Financial Modeling Of Value At Risk Portfolio - Essay Example

? FINANCIAL MODELING OF VALUE AT RISK PORTFOLIO By Presented to FINANCIAL MODELING OF VALUE AT RISK PORTFOLIO INTRODUCTION The following report has been based on total return index data. This information will be used to analyze, justify, explain, recommend and conclude on the financial modeling outcomes of four shares of four different companies. Probability measures have been used to determine how frequent we anticipate various results to take place should we repeat a provided experiment repeatedly. The stakeholders of the four companies choose investment as a probability approach. The following data analysis is to present a standard report on the development of an event study of a statistical model of shares market data. The analysis is carried out on the value at risk of a portfolio of four shares employing the techniques deployed in financial modeling. The report is also carried out on a 260-day value-at-risk (VAR) of the portfolio of the shares used to make the report. The shares have been analyzed on a daily basis, to normalize the matching volumes of the traded shares. Various plans, methods and project formulae have been utilized to consider the application to be obtained for a determining process. The data used in the analysis uses closing prices to depict how the entire analysis and procedural VBA analysis operates. The shares and dividends depicted in the data are collected from open sources that have been computerized and processed. Nevertheless, some of the information is slightly corrected in order to evade troubles cause by missing data in the analyzed time, share and stock trades patterns. Additionally, the data has been decreased to the industrial shares and stock trading. The data analysis will have a function at the opening part of non-changed stock market data that creates a stable statistical distribution. The methodologies used in this data analysis include stimulation employed in the Brownian motion concept, the analytic method of the VAR concept, the Monte Carlo concept, a historical analysis and non-parametric technique. The outline of the remaining sections of the analysis include a background analysis of the data sample, analytic VAR, Monte Carlo VAR, historical analysis and discussion section. BACKGROUND OF THE DATA SAMPLE The congruence model has put several considerations into deep concentration. These are the inputs, the components of an organization and the outputs of the organization, defining each of these components intensively. The inputs of an organization have been classified into three main categories, and an additional derivative input has been added. These are; the Environment related inputs, resources and organizational history inputs. The derivative input outlined by the model is strategy, as it determines the functionality, productivity and interrelation of the rest of the inputs (Charnes, 2011, p. 142). An organization has been broadly categorized into four key components which are the task, the individual, formal organization arrangements and relationships as well as information organizational aspects, such as leadership skills. From the components, the model has covered the outputs of an organization, which will be the core focus of our analysis. The outputs have been categorized into three main classes, which include Individual output, Group output and organizational output (Charnes, 2011, p. 142). Using the model, this paper will analyze a company outlining the various issues pertaining to the organization and the extent to which the organization has achieved efficiency as defined by the model and the creators. Table of summary statistics for each of your shares individually B(t) A(t) time Path 1 Path 2 Path 3 time Path 1 Path 2 Path 3 0 0 0 0 0 10 10 10 1 -1.5556 -0.8799 0.7468 1 9.5833 9.7860 10.2740 2 -2.6548 -0.1507 -0.8768 2 9.3036 10.0548 9.8370 3 -5.0247 0.0467 -1.8954 3 8.6426 10.1640 9.5814 4 -4.0943 -0.5172 -1.1894 4 8.9717 10.0448 9.8432 5 -3.9233 -1.2864 0.0331 5 9.0730 9.8641 10.2599 6 -1.1964 -1.1685 0.2872 6 9.9411 9.9494 10.3862 7 -0.1330 -0.3994 -0.4646 7 10.3101 10.2302 10.2106 8 -1.3660 1.4337 -0.6967 8 9.9902 10.8301 10.1910 9 -1.3713 0.6830 -1.3408 9 10.0386 10.6549 10.0478 10 -1.5116 1.0446 -1.8451 10 10.0465 10.8134 9.9465 11 -2.2723 2.1298 -2.2337 11 9.8683 11.1890 9.8799 12 -1.1180 2.3002 -0.8790 12 10.2646 11.2901 10.3363 13 -1.5981 0.7735 -0.6825 13 10.1706 10.8820 10.4453 14 -0.5915 -0.5241 0.5752 14 10.5225 10.5428 10.8726 15 -2.3509 -1.7074 -0.5114 15 10.0447 10.2378 10.5966 16 -1.2272 -2.6731 -0.5607 16 10.4319 9.9981 10.6318 17 -1.1170 -2.9715 -0.8721 17 10.5149 9.9586 10.5884 18 -1.7262 -2.1687 0.0003 18 10.3821 10.2494 10.9001 19 -3.1871 -1.4018 1.1856 19 9.9939 10.5295 11.3057 20 -2.2526 -1.2975 0.4015 20 10.3242 10.6108 11.1204 21 -1.5082 -3.3179 -0.0064 21 10.5975 10.0546 11.0481 22 -0.4126 -3.0971 0.5045 22 10.9762 10.1709 11.2514 23 0.7417 -1.8357 -0.5117 23 11.3725 10.5993 10.9965 24 0.6308 -2.0880 0.3634 24 11.3893 10.5736 11.3090 25 1.5005 -1.4747 0.5182 25 11.7002 10.8076 11.4055 According to Albrecher, Runggaldier and Schachermayer, 2009, economic and progress plan made and put down in the budgetary records, the unit is leading towards the growth of a financial development project. The project requires the Tasmanian government to concentrate towards a strategy aimed at setting up financial development most necessary concerns for Tasmania at a financially wide, divisional and regional level. The EDP (economic development plan) provides the overarching framework where they coordinate significant legislative approaches like infrastructure, expertise and originality. The EDP is mainly aimed at improving the durability of the citizens of Tasmania through the financial, political and environmental growth. Nevertheless, the education sector was opened with the closure of curricular systems for the construction of an improved curriculum, together with its infrastructure (Charnes, 2011, p. 142). According to Alexander, 2009, Political organizations have had a huge impact on the budgetary positions and additional negotiations and debates will hence become necessary. Recent press filings have indicated the labor unit of the government being shifted to an important path towards approving the representation the Tasmanian state took to elections. Glenora is one of the schools addressed in the state of Tasmania budgetary speeches towards earmarking for shutdown. Closure of the schools is capable of saving millions of state dollars. However, the minister will endure a huge cost at the expense of elections being around the corner. Stakeholders believe that the state is in financial troubles the state broadcasted in the budget it requires for academic development. Budgetary procedures involve school associations created in the past of a willing society, minded parents and allies of the school towards putting down expert academic and financial reasons for schools remaining open (Benninga and Czaczkes, 2000, p. 209). Every taxpayer is required to fill out chargeable earnings on yearly accounting phases known as the tax years. The IRS refers to all earning entities, regardless of whether they are businesses or individuals, as taxpayers. The normal calendar time schedule is the most frequently used tax year. Additional tax years used includes financial years and short tax years. A reliable accounting technique is used by every taxpayer. The technique usually involves a procedure for determining when to report earnings and expenditure (Alexander, 2009, p. 27). The most frequently implemented accounting techniques are the currency method and an accretion technique. With the currency technique, the taxpayer generally reports earnings within the tax year. Necessary deductions in terms of expenditure are made, and the taxpayer receives his net salary. With the accretion methodology of accounting, the taxpayer reports earnings made whether of the time it was received and the expenditures are withheld during the tax year and the taxpayer acquires them. Therefore, I don’t think businesses and individuals have different accounting systems for tax deduction because accounting for trade and individual expenditure under different accounting methods with cost the IRS more (Alexander, 2009, p. 27). Income transfers from the government of Australia have turned out to be an important source of finance for the states within the Australian regime. The transfers made are needed to handle the important inequality amid the corresponding income raising authorities and expenses duties of the Australian and Tasmanian authorities. The call for such profits transfers along with the strategies a running their allocation is stated in further details in the vertical financial imbalance and horizontal financial equalization divisions of the budgetary records. According to Albrecher, Runggaldier and Schachermayer, 2009, the finance department representatives have made it clear that all states presently take delivery of every GST profits gathered by the Australian government as GPP’s. The states repay the Australian for GST running expenses, making the GST compilations become allocated amongst the states in accordance with their commonwealth grants commission’s (CGS) techniques. From the above analysis, it evident that methodologies used by the commonwealth have a significant effect on the budgetary decisions and procedures applied. Beneath the techniques used by the CGC (certified Guarantee Company), the Tasmania allocation of the profits acquired in the company was discovered in accordance with the allocation of the countrywide population. The allocation was altered by a very important aspect termed as the GST relativity. The GST relativity mirrored the state’s evaluated the call for monetary assistance. The CGC decides the relativities for every state, in accordance with the strategy of HFE annually. Besides the population of the states and the GST relativity, the sum of GST reimbursed to Tasmania is also affected by the size of the GST pool of funds. The financial support from this division is propelled mainly by the performance of the countrywide financial system, mainly the consumption of taxable goods and service, along with real estate financial speculations. According to Albrecher, Runggaldier and Schachermayer, 2009, the commonwealth and its services are all externally experienced towards Tasmania, with all their effects being important to the budgetary procedures. After the formation of the federation, a monetary bond between the Australian regime and other state regimes have evolved whereby their prevailing distinctive is the basic imbalance amid the finance increasing authorities and functional duties of every arm of the government. While the starting point of the current VFI are in the first set of laws agreed by the federation, the technical restrictions to minimizing this disparity have been toughened by legitimate changes and by high court understanding of the charter. According to Albrecher, Runggaldier and Schachermayer, 2009, similar principles are relevant and applicable in the same service delivery and distribution. The CGC looks at the work that the states engage in while giving services that are proportionate to other states. Calculation of the level of services provided has to be carried out for the sake of services improvement. The standard intensity of services provided in the budgetary allocations is determined by the CGC and it caters to all the regions of state general government expenses. These expenses include health, education, justice and civic security. All these expenses are internal affairs, even though they are affected by the choices made by the commonwealth, an international body. The concepts and revenue figures included in this piece of writing are grounded on the theory developed by Kirton. The Adaption-Innovation hypothesis along with recent studies creates an investigative analysis used to look into the correlation between the theory’s trends. It also accounts for the disciplines and profession preferences of accounting aspirants. The journal provides outcomes that severally serve as preliminary proof that an affiliation between the adaptor-innovator approach and the well-being of accounting employees in different organizations. The Australian Accounting Review develops an understanding structure for environment management accounting (EMA), connecting trading and EMA methods. The planned framework gives an outline for managers to comprehend and evaluate the variety of surrounding management accounting techniques that have been presently enhanced, with the aim of pushing for their implementation. The structure systematically incorporates two main elements of ecological supervision accounting; they include monetary environmental management accounting (MEMA) and physical environmental management accounting (PEMA). The journal emphasizes the past against prospective and short against long lasting periods of various techniques and the frequency of data generation, prior to finishing with a short debate regarding the selection of the most significant methods (Fabozzi, Focardi, Focardi and Kolm, 2006, p. 123). Portfolio values and hence returns for each day The journal debates over a number of years’ accounting handling of civic property. The argument focuses on the attention of the correctness of the civic sector accounting standards commission. The board applies principles of the private sector to the growth of the civic sector accounting values. The situation discussed in the publication is examined and brought out as the reason behind the private sector accounting principles. These values are supposed to be correctly implemented to go well with an extremely varied and diverse operating environment in the civic sector. These variations are mainly ignored by the author with ending issues for the civic sector accounting principles. Australia and New Zealand share similar legacies, cultures, systematic and academic principles that are broadly valued (Charnes, 2011, p. 142). Nevertheless, accounting principles pioneers within this region have recently advocated that civic arts institutes like museums bring their heritage collections as resources for accounting purposes. There are no such needs in the United States, European Union and Canada. At the same time, the international accounting standards commission made the proposal after conducting reviews of present accounting activities. Obviously, the monumental art institutes in the English-speaking entity do not account for the collections for monetary reporting objectives. The journal is accountable for depicting that it is not systematically appropriate to realize artistic, heritage and scientific collections as resources for monetary reporting aims. Table of summary statistics for each of your shares for the portfolio Portfolio Weights Portfolio M&S Vodafone BSkyB S&S Expected Return StDev 1 19% 8% 15% 58% 0.0336% 1.2179% 2 27% 1% 2% 70% 0.0445% 1.2679% 3 36% -7% -11% 82% 0.0553% 1.4075% 4 45% -14% -24% 93% 0.0661% 1.6135% 5 53% -21% -37% 105% 0.0769% 1.8640% 6 62% -28% -50% 117% 0.0877% 2.1435% 7 71% -36% -63% 128% 0.0985% 2.4421% 8 79% -43% -76% 140% 0.1094% 2.7535% 9 88% -50% -89% 152% 0.1202% 3.0739% 10 96% -58% -102% 164% 0.1310% 3.4006% 11 105% -65% -115% 175% 0.1418% 3.7322% 12 114% -72% -128% 187% 0.1526% 4.0673% 13 122% -79% -141% 199% 0.1635% 4.4052% 14 131% -87% -155% 210% 0.1743% 4.7452% 15 140% -94% -168% 222% 0.1851% 5.0870% 16 148% -101% -181% 234% 0.1959% 5.4302% 17 157% -109% -194% 245% 0.2067% 5.7745% 18 165% -116% -207% 257% 0.2175% 6.1198% 19 174% -123% -220% 269% 0.2284% 6.4659% 20 183% -130% -233% 280% 0.2392% 6.8127% optimal portfolio 68% -33% -59% 125% 0.0951% 2.3462% risk-free rate         0.0000% 0.0000% 0.0000% 0.0000% Histogram of the empirical returns ANALYTIC VAR Certain criticisms of traditional budgeting arise from the descriptions of the significant terminologies used by economists and accountants in the government and organizations. A budget is an estimated total cost or income for an operation or activity covering a particular period (Jondeau, Poon and Rockinger, 2007, p. 316). A budget can also be an arrangement for the management and control of assets and expenses. Motivation in variance analysis involves control through a set of processes, instruments, performance measures that organizations or governments deploy to lead and inspire all workers to accomplish set goals. Human relations association forms part of the base for motivation in accounting to enhance an easy repetitive assignment involving financial compensation of all transactions in an organization. Performance evaluation is the valuable control of the chief tasks from diverse units. These units are normally situated at the very end of the production procedure to complement itinerant analysts. The opening output is checked by equipment after the pieces of equipment overshadow. According to Budlender (2010), the second budget paper supplied enough knowledge concerning the output that the Tasmanian government will be able to distribute in 2008 and 2009. Within this period, the budget will allocate funds for detailed monetary and non-fiscal data for regime unit, bureaus and general government division statutory authorities, in favor of the merger financial appropriation bills and the regime’s strategies as made clear by the treasurer in his budget speech. The incorporation of the archives headquarters of Tasmania and the country’s library heritage services into a fresh body recognized as heritage and Tasmania information services will advance and availability, conservation and organization of the traditional remembrance and documentary record of Tasmania, counting the lawful structure for regime recordkeeping. The digitization of Tasmania’s documentary heritage gives superior right of entry to these sole resources for all citizens and worldwide and the global audience (Jondeau, Poon and Rockinger, 2007, p. 316). As the Market capitalization of Netflix nears a 2 billion dollar mark, majority of financial analysts find it logic to carry out a study on the theories understood in the market capitalization. The present survey of more than 1000 dollars for each subscriber means that a ridiculously long flow of income from every client has been received by the company. Nevertheless, an imaginative license should not be used to analyze the customer’s duration value analysis on Netflix. A futuristic outlook should be used for an increasingly growing and counterintuitive, making an analysis with fewer errors. Currently, the net lifetime worth of every Netflix client stands at 70$, and the stir rate stands at a constant 5%. This $70 presumption is openhanded because it does not consider the dilutive impacts of stock-based payment. This reimbursement does not have an impact on the value for every consumer. However, it has a direct impact on the share of every shareholder on every customer’s value. Netflix’s stir rate can keep on reducing, causing other competences to rise. At the same time, Netflix’s may perhaps raise its prices, an approach that has previously been done numerous times. This strategy creates a favorable environment for the organization to stick with the $70 value for its customers (Alexander, 2009, p. 27). On a monthly basis, the compounded increase in new subscribers of Netflix is arranged in the order of 10%, 9%, 8.5%, 8%, 7.5%, 7%, 6.5% and 6% from 2004 to 2009 correspondingly. This matches the disposable increase of the client base of those years rating at 78%, 59%, 50%, 42%, 34%, and 26% correspondingly. The market capitalization of Netflix will rise by 8% annually through January 2012. Following this year’s increase in returns, earnings will constantly be rising at a rate of 8%. This will lead to a future appreciation of value of an approximately similar rate (Fabozzi, Focardi, Focardi and Kolm, 2006, p. 123). MONTE CARLO VAR Control in accounting management is the conduction of approaches reached in the tactical planning procedure. As a result, the organization accomplishes the set objectives and mission. Control becomes a device that facilitates accounting managers in making critical decisions. Time management is the establishment of interceding variables that improve the perception of time. This way, accounting managers are able to ease pressure on their behaviors and perceive control over time and operations assumed significant in variance analysis. Coordination and communication are skills that deploy signs used in organizational semiotics to bridge the gap between technical and social aspects of accounting. Coordination and communication skills are progressive volumes of information structures and technology (Benninga and Czaczkes, 2000, p. 209). Resource allocation within an organization or government implies the appliance of concepts of finances of higher education and management accounting breakthroughs. Zero-based budgeting is a mechanism of budgeting whereby all operations are reassessed every time a budget is produced (Jondeau, Poon and Rockinger, 2007, p. 316). Distinct levels of every operation or transaction is valued and a combination of selected to correspond with the finances that are currently accessible now. Incremental in zero-based budgeting involves a quick contrast that is inclined to begin with a balance that is similar to the previous financial year’s entire balance (Fabozzi, Focardi, Focardi and Kolm, 2006, p. 123). Rigidity is the implementation of flexible management that does not awaken the foundation of an organization’s management. To a certain extent of rigidity, management becomes a quality of assurance and both aspects mutually turn out to have a supplementary affiliation. Flexibility is an aspect of management that can be re-engineered to create rigidity required in settling of activities in an organization. Knowledge in accounting assists in the provision of precision and a well-timed report of monetary results (Fabozzi, Focardi, Focardi and Kolm, 2006, p. 123). This analysis implies that the existing valuation of Netflix is only logical if the company anticipates a constant return in the future (Alexander, 2009, p. 27). In this case, such a rate stands at 8%, and if the assumptions of the sample are collective, Netflix will expect pure profits in the future. By the year 2010, Netflix will have a sum value calculated as the collective lifetime value of every subscribers and will be equivalent to its present value on top of a standard return of 8%. As the time in the valuation pushes on, the preconceived notion of excluding the dilutive impacts of stock alternatives appears even bigger. From the perception of Netflix’s shareholders, doubling the shares of the shareholder is similar to reducing the lifetime customer value, making the attributed stock become reduced to half its current value. The bias of excluding the impacts of taxes appears much bigger as time in the analysis period increases (Charnes, 2011, p. 142). Currently, Netflix has accumulated losses that can do without its tax liability, making the tax liability of the organization substantially increase with time. The efficiency of its marketing prices and cost management could in principle, offset some effects that could lead to an increase in price (Alexander, 2009, p. 27). Marketing costs are highly significant in analyzing an organization’s Customer Lifetime Value since they are used to compare other figures that assess the effect of proposed strategies (Shuen, 2008, p. 181). Even though marketing cost figures have no significance in determining the value of customers’ loyalty, Netflix is an organization that can be apply such figures and determine the price, share and revenue trend to come. HISTORICAL ANALYSIS / BOOTSTRAP VAR Costs can be referred to as awful things experienced or fine things lost. Standard costing and variance analysis by any government involves expenditure, levying, loaning, regulating, altering assets liberties or liability regulations. Government or organizational action normally formulates both good and things in trade. The decisive issue in management accounting is whether the government, organization or consumer is more contented with the transaction or dealing made. Civic actions will tend to generate either more benefits or demerits that determine the advantages of traditional budgeting. Economists and accountants imply that two diverse fields in terms of cost and variance analysis. Therefore, when economists describe cost through variance analysis and standard costing, they include the sacrifice of opportunities and important choices. From an accountant’s perception, standard costing and traditional budgeting are prospective, subjective, and occasionally costs-evaded. The following paper will look into the alleged advantages, and demerits of standard costing, variance analysis and traditional budgeting in management accounting. Financial progress on the tourism and arts unit of the government develops financial and commerce development in Tasmania. Tourism and arts unit engages in foreign affairs of the country since tourists are supposed to go through certain units and organizations to thrive well within the country. The tourism and arts unit is accountable for delivering advertising and development programs in support of the state’s tourism commerce. Opportunities arise from the sport, recreation and physical operations and the Tasmanians, along with the security and promotion of several of the country’s considerable traditional resources as well as developing and promoting the arts of the tourism industry. According to Albrecher, Runggaldier and Schachermayer, 2009, the education unit does not actually serve an external purpose in the budgetary system of Tasmania. Nevertheless, the provision of education, tutoring and society services are obliged to go through three chief arms of residential identification. The arms required by the Tasmanians include citizenship by birth, training and experience, documents and data network institutes. Learning services act on four regions, two of which have complete external influence (Jondeau, Poon and Rockinger, 2007, p. 316). These services hold up the accomplishment of programs at a domestic level and give support for educational institutions for the launch and promotion of systems conditions and directions. DISCUSSION Accountants capture data related to the dealings and incidences of an enterprise to sum up operations in reports used by individuals with interest in the field. The task has a complicated nature when it comes to the dealings recorded into credentials. Such a task is accomplished through skilled and blending responsibilities of the innovation of technical information and measurement. The information is fully valued through lengthy investigations of the discipline. A factual comprehension of accounting is not simply acquired without perseverance. Employees should know that information concerning accounting is helpful to the success of the enterprise. When the essentials of the discipline are fully obtained, employees will develop interest in their profession and assist in development of the organization. An accountant’s tasks might also comprise of the production of interior monetary credentials, including the scheduled outside monetary reports. The work of accountant employees in the organization might be surveyed by a bookkeeper or manager from within the company, or by an accounting organization bonded by the firm. The operations carried out by the federal bureaus at local, state and national positions are regulated by the government or individual companies. Accountants who directly serve the government assure revenue and expenditure is correct and officially authorized. On the other hand, the federal government considers information from local institutions and media houses crucial that international information. Information from all corners of the world is indispensable to an accountant depending on records they deal with. The description of the allocated finances towards improving the educational sector can include the promotion and sustenance of the most efficient educational curricular system. Students are obliged to have a right of entry to an inexpensive, secure and long-term learning system. Such a system can handle and cater to all the needs of the students. The community and public at large are all factors that affect the educational system of Tasmania. Including both factors when allocating the funds reserved for the education sector will maintain the liberties of teachers, students and the community at large. According to Jones (2009), when the budgetary system decided to alter the curricula by closing the schools, the funds lost during admissions and charging fees could have been reimbursed in other sub-divisions of the educational sector. A structure could also be created where the stakeholders can be able to provide their knowledge on policy progression in a way that is in line with the goals and missions of the education sector. This way, the needs of the government, citizens, teachers and even students can be reflected with the creation of a committee, where ground for innovative ideas would be laid. The journals presented make nearly every field more effective and correct. They have given guides, accepted forms for dealings and records, and manage information in an improved manner. Increasing the right of entry to an organization’s information permits accountants to have rapid access to the data required by the organizations. A novel accounting software will also make work more effective and pleasant by getting rid of manual operations. The journals have presented means of resolving issues of geography through the Internet, making a contemporary accountant become knowledgeable with computer programs and accounting techniques. According to Alexander, 2009, p. 27, government services are responsible for the provision of information concerning the outputs made. In the Tasmanian budget, the output is composed of goods and services that the government is supposed to deliver between the years 2011 and 2012, as well as the financial eras that proceed afterwards in 2013 to 2015. Budget paper no. 2 provides the significance of government services while making the budget in Tasmania, Australia. The government services provide monetary and non-monetary data on the activities the government units, bureaus and Government Sector constitutional systems are engaged in. Government services serve as an external factor since they supply data on bodies and organizations within the published annual report, regardless of its origin. To what extent is your conclusion likely to be robust for all portfolios and to what extent is it driven by the articular features of your data sample? The conclusion to be made from the data analysis and report compiled above is likely to be very concrete based on the findings of the performance and trading trends of four shares of four companies. The specific aspects of the data gathered for the trade trending of the four shares of the companies have created a base for all portfolios used in the analysis. The report grows stronger under the breakdown of the data collected by the use of modeling methodologies used in the analysis. The conclusion made from the analysis is a key aspect to making the value at risk portfolio of the analysis more credible for the decision-making procedure of similar companies in the same industry, and the managerial level of the companies used in the study. References Albrecher, H., Runggaldier, W. J. and Schachermayer, W. 2009. Advanced Financial Modelling. California: Walter de Gruyter Alexander, C. 2009. Market Risk Analysis, Value at Risk Models. New York: John Wiley and Sons Antoniou, I., Ivanov, V., Ivanov, V. and Zrelov, P.V. 2004. On the log-normal distribution of stock market data. Physica A 331 (2004) 617 – 638 Benninga, S. and Czaczkes, B. 2000. Financial modeling, Volume 1. California: MIT Press Charnes, J. 2011. Financial Modeling with Crystal Ball and Excel. New York: John Wiley and Sons p. 142 Fabozzi, F. J., Focardi, S. M., Focardi, S. and Kolm, P. N. 2006. Financial modeling of the equity market: from CAPM to cointegration. New York: John Wiley and Sons Focardi, S. and Fabozzi, F. J. 2004. The mathematics of financial modeling and investment management. New York: John Wiley and Sons p. 391 Jondeau, E., Poon, S. and Rockinger, M. 2007. Financial modeling under non-Gaussian distributions. Boston: Springer Mackinlay, A. C. 1997. Event Studies in Economics and Finance. Journal of Economic Literature, Vol. XXXV (March), pp. 13–39 Manganelli, S. and Engle, R. F. 2001. Value at risk models in finance. London: European central bank 41 pages Read More