 | 49.50 | 24.40 | 10.80 | 11/05/2011 | 41.80 | 30.20 | 20.50 | 52.90 | 25.50 | 11.20 | 12/05/2011 | 44.20 | 31.70 | 21.90 | 49.50 | 26.00 | 10.90 | 13/05/2011 | 43.70 | 33.20 | 23.00 | 51.30 | 25.90 | 11.30 | 16/05/2011 | 43.40 | 34.80 | 23.50 | 50.60 | 25.60 | 11.50 | 17/05/2011 | 42.80 | 36.50 | 23.20 | 50.20 | 26.00 | 11.80 | 18/05/2011 | 42.30 | 38.30 | 23.30 | 50.40 | 25.10 | 11.70 | 19/05/2011 | 40.80 | 40.20 | 22.10 | 52.00 | 26.40 | 11.90 | 20/05/2011 | 43.20 | 42.20 | 23.60 | 51.90 | 25.90 | 12.30 | 23/05/2011 | 44.50 | 44.30 | 25.10 | 54.20 | 26.80 | 12.60 | 24/05/2011 | 45.80 | 46.50 | 26.80 | 53.70 | 27.00 | 12.90 | 25/05/2011 | 45.10 | 44.20 | 28.30 | 53.80 | 27.20 | 13.40 | 26/05/2011 | 44.00 | 42.00 | 27.80 | 53.80 | 26.00 | 13.30 | 27/05/2011 | 42.60 | 39.90 | 26.20 | 53.70 | 27.60 | 13.30 | 30/05/2011 | 44.70 | 38.00 | 27.90 | 53.50 | 27.70 | 13.60 | 31/05/2011 | 44.50 | 36.30 | 29.60 | 56.70 | 27.00 | 13.60 | 01/06/2011 | 44.00 | 34.50 | 29.40 | 55.70 | 27.00 | 13.20 | 02/06/2011 | 42.30 | 34.50 | 27.60 | 57.20 | 27.00 | 14.20 | 03/06/2011 | 42.50 | 36.20 | 27.70 | 57.90 | 28.30 | 15.10 | 06/06/2011 | 44.10 | 38.00 | 29.20 | 57.10 | 30.20 | 16.10 | 07/06/2011 | 46.00 | 39.90 | 31.00 | 58.60 | 31.70 | 17.20 | 08/06/2011 | 44.50 | 41.80 | 30.30 | 62.70 | 33.90 | 18.40 | 09/06/2011 | 45.60 | 43.00 | 31.70 | 66.00 | 36.20 | 17.60 | 10/06/2011 | 48.70 | 45.10 | 33.90 | 70.60 | 38.40 | 16.40 | 13/06/2011 | 52.10 | 47.30 | 36.20 | 75.50 | 36.20 | 15.30 | 14/06/2011 | 55.40 | 49.10 | 37.60 | 80.30 | 33.70 | 16.00 | 15/06/2011 | 53.80 | 51.50 | 35.20 | 81.20 | 34.80 | 15.20 | 16/06/2011 | 55.60 | 49.50 | 36.70 | 75.80 | 35.60 | 14.40 | 17/06/2011 | 57.50 | 50.00 | 37.40 | 78.30 | 34.40 | 13.50 | 20/06/2011 | 53.90 | 52.50 | 34.90 | 77.00 | 33.50 | 14.40 | 21/06/2011 | 50.50 | 55.00 | 32.50 | 72.40 | 32.60 | 14.70 | 22/06/2011 | 48.70 | 57.50 | 30.70 | 67.80 | 32.40 | 14.80 | 23/06/2011 | 51.40 | 60.00 | 32.40 | 69.20 | 33.00 | 14.60 | 24/06/2011 | 51.10 | 57.00 | 31.60 | 73.80 | 30.90 | 14.40 | 27/06/2011 | 48.00 | 56.50 | 29.50 | 69.80 | 29.10 | 13.90 | 28/06/2011 | 44.90 | 59.00 | 27.50 | 65.90 | 31.00 | 14.20 | 29/06/2011 | 47.60 | 61.50 | 28.60 | 62.40 | 30.20 | 13.80 | 30/06/2011 | 49.60 | 62.00 | 29.90 | 66.20 | 30.20 | 14.60 | 01/07/2011 | 49.60 | 59.00 | 30.00 | 70.20 | 29.30 | 14.50 | 04/07/2011 | 49.60 | 72.00 | 29.50 | 75.00 | 27.60 | 15.00 | 05/07/2011 | 50.00 | 75.50 | 27.90 | 70.10 | 25.70 | 14.40 | 06/07/2011 | 46.70 | 79.00 | 26.00 | 68.50 | 27.00 | 14.30 | 07/07/2011 | 47.50 | 75.50 | 26.50 | 70.60 | 27.00 | 14.00 | 08/07/2011 | 47.00 | 79.00 | 26.60 | 73.00 | 28.30 | 14.00 | 11/07/2011 | 48.70 | 77.00 | 27.90 | 71.20 | 28.10 | 14.10 | 12/07/2011 | 48.60 | 73.50 | 28.90 | 70.50 | 27.00 | 14.30 | 13/07/2011 | 48.30 | 70.00 | 28.70 | 70.50 | 27.40 | 14.20 | 14/07/2011 | 47.90 | 69.00 | 28.80 | 71.00 | 26.50 | 14.20 | 15/07/2011 | 46.80 | 68.00 | 28.20 | 70.60 | 25.80 | 14.20 | 18/07/2011 | 45.50 | 65.50 | 26.70 | 68.80 | 26.00 | 14.10 | 19/07/2011 | 45.10 | 62.50 | 26.60 | 72.20 | 27.10 | 14.60 | 20/07/2011 | 45.40 | 59.50 | 27.20 | 73.90 | 27.30 | 15.50 | 21/07/2011 | 46.20 | 62.00 | 28.80 | 75.20 | 26.50 | 15.20 | 22/07/2011 | 45.50 | 63.50 | 27.80 | 75.20 | 25.50 | 14.50 | 25/07/2011 | 43.20 | 66.50 | 26.00 | 74.20 | 26.10 | 15.00 | 26/07/2011 | 43.60 | 67.00 | 26.20 | 79.30 | 26.60 | 15.00 | 27/07/2011 | 43.50 | 65.00 | 26.50 | 83.50 | 27.00 | 15.40 | 28/07/2011 | 44.80 | 64.00 | 27.60 | 78.70 | 28.80 | 15.30 | 29/07/2011 | 47.90 | 63.00 | 29.50 | 84.00 | 30.20 | 15.40 | 01/08/2011 | 49.80 | 60.00 | 31.50 | 89.30 | 28.70 | 15.40 | 02/08/2011 | 48.20 | 58.50 | 33.70 | 88.10 | 29.00 | 15.30 | 03/08/2011 | 47.00 | 60.00 | 34.50 | 85.00 | 28.70 | 14.90 | 04/08/2011 | 45.60 | 60.00 | 32.80 | 85.60 | 30.10 | 14.90 | 05/08/2011 | 46.80 | 58.50 | 34.70 | 90.50 | 30.10 | 15.40 | 08/08/2011 | 46.70 | 56.00 | 34.70 | 92.30 | 29.60 | 15.60 | 09/08/2011 | 47.30 | 55.00 | 35.70 | 94.30 | 29.00 | 15.40 | 10/08/2011 | 47.10 | 54.00 | 35.60 | 92.70 | 29.10 | 15.30 | 11/08/2011 | 47.00 | 56.50 | 35.20 | 82.80 | 28.80 | 15.30 | 12/08/2011 | 46.70 | 59.00 | 34.30 | 80.90 | 29.50 | 15.20 | 15/08/2011 | 46.90 | 61.50 | 35.20 | 77.20 | 29.20 | 15.50 | 16/08/2011 | 46.80 | 64.50 | 34.80 | 76.90 | 29.40 | 15.60 | 17/08/2011 | 47.00 | 64.00 | 35.20 | 74.70 | 31.00 | 15.70 | 18/08/2011 | 48.00 | 63.00 | 36.50 | 73.00 | 30.40 | 16.00 | 19/08/2011 | 47.70 | 66.00 | 35.80 | 70.80 | 30.20 | 15.80 | 22/08/2011 | 47.30 | 66.00 | 35.40 | 72.90 | 29.10 | 16.10 | 23/08/2011 | 46.90 | 68.50 | 34.90 | 73.60 | 30.90 | 16.20 | 24/08/2011 | 47.10 | 70.50 | 35.20 | 75.50 | 30.90 | 16.40 | 25/08/2011 | 47.10 | 69.50 | 35.50 | 76.90 | 30.40 | 16.90 | 26/08/2011 | 47.80 | 68.50 | 37.50 | 77.00 | 30.30 | 16.90 | 29/08/2011 | 48.00 | 71.00 | 38.50 | 74.40 | 31.40 | 16.80 | 30/08/2011 | 47.80 | 70.50 | 38.20 | 72.30 | 32.60 | 16.70 | 31/08/2011 | 47.40 | 70.00 | 37.70 | 71.80 | 33.50 | 16.30 | 01/09/2011 | 46.70 | 70.50 | 37.20 | 73.90 | 34.50 | 16.50 | 05/09/2011 | 46.70 | 71.50 | 37.60 | 74.10 | 35.50 | 16.90 | 06/09/2011 | 48.00 | 69.50 | 39.20 | 75.10 | 35.30 | 17.80 | 07/09/2011 | 47.70 | 69.00 | 39.30 | 74.90 | 33.00 | 18.50 | 08/09/2011 | 47.20 | 70.50 | 38.60 | 73.10 | 32.60 | 18.80 | 09/09/2011 | 46.80 | 70.50 | 37.40 | 73.20 | 30.80 | 18.90 | 12/09/2011 | 46.10 | 72.50 | 37.60 | 73.20 | 32.20 | 18.40 | 13/09/2011 | 46.60 | 74.00 | 38.60 | 74.10 | 32.40 | 18.10 | 14/09/2011 | 46.30 | 73.50 | 39.20 | 74.40 | 31.90 | 18.10 | 15/09/2011 | 45.90 | 73.50 | 39.00 | 72.40 | 32.40 | 18.30 | 16/09/2011 | 46.00 | 72.50 | 39.60 | 72.80 | 32.00 | 17.90 | 19/09/2011 | 46.00 | 73.00 | 39.50 | 72.90 | 32.20 | 18.00 | 20/09/2011 | 46.20 | 75.00 | 40.90 | 74.80 | 32.20 | 18.00 | 21/09/2011 | 48.30 | 75.00 | 42.60 | 77.50 | 32.20 | 17.90 | 22/09/2011 | 48.20 | 75.00 | 41.10 | 76.70 | 32.30 | 18.00 | 23/09/2011 | 47.10 | 75.50 | 40.50 | 77.80 | 33.40 | 18.20 | 26/09/2011 | 46.70 | 77.00 | 41.20 | 78.20 | 33.40 | 19.30 | 27/09/2011 | 46.20 | 80.50 | 42.80 | 79.30 | 33.50 | 20.20 | 28/09/2011 | 47.00 | 80.50 | 45.20 | 78.00 | 32.80 | 18.90 | 29/09/2011 | 46.30 | 79.00 | 45.40 | 76.10 | 32.40 | 18.70 | 30/09/2011 | 46.70 | 79.50 | 46.00 | 75.90 | 32.10 | 18.90 | 03/10/2011 | 47.20 | 78.50 | 49.00 | 77.50 | 32.30 | 19.30 | 04/10/2011 | 47.20 | 80.50 | 50.90 | 77.70 | 31.80 | 19.60 | 05/10/2011 | 46.60 | 82.00 | 48.60 | 77.20 | 30.30 | 19.90 | 06/10/2011 | 45.90 | 80.00 | 48.20 | 73.70 | 29.10 | 20.70 | 07/10/2011 | 44.50 | 81.00 | 45.30 | 73.20 | 29.30 | 22.10 | 10/10/2011 | 44.20 | 85.00 | 45.70 | 76.40 | 29.80 | 23.60 | 11/10/2011 | 44.20 | 85.00 | 45.50 | 74.20 | 30.90 | 25.20 | 12/10/2011 | 44.50 | 83.00 | 46.20 | 76.60 | 30.70 | 24.30 | 13/10/2011 | 44.50 | 78.50 | 46.20 | 77.10 | 32.30 | 24.50 | 14/10/2011 | 45.00 | 80.00 | 47.20 | 78.60 | 33.20 | 25.90 | 17/10/2011 | 45.60 | 82.00 | 48.60 | 79.20 | 34.10 | 26.10 | 18/10/2011 | 45.10 | 80.00 | 47.90 | 78.00 | 32.50 | 26.30 | 19/10/2011 | 46.10 | 82.50 | 37.90 | 78.90 | 34.70 | 26.80 | 20/10/2011 | 48.30 | 86.50 | 40.50 | 82.20 | 34.50 | 27.20 | 21/10/2011 | 46.90 | 90.50 | 41.30 | 87.50 | 35.50 | 28.50 | 24/10/2011 | 46.30 | 93.00 | 41.20 | 93.50 | 37.90 | 30.40 | 25/10/2011 | 46.30 | 97.50 | 41.20 | 100.00 | 40.50 | 31.50 | 26/10/2011 | 46.60 | 102.00 | 40.50 | 107.00 | 43.30 | 33.30 | 27/10/2011 | 48.30 | 107.00 | 40.90 | 114.30 | 43.00 | 33.40 | 28/10/2011 | 49.40 | 102.00 | 39.80 | 119.50 | 42.90 | 32.00 | 31/10/2011 | 47.80 | 100.00 | 37.70 | 117.20 | 43.40 | 29.80 | 01/11/2011 | 46.30 | 98.00 | 36.80 | 109.60 | 43.80 | 27.80 | 02/11/2011 | 46.10 | 98.00 | 36.50 | 103.50 | 41.50 | 28.40 | 03/11/2011 | 44.70 | 94.00 | 34.30 | 97.30 | 43.40 | 26.60 | 04/11/2011 | 45.30 | 96.00 | 35.10 | 104.10 | 40.60 | 25.20 | 07/11/2011 | 43.10 | 91.50 | 32.70 | 97.70 | 38.40 | 26.30 | 08/11/2011 | 42.30 | 87.00 | 30.80 | 91.40 | 39.90 | 27.40 | 09/11/2011 | 42.80 | 86.50 | 31.30 | 96.90 | 42.00 | 28.40 | 10/11/2011 | 43.20 | 89.50 | 32.60 | 98.90 | 42.60 | 26.80 | 11/11/2011 | 43.30 | 88.50 | 33.50 | 101.10 | 39.30 | 25.80 | 14/11/2011 | 41.70 | 84.50 | 31.50 | 94.10 | 38.10 | 26.30 | 15/11/2011 | 41.30 | 82.50 | 30.30 | 95.20 | 38.00 | 26.00 | 16/11/2011 | 41.60 | 84.50 | 31.20 | 97.90 | 39.60 | 25.20 | 17/11/2011 | 42.00 | 85.50 | 31.90 | 98.40 | 37.70 | 25.30 | 18/11/2011 | 41.30 | 86.00 | 31.20 | 93.40 | 38.20 | 25.60 | 21/11/2011 | 41.10 | 84.50 | 31.10 | 96.70 | 37.90 | 24.50 | 22/11/2011 | 40.30 | 85.00 | 31.00 | 96.40 | 38.20 | 22.80 | 23/11/2011 | 40.00 | 85.50 | 31.20 | 99.20 | 38.40 | 21.40 | 24/11/2011 | 40.10 | 89.50 | 32.20 | 100.70 | 38.50 | 21.70 | 25/11/2011 | 40.10 | 88.50 | 32.00 | 97.50 | 38.50 | 22.70 | 28/11/2011 | 39.20 | 85.50 | 30.90 | 93.80 | 38.50 | 22.60 | 29/11/2011 | 38.50 | 84.00 | 30.40 | 90.00 | 36.60 | 21.40 | 30/11/2011 | 36.20 | 80.00 | 28.50 | 86.60 | 35.80 | 22.30 | 01/12/2011 | 34.10 | 76.00 | 26.60 | 80.70 | 35.30 | 20.90 | 02/12/2011 | 34.40 | 74.50 | 25.40 | 77.70 | 37.00 | 20.40 | 05/12/2011 | 36.40 | 78.00 | 26.00 | 83.00 | 38.20 | 19.00 | 06/12/2011 | 38.80 | 81.50 | 27.50 | 88.70 | 38.80 | 19.50 | 07/12/2011 | 38.60 | 77.50 | 26.90 | 83.60 | 38.60 | 18.60 | 08/12/2011 | 37.20 | 78.50 | 26.30 | 80.00 | 38.90 | 19.40 | 09/12/2011 | 37.00 | 79.00 | 26.30 | 81.50 | 38.40 | 19.50 | 12/12/2011 | 37.10 | 79.00 | 26.70 | 82.00 | 38.70 | 20.30 | 13/12/2011 | 36.30 | 76.50 | 26.20 | 84.70 | 38.10 | 19.70 | 14/12/2011 | 34.70 | 73.50 | 24.50 | 79.40 | 38.10 | 19.60 | 15/12/2011 | 35.10 | 72.00 | 23.50 | 84.20 | 35.50 | 20.50 | 16/12/2011 | 34.90 | 68.50 | 22.00 | 79.50 | 37.30 | 20.00 | 19/12/2011 | 36.90 | 71.50 | 22.50 | 82.80 | 38.60 | 19.30 | 20/12/2011 | 37.30 | 70.00 | 22.40 | 85.90 | 38.60 | 19.90 | 21/12/2011 | 36.10 | 66.50 | 21.00 | 80.00 | 38.40 | 20.40 | 22/12/2011 | 36.00 | 67.00 | 20.10 | 78.80 | 38.70 | 20.60 | 23/12/2011 | 37.70 | 70.00 | 21.40 | 82.00 | 39.00 | 21.30 | 26/12/2011 | 38.40 | 73.50 | 22.80 | 82.60 | 39.80 | 21.40 | 27/12/2011 | 37.70 | 73.50 | 24.20 | 80.80 | 39.40 | 20.60 | 28/12/2011 | 37.20 | 74.50 | 24.90 | 81.70 | 37.60 | 21.30 | 29/12/2011 | 37.00 | 78.00 | 26.20 | 79.90 | 38.20 | 21.50 | 30/12/2011 | 37.70 | 81.50 | 28.00 | 81.60 | 38.70 | 22.70 | 03/01/2012 | 37.00 | 81.50 | 28.50 | 82.20 | 38.70 | 23.10 | 04/01/2012 | 36.50 | 80.00 | 27.60 | 83.30 | 39.00 | 23.50 | 05/01/2012 | 36.70 | 82.50 | 28.60 | 81.60 | 40.00 | 24.00 | 06/01/2012 | 37.10 | 84.50 | 30.50 | 86.80 | 41.00 | 24.70 |

Appendix 2: The bid-ask price of two portfolios in one year period Date | ask | bid | ask | bid | ask | bid | ask | bid | ask | bid | ask | bid | | ACB | | SSI | | KLS | | DTC | | HAI | | BPC | | 04/01/2011 | 28.20 | 27.80 | 27.70 | 27.20 | 13.20 | 12.20 | 43.00 | 41.00 | 21.50 | 21.50 | 10.00 | 10.00 | 05/01/2011 | 28.00 | 27.80 | 28.30 | 26.50 | 13.30 | 12.90 | 44.00 | 43.50 | 21.50 | 21.50 | 10.10 | 9.80 | 06/01/2011 | 28.90 | 28.00 | 27.30 | 26.50 | 12.60 | 12.10 | 43.00 | 43.00 | 22.00 | 20.50 | 10.10 | 9.80 | 07/01/2011 | 29.40 | 28.70 | 27.00 | 26.60 | 12.20 | 11.30 | 45.90 | 42.00 | 22.00 | 21.00 | 10.20 | 9.90 | 10/01/2011 | 29.00 | 28.30 | 26.80 | 26.50 | 12.40 | 11.70 | 42.00 | 41.60 | 22.00 | 20.50 | 10.10 | 9.80 | 11/01/2011 | 28.70 | 28.40 | 26.20 | 25.40 | 13.10 | 12.10 | 44.50 | 42.00 | 22.00 | 21.00 | 9.70 | 9.70 | 12/01/2011 | 28.60 | 28.30 | 24.90 | 24.50 | 13.00 | 12.30 | 42.60 | 42.60 | 22.00 | 21.90 | 10.00 | 9.70 | 13/01/2011 | 28.50 | 28.10 | 25.30 | 24.20 | 12.40 | 12.10 | 42.60 | 42.60 | 21.90 | 20.50 | 10.00 | 9.70 | 14/01/2011 | 28.40 | 28.10 | 24.30 | 23.50 | 12.50 | 11.90 | 42.60 | 42.60 | 22.00 | 21.10 | 9.90 | 9.70 | 17/01/2011 | 28.20 | 27.90 | 22.80 | 22.40 | 12.40 | 11.90 | 40.00 | 40.00 | 22.00 | 21.80 | 9.90 | 9.60 | 18/01/2011 | 28.20 | 28.00 | 21.30 | 21.30 | 12.10 | 11.70 | 40.00 | 40.00 | 21.90 | 21.00 | 9.80 | 9.70 | 19/01/2011 | 28.30 | 28.00 | 22.30 | 21.50 | 12.10 | 11.90 | 40.50 | 40.50 | 22.00 | 21.50 | 9.60 | 9.30 | 20/01/2011 | 28.20 | 27.90 | 22.30 | 21.20 | 12.00 | 11.60 | 40.50 | 40.50 | 22.00 | 21.90 | 9.80 | 9.30 | 21/01/2011 | 28.10 | 27.80 | 21.80 | 20.30 | 11.60 | 11.40 | 41.00 | 40.50 | 22.00 | 22.00 | 9.90 | 9.50 | 24/01/2011 | 28.20 | 28.00 | 21.80 | 21.20 | 11.40 | 11.20 | 40.70 | 40.00 | 22.00 | 22.00 | 10.00 | 9.60 | 25/01/2011 | 28.40 | 28.00 | 21.20 | 20.60 | 11.80 | 11.20 | 40.50 | 40.50 | 22.00 | 20.50 | 9.70 | 9.60 | 26/01/2011 | 28.30 | 27.80 | 21.00 | 20.50 | 12.00 | 11.70 | 40.00 | 40.00 | 21.00 | 21.00 | 9.90 | 9.90 | 27/01/2011 | 28.00 | 26.80 | 21.60 | 21.10 | 12.00 | 11.40 | 42.80 | 41.00 | 21.00 | 20.00 | 9.70 | 9.70 | 28/01/2011 | 27.40 | 26.60 | 21.30 | 20.70 | 11.40 | 10.90 | 44.60 | 40.00 | 20.10 | 20.00 | 10.00 | 9.30 | 08/02/2011 | 27.00 | 25.60 | 21.30 | 20.80 | 11.50 | 11.00 | 44.00 | 44.00 | 20.10 | 19.50 | 9.80 | 9.70 | 09/02/2011 | 26.50 | 25.50 | 21.40 | 20.70 | 11.20 | 10.60 | 44.00 | 42.00 | 20.50 | 20.00 | 9.90 | 9.70 | 10/02/2011 | 27.80 | 26.50 | 22.20 | 21.60 | 11.30 | 10.60 | 44.00 | 41.00 | 20.50 | 20.10 | 9.80 | 9.70 | 11/02/2011 | 27.30 | 26.40 | 22.40 | 21.30 | 11.50 | 11.10 | 42.00 | 41.00 | 20.30 | 20.30 | 10.00 | 9.70 | 14/02/2011 | 26.50 | 25.70 | 22.10 | 21.70 | 11.40 | 10.90 | 44.00 | 41.30 | 20.30 | 20.00 | 9.80 | 9.80 | 15/02/2011 | 26.40 | 26.00 | 22.40 | 21.80 | 10.90 | 10.60 | 43.00 | 43.00 | 20.30 | 20.00 | 10.00 | 10.00 | 16/02/2011 | 26.30 | 25.80 | 23.40 | 23.20 | 10.90 | 10.60 | 43.00 | 42.00 | 20.30 | 19.30 | 10.20 | 9.70 | 17/02/2011 | 26.20 | 25.60 | 24.50 | 24.50 | 10.80 | 10.50 | 41.70 | 41.70 | 20.00 | 19.00 | 10.20 | 9.90 | 18/02/2011 | 25.80 | 25.00 | 25.70 | 24.50 | 10.80 | 10.40 | 44.60 | 44.60 | 20.20 | 19.50 | 9.90 | 9.90 | 21/02/2011 | 25.00 | 24.00 | 25.70 | 24.50 | 10.40 | 10.00 | 47.70 | 46.50 | 19.30 | 19.30 | 10.00 | 9.60 | 22/02/2011 | 24.90 | 24.00 | 24.80 | 24.00 | 10.00 | 9.50 | 48.00 | 44.30 | 19.40 | 19.40 | 9.90 | 9.60 | 23/02/2011 | 25.00 | 24.10 | 25.20 | 25.00 | 10.00 | 9.60 | 42.70 | 42.60 | 19.00 | 18.10 | 10.00 | 10.00 | 24/02/2011 | 24.20 | 23.10 | 26.40 | 24.90 | 9.80 | 9.60 | 42.60 | 42.60 | 18.60 | 18.00 | 10.30 | 9.80 | 25/02/2011 | 23.40 | 22.50 | 27.70 | 26.90 | 9.60 | 9.10 | 42.60 | 40.10 | 18.50 | 18.20 | 9.80 | 9.50 | 28/02/2011 | 24.20 | 22.70 | 29.00 | 27.70 | 9.00 | 8.60 | 41.10 | 40.60 | 19.50 | 18.70 | 10.10 | 9.90 | 01/03/2011 | 25.50 | 23.40 | 28.50 | 27.30 | 9.30 | 8.90 | 40.80 | 40.80 | 19.50 | 18.10 | 10.10 | 9.60 | 02/03/2011 | 25.50 | 24.00 | 28.00 | 27.20 | 9.80 | 8.70 | 40.70 | 40.20 | 19.90 | 18.00 | 9.90 | 9.80 | 03/03/2011 | 25.40 | 24.20 | 28.80 | 28.40 | 9.30 | 8.60 | 40.80 | 40.80 | 19.00 | 18.60 | 10.00 | 9.70 | 04/03/2011 | 24.60 | 23.90 | 30.20 | 29.80 | 9.30 | 8.70 | 41.00 | 41.00 | 20.10 | 18.00 | 9.90 | 9.70 | 07/03/2011 | 24.40 | 23.80 | 31.70 | 31.70 | 9.00 | 8.60 | 42.50 | 42.50 | 19.50 | 19.00 | 10.30 | 9.80 | 08/03/2011 | 25.50 | 24.80 | 33.20 | 33.20 | 9.10 | 8.80 | 40.70 | 40.50 | 19.90 | 19.00 | 9.90 | 9.90 | 09/03/2011 | 26.00 | 25.10 | 34.80 | 34.00 | 9.50 | 9.00 | 41.00 | 41.00 | 19.90 | 19.90 | 9.90 | 9.50 | 10/03/2011 | 26.90 | 25.70 | 36.50 | 36.00 | 9.30 | 8.90 | 42.10 | 42.00 | 19.90 | 19.50 | 10.20 | 9.90 | 11/03/2011 | 28.10 | 27.00 | 38.30 | 38.30 | 9.40 | 9.10 | 0.00 | 0.00 | 20.00 | 18.50 | 10.30 | 9.90 | 14/03/2011 | 27.90 | 26.70 | 40.20 | 40.20 | 9.90 | 9.20 | 0.00 | 0.00 | 20.00 | 19.30 | 10.50 | 9.80 | 15/03/2011 | 28.00 | 26.80 | 42.20 | 42.20 | 10.30 | 9.90 | 43.00 | 41.00 | 20.90 | 19.50 | 10.60 | 9.80 | 16/03/2011 | 27.70 | 27.10 | 44.30 | 43.20 | 11.00 | 9.90 | 43.00 | 40.50 | 20.10 | 19.50 | 10.00 | 10.00 | 17/03/2011 | 28.00 | 26.80 | 46.50 | 46.00 | 11.00 | 10.40 | 43.00 | 40.20 | 20.20 | 6.00 | 10.10 | 10.00 | 18/03/2011 | 27.70 | 27.10 | 46.90 | 44.20 | 10.90 | 10.40 | 42.00 | 40.70 | 20.20 | 20.10 | 10.30 | 10.00 | 21/03/2011 | 28.30 | 27.00 | 42.00 | 42.00 | 11.40 | 10.60 | 40.80 | 40.00 | 21.00 | 20.50 | 10.60 | 10.20 | 22/03/2011 | 29.70 | 29.60 | 39.90 | 39.90 | 12.20 | 12.10 | 43.00 | 40.30 | 20.50 | 19.50 | 10.80 | 10.60 | 23/03/2011 | 31.60 | 27.60 | 39.80 | 38.00 | 12.80 | 12.20 | 42.90 | 41.00 | 20.50 | 19.50 | 10.30 | 10.10 | 24/03/2011 | 29.60 | 27.90 | 38.90 | 36.30 | 13.40 | 12.20 | 42.50 | 40.20 | 20.90 | 19.70 | 10.20 | 9.90 | 25/03/2011 | 28.70 | 27.60 | 35.20 | 34.50 | 12.80 | 12.00 | 42.30 | 40.40 | 20.90 | 19.80 | 10.70 | 10.30 | 28/03/2011 | 29.90 | 29.30 | 22.80 | 22.40 | 13.00 | 12.80 | 42.90 | 40.90 | 20.50 | 19.50 | 10.70 | 10.20 | 29/03/2011 | 30.50 | 29.00 | 21.30 | 21.30 | 13.70 | 12.20 | 42.00 | 41.30 | 20.00 | 19.50 | 9.80 | 9.80 | 30/03/2011 | 30.90 | 30.10 | 22.30 | 21.50 | 14.00 | 13.40 | 44.00 | 42.70 | 20.50 | 19.50 | 10.10 | 9.70 | 31/03/2011 | 30.80 | 29.50 | 22.30 | 21.20 | 14.10 | 12.90 | 45.80 | 43.00 | 20.30 | 19.50 | 10.00 | 9.70 | 01/04/2011 | 29.70 | 28.40 | 21.80 | 20.30 | 13.30 | 12.60 | 45.50 | 42.00 | 20.00 | 19.50 | 10.00 | 10.00 | 04/04/2011 | 29.20 | 28.10 | 21.80 | 21.20 | 13.00 | 12.00 | 42.90 | 41.30 | 20.50 | 20.20 | 10.40 | 10.40 | 05/04/2011 | 30.20 | 28.90 | 21.20 | 20.60 | 13.30 | 13.00 | 41.50 | 41.50 | 20.50 | 19.90 | 10.30 | 10.10 | 06/04/2011 | 31.00 | 30.10 | 21.00 | 20.50 | 14.20 | 13.60 | 43.00 | 42.90 | 20.90 | 20.50 | 10.40 | 10.30 | 07/04/2011 | 32.60 | 30.70 | 21.60 | 21.10 | 15.00 | 14.80 | 44.00 | 42.80 | 21.30 | 20.00 | 10.50 | 10.20 | 08/04/2011 | 34.40 | 32.50 | 21.30 | 20.70 | 16.00 | 15.50 | 46.00 | 44.00 | 20.80 | 20.00 | 10.60 | 10.30 | 13/04/2011 | 35.50 | 33.00 | 21.30 | 20.80 | 17.10 | 15.70 | 48.50 | 46.90 | 21.00 | 20.60 | 10.50 | 10.20 | 14/04/2011 | 35.20 | 33.60 | 21.40 | 20.70 | 17.60 | 16.50 | 46.00 | 45.10 | 22.20 | 20.10 | 10.70 | 10.40 | 15/04/2011 | 36.70 | 36.00 | 22.20 | 21.60 | 18.40 | 18.40 | 47.00 | 42.20 | 22.50 | 21.00 | 11.10 | 10.60 | 18/04/2011 | 39.20 | 39.20 | 22.10 | 21.30 | 19.60 | 19.60 | 46.20 | 45.00 | 22.50 | 21.50 | 11.60 | 11.40 | 19/04/2011 | 41.90 | 40.10 | 22.10 | 21.70 | 20.90 | 20.50 | 49.30 | 49.30 | 21.50 | 21.00 | 11.60 | 11.10 | 20/04/2011 | 43.10 | 40.60 | 22.40 | 21.80 | 22.30 | 20.50 | 52.70 | 50.50 | 22.30 | 21.00 | 11.00 | 10.70 | 21/04/2011 | 44.10 | 41.60 | 23.40 | 23.20 | 23.40 | 23.00 | 52.50 | 48.90 | 21.50 | 20.60 | 11.00 | 10.50 | 22/04/2011 | 44.00 | 39.50 | 24.50 | 24.50 | 25.00 | 21.80 | 53.00 | 46.40 | 20.50 | 19.60 | 10.10 | 10.00 | 25/04/2011 | 39.00 | 37.60 | 25.70 | 24.50 | 21.30 | 21.30 | 51.30 | 51.10 | 20.10 | 19.50 | 10.60 | 9.60 | 26/04/2011 | 40.00 | 35.00 | 25.70 | 24.50 | 19.90 | 19.90 | 54.80 | 52.00 | 20.00 | 19.50 | 11.00 | 10.90 | 27/04/2011 | 37.40 | 35.20 | 24.80 | 24.00 | 19.00 | 18.60 | 52.80 | 49.20 | 20.60 | 19.60 | 11.00 | 10.40 | 28/04/2011 | 39.00 | 36.00 | 26.80 | 25.00 | 17.30 | 17.30 | 53.50 | 53.00 | 20.20 | 20.00 | 10.70 | 10.40 | 29/04/2011 | 37.00 | 34.60 | 26.40 | 24.90 | 16.10 | 16.10 | 53.50 | 49.60 | 21.00 | 20.00 | 10.40 | 10.00 | 04/05/2011 | 36.40 | 35.00 | 27.70 | 26.90 | 16.00 | 15.00 | 52.00 | 49.50 | 21.40 | 19.50 | 10.40 | 10.20 | 05/05/2011 | 36.50 | 35.00 | 29.00 | 27.70 | 16.10 | 14.30 | 46.00 | 46.00 | 21.20 | 20.50 | 10.40 | 10.00 | 06/05/2011 | 37.50 | 35.80 | 28.50 | 27.30 | 17.00 | 16.80 | 46.00 | 42.90 | 22.40 | 22.40 | 10.80 | 10.80 | 09/05/2011 | 39.20 | 39.20 | 28.00 | 27.60 | 18.10 | 18.10 | 46.70 | 45.00 | 23.90 | 23.80 | 11.30 | 11.20 | 10/05/2011 | 41.90 | 41.90 | 30.00 | 29.60 | 19.30 | 19.30 | 49.60 | 49.00 | 25.50 | 23.10 | 10.80 | 10.80 | 11/05/2011 | 44.00 | 40.40 | 34.30 | 32.30 | 20.60 | 19.50 | 52.90 | 52.40 | 26.00 | 24.40 | 11.30 | 11.20 | 12/05/2011 | 44.70 | 42.70 | 36.00 | 33.50 | 21.90 | 21.90 | 50.00 | 24.50 | 27.00 | 24.60 | 11.00 | 10.80 | 13/05/2011 | 45.00 | 41.20 | 38.90 | 35.90 | 22.40 | 21.40 | 52.40 | 49.00 | 26.10 | 25.50 | 11.30 | 11.20 | 16/05/2011 | 45.80 | 42.80 | 42.00 | 41.00 | 24.60 | 22.00 | 52.30 | 49.00 | 26.30 | 25.00 | 11.70 | 11.00 | 17/05/2011 | 43.60 | 41.60 | 41.00 | 40.00 | 24.80 | 21.90 | 51.00 | 50.00 | 26.50 | 25.70 | 12.00 | 11.50 | 18/05/2011 | 43.50 | 41.60 | 44.00 | 41.00 | 24.60 | 22.20 | 52.00 | 50.00 | 25.20 | 25.00 | 11.90 | 11.40 | 19/05/2011 | 42.00 | 39.40 | 43.20 | 41.20 | 23.30 | 22.60 | 53.50 | 49.50 | 26.80 | 26.00 | 12.00 | 11.80 | 20/05/2011 | 42.60 | 42.30 | 42.20 | 42.20 | 23.20 | 22.80 | 54.50 | 51.00 | 26.50 | 25.50 | 12.40 | 12.00 | 23/05/2011 | 46.20 | 43.60 | 44.30 | 40.20 | 25.20 | 24.20 | 54.50 | 54.00 | 27.00 | 25.50 | 12.80 | 12.30 | 24/05/2011 | 47.00 | 45.00 | 45.50 | 41.30 | 26.80 | 26.80 | 54.50 | 53.00 | 27.50 | 26.50 | 13.30 | 12.20 | 25/05/2011 | 45.90 | 44.40 | 44.00 | 42.80 | 28.60 | 27.40 | 55.00 | 53.00 | 28.00 | 27.00 | 13.60 | 13.20 | 26/05/2011 | 44.80 | 43.80 | 41.20 | 39.80 | 28.00 | 26.80 | 54.50 | 53.30 | 26.00 | 26.00 | 13.50 | 12.90 | 27/05/2011 | 43.50 | 42.00 | 39.90 | 36.20 | 27.30 | 25.90 | 53.80 | 53.10 | 27.80 | 26.00 | 13.50 | 13.00 | 30/05/2011 | 45.40 | 42.60 | 39.80 | 36.13 | 28.00 | 26.20 | 54.00 | 53.40 | 28.50 | 27.00 | 13.70 | 13.40 | 31/05/2011 | 46.50 | 44.00 | 38.90 | 36.80 | 29.80 | 28.60 | 57.20 | 53.50 | 27.20 | 26.60 | 13.80 | 13.40 | 01/06/2011 | 45.40 | 43.30 | 35.20 | 33.40 | 31.50 | 28.50 | 60.00 | 54.50 | 28.00 | 25.80 | 13.20 | 13.10 | 02/06/2011 | 43.00 | 41.90 | 35.90 | 33.60 | 28.50 | 27.40 | 58.30 | 55.90 | 27.50 | 26.50 | 14.20 | 14.20 | 03/06/2011 | 43.30 | 41.80 | 36.20 | 35.20 | 29.00 | 26.00 | 58.40 | 56.00 | 28.70 | 27.90 | 15.10 | 15.10 | 06/06/2011 | 44.50 | 43.20 | 38.00 | 37.60 | 29.60 | 28.20 | 57.50 | 57.00 | 30.20 | 30.00 | 16.90 | 16.10 | 07/06/2011 | 46.70 | 45.10 | 39.90 | 39.90 | 31.20 | 30.40 | 59.00 | 57.10 | 32.30 | 30.50 | 17.20 | 17.20 | 08/06/2011 | 45.20 | 43.60 | 41.80 | 41.80 | 33.10 | 29.80 | 62.70 | 62.50 | 33.90 | 33.50 | 18.40 | 18.00 | 09/06/2011 | 46.90 | 44.00 | 43.80 | 42.30 | 32.40 | 29.50 | 67.00 | 63.50 | 36.20 | 35.50 | 19.50 | 17.20 | 10/06/2011 | 48.70 | 47.50 | 45.10 | 45.10 | 33.90 | 33.30 | 70.60 | 70.50 | 38.70 | 37.50 | 16.80 | 16.40 | 13/06/2011 | 52.10 | 52.10 | 47.30 | 46.50 | 36.20 | 36.20 | 75.50 | 75.50 | 38.30 | 35.80 | 16.30 | 15.30 | 14/06/2011 | 55.70 | 53.10 | 49.60 | 47.30 | 38.70 | 36.20 | 80.70 | 78.00 | 34.50 | 33.73 | 16.30 | 15.30 | 15/06/2011 | 56.20 | 53.60 | 51.50 | 48.20 | 37.60 | 35.00 | 85.90 | 80.00 | 36.00 | 32.00 | 16.00 | 15.00 | 16/06/2011 | 56.60 | 52.90 | 52.50 | 49.50 | 37.00 | 35.00 | 76.30 | 75.60 | 36.40 | 34.20 | 15.30 | 14.20 | 17/06/2011 | 59.00 | 55.70 | 50.00 | 47.10 | 37.30 | 34.20 | 81.10 | 75.60 | 35.60 | 33.20 | 13.80 | 13.40 | 20/06/2011 | 57.50 | 53.50 | 52.50 | 51.00 | 37.40 | 34.80 | 83.00 | 73.70 | 34.40 | 32.00 | 14.40 | 14.40 | 21/06/2011 | 53.00 | 50.20 | 55.00 | 53.00 | 32.50 | 32.50 | 74.00 | 71.70 | 34.50 | 31.20 | 15.30 | 14.00 | 22/06/2011 | 52.00 | 48.90 | 57.50 | 57.50 | 32.60 | 30.30 | 72.30 | 67.40 | 33.00 | 32.00 | 15.00 | 14.60 | 23/06/2011 | 52.00 | 49.90 | 60.00 | 57.00 | 32.80 | 30.90 | 70.00 | 67.80 | 34.00 | 31.60 | 15.20 | 14.40 | 24/06/2011 | 53.50 | 50.10 | 61.50 | 57.00 | 34.00 | 32.10 | 74.00 | 73.00 | 31.00 | 30.70 | 14.90 | 14.20 | 27/06/2011 | 51.50 | 47.60 | 57.00 | 54.50 | 31.60 | 29.40 | 78.20 | 69.00 | 30.00 | 28.80 | 14.10 | 13.60 | 28/06/2011 | 46.00 | 44.70 | 59.00 | 59.00 | 27.50 | 27.50 | 66.50 | 65.20 | 31.10 | 30.90 | 14.40 | 13.90 | 29/06/2011 | 48.00 | 45.20 | 61.50 | 60.00 | 29.40 | 27.20 | 66.90 | 61.70 | 33.00 | 29.00 | 14.10 | 13.70 | 30/06/2011 | 50.90 | 48.10 | 64.50 | 60.50 | 30.60 | 28.60 | 66.70 | 66.00 | 30.20 | 30.20 | 14.70 | 14.20 | 01/07/2011 | 52.50 | 48.80 | 62.00 | 59.00 | 31.90 | 28.90 | 70.80 | 69.50 | 30.20 | 28.50 | 14.50 | 14.40 | 04/07/2011 | 51.00 | 49.00 | 72.00 | 72.00 | 30.20 | 29.00 | 75.10 | 74.00 | 29.00 | 27.50 | 15.00 | 15.00 | 05/07/2011 | 52.50 | 48.00 | 75.50 | 75.50 | 31.50 | 27.50 | 71.00 | 70.00 | 26.50 | 25.70 | 14.90 | 14.20 | 06/07/2011 | 48.80 | 46.50 | 79.00 | 75.50 | 27.70 | 26.00 | 68.50 | 68.40 | 27.40 | 26.50 | 14.40 | 14.10 | 07/07/2011 | 48.40 | 46.40 | 77.00 | 75.50 | 27.50 | 25.20 | 73.10 | 68.50 | 28.30 | 26.00 | 14.00 | 13.80 | 08/07/2011 | 47.90 | 45.50 | 79.00 | 76.00 | 27.30 | 25.10 | 73.00 | 73.00 | 28.70 | 28.00 | 14.00 | 13.90 | 11/07/2011 | 49.60 | 47.00 | 82.00 | 76.50 | 28.40 | 26.60 | 73.80 | 70.50 | 28.20 | 28.00 | 14.30 | 14.00 | 12/07/2011 | 50.00 | 48.20 | 77.50 | 73.50 | 29.80 | 28.00 | 71.20 | 70.00 | 27.50 | 26.50 | 14.60 | 14.20 | 13/07/2011 | 48.80 | 47.60 | 70.00 | 70.00 | 29.30 | 27.80 | 70.50 | 70.50 | 28.00 | 27.10 | 14.60 | 14.20 | 14/07/2011 | 48.60 | 47.40 | 69.00 | 66.50 | 29.10 | 28.50 | 71.00 | 71.00 | 27.20 | 26.50 | 0.00 | 0.00 | 15/07/2011 | 48.00 | 46.00 | 70.00 | 67.00 | 29.00 | 27.60 | 71.50 | 70.50 | 25.80 | 25.80 | 14.30 | 14.10 | 18/07/2011 | 46.80 | 45.10 | 68.50 | 65.00 | 28.00 | 26.30 | 71.00 | 66.00 | 26.00 | 25.90 | 14.10 | 14.10 | 19/07/2011 | 46.70 | 44.30 | 63.50 | 62.50 | 28.10 | 25.80 | 72.50 | 72.00 | 27.50 | 25.00 | 14.80 | 14.30 | 20/07/2011 | 46.00 | 45.00 | 60.50 | 59.50 | 27.70 | 26.90 | 74.10 | 73.50 | 27.40 | 27.10 | 15.60 | 14.60 | 21/07/2011 | 47.50 | 45.50 | 62.00 | 62.00 | 29.10 | 28.30 | 75.50 | 74.90 | 27.40 | 26.00 | 15.60 | 15.00 | 22/07/2011 | 46.50 | 45.00 | 65.00 | 63.50 | 29.10 | 27.00 | 79.50 | 72.00 | 26.00 | 24.80 | 15.40 | 14.40 | 25/07/2011 | 45.00 | 42.70 | 66.50 | 63.00 | 27.50 | 25.90 | 77.00 | 72.00 | 27.20 | 25.50 | 15.40 | 14.80 | 26/07/2011 | 44.40 | 43.00 | 68.00 | 66.00 | 27.00 | 25.90 | 79.30 | 79.30 | 27.50 | 26.20 | 15.50 | 14.80 | 27/07/2011 | 44.00 | 43.40 | 65.50 | 65.20 | 27.00 | 26.20 | 84.80 | 81.00 | 27.00 | 26.50 | 15.50 | 15.20 | 28/07/2011 | 45.30 | 45.00 | 64.50 | 64.00 | 28.00 | 27.80 | 84.50 | 77.80 | 28.80 | 28.80 | 15.40 | 15.00 | 29/07/2011 | 47.90 | 46.50 | 64.00 | 61.00 | 29.50 | 29.50 | 84.20 | 83.50 | 30.50 | 30.00 | 15.80 | 15.10 | 01/08/2011 | 51.00 | 48.10 | 63.00 | 60.00 | 31.50 | 31.50 | 89.80 | 86.00 | 28.80 | 28.60 | 15.60 | 15.00 | 02/08/2011 | 50.00 | 47.30 | 60.50 | 58.00 | 33.70 | 33.00 | 89.30 | 84.00 | 29.00 | 28.50 | 15.60 | 15.00 | 03/08/2011 | 48.50 | 46.00 | 61.00 | 59.00 | 36.00 | 32.50 | 87.00 | 83.00 | 29.40 | 28.00 | 15.50 | 14.50 | 04/08/2011 | 46.30 | 45.10 | 62.00 | 60.00 | 34.50 | 32.10 | 87.00 | 84.80 | 30.10 | 30.10 | 15.00 | 14.90 | 05/08/2011 | 47.40 | 46.00 | 59.50 | 58.00 | 35.00 | 33.50 | 91.30 | 88.00 | 30.50 | 29.90 | 15.60 | 15.00 | 08/08/2011 | 48.00 | 46.20 | 57.50 | 56.00 | 35.70 | 34.00 | 96.80 | 90.50 | 30.10 | 29.00 | 15.60 | 15.50 | 09/08/2011 | 48.00 | 46.90 | 57.00 | 55.00 | 37.00 | 35.00 | 97.00 | 93.00 | 29.40 | 28.60 | 15.60 | 15.20 | 10/08/2011 | 47.50 | 46.50 | 56.00 | 54.00 | 36.00 | 34.60 | 97.50 | 90.00 | 29.30 | 28.80 | 15.50 | 15.20 | 11/08/2011 | 47.50 | 45.20 | 56.50 | 52.50 | 36.00 | 34.50 | 85.70 | 81.00 | 29.40 | 28.70 | 15.50 | 15.10 | 12/08/2011 | 46.90 | 46.50 | 59.00 | 59.00 | 34.90 | 34.60 | 82.00 | 79.50 | 30.00 | 29.40 | 15.30 | 15.00 | 15/08/2011 | 47.40 | 47.00 | 61.50 | 61.50 | 35.00 | 34.60 | 80.50 | 75.90 | 29.50 | 29.10 | 15.60 | 15.20 | 16/08/2011 | 47.20 | 46.70 | 64.50 | 64.00 | 35.40 | 34.50 | 82.60 | 76.00 | 29.50 | 29.00 | 15.80 | 15.30 | 17/08/2011 | 47.80 | 46.50 | 67.00 | 64.00 | 36.00 | 34.10 | 78.50 | 72.20 | 31.40 | 29.80 | 16.40 | 15.40 | 18/08/2011 | 49.00 | 47.50 | 64.50 | 61.00 | 37.60 | 35.60 | 75.00 | 71.00 | 31.00 | 30.00 | 16.30 | 15.50 | 19/08/2011 | 48.60 | 47.50 | 66.00 | 64.00 | 36.50 | 35.40 | 72.50 | 67.90 | 30.30 | 30.00 | 16.00 | 15.60 | 22/08/2011 | 47.80 | 47.00 | 68.00 | 65.00 | 36.00 | 34.90 | 75.00 | 71.00 | 31.00 | 28.50 | 16.20 | 16.00 | 23/08/2011 | 47.20 | 46.10 | 69.00 | 67.00 | 35.20 | 33.90 | 74.90 | 73.00 | 31.10 | 30.30 | 16.30 | 16.00 | 24/08/2011 | 47.40 | 46.90 | 70.50 | 67.50 | 35.60 | 34.70 | 76.00 | 75.00 | 31.30 | 30.00 | 16.60 | 16.20 | 25/08/2011 | 48.00 | 46.90 | 73.00 | 69.50 | 36.00 | 35.30 | 80.70 | 75.50 | 31.00 | 30.00 | 17.30 | 16.60 | 26/08/2011 | 49.00 | 47.20 | 70.00 | 68.50 | 37.90 | 35.80 | 78.30 | 74.50 | 32.00 | 30.10 | 17.10 | 16.70 | 29/08/2011 | 48.90 | 47.80 | 71.50 | 69.00 | 39.80 | 37.60 | 77.00 | 73.00 | 32.40 | 30.30 | 16.90 | 16.30 | 30/08/2011 | 48.20 | 47.30 | 72.00 | 70.00 | 39.00 | 37.60 | 72.50 | 72.00 | 33.00 | 31.50 | 17.00 | 16.30 | 31/08/2011 | 47.70 | 47.20 | 72.00 | 70.00 | 38.20 | 37.00 | 72.30 | 71.00 | 33.80 | 32.60 | 16.60 | 16.00 | 01/09/2011 | 47.30 | 46.00 | 72.00 | 70.50 | 37.80 | 37.00 | 74.00 | 73.50 | 34.80 | 31.20 | 16.70 | 16.30 | 05/09/2011 | 47.40 | 46.40 | 71.50 | 70.00 | 38.10 | 37.10 | 74.80 | 73.80 | 36.50 | 33.10 | 17.10 | 16.40 | 06/09/2011 | 48.50 | 47.30 | 72.00 | 69.50 | 40.00 | 38.60 | 76.00 | 74.00 | 36.00 | 34.00 | 18.00 | 17.00 | 07/09/2011 | 48.20 | 47.40 | 70.00 | 68.50 | 39.90 | 38.60 | 75.30 | 74.00 | 33.20 | 32.90 | 19.00 | 18.20 | 08/09/2011 | 47.50 | 47.00 | 70.50 | 69.00 | 40.50 | 38.00 | 74.00 | 72.00 | 33.20 | 31.00 | 19.00 | 18.40 | 09/09/2011 | 47.30 | 46.30 | 71.50 | 70.00 | 39.20 | 36.10 | 74.00 | 72.80 | 31.50 | 30.50 | 19.00 | 18.50 | 12/09/2011 | 47.00 | 45.50 | 74.00 | 72.50 | 37.90 | 35.70 | 73.50 | 73.00 | 32.50 | 31.50 | 18.90 | 18.00 | 13/09/2011 | 47.00 | 46.00 | 75.50 | 73.00 | 39.20 | 37.20 | 75.00 | 74.00 | 32.80 | 32.20 | 18.70 | 17.80 | 14/09/2011 | 46.90 | 46.00 | 74.50 | 73.00 | 39.80 | 38.60 | 74.70 | 74.00 | 32.80 | 31.00 | 18.50 | 18.00 | 15/09/2011 | 46.30 | 45.50 | 74.50 | 73.00 | 39.60 | 38.60 | 73.50 | 72.20 | 33.00 | 31.90 | 18.50 | 18.10 | 16/09/2011 | 46.50 | 45.80 | 73.50 | 72.50 | 41.70 | 39.10 | 73.20 | 72.50 | 32.20 | 32.00 | 18.20 | 17.80 | 19/09/2011 | 46.50 | 45.80 | 73.50 | 72.00 | 39.90 | 39.10 | 76.00 | 72.10 | 32.80 | 32.00 | 18.30 | 17.80 | 20/09/2011 | 46.50 | 45.90 | 75.00 | 73.00 | 42.00 | 39.60 | 76.00 | 73.00 | 32.50 | 32.00 | 18.10 | 17.70 | 21/09/2011 | 49.20 | 46.50 | 77.00 | 75.00 | 43.50 | 41.70 | 78.00 | 75.00 | 32.40 | 32.10 | 18.00 | 17.70 | 22/09/2011 | 49.60 | 47.20 | 76.00 | 74.00 | 42.80 | 40.00 | 80.00 | 75.10 | 32.50 | 31.50 | 18.10 | 17.90 | 23/09/2011 | 47.90 | 46.90 | 76.50 | 75.00 | 41.70 | 40.10 | 78.80 | 76.00 | 34.50 | 32.30 | 18.40 | 18.00 | 26/09/2011 | 47.20 | 46.40 | 79.00 | 75.50 | 42.00 | 40.80 | 81.00 | 77.10 | 33.50 | 33.00 | 19.40 | 18.60 | 27/09/2011 | 46.80 | 45.90 | 80.50 | 78.50 | 44.00 | 41.30 | 83.00 | 79.00 | 34.00 | 33.40 | 20.60 | 19.50 | 28/09/2011 | 48.00 | 46.20 | 83.00 | 80.50 | 45.70 | 43.10 | 79.40 | 76.50 | 33.00 | 32.70 | 19.50 | 18.80 | 29/09/2011 | 46.80 | 46.10 | 80.50 | 77.50 | 47.50 | 43.60 | 77.00 | 74.20 | 33.00 | 31.60 | 19.00 | 18.50 | 30/09/2011 | 47.50 | 45.80 | 79.50 | 77.50 | 46.80 | 45.00 | 77.00 | 75.00 | 32.40 | 32.00 | 19.30 | 18.50 | 03/10/2011 | 49.00 | 47.00 | 80.00 | 78.50 | 49.20 | 46.50 | 80.00 | 76.00 | 32.60 | 32.00 | 20.00 | 19.00 | 04/10/2011 | 48.00 | 46.70 | 82.00 | 77.50 | 52.40 | 49.60 | 78.00 | 77.50 | 32.00 | 31.50 | 20.00 | 19.30 | 05/10/2011 | 47.00 | 46.30 | 84.50 | 82.00 | 50.90 | 47.50 | 77.80 | 76.60 | 30.50 | 30.00 | 20.50 | 19.60 | 06/10/2011 | 46.50 | 45.60 | 83.00 | 80.00 | 52.40 | 46.20 | 76.10 | 71.80 | 29.60 | 29.00 | 21.20 | 20.00 | 07/10/2011 | 45.30 | 42.70 | 81.00 | 79.50 | 47.90 | 44.90 | 74.20 | 72.00 | 31.00 | 29.10 | 22.10 | 22.00 | 10/10/2011 | 45.00 | 43.60 | 85.00 | 85.00 | 47.00 | 44.50 | 76.40 | 76.40 | 30.40 | 29.70 | 23.60 | 22.10 | 11/10/2011 | 44.60 | 44.00 | 89.00 | 85.00 | 46.50 | 45.00 | 77.00 | 73.60 | 31.00 | 30.50 | 25.20 | 25.00 | 12/10/2011 | 44.80 | 44.10 | 85.50 | 83.00 | 47.50 | 45.30 | 77.00 | 76.40 | 31.40 | 30.20 | 26.90 | 23.50 | 13/10/2011 | 45.00 | 44.80 | 82.00 | 81.50 | 47.00 | 46.70 | 77.50 | 76.90 | 32.80 | 31.00 | 25.50 | 24.00 | 14/10/2011 | 45.80 | 44.50 | 80.50 | 79.00 | 48.00 | 46.50 | 80.00 | 78.00 | 34.00 | 32.60 | 26.20 | 25.20 | 17/10/2011 | 46.50 | 45.10 | 82.50 | 81.00 | 49.90 | 48.00 | 80.00 | 78.00 | 35.00 | 33.30 | 26.50 | 25.90 | 18/10/2011 | 46.00 | 44.80 | 82.00 | 80.00 | 49.50 | 47.50 | 78.00 | 78.00 | 34.60 | 32.00 | 27.00 | 25.80 | 19/10/2011 | 48.00 | 44.40 | 82.50 | 79.50 | 37.90 | 37.90 | 79.80 | 76.00 | 34.70 | 34.50 | 28.10 | 26.20 | 20/10/2011 | 49.30 | 47.40 | 86.50 | 84.00 | 40.50 | 40.50 | 83.00 | 81.00 | 36.00 | 34.00 | 28.00 | 26.50 | 21/10/2011 | 48.30 | 46.10 | 90.50 | 86.00 | 43.30 | 40.10 | 87.90 | 83.00 | 36.80 | 34.40 | 29.10 | 26.00 | 24/10/2011 | 47.00 | 46.00 | 94.50 | 90.50 | 44.00 | 40.70 | 93.60 | 90.00 | 37.90 | 37.90 | 30.40 | 30.10 | 25/10/2011 | 47.00 | 46.00 | 97.50 | 94.50 | 42.30 | 40.70 | 100.00 | 100.00 | 40.50 | 40.50 | 32.50 | 29.00 | 26/10/2011 | 49.00 | 45.70 | 102.0 | 102.0 | 41.10 | 40.20 | 107.00 | 105.00 | 43.30 | 43.30 | 33.70 | 32.50 | 27/10/2011 | 49.80 | 47.50 | 107.0 | 105.0 | 42.00 | 39.90 | 114.40 | 114.00 | 46.30 | 41.00 | 35.60 | 31.00 | 28/10/2011 | 51.00 | 48.30 | 110.0 | 102.0 | 41.10 | 38.70 | 122.30 | 107.00 | 44.50 | 42.80 | 32.30 | 31.10 | 31/10/2011 | 49.20 | 47.10 | 107.0 | 99.50 | 39.60 | 37.10 | 119.50 | 111.50 | 45.90 | 39.90 | 29.80 | 29.80 | 01/11/2011 | 47.20 | 45.00 | 99.50 | 95.50 | 40.30 | 35.50 | 114.00 | 109.00 | 45.90 | 42.00 | 27.90 | 27.80 | 02/11/2011 | 46.90 | 45.50 | 100.0 | 97.00 | 37.40 | 35.00 | 107.00 | 102.00 | 43.80 | 40.80 | 29.70 | 27.50 | 03/11/2011 | 45.80 | 44.00 | 95.50 | 93.50 | 36.00 | 34.00 | 102.00 | 96.50 | 44.40 | 42.20 | 26.80 | 26.50 | 04/11/2011 | 46.50 | 44.70 | 98.00 | 95.00 | 36.20 | 34.30 | 104.10 | 99.20 | 41.40 | 40.40 | 27.90 | 24.80 | 07/11/2011 | 45.50 | 42.50 | 92.50 | 91.50 | 34.00 | 32.70 | 107.00 | 96.90 | 40.70 | 37.80 | 26.50 | 25.90 | 08/11/2011 | 43.50 | 42.00 | 89.00 | 87.50 | 32.00 | 30.50 | 93.00 | 90.90 | 41.00 | 37.00 | 27.90 | 27.00 | 09/11/2011 | 43.50 | 42.00 | 89.00 | 85.00 | 32.30 | 29.90 | 97.00 | 96.80 | 42.60 | 41.50 | 28.40 | 27.70 | 10/11/2011 | 43.50 | 42.60 | 90.00 | 86.50 | 33.40 | 31.50 | 100.00 | 97.00 | 43.50 | 41.90 | 29.70 | 26.50 | 11/11/2011 | 44.90 | 42.60 | 92.50 | 88.50 | 34.70 | 32.50 | 102.00 | 100.00 | 42.00 | 38.00 | 26.80 | 25.10 | 14/11/2011 | 43.30 | 41.20 | 87.50 | 84.50 | 32.60 | 31.20 | 94.60 | 94.10 | 39.30 | 36.60 | 27.10 | 25.00 | 15/11/2011 | 42.50 | 40.50 | 85.50 | 80.50 | 32.50 | 29.40 | 99.90 | 91.50 | 38.10 | 36.20 | 26.50 | 25.50 | 16/11/2011 | 42.00 | 41.10 | 84.50 | 81.50 | 32.10 | 29.90 | 100.00 | 93.00 | 40.60 | 37.00 | 26.00 | 25.00 | 17/11/2011 | 42.40 | 41.50 | 87.00 | 84.00 | 32.40 | 31.30 | 100.00 | 97.00 | 39.60 | 36.90 | 26.50 | 25.00 | 18/11/2011 | 41.90 | 41.60 | 86.50 | 85.50 | 31.80 | 31.70 | 95.00 | 93.30 | 38.50 | 37.50 | 26.30 | 24.50 | 21/11/2011 | 41.10 | 40.80 | 86.00 | 85.30 | 31.50 | 31.20 | 99.90 | 93.70 | 38.50 | 36.50 | 26.80 | 23.90 | 22/11/2011 | 41.00 | 40.70 | 85.00 | 84.80 | 31.00 | 30.80 | 100.00 | 95.00 | 38.80 | 37.90 | 22.80 | 22.80 | 23/11/2011 | 40.50 | 39.60 | 84.50 | 84.00 | 32.00 | 30.10 | 100.10 | 96.50 | 39.00 | 36.80 | 23.00 | 21.30 | 24/11/2011 | 40.40 | 40.00 | 89.50 | 85.50 | 32.80 | 31.30 | 102.50 | 99.00 | 38.60 | 37.30 | 22.50 | 20.50 | 25/11/2011 | 40.50 | 39.80 | 92.00 | 88.50 | 33.00 | 31.50 | 98.10 | 96.00 | 38.50 | 38.40 | 22.90 | 22.50 | 28/11/2011 | 40.00 | 38.80 | 89.00 | 85.00 | 32.00 | 30.30 | 97.50 | 92.50 | 39.00 | 38.40 | 22.70 | 21.80 | 29/11/2011 | 40.00 | 38.10 | 86.00 | 83.50 | 31.40 | 29.80 | 90.10 | 90.00 | 38.60 | 35.90 | 21.50 | 21.20 | 30/11/2011 | 38.50 | 35.90 | 83.00 | 80.00 | 30.10 | 28.30 | 95.10 | 83.70 | 36.50 | 34.10 | 22.40 | 22.00 | 01/12/2011 | 36.00 | 33.70 | 76.50 | 76.00 | 27.00 | 26.60 | 81.20 | 80.60 | 36.00 | 33.30 | 21.10 | 20.80 | 02/12/2011 | 36.40 | 35.00 | 77.50 | 74.50 | 26.50 | 25.80 | 85.90 | 75.10 | 37.70 | 35.00 | 21.10 | 20.10 | 05/12/2011 | 36.80 | 35.10 | 78.00 | 74.50 | 27.00 | 25.10 | 83.10 | 81.90 | 39.30 | 38.00 | 19.60 | 19.00 | 06/12/2011 | 38.90 | 38.00 | 81.50 | 79.50 | 27.80 | 26.50 | 88.80 | 88.50 | 39.00 | 38.50 | 20.00 | 18.00 | 07/12/2011 | 39.00 | 38.00 | 82.00 | 77.50 | 28.00 | 26.80 | 90.00 | 79.00 | 39.00 | 37.90 | 18.60 | 18.50 | 08/12/2011 | 37.80 | 36.50 | 78.50 | 75.50 | 27.00 | 25.30 | 80.00 | 79.50 | 39.50 | 36.50 | 19.60 | 18.60 | 09/12/2011 | 37.50 | 36.60 | 79.50 | 78.00 | 26.80 | 25.80 | 82.40 | 81.00 | 40.22 | 37.10 | 19.50 | 19.50 | 12/12/2011 | 37.00 | 36.80 | 78.70 | 78.00 | 27.10 | 26.30 | 82.90 | 81.50 | 39.50 | 37.10 | 20.50 | 19.30 | 13/12/2011 | 37.20 | 36.90 | 79.00 | 78.60 | 25.60 | 25.50 | 85.00 | 84.00 | 39.00 | 37.00 | 20.50 | 18.90 | 14/12/2011 | 34.80 | 34.60 | 76.00 | 75.60 | 25.20 | 25.00 | 80.00 | 79.10 | 39.00 | 37.00 | 19.70 | 19.70 | 15/12/2011 | 36.00 | 34.50 | 75.00 | 73.00 | 25.10 | 22.80 | 84.80 | 83.50 | 36.00 | 35.50 | 20.90 | 20.40 | 16/12/2011 | 35.50 | 34.60 | 72.00 | 71.00 | 23.20 | 21.90 | 87.90 | 78.40 | 37.90 | 36.50 | 21.30 | 19.10 | 19/12/2011 | 37.30 | 35.00 | 71.50 | 68.50 | 23.40 | 22.80 | 82.80 | 82.80 | 39.50 | 35.10 | 20.00 | 19.00 | 20/12/2011 | 38.50 | 36.90 | 72.50 | 70.00 | 23.20 | 21.80 | 87.70 | 84.00 | 39.70 | 35.90 | 20.00 | 19.70 | 21/12/2011 | 37.20 | 35.70 | 69.00 | 66.50 | 22.00 | 20.90 | 80.00 | 79.90 | 38.80 | 37.00 | 21.00 | 20.10 | 22/12/2011 | 37.10 | 35.80 | 67.00 | 65.00 | 21.30 | 20.80 | 85.60 | 74.40 | 39.00 | 38.00 | 21.50 | 19.80 | 23/12/2011 | 38.20 | 36.50 | 70.00 | 68.50 | 21.50 | 20.30 | 82.00 | 82.00 | 39.00 | 38.90 | 22.00 | 19.40 | 26/12/2011 | 38.80 | 37.40 | 73.50 | 72.00 | 22.80 | 22.70 | 85.90 | 77.10 | 40.90 | 39.00 | 22.50 | 20.50 | 27/12/2011 | 38.90 | 37.40 | 76.00 | 72.50 | 24.30 | 23.70 | 84.40 | 78.50 | 39.80 | 38.50 | 22.10 | 20.00 | 28/12/2011 | 37.50 | 37.00 | 75.50 | 73.50 | 25.80 | 23.10 | 83.40 | 80.00 | 37.60 | 37.60 | 21.60 | 21.20 | 29/12/2011 | 39.50 | 36.50 | 78.00 | 73.00 | 27.60 | 25.10 | 81.00 | 78.00 | 40.20 | 37.70 | 23.60 | 20.00 | 30/12/2011 | 37.20 | 37.00 | 81.30 | 81.30 | 27.80 | 27.40 | 85.00 | 80.00 | 40.50 | 37.50 | 23.00 | 20.10 | 03/01/2012 | 37.80 | 37.60 | 81.00 | 80.80 | 28.60 | 28.30 | 86.40 | 81.60 | 39.75 | 38.70 | 24.00 | 21.20 | 04/01/2012 | 37.00 | 36.80 | 82.50 | 80.90 | 28.80 | 28.50 | 85.50 | 80.00 | 40.00 | 38.80 | 25.00 | 22.20 | 05/01/2012 | 37.00 | 36.40 | 84.00 | 82.00 | 29.50 | 26.90 | 84.90 | 80.00 | 40.50 | 38.40 | 25.10 | 21.70 | 06/01/2012 | 37.60 | 36.40 | 85.50 | 84.00 | 30.60 | 29.10 | 87.30 | 82.40 | 41.50 | 38.00 | 24.90 | 23.10 |

Appendix 3: The histograms of daily normal return (VND)

Figure [ 13 ]: Histogram of daily normal return of ACB

Figure [ 14 ]: Histogram of daily normal return of SSI

Figure [ 15 ]: Histogram of daily normal return of KLS

Figure [ 16 ]: Histogram of daily normal return of DTC

Figure [ 17 ]: Histogram of daily normal return of HAI

Figure [ 18 ]: Histogram of daily normal return of BPC

--------------------------------------------
[ 2 ]. Vietstock financial information is one of the leading online financial and securities information portals in Vietnam, attracting millions of visits per day. Information portal and services are provided on the Vietstock’s homepage incorporated under the Tai Viet Joint Stock Company. Available from: http://www.vietstock.vn/tianyonen/Index.aspx?Component=Introductions&ChannelID=36