expectation-maximization algorithm

Value at risk is one of the most widely used risk measurement criteria. Period value at risk extends the concept of value at risk for an investment with a set of maturity horizons, thus neutralizing the model's sensitivity to a point investment horizon. This reduces the impact of liquidity risk and the investor has ample opportunity to sell and can make the right decision in an interval. In the present study, two stock portfolio models are designed based on the period value at risk, the first based on historical simulation and the second is parametric and based on the distribution of normal-Laplace mixture for proper fitting of tail data. The result of the experimental study of the models designed on a stock portfolio with eight indices of the Tehran Stock Exchange in the period 1390 to 1399 shows that the parametric approach in the test data in average return and Sharp ratio criteria has a better performance than the historical scenario. Also, the relative error between the period risk value predicted by the stock portfolio and its estimation in the test data in the parametric approach is less.