Research On Portfolio Under Non-normal Stable Distributions

The mean-variance portfolio model by Markowitz was the milestone of the mod-ern portfolio theory, and the essence of diversification has been the principles of modern institutional investing. The model assumes that the return on assets follows the normal distribution which makes the model simple and analytical. Because of the above advantages, this model has been the industry standard model. Markowitz’s classical mean-variance portfolio model must be dependent in return on assets rate fol-lows the normal distribution and variance exists. However, a lot of financial practice and empirical studies showed that the distribution of asset returns behaved sharper peak and thicker tail than the normal distribution. The Markowitz’s mean-variance portfolio selection model of input parameters demanding, could not provide a precise prediction of future assets report, and in the different economic environment, the correlation between each asset is the change, it is difficult to accurately forecast.In view of the above problems, in this paper the non-normal stable distribution, which better describes the sharp peak、thick tail phenomena of asset returns, is in-troduced to improve the standard portfolio allocation model. And the calculation complexity of the model is solved by an efficient numerical calculation method. The mean-absolute deviation model is established under different distributions, and the empirical studies show that the new model based on the non-normal stable distribu-tion is more appropriate for the capital markets. In this paper, the price earnings ratio is applied to the dynamic rebalancing of the portfolio, which is helpful to improve the efficiency of portfolio investment.