A Study On Portfolio Selection Of Different Risk Measurement Model Based On Stable Distribution

As a core topic of modern finance, portfolio problem researches mainly under the condition of uncertainty on the optimal allocation and selection of assets, thus achieving the balance between return maximization and the risk minimization. In the year 1952,Markowitz applied the variance of the assets returns for measuring risk and proposed the mean variance portfolio selection theory for the first time [1], which is considered to have pioneered the modern portfolio theory and laid the foundation of the quantitative study of financial investment problems. However, Markowitz based his mean-variance portfolio model on the condition that the asset returns follows the normal distribution and that the variance does exist. However, large numbers of empirical study show that both the normal distribution assumption of returns and the existence of variance are questionable.In addition, based on Markowitz’s theoretical framework, the portfolio model is strict in input parameters. However, it is very diffcult to predict the future asset returns accurately and to forecast the correlation among the future assets in diferent economic environment due to the time-varying correlation among assets.In view of the above problem, this paper will study the portfolio theory with different risk measures and the stable distribution characterized of heavy tails. Considering that the stable distribution is a four-parameter distribution and that there is no explicit density function, this paper studies high efcient algorithms to reduce the computational complexity that the stable distribution brings to the model. In the empirical research part, each model is analyzed, compared with the corresponding models under the normal distribution,the mean-absolute deviation model and the mean-semi-absolute deviation model based on the stable distribution, whose efcient frontier move to the upper left, and have a better investment effect of the optimal proportion through calculation. In addition, this paper also introduces the risk parity theory and improve the model under this theory and then obtains the optimal proportion of the model.