In this research, the application of Monte Carlo simulation based Principal component analysis (PCA), as a nonparametric approach for calculating value at risk and expected shortfall, has been studied. This method tries to overcome some problems of conventional Monte Carlo simulation method such as excessive and time consuming calculation, . In this order, by applying Monte Carlo simulation based PCA method, we calculate VaR and ES for Tehran Stock Exchange industrial indices and compare its results with the results obtained by RISKMETRICS method and conventional Monte Carlo simulation method. Results from backtesting technics show Monte Carlo simulation based PCA and conventional Monte Carlo simulation method both have the same accuracy in estimating VaR and ES, but RISKMETRICS could not estimate VaR and ES as well like last methods. Also, assessing time needed for estimating VaR and ES shows Monte Carlo simulation based PCA a quicker method than conventional Monte Carlo simulation.

In recent years the main models for measuring Market risk is Value-At-Risk models. Market risk is the risk that the portfolio investment value or asset value of financial institution will decrease due to some factors Such as: changes of asset prices, interest rate, market Volatility or market liquidity.In the following Research, We are trying to evaluate the efficiency of Risk metrics model of J.P Morgan corporation And GARCH Type model for VAR estimation via index volatilities.For this purpose, we use TSE index data between 1382-1386 years in order to design and test model efficiency. This is done using a 1382-1384 TSE index data to estimate parameters of model and real data of 1385 and 1386 for credit viability of these models. Kupiec Likelihood Ratio (LR) that Calculate failure probability show us: it does not have a meaning difference between Risk metrics and GARCH type models for market risk estimation in 95% and 99% confidence levels. Both of these models are efficient to estimate market risk (VAR).

Initially In this study, we introduce a new index called Revised Sharp (R-Sharp) for evaluation of portfolio in investment companies in Tehran Stock Exchange, and then examine this index were compared with the Sharp index. In the R-Sharp index, value at risk concept was used due to the properties of VaR and its application in the international financial institutions.The results indicate that the VaR calculation by GARCH is not applicable since time series data have not heteroscedasticity. Therefore, VaR was calculated for 10 investment companies by Risk Metrics method with  l=0.94 in coefficient level at 99.9%, 99% and 95% for I-day and 10-day. In order to assess the accuracy of VaR calculation, the Wilcoxon signed ranks test was utilized. The results indicate that VaR Backtesting at 95% and one-day period for all companies, were reliable.In this study, after calculating VaR and VaR Backtesting, R-SHARP and SHARP indexes calculated for the period of study (2007-2010). The results show that there are some differences in the ranking of R-SHARP and SHARP indexes. So we tested the difference of R-SHARP and SHARP indexes by nonparametric tests such as Wilcoxon signed ranks test. Results of these tests indicate that sleight insignificant differences of indexes.

Initially In this study, we introduce a new index called Revised Sharp (R-Sharp) for evaluation of portfolio in investment companies in Tehran Stock Exchange, and then examine this index were compared with the Sharp index. In the R-Sharp index, value at risk concept was used due to the properties of VaR and its application in the international financial institutions.The results indicate that the VaR calculation by GARCH is not applicable since time series data have not heteroscedasticity. Therefore, VaR was calculated for 10 investment companies by Risk Metrics method with  l=0.94 in coefficient level at 99.9%, 99% and 95% for 1-day and 10-day. In order to assess the accuracy of VaR calculation, the Wilcoxon signed ranks test was utilized. The results indicate that VaR Back testing at 95% and one-day period for all companies, were reliable.In this study, after calculating VaR and VaR Back testing, R-SHARP and SHARP indexes calculated for the period of study (2007-2010). The results show that there are some differences in the ranking of R-SHARP and SHARP indexes. So we tested the difference of R-SHARP and SHARP indexes by nonparametric tests such as Wilcoxon signed ranks test. Results of these tests indicate that sleight insignificant differences of indexes.