Dama International Journal of Researchers ISSN: 2343-6743, Scientific Journal Impact Factor: 5.968 & ISI Impact Factor: 1.018, Dama Academia Pubisher: Vol 3, Issue 06, June, 2018, Pages 09 - 15, Available @ www.damaacademia.com Dama International Journal of Researchers, www.damaacademia.com, editor@damaacademia.com 9 Historical Simulation (HS) Method on Value-at-Risk & its Approaches Peter Kwasi Sarpong 1 , Jones Osei 2 , Samuel Amoako 3 Email: kp.sarp@yahoo.co.uk, oseijones2013@gmail.com, Samkamoako2016@gmail.com Mathematics Department, Kwame Nkrumah University of Sciene & Technology Abstract Value at risk (VaR) is a management tool for measuring and controlling risk. Individual and institutional investors rely their investment decisions increasingly on the risk inherent in a security. In this theses, calculating of Va R are implemented using Historical Simulation and Monte Carlo approach on stock portfolio. Different Values of confidence levels are also used for each of the method. The study is conducted on six fundamentally different stocks. Data on daily prices on collected for a period of eight years (2007-2014) for all stocks assets and their corresponding log returns calculated. From our analysis, Monte Carlo Simulation had an optimal values of VaR as compared to Historical simulation in both the VaR 95% and VaR 99% confidence levels. Nonetheless, the VaR 95% has the highest simulation time. Keywords: Value at Risk, Risk Approach, Risk Simulation I. INTRODUCTION Risk estimation has engrossed financial market participants since the beginning of financial history. Be that as it may, numerous past endeavors have turned out to be unreasonably perplexing. For instance, upon its presentation, Harry Markowitz’s Nobel prize-winning theory of portfolio risk measurement was not embraced practically speaking as a result of its burdensome information prerequisites. In fact, it was Sharpe (2000) who, alongside others, made portfolio theory the standard of financial risk measurement in real world applications through the appropriation of the rearranging suspicion that all risk could be decomposed into two parts: systematic, market risk and the residual, company-specific or idiosyncratic risk. The resulting Capital Asset Pricing Model theorized that since just undiversifiable market risk is relevant for securities pricing, only the market risk measurement β is necessary, along these lines extensively decreasing the required information inputs, (Sharpe, 2000). This model yielded a promptly quantifiable evaluation of risk that could be practically applied in a real time market environment. The main issue was that β demonstrated to have just a tenuous connection with real security returns in this way throwing questions on β designation as the genuine danger measure. With β addressed, and with asset pricing all in all being at somewhat of a chaos as for whether the thought of “priced risk” is truly pertinent, market practitioners hunt down a replacement risk measure that was both precise and generally modest to evaluate. In spite of the thought of numerous different measures and models, VaR has been broadly received. Part of the reason prompting the widespread adoption of VaR was the choice of JP Morgan to make a straightforward VaR estimation model, called Risk Metrics. Risk Metrics was upheld by an openly accessible database containing the basic inputs required to appraise the model. I. REVIEW OF RELATED LITERATURE Markowitz (1952) conducted spearheading work in the field of statistical market risk analysis in the mid-fifty’s by presenting the Modern Portfolio Theory (MPT). In MPT, market risk is measured as the standard deviation of returns, which are expected to follow normal distribution. Market risk in MPT context thus entails both upside and drawback potential. In recent years a concept called VaR has increased much consideration among scholastics and professionals. VaR gives an alternate way to deal with business sector risk: it is a measure of investment portfolio loss potential. VaR concentrates on the drawback risk the portfolio is presented to. Approach to risk management perceives that the risks happen just to the extent they cause financial losses. Formally VaR is characterized as the greatest expected risk over a given horizon period at a given level of confidence, (Dowd, 1998) Mandelbrot (1963) observed that volatilities of market factors are time-dependent. This phenomenon known as volatility clustering has been affirmed by numerous studies from that point forward. Therefore, in modelling market factor distributions conditional methods (time-dependent) have appeared superior to unconditional methods (time- independent) in modelling market factor distributions for VaR calculations in many empirical studies (see, e.g., JP Morgan, 1996, Goorbergh et al., 1999a). Conditional methods represent time re- liance of business sector component conveyances while unconditional methods assume that market factor distributions stay consistent after some time and are free of past realizations.