Portfolio Choice Under The Mean-Variance Model With Uncertainty

The traditional mean-variance portfolio in the market trading friction is under the strict assumptions, by quantifying the portfolio return and risk, the proportion of the distribution of wealth by the optimization rule obtained portfolio. Actually, investors in decision-making for risk assets in the model of income expectation, variance and covariance parameters of real value is often unknown, the empirical analysis is often based on historical data obtained from its estimated value, which leads to estimate risk parameters, that is, the existence of model parameter uncertainty problem, then estimation bias would bring the estimated risk; at the same time, market transaction friction exists objectively, and the transaction cost is one of the typical. Transaction cost is not fixed with the development of the security market, that is, there are variable transaction costs. Not only the model parameter uncertainty but also the variable transaction cost influence the stability and performance of the asset portfolio in varying degrees. Therefore, considering the uncertainty of the model parameter and the variable transaction cost has become a hot issue in the academic circles in recent years.Assuming that the investor is uncertainty-aversion, this paper studies model parameter uncertainty and the variable transaction cost under the portfolio selection problem based on the mean-variance model, and discuss the inner links from the perspective of portfolio’s stability and performance. Based on the traditional mean-variance model, this article introduces a set of constraint constants to measure the degree of model parameter’s uncertainty and the V-style transaction cost function to measure the variability of transaction cost, then constructs the max-min multi-prior portfolio model and obtains the analytical expressions of the model by using Lagrange method and makes the theoretical analysis. The thesis does an empirical study based on the sample of eight stock’s monthly return data from July 2011 to June 2014 in Shanghai Exchange 50 Index. Results show, the weight of multi-prior portfolio is a weighted average of the weight of mean-variance portfolio and that of min-variance portfolio and the stability of multi-prior portfolio is better than the minimum variance portfolio; the stability of mean-variance portfolio is increasing with the increasing degree of the model parameter uncertainty and the continuous decline of transaction cost; moderate consideration of model parameter uncertainty can enhance the performance of that portfolio, what’s more, the lower the transaction cost, the more obvious the promotion.Study show the relationship between model parameter uncertainty with transaction cost and the asset portfolio, it points that moderate model parameter uncertainty and the appropriate transaction cost can improve not only the performance of the mean-variance portfolio but also the stability of it, which is also conducive to the stable and healthy development of the securities market. However, the real investment decisions are dynamic, so the problem of multi stage portfolio selection under the uncertainty is worth further researching.