| With the development of the China’s capital market, stock investment has become an important way to invest in normal people’s life. However, higher yield is often accompanied by higher risk. From the perspective of risk control, this paper first introduces the concept of VaR(Value at Risk), and introduces several traditional methods in calculating Value at Risk. The traditional methods are Historical Simulation(HS), Parametric Method(Variance-Covariance) and Monte Carlo Simulation.However, almost all the existing models assume the distribution of return as a single distribution such as normal distribution or student-t distribution. This makes the estimates of loss have limitations. So, we then introduce the mixed normal distribution.Mixed normal distribution can fit the financial return series more flexible and more accurately comparing with the single distribution model. Moreover, mixed normal distribution can generate an asymmetric and fat tailed distribution of financial return series accurately. By constructing an instance of mixed normal distribution models, we have a preliminary understanding it. After that, this paper introduces the method of parameters estimation of mixed normal distribution: maximum likelihood estimation and EM algorithm. In the last part of the paper, we make an empirical analysis. We choose six stocks from different stock exchanges in China, and select 200 daily returns of each stock as the analysis data. In the next step, combine the six stocks in different weights as a portfolio, and use the mixed normal distribution to fit the return series.Then choose the best fitted model with AIC criterion. Finally, calculate the VaR of every portfolio under the best mixed normal distribution and get the optimal portfolio with the smallest VaR. |
