Portfolio Optimization Based On The VaR-ARCH Framework

In the first part of this paper, I use ARCH style models, such as GARCH, EGARCH and GARCH in mean, to compute financial asset's Value at Risk, which are based on Normal, t or General Error distribution separately. To do so, computer program and Monte Carlo simulation technique are employed. As a consequence, a mechanism is built which can select the best model concerning the accuracy of VaR calculation. In addition, EWMA model is also studies, which is the core algorithm of J.P.Morgan's RiskMetrics, to compare with ARCH style models. Empirical study suggest that some ARCH style models are more accurate than EWMA in VaR calculation.In the second part, I brought out the VaR-ARCH optimization framework for investment decision based on the mechanism built above. In this framework, CVaR is the optimization target, the optimal asset proportion is the final result after working out a mathematical program problem. In order to show how VaR-ARCH framework works, I select three stocks , without lose the generality, from ShangZhen50 index's member stocks to make single-period and multi-period mock investment abide by VaR-ARCH framework. As the result, the mean-CVaR and mean-VaR efficient frontier, which are familiar with the mean-variance efficient frontier of Markovtiz, under different confidential level are given. It proves the VaR-ARCH framework's feasibility and rationality. Meanwhile, the VaR-ARCH framework can increase the portfolio's expected revenue and decrease the VaR significantly according to the multi-period mock investment. As a conclusion, the VaR-ARCH framework has an actively practical meaning.