Improvement And Application Of Mean-variance Model

Portfolio selection is very important in improving the efficiency of capital use and preventing financial risks.It concerns to obtain higher returns with lower risks.The mean-variance model is the earliest portfolio optimization model,which uses the mean and variance of returns to measure the returns and risks of portfolios.However,it is difficult to calculate the mean and covariance matrix accurately,and the model is very sensitive to them,especially when the returns of selected assets are highly correlated.Therefore,some improved solutions have been proposed,such as eliminating highly correlated assets,multi-factor models,using better risk factors,robust optimization model,and so on.This article will further improve the mean-variance model on this basis,reduce sensitivity to it,and hope to obtain higher returns with lower risks.First,based on the characteristics that the change in the return rate of a single asset is highly correlated with the change in the return rate of the industry in which it is located,and the trend of change is relatively consistent,we consider to add the overall risk of the asset’s industry to the mean-variance model to establish a mean-variance model with background risk.Then,an example is used to prove that appropriately increasing the weight of the background risk can effectively increase the return rate of the portfolio.We also compare the proposed model with the mean-Var model to further verify the effectiveness of the model.Drawing lessons from previous scholars’ research ideas on the mean-variance model,we analyze the impact of historical returns with different time spans on the effective frontier curve of the mean-variance model with background risk when the mean change,variance change,mean and variance both change.We take the point that maximizes Sharpe’s ratio as the optimal portfolio,calculate its return,and find that a proper reduction of the time span helps to obtain a better portfolio.We also combined the mean-variance model with background risk and the method of using ARIMA and GARCH model to predict the return on assets,and obtain better expected results.