Quantifying and Managing the Risk - Assignment Example

?Introduction This assignment is aimed at quantifying and managing the risk of a portfolio by measuring financial risk analysis of the 260-day Value at Risk (VAR) of a portfolio of 4 shares that include: . National Grid PLC, Tate & Lyle PLC, Imperial Tobacco Group PLC and Investec PLCA. In the analysis, it is important to start by conducting a short discussion of Value at Risk in general, followed by a summary of the data analysis that includes presentation of the main findings of the analysis, along with a discussion of any limitations and possible recommendations. Finally a conclusion is made on the data that has been analysed and presented. Background Hofler (2008) asserted that Value-at-Risk was first used in the late 1980’s by investment banks and security houses to measure the risk of their trading portfolios. In fact the word value at risk was first published in a G-30-report in 1993. However, the analysis became more prominent after the 2007 financial crisis after JP Morgan gave a presentation on quantitative tool that can measure market risk through VAR. The VAR of a portfolio is the maximum loss expected to occur with a certain probability over a given time period given a probability (usually between 5 percent and 1 per cent) that the portfolio will perform below expectation (Papaioannou et al, 2006). VAR is an analysis tool that is used to pinpoint risks that exist in a given portfolio (Best, 1998). Many financial traders often apply some sort of VAR regime, which help them set their limits. Therefore, VAR is widely used by various companies worldwide with managers in brokerage firms, investment funds and corporate using it to measure their financial risk (Alexander, 2009). In the banking sector, bank regulators use Value-at-Risk in determining how much capital a bank and other financial institutions should possess in line with the market risks it is bearing (Grant, 2004). The aim of this study is to use Analytic VAR, historical (Bootstrap) VAR and Monte Carlo (MC) VAR simulation as alternative approaches of calculating VAR. The listed companies being analysed are listed in the FTSE 100 index in the London Stock Exchange. The first company in the analysis is Imperial Tobacco Group PLC. The company was founded in 1901 and is involved in manufacturing, marketing, distribution, and sale of tobacco and tobacco-related products that include cigarettes, fine cut tobacco, cigars, snus, tubes, filters, and rolling paper products, as well as roll your own, make your own, and pipe tobaccos. Imperial Tobacco Group PLC also provides logistics services for tobacco product manufacturers, as well as to various customers in the convenience, telecommunications, transportation, pharmaceutical, publishing, and lottery sectors. The company is based in Bristol, the United Kingdom and has a market capitalization of 24,560.76 million pounds (Imperial Tobacco Group PLC, 2011). The second company in the analysis is Tate & Lyle PLC. The company is headquartered in London; the United Kingdom and offers its products primarily in Europe, the Middle East, Africa, the Asia Pacific, and the Americas. This includes manufacturing and sale of ingredients and solutions to the food, beverage, industrial, animal feed, pharmaceutical, and personal care markets. Tate & Lyle PLC has a market capitalization of 3,361.55 million pounds (Tate & Lyle PLC, 2011). The third company in the analysis is National Grid plc. The company owns and operates regulated electricity and gas infrastructure networks in the United Kingdom and northeastern United States. The company operates high voltage electricity transmission networks, electricity interconnectors, gas distribution systems and liquefied natural gas storage activities in the Great Britain, New York, Canada and New England. The company serves residential and commercial consumers through the delivery of gas, generation and distribution of electricity to approximately 8 million customers in New England, upstate New York and Long Island. National Grid plc was founded in 1990 and is based in London, the United Kingdom with a market capitalization of 34,848.68 pounds (National Grid Plc, 2011). The fourth company of analysis is Investec plc. The company is an international, specialist bank and asset manager that provides a diverse range of financial products and services that include advisory, structuring, lending, securities trading, market making and principal transactions to a selected client base Investec plc and Investec Limited have subsidiary companies that include Investec Bank plc (IBP) and Investec Bank Limited (IBL) respectively. At the same time Bank (Australia) Limited (IBAL) is a subsidiary of IBP. Investec also has interests in Lease direct Finance Limited (LDF) and Investec Asset Management Namibia (Pty) Ltd. Investec PLC has a market capitalization of 3,180.63 million pounds (Investec plc 2011). These companies are listed in the FTSE index since the meet the requirements set out by the FTSE Group, including having a full listing on the London Stock Exchange and meeting certain tests on nationality, free float, and liquidity. Data analysis Choudhry (2011) asserts that a VAR statistic is composed of a time period (a day, a month or a year), a confidence level (typically either 95% or 99%), and a loss amount (expressed either in percentage or loss in currency) and correlation is also the main component of many VAR models. In conducting our analysis using Analytic VAR, historical (Bootstrap) VAR and Monte Carlo (MC) VAR simulation we are going to use data from 4 portfolios provided to measure financial risk. Value at Risk records the actual loss that would occur if the returns were below a certain probability threshold of the distribution. We are using the total return index to analyse the performance of the portfolio investment, because it is an accurate measure of actual performance that includes dividends, interest, rights offerings and other distributions realized over a given period of time. Using the solver to be able to invest in a portfolio of investment the results are shown below: The total weight is 19.07% and an expected return of 0.01% and the respective portfolio weights are: 1) National Grid PLC=0.00% 2) Tate & Lyle PLC=16.91% 3) Imperial Tobacco Group PLC=2.16% 4) Investec PLC=0.00% From the respective total weights, some shares that will bring a higher return than other. The expected returns are shown below: Minimum Expected Return 0.0337% Maximum Expected Return 0.0639% As a result, these figures are supported by the following portfolio graph that shows the portfolio investment with the expected returns and the standard deviation. In analysing the efficient frontier curve to analyse the portfolio of investment, the efficient frontier curve is shown below: The efficient frontier curve has a slope of 0.039124754 with the optimal portfolio weight being: 1) National Grid PLC=0% 2) Tate & Lyle PLC=23% 3) Imperial Tobacco Group PLC=73% 4) Investec PLC=5% The result of our portfolio shows the relationship between their mean and their standard deviation in the four shares as: National Grid PLC Tate & Lyle PLC Imperial Tobacco Group PLC Investec PLC Mean Return 0.034% 0.051% 0.064% 0.050% Stdev of Returns 1.380% 1.906% 1.457% 2.712% CORRELATIONS BETWEEN RETURNS National Grid PLC Tate & Lyle PLC Imperial Tobacco Group PLC Investec PLC National Grid PLC 100% 19% 40% 22% Tate & Lyle PLC 19% 100% 20% 23% Imperial Tobacco Group PLC 40% 20% 100% 22% Investec PLC 22% 23% 22% 100% In the table provided above, National Grid PLC has mean of 0.034% and a standard deviation of 1.380% bins frequency -6.45% 8 -3.45% 25 -0.45% 764 2.55% 1734 5.55% 62 8.55% 4 11.55% 0 14.55% 0 17.55% 1 Its return distribution is of a normal curve with its share price being around 2.55% more than 14734 days. This relationship can be shown in the histogram below: The graph shows that the share prices have been normally distributed. Tate & Lyle PLC has a mean of 0.051% and a standard deviation of 1.906%. The values of its returns are shown in the table below: bins frequency -9.85% 0 -7.85% 2 -5.85% 5 -3.85% 23 -1.85% 144 0.15% 1262 2.15% 1006 4.15% 131 6.15% 20 This value in the above table shows that the price of Tate & Lyle PLC are normally distributed with it rate of return at 0.15% at most of the time; this is shown that it has a normal curve which is normally distributed in the histogram below that. Imperial Tobacco Group PLC has a mean of 0.064% and a standard deviation of 0.074% with a normal distribution as shown below: bins frequency -9.85% 0 -7.85% 2 -5.85% 5 -3.85% 23 -1.85% 138 0.15% 1218 2.15% 963 4.15% 124 6.15% 20 8.15% 1 10.15% 3 The figure above shows that Imperial Tobacco Group PLC is normally distributed with its prices bringing a rate of return of 0.15% almost 1218 times. Finally, Investec PLC has a mean of 0.050% and a standard deviation of 2.712%. It has a normally distributed curve that is described by the table and graph below. bins frequency -16.93% 0 -12.93% 4 -8.93% 11 -4.93% 66 -0.93% 588 3.07% 1536 7.07% 171 11.07% 26 15.07% 6 Both the table and the graph show that it is normally distributed with a normal curve a rate of return of around 3.07% in almost 1536 days. 1. Historical Method Calculating VAR This method involves use of actual historical returns, and organizing them in order from worst to best. As a result, we use the method to calculate each daily return assuming that historical perspectives will be repeated. In a histogram that compares the frequency of return. The above graph shows National Grid PLC. In the graph, the "left tail" of the histogram shows the lowest 5% and 1% of daily returns. In analysing the histogram, we can say with 95% confidence that the worst daily loss will not exceed 0%. Put another way, we expect with 95% confidence that our gain will exceed 0%. At the same time, with 99% confidence, the worst daily loss will not exceed 4%. And with 95% confidence the gains realised will not exceed 4% The above graph shows Tate & Lyle PLC. In the graph, the "left tail" of the histogram shows the lowest 5% and 1% of daily returns. In analysing the histogram, we can say with 95% confidence that the worst daily loss will not exceed 0%. Put another way, we expect with 95% confidence that our gain will exceed 0%. At the same time, with 99% confidence, the worst daily loss will not exceed 3%. And with 95% confidence the gains realised will not exceed 3.5% The above graph shows Imperial Tobacco Group PLC. In the graph, the "left tail" of the histogram shows the lowest 5% and 1% of daily returns. In analysing the histogram, we can say with 95% confidence that the worst daily loss will not exceed 0%. Put another way, we expect with 95% confidence that our gain will exceed 0%. At the same time, with 99% confidence, the worst daily loss will not exceed 3.5 %. And with 95% confidence the gains realised will not exceed 4.2%. The above graph shows Imperial Investec PLC. In the graph, the "left tail" of the histogram shows the lowest 5% and 1% of daily returns. In analysing the histogram, we can say with 95% confidence that the worst daily loss will not exceed 0.3%. Put another way, we expect with 95% confidence that our gain will exceed 0.3%. At the same time, with 99% confidence, the worst daily loss will not exceed 2.1 %. And with 95% confidence the gains realised will not exceed 2.5%. Advantages: Historical simulation method is fast and simple to implement and interpret. It is used to compute risks of portfolios with many options. According to Meric and Meric (2001) and et al (2008), historical simulation allows distribution of risk factors to be considered. Disadvantages It is not possible to do scenario analysis using this method and it can compute misleading VAR estimates especially when the immediate past is not represented. It is not suitable for estimating low quantiles of changes in prices on small data (Rachev, 2003). The Historical Simulation method is cumbersome for large portfolios with complicated structures. The historical simulation approach normally has difficulty in dealing with new risks and assets if they do not have sufficient historical prices and data. 2. The Variance-Covariance Method The variance covariance method assumes that stock returns are normally distributed. It is used to calculate efficient portfolios (Benninga and Czaczkes 2000). Hence we use the expected (or average) return and standard deviation and are able to automatically know where the worst 5% and 1% lie on the curve. Using the mean and standard deviation of the 4 portfolio of assets, The VaR metric is 260 day 95% and 99%, we can calculate VaR and find results above as: National Grid PLC Tate & Lyle PLC Imperial Tobacco Group PLC Investec PLC Stdev of Returns 1.380% 1.906% 1.457% 2.712% Hence in using the above data: we are able to see the worst 5% and 1% of the 4 shares with 95% and 95% respectively. Confidence National Grid PLC Tate & Lyle PLC Imperial Tobacco Group PLC Investec PLC 95% -1.65 x 1.380%=-2.27% -1.65 x 1.906%= -3.14% -1.65 x 1.457%=-2.4% -1.65 x 2.712%=-4.47% 99% -2.33 x 1.380%=- 3.21% -2.33 x 1.906%=-4.44% -2.33 x 1.457%=- 3.39% -2.33 x 2.712%=-6.31% Advantages First, it is fast and easy to compute. Second, it can be easily explained to senior management. Third, it is easy to investigate various assumptions concerning variance and correlations in when scenario analysis is performed. Disadvantages According to Benninga and Czaczkes (2000), first, it is not possible to calculate risk of portfolios with options when the holding period is long. Secondly, it is difficult to explain this method to senior management. Thirdly, it can result in misleading VAR estimates when the immediate past is non-representative. Fourth, it only assumes stable correlations (Cima, 2000). Lastly, it may be difficult to examine other options concerning the distribution of factors affecting the market using this method. 3. Monte Carlo Simulation According to McLeish (2011), the Monte Carlo Simulation involves developing a model for future stock price returns and running multiple hypothetical trials through the model. As a result, based on its historical trading pattern and after running 1000 trial, with 99% probability, the stock price of National Grid PLC would not climb to more than 247.71 and its future price fall to more less than 220.766. At the same time, with 95% confidence level, the 5% lowest share price is 221.994. Hence there is 5% likelihood that if the share falls to this point, we will experience a loss of 7.9. At the same time, the 5% highest share price would be 242.702 in which we will experience a gain of 12.802. This gain is our VaR estimate at 95% confidence level for the share. The following histogram shows the movement For Tate & Lyle PLC, after 1000 runs to get the VaR at a 99% confidence level, the 1% lowest stock price, is 771.886. The original stock price was 779.8. There is a 1% likelihood that the share will rise to 795.064. If that happens, we will experience a gain of at least 15.264. This gain is our VaR estimate at a 99% confidence level for one share. At 95% confidence level, the 5% lowest stock price is 772.982. Hence there is 5% likelihood that if the share falls to this level, we will experience a loss of 6.818. This gain is our VaR estimate at 95% confidence level for the share. Its histogram is shown below: After 1000 runs to get the VaR at a 99% confidence level, for Imperial Tobacco PLC the 1% lowest stock price, is 212.078. The original stock price was 222.8. There is a 1% likelihood that the share will rise to 236.35. If that happens, we will experience a gain of at least 13.55. This gain is our VaR estimate at a 99% confidence level for one share. At the same time, after 1000 runs to get the VaR at 95% confidence level, the 5% lowest stock price is 215.699. Hence there is 5% likelihood that if the share rises to 235.088, we will experience a gain of 19.389. This is shown in the histogram below: In analysing Investec PLC, after 1000 runs to get the VaR at a 99% confidence level, the 1% lowest stock price, is 90.462. The original stock price was 100. There is a 1% likelihood that the share will rise to 116.08. If that happens, we will experience a gain of at least 16.08. This gain is our VaR estimate at a 99% confidence level for one share. At the same time, the VaR at 95% confidence level, the 5% lowest stock price is 93.92. Hence there is 5% likelihood that if the share falls to this level, hence we will experience a loss of 6.08. This gain is our VaR estimate at 95% confidence level for the share. The histogram is shown below: Advantages: Using the Monte Carlo method, an analyst is able to use various distributional assumptions like normal as well as nonnormal distributions and T-distribution. In addition, it is possible to do scenario analysis using this method. Disadvantages: If an analyst makes further runs, he/she will eventually get results that will not be the same as the former due to data requirements and computational powers. In addition, computations cannot be made quickly when there is a relatively large portfolio. Explaining Monte Carlo simulation to senior management is quite difficult (Amenc and Sourd 2003). Finally, this method has risks of failure due to the requirements on specific stochastic methods and different methods of pricing financial products. Discussion: The assignment is aimed at quantifying and managing the risk of a portfolio by measuring financial risk analysis of the 260-day Value at Risk (VAR) of a portfolio of 4 shares that include: National Grid PLC, Tate & Lyle PLC, Imperial Tobacco Group PLC and Investec PLCA. The VAR of the portfolio was conducted to analyse the maximum loss expected to occur with a certain probability over a given time period given a probability that the portfolio will perform below expectation. The study used Analytic VAR, historical (Bootstrap) VAR and Monte Carlo (MC) VAR simulation as alternative approaches of calculating VAR using data from 4 portfolios provided to measure financial risk. Value at Risk records the actual loss that would occur if the returns were below a certain probability threshold of the distribution. The discussions on the findings are provided below: National Grid PLC has a portfolio weight of 0% and using the efficient frontier curve, its total weight of 0% and its share price return is normally distributed at around 2.55% being more dominant. This is supported by the historical method whereby, with 95% confidence that the worst daily loss will not exceed 0% and gains realised will not exceed 5%. At the same time, with 99% confidence, the worst daily loss will not exceed -4%. In comparison with variance covariance method to calculate VAR with 95% the daily lose would not exceed -2.27% and at 99% daily rate of return would not exceed -3.21%. When using the Monte Carlo simulation. As a result, based on its historical trading pattern with 95% confidence level, the shares might experience a loss of 7.9. The shares do not have a bigger weight as a result, coupled with the anticipated losses at both 95% and 99% confidence. When comparing the three methods, they almost have similar result in the same direction with small differences. The shares would not be added in the portfolio since they do not fall in the efficient frontier curve. Tate & Lyle PLC has the highest portfolio weight of 16.91% efficient frontier weight of 23%. The company has a mean of 0.051% and a standard deviation of 1.906%. Using the historical method, with 95% confidence that the worst daily loss will not exceed 0%. At the same time, with 99% confidence, the worst daily loss will not exceed 3%. And with 95% confidence the gains realised will not exceed 3.5%. Using the variance covariance method, with 95% confidence, the daily loss rate of return would not exceed -3.14% and at 99% confidence, the daily loss rate of return would not exceed -4.44%. Using the Monte Carlo VaR at 99% confidence level, we will experience a gain of at least 15.264. At 95% confidence level, we will experience a loss of 6.818. The three methods have almost similar result, supporting the conclusion that these shares would be added in a portfolio investment as they also fall in the efficient frontier curve with a weight of 23%. Imperial Tobacco Group PLC has a total weight of 2.16% efficient frontier with a total weight of 2.16%. The company has a mean of 0.064% and a standard deviation of 0.074% with a normal distribution with prices bringing a rate of return of around 0.15%. Using the variance covariance method, at 95% confidence that the worst daily loss will not exceed 0% and with 99% confidence, the worst daily loss will not exceed 3.5 %. Using the Monte Carlo method, at 99% confidence level, the share price would experience a gain of at least 13.55 and at 95% confidence level, the shares would gain 19.389. The results using the three methods have the same results in the same direction thus supporting the findings by the efficient frontier curve whereby it falls in the efficient frontier curve with a weight of 73%. Investec PLC having a portfolio weight of 0%. Using the efficient frontier, the company has a weight of 5% with a mean of 0.050% and a standard deviation of 2.712%. It has a normally distributed curve and a rate of return of around 3.07%. Using the historical method, with 95% confidence that the worst daily loss will not exceed 0.3%. At the same time, with 99% confidence, the worst daily loss will not exceed 2.1 %. And with 95% confidence the gains realised will not exceed 2.5%. Using the variance covariance method, at 95% confidence, the daily loss in terms of rate of return would not exceed-4.47% and at 99% confidence, the daily loss in terms of rate of return would not exceed -6.31%. When analysing the Monte Carlo method, 99% confidence level, we will experience a gain of at least 16.08. At the same time, the VaR at 95% confidence level, we will experience a loss of 6.08. When comparing the three methods, the Monte Carlo method has different results showing positive returns at 99% confidence and negative result at 95% confidence. However, this share would be added in the portfolio investment, however with a smaller percentage as seen in the efficient frontier with a weight of 5%. When analysing the four shares, Imperial Tobacco Group PLC, Tate & Lyle PLC and Investec PLC have the highest probability of being put in an investment. As an investor, it would be important to use all the methods to make informed decision on the portfolio investment due to the fact that they all base their decisions on historical and future expectations and none can be more perfect than the other. The only difference would be on the weight to be placed on the VaR method to be used. As a result, Monte Carlo and historical method would be the best to use but not in isolation since they all provide the same results and are easy to use in as long as the investor has the necessary data. References Alexander, C 2009, Market Risk Analysis, Value at Risk Models, John Wiley & Sons, New York. Amenc, N. and Sourd V 2003, Portfolio theory and performance analysis, John Wiley & Sons, New York. Benninga, S & Czaczkes, B 2000, Financial modeling, Volume 1, 2nd edn, MIT Press, Cambridge. Best, P 1998, Implementing value at risk, John Wiley & Sons, New York. Choudhry, M 2011, Structured Credit Products: Credit Derivatives and Synthetic Securitisation, 2nd edn, John Wiley and Sons, New York. Cima 2000, Management Accounting Information Strategy Beyond 2000 Pilot Paper, Elsevier, London. Grant LK 2004, Trading risk: enhanced profitability through risk control, John Wiley and Sons, New York Hofler, B 2008, Risk Measures - Value at Risk and Beyond, GRIN Verlag, Munich. Imperial Tobacco Group PLC 2011, Annual Report and Accounts 2011, viewed 6 January 2012 http://www.imperialtobacco.com/files/financial/reports/ar2011/files/pdf/2011AnnualReport.pdf Investec plc 2011, Group Financial Results 2011, viewed 6 January 2012 http://www.investec.co.uk/#home/investor_relations/Financial_Information/Financial_Results.html McLeish, LD 2011, Monte Carlo Simulation and Finance, John Wiley and Sons, New York. Meric, L & Meric, G 2001, Global financial markets at the turn of the century, Emerald Group Publishing, Bingley. National Grid Plc 2011, Annual Report 2011, viewed 6 January 2012 http://www.nationalgrid.com/nr/rdonlyres/03ec114b-2f87-45b8-b870-a429db233115/47508/bny91576bny010_edgr_n_cpo_1242.pdf Papaioannou, M, IMF & CMD 2006, A Primer for Risk Measurement of Bonded Debt from the Perspective of a Sovereign Debt Manager, International Monetary Fund, Washington. Rachev, TS 2003, Handbook of heavy tailed distributions in finance, Elsevier, London. Clayman RM, Fridson, SM & Troughton, HG 2008, Corporate Finance: A Practical Approach, John Wiley & Sons, New York. Resti, A & Sironi, A 2007,Risk management and shareholders' value in banking: from risk measurement models to capital allocation policies, John Wiley and Sons, New York. Tate & Lyle PLC 2011, Annual Report 2011, viewed 6 January 2012 http://www.tateandlyle.com/InvestorRelations/Documents/Annual%20Reports/Annual%20Report%202011.pdf Read More