Value at risk - Assignment Example

? Value at risk Introduction In the paper below, analysis of four portfolio shares of 4 different companies in the stock exchange are going to be evaluated and the value at risk is calculated. Since no investors or companies wish to get losses while dealing in shares (Jorion 2007, p.2). Value at risk provides a way to depict the probability of on making losses. In the paper below, various methodologies are going to be used to calculate the value at risk of the 4 portfolio shares for the given year. The methodologies that would be use include: The historical simulation, the Monte Carlo simulation and the parametric approach. In each of the following, there are various crucial steps that would be used in calculation of value at risk in the value at risk to come up with conclusions for the various portfolio shares. The structure of the paper would mostly be description based of the following approaches mentioned above. While calculating value at risk in a specific methodology, the following will need to be observed carefully. In each methodology, a description on how one is going to arrive at the specific value at risk for the given portfolio is going to be calculated and even a histogram plotted where necessary. In addition, one would be expected to comment on the important steps used and give a final verdict of the advantages and the disadvantages of using the given method. After calculating value at risk using the three approaches mentioned above, then a discussion will be conducted to compare the differences in the three methods while attempting to get the value at risk (Jorion 2007, p.6). Then the paper would end with a conclusion that would comment on the value at risk of the 4 portfolio shares used. Both non-parametric and parametric approaches used for estimating Value at risk have advantages as well as disadvantages (Jorion 2007, p.67). The parametric methods often require one to make strong assumptions concerning a given distributions of assets returns, though are simple to compute when one got the assumptions already made. On the other hand, the non-parametric approaches often require no assumption; though implicitly assume that a given data used in simulation is the representative sample of risks looked forward. Because the end product of any of the two approaches will be to estimate value at risk, often the most important points remain on whether results calculated by other different methods may differ from each other. In addition, one would still like to know which approach is the most reliable in estimating value at risk. Generally, intuitiveness shows that non-parametric methods, like the historical simulation as well as the parametric methods i.e. Risk metrics, will often yield the same Value at risk if historical returns data will be normally distributed. In addition, empirical studies also shown that the given predicted results from different Value at risk methodologies are often not close (Choudhry 2006, p.7. The historical simulation often does not impose a given distributional assumptions, sometimes it can be limited when used to forecast the range of certain portfolio value changes since it incorporates no volatility updating plus it produces inaccurate values once the future succumbs to extreme events. In contrast, the Risk metrics, is relatively easy to put in practice. Nonetheless, a given empirical observations on a given returns of financial instruments often do not exhibit the given normal distribution and hence the method do not fit data with certain heavy tails. Background to the data sample The following 4 companies have been chosen to have the analysis of their value at risk of their share portfolios calculated. They are Aggreko PLC, Admiral Group PLC, Amec PLC and the Anglo- American PLC. The Aggreko PLC is a very large international company that deals with supplying temporary power plus dealing with temperature control too. Admiral Group PLc is a large motor insurance company that has a head office at Wale, Cardiff . The Amec PLC is hence a global consultancy, project management and engineering company that is majorly based in Warrington. The Anglo-American PLC is therefore the largest mining companies that focus majorly on mining platinum metals, copper, diamonds, iron ores and many other precious types of metals. The four were chosen since their return indexes were close to each other and would help in not bringing major errors in the final results. The return index will be the one used in then calculations below since it is much easier to use than the price index figure that requires a lot of calculation before reaching the final figure. In the analysis of the portfolio below, the data to be used for the 4 companies have already been given in the given spread sheet and the historical values start range from 14th October, 2011 to 26th October, 2001. Often, there are a number of classifications that have been used by the given four portfolios. The given data used to analyze the given figures more so is dependent on four strategies: Multi-strategy, Arbitrage, CTA/Managed Futures and Long-Short equities. The arbitrage strategy often trades on the basis that the statistical mispricing of a given assets with respect to the market values. Often, such a strategy may expose the given fund to liquidity and credit risks. The Commodity Trading Advisor (CTA) or the Managed futures strategy sometimes involves taking both short and long positions for a wide range of asset classes. The short-long equities strategy often involves taking both short and long positions exclusively in equities. Moreover, there is always a tendency for taking the net long positions. In addition, some funds that employee this strategy often focus on investing in certain regions or industries. The multi-strategy approach aims majorly at diversifying the fund’s position through investing in a portfolio that comprise of various strategies, with the bid of reducing volatility plus smooth returns. Data When analyzing data given in the spreadsheet for the 4 companies over a period of 10 years. It includes monthly arithmetic returns plus monthly AUM for each given fund in the sample. Moreover, it is only funds that have remained more active over the 10 year period. Arbitrage funds CTA future funds Long Short equity funds Multi strategy funds Small funds 3 5 5 3 Large Funds 6 7 8 9 Analytic value at risk Concerning parametric approaches, the given portfolio returns are often characterized by certain parametric distribution, like the t-distribution, the normal distribution or a certain mixture of any given set of distributions. Often the parametric approaches are implemented by fitting certain probability density curves to a given data and then inferring Value at risk from the fitted curves. Parametric approaches are often more powerful compared to the non-parametric approach because they often do not entirely rely on certain sample observations, though they make some use of additional data found when assuming the distribution function. Mathematically, parametric approaches are majorly based on 4 distributional parameters, standard deviation, mean, kurtosis and skewness. The histogram above was drawn using the values of the 4 portfolio shares. Using the 99 percent confidence level given, one could calculate the value at risk of the given shares. Assuming that the mean loss could be 0.67 percent, then the value at risk would be 99 percent multiplied by 0.67 percent to get 0.66percent. This value at risk value is very minute and investors could invest in such portfolio. Using the 95 percent confidence level and assuming the mean loss is still 0.67 percent, the value at risk would then be 95 percent multiplied by 0.67 percent giving 0.63 percent. Monte Carlo VaR The Monte Carlo simulation often involve developing a given model for predicting future stock price returns plus in running multiple hypothetical trials through the model. The Monte Carlo simulation often refers to any method which randomly generates trials, though by itself does not show us anything concerning the underlying methodology. The following histogram for Monte Carlo simulation was drawn using the return index values of the four portfolio shares. Using the 99 percent confidence level given, one could calculate the value at risk of the given shares. Assuming that the mean loss could be 2.1 percent, then the value at risk would be 99 percent multiplied by 2.1 percent to get 1.98 percent. This value at risk value is very minute and investors could invest in such portfolio. Using the 95 percent confidence level and assuming the mean loss is still 2.1 percent, the value at risk would then be 95 percent multiplied by 2.1 percent giving 1.9 percent. Historical analysis This approach mathematically is relatively straight forward since it usually estimates the value at risk without making any strong assumptions concerning the distribution of loss or profit (Pietro 2001, p.2). Furthermore, the main assumption of the historical simulation (Non-parametric approaches) is that recent past provides a good predictor for the future. Historical simulation is one of the non-parametric approaches that can be used in the calculation of value at risk. Value at risk often can be calculated using the empirical (CDF) Cumulative Distribution Function of a given historical simulated returns. That means that tomorrow’s Value at risk could be calculated based on past figures plus the given distribution of portfolio returns that does not shift for a certain period of time. In order for one to find value at risk using historical simulation, one should confirm that a certain past returns have been sorted in ascending order plus the value at risk is got as that return and should lie between 5% or 1% lower percentile (Jorion 2007, p.56). The advantage which the historical simulation have is that it is easy to interpret and simple to calculate (Pietro 2001, p.3). Other advantage of using historical simulation is that it does not make any assumptions concerning the shape of a given distribution of a given risk factor that may affect a given portfolio’s value. Therefore, it often does not make any given parametric assumptions concerning the distribution of returns. Since the distribution of certain risk factors, like assets returns, can be often fat-tailed, the historical simulation technique might provide an improvement over other Value at risk methods that assume that a given risk factors may be normally distributed. In the event of turbulent events, there is no influence in the historical simulation when estimating value at risk. Using the 99 percent confidence level given, one could calculate the value at risk of the given shares. Assuming that the mean loss could be 0.5 percent, then the value at risk would be 99 percent multiplied by 0.5 percent to get 0.48 percent. This value at risk value is very minute and investors could invest in such portfolio. Using the 95 percent confidence level and assuming the mean loss is still 0.5 percent, the value at risk would then be 95 percent multiplied by 0.5 percent giving 0.9 percent. Discussion COMPARISON AMONG DIFFERENT VALUE AT RISK METHODS Both non-parametric and parametric approaches used for estimating Value at risk have advantages as well as disadvantages (Jorion 2007, p.67). The parametric methods often require one to make strong assumptions concerning a given distributions of assets returns, though are simple to compute when one got the assumptions already made. On the other hand, the non-parametric approaches often require no assumption; though implicitly assume that a given data used in simulation is the representative sample of risks looked forward. Because the end product of any of the two approaches will be to estimate value at risk, often the most important points remain on whether results calculated by other different methods may differ from each other. In addition, one would still like to know which approach is the most reliable in estimating value at risk. Generally, intuitiveness shows that non-parametric methods, like the historical simulation as well as the parametric methods i.e. Risk metrics, will often yield the same Value at risk if historical returns data will be normally distributed. In addition, empirical studies also shown that the given predicted results from different Value at risk methodologies are often not close (Choudhry 2006, p.7. The historical simulation often does not impose a given distributional assumptions, sometimes it can be limited when used to forecast the range of certain portfolio value changes since it incorporates no volatility updating plus it produces inaccurate values once the future succumbs to extreme events. In contrast, the Risk metrics, is relatively easy to put in practice. Nonetheless, a given empirical observations on a given returns of financial instruments often do not exhibit the given normal distribution and hence the method do not fit data with certain heavy tails. BACKTESTING OF VALUE AT RISK In order to check for the validity of a given risk model, there are often risk managers in place that use various statistical ways to know if a given model’s risk estimate will be consistent with the various assumptions of which the given model is based. Backtesting is hence a formal statistical framework which tests if actual losses are anywhere in line with the projected losses. By doing so, it hence systematically compares the given forecasting Value at risk with the actual Value at risk. For example, in case the given model was developed on a 1-day 99% value at risk, then backtesting entail looking for how many days the ex-post losses would exceed the 1-day 99% ex-ante value at risk (Jorion 2007, p.88). Often, days that actual loss try to exceed value at risk are often called exceptions, exceedences or violations. If the actual exceptions are approximately1%, then such a model is taken as reliable. In case they are, say, approximately 8%, then such a model is termed as underestimating the given model. In case the exceptions are, say, 0.3%, then such a model often overestimates the loss. As many people may argue, the sole purpose of the backtesting is to try and examine if the failure rate of a given model is statistically equal to the expected one (unconditional coverage) and to investigate if the Value at risk violations are also independently distributed (conditional coverage). VAR BACKGROUND INFORMATION Value at risk is usually a category of risk metrics that hence describes probabilistically the market risk for a given trading portfolio (Choudhry 2006, p.9). Value at risk has widely been used by securities firms, banks, securities firms, energy merchants, commodity merchants and other trading organizations. Therefore, such firms often track their given portfolio market risk through using historical volatility for risk metric. In addition, they may do so through calculating the given historical volatility of the portfolio's market value in a rolling hundred trading day period. The only problem such would provide the retrospective indication of a give risk. Often, the historical volatility does illustrate how risky a given portfolio had become over the previous hundred days. The most traditional and popular measure of risk is the use volatility. The problem with volatility is that it often does not care of the direction of a given investment’s movement: a certain stock can be volatile since it suddenly jumps higher. Investors are often not distressed by gains. Most investors risk about the notion of losing their money while investing and Value at Risk may be based on that given common- sense fact. Since nobody strives to be a loser in any investment, value at risk comes into play to help solve such issues (Choudhry 2006, p.10). Risk is always about the odds of losing while value at risk is more so based on common-sense. When assuming that investors care more about the odds of getting big losses in their investment, value at risk tries to answer some of their questions like, “ What could be the worst case-scenario?” or “ What quantity of money can one lose at an investment? Some times the value at risk is usually a category of risk metrics that hence describes probabilistically the market risk for a given trading portfolio. Value at risk has widely been used by securities firms, banks, securities firms, energy merchants, commodity merchants and other trading organizations. Therefore, such firms often track their given portfolio market risk through using historical volatility for risk metric. In addition, they may do so through calculating the given historical volatility of the portfolio's market value in a rolling hundred trading day period. The only problem such would provide the retrospective indication of a give risk. Often, the historical volatility does illustrate how risky a given portfolio had become over the previous hundred days. The most traditional and popular measure of risk is the use volatility. The problem with volatility is that it often does not care of the direction of a given investment’s movement: a certain stock can be volatile since it suddenly jumps higher. Investors are often not distressed by gains. Most investors risk about the notion of losing their money while investing and Value at Risk may be based on that given common- sense fact (Holton 2004, p.23). Since nobody strives to be a loser in any investment, value at risk comes into play to help solve such issues. Risk is always about the odds of losing while value at risk is more so based on common-sense. When assuming that investors care more about the odds of getting big losses in their investment, value at risk tries to answer some of their questions like, “ What could be the worst case-scenario?” or “ What quantity of money can one lose at an investment? To be more specific, value at risk statistic got three components: Confidence level, a time period and a loss amount or just loss percentage. Keeping the three parts in mind, one can be able to see the variations which the questions value at risk tries to answer: For example, What can I do most - with a 99% or 95% level of confidence - one expects to lose money in dollars over the next one year? What maximum percentage can I - with 99% or 95% confidence - expect one to lose in the next one year? From the given example, one could be able to analyze how the ‘value at risk’ has the three elements. It does possess a high level of confidence (either 99% or 95%), a time frame and an estimate of a given investment loss (either expressed in dollar or in percentage terms) (Choudhry 2006, p.16). COMPONENTS OF VALUE-AT-RISK MEASURES The implementation of value at risk often requires background information of some of their components. Distribution assumptions The value at risk from a statistical view point is the quantile of profit or loss (P&L) distribution of any given portfolio over a specific holding period. Therefore, the key element in implementing value at risk is hence to obtain very accurate estimates for a given tails based on the relevant distributional assumption of given returns. Though some individual argue out that the distributional assumptions can also be a controversial issue (Holton 2004, p.44). Usually, the parametric-value at risk methods try to assume that a given portfolio returns can be characterized by a given parametric distribution, like the normal distribution, or the student t-distribution plus or even a mixture of both sets of distributions. Unfortunately, the approaches are subjected to “model risk” of which the given distributional assumptions could even be inaccurate. Therefore, there exist many empirical studies that show that a certain financial time-series might have violated the normality assumption, exhibited asymmetric, platykurtic or leptokurtic distributions that got heavy tails. Often, the non-parametric techniques do not impose a certain distributional assumptions, hence, are free of “parameter estimation” risk and model risk (Choudhry 2006, p.25). The window length of data The window length refers to the length of which an observation period can be used for estimating Value at risk. Often, the window length choice tries to relate to some sampling issues plus the availability of databases of which some may be controversial (Pietro 2001, p.3). Some people argue that the given sample size often affects the value at risk estimates accuracy, with a longer sample size giving the most precise estimations. Furthermore, other people try to maintain that on adding more historical data would indicate adding older data that could be inappropriate for forecasting the future and hence would be beneficial in using smaller sample size because it could accommodate structural changes of a given trading behaviour. Similarly, in terms of value at risk stability, some people argue out that the Value at risk often increase with the expanding observation intervals, and the value at risk measures often become more stable with longer observation periods (Jorion 2007, p.22). Time horizon (holding period) effect on the Value at risk values Often, the time horizon may take any time value. When in practice, it might vary from 1 day to 2 weeks i.e. 10 trading days plus it may depend on liquidity of assets and the frequency of a given trading transactions. In according to the Basle Committee, it is recommended to use the ten day holding period whereas other people argue that the given time frame of ten days is insufficient for. It is argued that it is insufficient for the given traded instruments plus might be restrictive in case of illiquid assets. Generally, the long holding periods are often recommended for portfolios that got illiquid instruments. The empirical studies often reveal that the longer a given holding period, then the higher the VaR is (Holton 2004, p.56). Confidence level effect on the Value at risk values When it comes to risk management, often the confidence level tries to reveal the given internal acceptable requirements for a given financial institutions plus therefore may be different across the various institutions based on attributes like confidence and tolerance (Jorion 2007, p.24). The Risk Metrics system often uses the 95% confidence level, while the Basel committee uses the 99% confidence level. Some people support that the Basel committee’s choice of confidence level is hence the reflection of a given tradeoff between a certain desires of regulators and is supposed to ensure a stable and safe financial system plus existence of high level capital requirements reserve. In general, whenever the given confidence level is high, means the value at risk will be high too. VALUE AT RISK APPROACHES Although Value at risk is an intuitive concept, sometimes its measurement may be a very challenging problem (Holton 2004, p.67). There is usually a number of useful models that can be employed in the calculation of the value at risk and often employ various methodologies. In addition, they also reveal that the given methodologies often follow some general structure that can be summarized in 3 points; i) Mark-to-market a given portfolio ii) Try to estimate the given distribution of portfolio returns iii) Ensure one computes the value at risk of the portfolio. Furthermore, there are some people that argue out that there existed some key differences among the value at risk methods. The people generally explain that the major differences are more so related to one estimating the given distribution of portfolio returns. Conclusion From the above analysis of the value at risk of the four given share portfolio, we realized the differences in the methods used and the advantages and the disadvantages of the methodologies (Pietro 2001, p.6). It is always the pride of any good investor to know what is the value of risk of a given share while investing so as to know whether the outcomes would lead to losses or profits. In the present, a lot of people are using value at risk calculating their probabilities of making losses while investing in shares (Pietro 2001, p.3). Bibliography Ado, A., 2008, Value-at-Risk, New York: Lambert Academic Publishing. Alexander, C., 2009, Market Risk Analysis, Value at Risk Models, New York: John Wiley & Sons. Best, P., 2011, Implementing value at risk, New York: John Wiley & Sons. Choudhry, M., 2006, An introduction to value-at-risk. New York: John Wiley and Sons. Holton, G. A., 2004, Value-at-risk: theory and practice, Michigan: Academic Press. Jorion, P., 2011, Value at risk: the new benchmark for controlling market risk, New York: Irwin Professional Pub. Jorion, P., 2007, Value at risk: the new benchmark for managing financial risk, New York: McGraw-Hill Professional. Pietro Penza, V. K., 2001, Measuring market risk with value at risk, New York: John Wiley and Sons. Read More