Value-at-Risk Models And Their Applications To Portfolio Theory

VaR-at-Risk (VaR) is a standard measure that financial analysts use to quantify market risk in recent years. It can help the asset managers know how to determine the market risk quickly. It is also a focus problem for the financial organization to deal with the new risk appeared.Every use of VaR requires choosing among different VaR forecasting models. In this paper, we consider a two-stage model selection procedure. In the first stage we test the ARCH type models for statistical accuracy. If multiple models survive rejection with the tests, we perform a second stage filtering of the surviving models using subjective loss function. Through the two-stage model selection procedure, we found that EGARCH (1, 1) and EGARCH (1, 1)-M model are not appropriate in the first stage meanwhile GARCH (1, 1)-M model is the best model compared with the other models.Follow this conclusion, we put forward a new model, factor-GARCH-M model, to compute the VaR. A case study for Shanghai stock market is performed to demonstrate how the new models can be implemented. It provides a new idea for taking a major policy decision.A new approach of risk management CVaR introduced by Rockafeller and Uryasev has significant advantages over VaR and more reasonable economic implications than VaR. In this paper, on the base of classical M-V models, we consider a new optimal portfolio model as a minmax problem by using risk measure index CVaR. And we can get the value of VaR from the process of solving the optimal problem.