Report on Analysis of the 260-Day Value at Risk (VAR) of Portfolio of Shares

Table of Contents

Introduction

Background to the Data Sample

Analytic VAR

Monte Carlo VAR 800

Historical Analysis/Bootstrap VAR

Discussion

Conclusion

References

Introduction

For quite a long time now the main concern for investors as well as regulators of financial markets has been the risk of catastrophic market and the sufficiency of capital needed to counter such kind of risk when it occurs. Many institutions have undergone loses despite their gigantic nature and good forecasting and this has been associated with inappropriate forms of pricing and poor management together with the fraudulent cases, factors that have always brought the issue of managing risk and regulating these financial markets to the level of public policy as well as discussion. A basic tool that has been identified as being effective in the assessment of financial risk is the Value at Risk (VaR) process (Artzner, et al., 1997). The VaR has been figured out as being an amount that is lost on a given form of portfolio including a small probability in a certain fixed period of time counted in terms of days. VaR however poses a major challenge during its implementation and this has more to do with the specification of the kind of probability distribution having extreme returns that is made use of during the calculation of the estimates used in the VaR analysis (Mahoney, 1996; McNeil & Frey, 2000; Dowd, 2001). As has been noted, the nature of VaR estimation majorly does depend on the accurate predictions of some uncommon events or risks that are catastrophic. This is attributed to the fact that VaR is a calculation made from the lowest portfolio returns. For this reason, any form of calculation that is employed in the estimation of VaR must be able to encompass the tail events’ prediction and make this its primary goal (Chiang, et al., 2007; Engle, 2002; Engle & Kroner, 1995; Engle & Rothschild, 1990; Francis, et al., 2001). There have been statistical techniques as well as thumb rules that many researchers argue as having been very instrumental in the prediction and analysis of intra-day and in most cases day-to-day risk. These are however; not appropriate for the analysis of VaR. The predictions of VaR now fall under parametric predictions that encompass conditional volatilities and non-parametric prediction that incorporate the unconditional volatilities (Jorion, 2006; Jorion, 2007).

This report takes a keen look at the analysis of VaR based on a portfolio of four shares that have been monitored in a 260-day period. A background of the data sample has been done in order to shed more light on the data that has been applied in this process for the four shares in the 260-day period of time that was given in the spread sheet. The analysis includes the various methods of analysing VaR, which have been proven as useful tools in the financial modelling. The analysis of the four shares could be done by use of either the pricing index or the total return index data on shares. The process will look at the analytic VaR, Monte Carlo VaR, and the Historical Analysis/Bootstrap VaR. these will be based on the calculations of the data given for the four shares and advantages and disadvantages of each method given in details. A discussion of the analysis will then be carried out in the subsequent section and a conclusion made. The importance of VaR analysis methods cannot be ignored and thus have been given due consideration in looking at the data for the four portfolio of shares. The confidence level identified is p = (1-a) that is meant to define the maximum loss probability that is expected. The risk surface of the market will be analysed by use of the confidence level that varies between 95% and 99%. The method chosen for any calculation will majorly depend on the accuracy of the output to be estimated and the required timing that could create such an output (Bekaert & Harvey, 1997).

Background to the Data Sample

The assets that form the sample for this portfolio of four shares include the Sage Group PLC, Xtrata PLC, Royal Dutch Shell PLC, and the Severn Trent PLC, which are their equity names. Sage Group PLC is involved in the Information Technology industry where it deals in the provision of software for business, and offers support and services to both small and medium scale businesses. Specific and larger business firms are also covered. The company tries to provide services that make it easier for other business organizations to conduct their businesses. Sage Group PLC is listed on the London stock exchange and has been among the best performing firms in the financial market.

Xtrata PLC is a global company that is involved in the mining industry and has its headquarters in Switzerland and has registered its office in London. It majorly produces coal, a leading exporter of coal, and mines other minerals and metals such as copper, vanadium, zinc, and nickel. It is also a leading producer of ferrochrome in the world. This company has major operations in over 19 countries across Africa, Asia, Europe, South America, North America, and Australia. It has its primary listing done on the London stock exchange and forms part of the FTSE 100 index. It also has a secondary listing done on the SIX Swiss exchange and has Glencore International as its largest shareholder. The company has experienced some numerous acquisitions. It has revenue of over 30 million USD with an operating income of over 7 million USD.

Royal Dutch Shell PLC is a global company that is involved in the energy and petrochemical industry. It has its roots in England and Wales. The company operates in over 90 countries across all continents with over 93, 000 employees. Its 48% of production involves natural gas and produces over 3.3 million barrels daily. It owns three refineries as well as chemical plants. It is thus involved in the extraction of crude oil and gas, while it refines this and supplies, trades and eventually ships the products to international markets. It has employed high technology in its management and innovation has seen it through many hurdles. It recorded over 360 billion USD in revenue in 2010 with an income of over 20 billion USD.

Severn Trent PLC is a public utility company in Britain and is traded at the London stock exchange. It is part of the FTSE 100Index. It employs over 15, 000 people and operates in UK, Europe, US, and the Middle East. It is constituted of two major companies which are Severn Trent Water and Severn Trent Services. This company does supply over 3.7 households as well as companies in the locations covered. Severn Trent PLC has recorded over 1600 million USD in revenue in 2010 and has operating income of over 557 million USD according to the 2010 figures with a net income of over 250 million USD.

The currency employed was in sterling pounds. The sample was selected for a period that traverses two years starting from 18th October 2010 to 14th October 2011 which forms a 260-day period that was needed for the sample. The samples in the data have been presented on a daily basis for each and every share traded. The data represent some of the most liquid stocks that have been observed on the financial market and have thus been filtered and adapted adequately for the benefit of creating the necessary inputs needed in the calculation of the risk factors (Angelidis, et al., 2004).

In many cases, multiple samples are normally used in constructing a portfolio. Portfolio returns could be simulated by use of post fitting or pre-sampling. In this data sampling, for the benefit of this report, pre-sampling technique was made use of. This is because each and every asset was sampled independent of the other avoiding the hybrid extreme value estimator and the concept of empirical distribution and thus it was scaled in order to get the well-correlated returns that were needed (Jorion, 2006; Jorion, 2007). This allows us to calculate the value of the portfolio of the four shares. It is very possible to make use of the covariant matrices that are different for the sample portions as opposed to the whole sample. This approach is very crucial given the fact that the samples are not fixed over time and as such will change depending on the market trends. The four samples were selected on a period of 260 days, at least over 100 days given the fact that for 1% of VaR, a time of less than 260 days is not enough to make an accurate estimation of the VaR. In this case therefore; a large sample was used. The testing for performance was initiated on 18th October 2010 and the sample of a 260-day period thus ends on 14th October 2011. As has been noted in other studies on returns, the returns normally do exhibit a number of properties that are common and do not depend on the asset. This could be extended to what is considered to be the tail of such returns. Extreme events have been included in the samples in order to bring about an accurate prediction of the results. For all the methods used in the estimation of VaR, the size of the sample still matters. In this case, the 260 days sample was found to be a bit low and thus the accuracy of the predictions cannot be guaranteed. This is because of the need to have a sample that is as large as possible. Lower forms of correlations were expected in the extremes when stocks were being considered than when other assets such as currency were used (Artzner, et al., 1997).

Table 1: Summary statistics

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Table 2: Correlation matrix for the 4 share portfolio

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