Analysis of Financial Modeling - Literature review Example

?Financial Modeling Summary: The chapter below is the discussion of the financial modeling, the financial model discussed in the chapter mainly consists of the various approaches used in the modeling. The different kind of the modeling discussed here are the value at risk, Mont Carlo VaR analysis, bootstrap method of analysis and the portfolio analysis. The main intention of the study is to conduct an analysis of the Value at Risk (VaR) of a portfolio of 4 shares using the methods discussed in the above Financial Modeling. The four companies are taken into account for calculation of the shares and the Companies used for the analysis and they are the British Land Company PLC, Marks & Spencer Group PLC, Cairn Energy PLC and the Land Securities Group PLC.A clear analysis and the calculations are made in the study below. We begin the chapter with the general idea of the VaR and the various approaches to the VaR, the historic application and the application of the same. We also include the evaluation of the VaR at the different possible approaches in the study; a final conclusion is made by the calculations carried out in the study. Introduction: The ‘value at risk’ is an extensively employed risk measure concept in the risk of loss on a particular portfolio of fiscal assets. For a specified portfolio, probability and time horizon, VaR is described as a threshold price such that the possibility that the market loss on the portfolio above the particular time horizon go beyond this value is the known probability level. VaR has different important uses in finance risk management, risk assessment, financial control, reporting of the financial statement and calculating the capital regulation by analyzing the Various concepts. VaR can also be used in non-financial aspects. The VaR risk assessment defines risk as a market loss on a permanent portfolio over an unchanging time horizon, by analyzing the normal markets. There are many option risk procedures in finance. As a substitute of mark-to-market, which makes use of the market value to define loss, loss is frequently defined as transformation in principal value. For instance, if an organization hold a loan that decline in market price as the interest charge go up, but has no alteration in cash flows or credit quality, some systems do not identify a loss. Or we can try to integrate the economic price of possessions, which was not calculated in every day financial statements, such as loss of market assurance or employee confidence, destruction of brand names etc. “VaR measures are inherently probabilistic” (Holton 2003, p. 107). Moderately assuming an unchanging portfolio above a fixed time horizon, several risk measures integrate the consequence of probable operation and believe the expected investment period of position. Lastly, some risk procedures adjust for the probable effects of irregular markets, rather than excluding them from the calculation. Aim of the Study: The aim of the assignment is to conduct an analysis of the Value at Risk (VaR) of a portfolio of 4 shares using the methods discussed in ASB4416 Financial Modeling. The 4 shares of the four companies are used for the analysis and they are the British Land Company PLC, Marks & Spencer Group PLC, Cairn Energy PLC and the Land Securities Group PLC. The study mainly aims to analyze the shares by the various financial models used and by the various analyses of the statistical models like the multivariate analysis, boot strap method and the analytical Variation method for the study. We assess Variation that has been developed on a frequent measure, in some instances to agree with diverse type of risk and in extra cases, as an answer to the boundaries of VaR. In the concluding section, we assess how VaR fits into and compare with the other risk evaluation measures. Methodologies Used: There are three fundamental approaches that used for calculating the Value at Risk, although there are abundant Variations inside each approach. The measures can be calculated logically by building assumption about return distributions in the market risks, and by using the Variances and co-variances transversely in these risks. It can in additionally expected by operating hypothetical portfolios throughout chronological data or from Monte Carlo model. Data and Analysis: In this segment, we explain and contrast the various approaches, Variance Covariance Method: As value at Risk measures the chance that the worth of a portfolio will fall below a particular value in a fastidious time period, it should be reasonably easy to work out if we can obtain a probability distribution of possible values. That is essentially calculated in the Variance covariance method, a method that has the advantage. There are different steps occupied in the process and they are as follows. The first step necessitates us to take every asset in a portfolio and chart that asset onto easier, consistent instruments. For example, a ten-year voucher bond with annual coupons C, for occasion, can be busted down into ten zero coupon bonds, with corresponding cash flows: The first coupon match up to a one-year zero voucher bond with a face value of C, the second coupon with a two-year zero coupon link with a face value of C and so until the tenth cash flow, which is coordinated up with a 10-year zero coupon bond with a face value of FV (equivalent to the face value of the 10-year acquaintance) plus C. The planning process is more difficult for more compound assets like the stocks and options, but the essential perception does not change. We try to map each financial benefit hooked on a set of instrument symbolizing the original market risks. In the next step, each monetary asset is confirmed as a set of position in the consistent market instrument. This is easy for the 10-year coupon bond, where the transitional zero coupon bonds have face values that equal the coupons and the final zero voucher bond has the face value, in adding up to the coupon in that era. As with the map, this process is more complex when functioning with exchangeable bonds, stock or derivative. Once the consistent instruments that influence the assets in a portfolio are recognized, we have to approximate the variances in each of these instruments and the covariance throughout the instrument in the subsequent step. In observation, these difference and covariance estimate are acquired by glancing at chronological data. They are the inputs in approximating the VaR. In the ultimate step, the Value at Risk for the portfolio is calculated by means of the weights on the standardized instrument to identify the Variances and covariance in analyzing the shares. Each of the three concepts for estimating Value at Risk has benefits and comes with belongings. The variance-covariance advance, with its delta regular and delta gamma variations, involve us to make tough assumption about the go back distributions of consistent assets, but is easy to compute, once those assumptions have been made. The chronological replication advance require no statement about the nature of return distributions but completely assume that the data used in the replication is a representative sample of the risks looking further. The Monte Carlo simulation approach allow for the most elasticity in terms of choosing distributions for earnings and bring in subjective judgment and external data, but is the majority complex from a computational standpoint. Background to the Data Sample: Portfolio analysis is an efficient way to evaluate the services and products that make up an association's industry portfolio. All associations are involved in excess of one business. Some of these contain meetings and conventions, publishing, education and training, research, government representation, public relations, standards setting, etc. Portfolio analysis assists to decide which of these services and products should be highlighted and which should be phased out, founded on objective criteria. “Portfolio analysis is a quantitative method for selecting an optimal portfolio that can strike a balance between maximizing the return and minimizing the risk in various uncertain environments” (Huang 2010, p. 1). Portfolio analysis consists of focusing each of the association's services and products through a succession of finer screens. “Financial risk refers to the uncertainty of expected returns from a security attributable to possible changes in the financial capacity of the security issuer to make future payments to the security owner. If the chance to the terms of the instrument is high, then the financial risk is said to be high” (Keown, Scott, Martin. & William 2004). It is clear that the financial risk connected with grasping commercial paper, which we will view shortly is nothing above a corporate IOU, go beyond that of holding securities distributed by the United States treasury. In both research and economic practice, when calculate approximately of risk free returns are preferred, the yields obtainable on Treasury securities are referred to and the safety of other monetary devices is weighted against them. As the profitable securities portfolio is calculated to give a return on funds that would or else be tied up in idle cash detained for dealings or precautionary reasons, the financial officer will mot typically be willing to imagine much financial risk in the hope of better return within the structure of the portfolio. During a time of scarce resources, it is necessary to screen out services and programs that are not important to most members. Those who appeal to a further limited part can be funded by those desiring the service or product rather than by dues. The main aim of the project is to conduct an analysis of the Value at Risk (VaR) of a portfolio of 4 shares using the process discussed in ASB4416 Financial Modeling. This portfolio analysis includes the four shares are British Land Company PLC, Marks & Spencer Group PLC, Cairn Energy PLC and Land Securities Group PLC. The study mostly aims in analyzing the shares by the different financial models utilized and by the various analyses of the statistical models like the boot strap method, multivariate analysis and the analytical Variation method. Table of Portfolio Analysis: The 4 shares of the four companies are used for portfolio analysis are the British Land Company PLC, Marks & Spencer Group PLC, Cairn Energy PLC and the Land Securities Group PLC. Year price/share 1 (17) price/share 2 (58) price/share 3 (22) price/share 4 (53) 2001 33.4 54.6 36.5 67.6 2002 24.8 56.3 25.4 67.8 2003 26.4 54.2 23.4 66.5 2004 26.3 55.8 26.5 66.7 2005 36.8 66.5 35.4 74.2 2006 39.5 63.2 42.6 65.3 2007 29.8 65.8 45.8 74.2 2008 26.4 59.8 36.9 75.6 2009 33.6 58.7 42.5 68.5 2010 38.4 56.3 43.6 63.2 The above table shows portfolio analysis of each company. Following are the mean and standard deviation of each company: Histogram: “A histogram is a series of contiguous bars or rectangles that represent the frequency of data in given class intervals. If the class intervals used along the horizontal axis are equal, then the height of the bars represent the frequency of values in a given class intervals” (Black 2010, p. 21). Graph showing the empirical return of the each share and portfolio. 3. Analytic VaR: The VaR risk assessment defines risk as a market loss on a permanent portfolio over an unchanging time horizon, by analyzing the normal markets. There are three fundamental approaches that used for calculating the Value at Risk that are analytic VaR, Monte Carlo and historical analysis. The measure can be computed logically by building assumption on the subject of return distributions in the market risks, and by using the Variances in and covariance’s transversely in these risks. It can in additionally expected by operating hypothetical portfolios throughout chronological information or from Monte Carlo model. “The process of risk decomposition is essential to Analytic VaR” (Das 2006, p. 106). There are many option risk procedures in finance, Analytical VaR is also called Parametric VaR for the reason that one of its basic statements is that the return allocation belongs to a family of parametric distributions; for instance the lognormal or normal distributions. Analytical VaR can basically be expressed as: “ Where: VaR? is the estimated VaR at the confidence level 100 ? (1 - ?) %. x? is the left-tail ? percentile of a normal distribution  . x? is described in the expression where R is the expected return. In order for VaR to be meaningful, we generally choose a confidence level of 95% or 99%. x? is generally negative. P is the marked-to-market value of the portfolio” (Berry 2011). Following are the calculation of Analytical VaR: Analytical VaR of (95%) ( 99%) British Land Company PLC, Price/share 1 (17) -77.07 -76.33 Marks & Spencer Group PLC, Price/share 2 (58) -146.02 -145.28 Cairn Energy PLC, Price/share 3 (22) -87.87 -87.13 Land Securities Group PLC, Price/share 4 (53) -170.62 -169.88 Expected Returns: British Land Company PLC, Price/share 1 (17) - 78.85. Marks & Spencer Group PLC, Price/share 2 (58) – 147.8 Cairn Energy PLC, Price/share 3 (22) – 89.65 Land Securities Group PLC, Price/share 4 (53) - 172.4 Advantages and Limitations: Analytical VaR is the simple methodology to calculate VaR and is rather easy to apply for a fund. The input data is rather restricted, and because there are no simulations involved, the calculation time is smallest. Its simplicity is also its main disadvantage. Firstly, Analytical VaR presumes that not only the past incomes follow a regular division, but also that the transforms in cost of the assets restricted in the portfolio follow a regular distribution. And this very rarely subsists the test of reality. Secondly, analytical VaR does not manage allocation like mortgage-backed securities. Finally, if our historical chains exhibits heavy tails, then calculating Analytical VaR using a normal distribution will underrate VaR at overestimate VaR and high confidence levels at low confidence levels. Monte Carlo VaR Method:  Monte Carlo VaR method involves developing the future stock price returns by running many hypothetical trials. This is the trial and error method. We need to repeat the steps until the formula yield the solution. Drawing the random numbers over a large number of times will give an idea about what output should be. Here in the following calculation we repeat the test for 100 times and get one result but the result may change if repeat it one more time. This trial and error method is time consuming and not very accurate.  Advantages in using the Monte Carlo method of VaR Simulation:  Monte Carlo method is non- linear and path dependent pay off function. Monte Carlo simulation VaR is not much affected by the extreme events. The statistical distribution can be used to simulate the returns so that we feel comfortable with the underlying assumptions that justify the use of particular distribution.  Disadvantages in using the Monte Carlo Simulation method:  The Monte Carlo calculation is a time consuming process. Monte Carlo method demands more calculations to complete all simulations Higher cost to develop a Monte Carlo VaR engine that can perform Monte Carlo simulations. The steps involved in the calculation of VaR using the Monte Carlo method: Step 1 – To Determine the length of the analysis limit and divide it equally into a large number by small time increments   Step 2- Then take a random number from a random number generator and update the price of the asset at the end of the first time increment.  Step 3 – Then Repeat Step 2 until reaching the end of the analysis limit by doing maximum round up  Step 4 – Then Repeat Steps 2 and 3 a large number of times to generate different paths for the stock over   Step 5 – Then Rank the full terminal stock prices from the smallest to the largest, read the simulated value in this series that represents the desired (1-?)% confidence level (95% or 99% generally) and deduce the relevant VaR. We can use the below equation to do the simulation  “ Ri = (Si+1 - Si) / Si = ? ?t + ? ? ?t1/2 Where Ri is the return of the stock on the ith day Si is the stock price on the ith day Si+1 is the stock price on the i+1th day ? is the sample mean of the stock price ?t is the time step ? is the sample volatility (standard deviation) of the stock price ? is a random number generated from a normal distribution” (Berry 2011). Calculation is attached herewith in excel spreadsheet.  Historical Analysis / Bootstrap VaR Method: The historical method is simply reorganizing the actual historical data. As the name indicates this is the method in which the past performance of the company is taken into consideration. The assumptions are made by analyzing the past performances. The past data will be a good indicator for the near future. As our market is so volatile, this method only depend the past data. This method assumes that the history will repeat itself. Advantages of the Historical Analysis: There is no need to make any assumptions No need of bothering about volatilities and correlations Only real facts and figures are taken into consideration. The distribution and all extreme events are considered. Disadvantages of the historical analysis:  Historical analysis/bootstrap VaR completely relies on historical data and it may biased Historical VaR cannot accommodate the changes in the present market Historical analysis lags when the portfolio contains complex securities. It cannot handle the sensitivity analysis easily  The steps in the calculation of VaR using the historical method: Step 1 – First Calculate the returns or price changes of all the assets in the portfolio between every time interval.  Step 2 – Then apply the current market value and revalue the portfolio  Step 3 – Then Sort the redefined portfolio values in the ascending order  Step 4 – Finally the simulated value should assign to the desired confidence level.  These steps can be formulated as follows.  “ VaR1-? =µ(R)- R?   Where: VaR1-? is the estimated VaR at the confidence level 100 ? (1 - ?)% ?(R) is the mean of the series of simulated returns or P&Ls of the portfolio R? is the ?th worst return of the series of simulated P & Ls of the portfolio or, in other words, the return of the series of simulated P & Ls that corresponds to the level of significance ?” (Berry 2011). The calculation are attached herewith in excel spreadsheet. Discussion: The assignment’s main idea is to conduct an analysis of the value at risk (VaR) of a portfolio of 4 shares. Report is to be submitted of the analysis of the 260 day VaR of the portfolio of shares. VaR is a measure, which is used to measure the risk of loss on a definite portfolio of shares. VaR is used for management and measurement of risk, for financial controlling and financial reporting. VaR helps in the appropriate maintenance of portfolio of shares. Here VaR is calculated using the Analytical method, the Monte Carlo Simulation and the Historical / Bootstrap method. “All methods have a common base but then diverge in how they actually calculate value at risk” (Farid & Salahuddin 2006, pp. 5-31). Analytic VaR: Results from Analytic VaR: Here, 260 day VAR is estimated for the portfolio of 4 shares using the Analytic VaR method and the confidence intervals used are 95% and 99% confidence levels. In this approach, the data consists of share price from 2001 to 2010 for the four portfolios of shares (company numbers: 17.58.22.53). Mean and standard deviation is first calculated for the portfolio of shares. Then using the confidence intervals of 95 % and 99% VaR is calculated. The VaR at 95% confidence level that is obtained is 481.58 while the VaR at 99% confidence level is obtained as 478.62. This implies that at the confidence interval of 95% 481.5 is the VaR while at the 99% confidence interval it is less and is 478.62. Advantages of Analytic VaR: Analytic VaR is very easy to implement especially in finding the VaR. In this method the input data is very limited and there are no simulations involved. Similarly the computation time in the case of Analytical VaR is also very minimal. Disadvantages of Analytic VaR: The drawbacks of Analytic VaR are that this method assumes that the historical returns follow a normal distribution and this is quite a rare case in reality. This method is not suitable for those portfolios, which have a “non linear pay off distribution like options or mortgage backed securities” (Berry 2011). Computation of VaR using the analytical VaR, which is usually done using a normal distribution, underestimates the value of VaR at high confidence levels and this also results in the alternative position where VAR is overestimated especially at low confidence intervals. Monte Carlo VaR: Results from Monte Carlo VaR: The Monte Carlo VaR generates market scenarios and also estimates the change in the value of the portfolio according to the change in the scenario. The Monte Carlo simulation allows using the actual historical distribution rather than normal returns. The results from Monte Carlo VaR suggest that for 95% confidence interval the VaR is estimated to be 35.192 while for 99.9% VaR is estimated to be 20.71. Thus at 99% confidence level the VaR is far lower. “The reason that one would choose Monte Carlo VAR over historical VAR is typically because the past is not trusted to be a good predictor of future” (Weert 2011, p. 88). Advantages of Monte Carlo VaR: This method is very realistic as compared to the other two methods and helps in the estimation of VaR more accurately. This method can be very accurately done using computers. The advantage is that the data obtained using the Monte Carlo method is more realistic as there are no assumptions. In this simulation no unrealistic assumptions with respect to returns are considered. “Random number generation is the first step in a Monte Carlo simulation algorithm” (Alexander 2008, p. 203). Disadvantages of Monte Carlo VaR: The main cause for this is the high number of probability distributions, which have to be estimated. This method cannot be done using a small amount of data and requires loads of data. Also another major difficulty is the number of simulations, which needs to be, ran in order to obtain the estimate of VaR. The drawback in the case of Monte Carlo simulation is that it is highly dependent in finding a very appropriate and realistic risk factor return model. Bootstrap VaR / Historical Analysis: Results from Bootstrap VAR / Historical Analysis: In the historical method, VaR is calculated using the historical returns that have been obtained from the previous years. Daily returns are calculated and a set of points is reached. At confidence level of 95% the VaR using the historical method is 28.83% while at the confidence interval of 99% the VAR is calculated at 31.49%. Therefore the VaR at 95% is lower than the VaR at 99%. The steps used in this approach are traditional and the first step is calculating the returns in the portfolio between each time interval. Then applying the price changes to the current market value of the shares and then revaluing the portfolio. The third step is sorting of the series of the portfolio stimulated from the lowest to the highest value. Then the stimulated value which corresponds to the desired confidence level is selected. Advantages of Bootstrap VAR / Historical Analysis: The advantages of this model are that in this model no assumptions are to be made with respect to the nature and the distribution of returns. “Historical VaR is also not limited to linear portfolios, as the parametric linear VaR model” (Alexander 2008, p. 141). Disadvantages of Bootstrap VaR / Historical Analysis: The disadvantage of this model is that this model accepts the future returns as same as the past returns. Another disadvantage of historical VaR is that “the result is often dominated by a single, recent, specific crisis, and it is very difficult to test other assumptions” (Marrison 2002, p. 118). The difficulty in applying the historical VAR is that it is quite difficult to apply this model with a wide horizon or more than a number of specified days. Conclusion: Using the three models there are high Variations especially comparing the analytical VaR method with the Monte Carlo and the Historical method. This is due to mainly the data change and the method in which the computation has been arrived in the three methodologies. The Monte Carlo and the Historical approach have more or less similar VaR but the Analytical VaR is very high as compared to both these methods. Both the historical as well as the Monte Carlo VaR can be applied to all types of portfolio. Risk can be measured to a high extent with the implementation of VaR but it is very necessary to input the correct details which are necessary for VaR calculation for example the correct details of portfolio composition, the time horizon and all the other parameters then VAR can be successfully implemented. 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