The Research On Minimax Portfolio Based On Nonparametric Estimation

The optimal portfolio of Minimax rule is the solution to a simple linear programming problem.The portfolio uses minimum return rather than variance as a measure of risk.The portfolio is chosen that minimizes the maximum loss over all past observation periods,for a given level of return.This objective function avoids the logical problems of a quadratic(non-monotonous)utility function implied by mean-variance portfolio selection rules.The minimax portfolio has more inclusive.For normal returns data,the portfolios are nearly equivalent to those chosen by a mean-variance rule.When the return data is not normally distribution,the mean-variance rule isn't applicable but the minimax portfolio is applicable.In addition,the portfolio research is based on a large number of financial data.In theory,the ideal results are obtained when the sample size tends to infinity.However,the sample data is limited in actual research and the little change of sample data will cause the fluctuation of the optimal solution.Therefore the portfolio frontier presents some discontinuities and is not very smooth.In order to overcome that,we use nonparametric estimation method to estimate the sample data.In this paper,the nonparametric kernel mean return estimation method and kernel median return estimation method are applied to the minimax model for the first time.At first,we present the formula for estimating the return on assets using the nonparametric kernel mean method and the nonparametric kernel median method.A minimax portfolio model based on nonparametric is formed.Then,we choose the data from China stock exchange market and American stock exchange market and use MATLAB statistical software for empirical analysis.The empirical analysis is made up of two parts.In the first,we construct effective border of the minimax portfolio model and the model with nonparametric estimates and calculate the minimum returns(that is model's risk measure).The second part is in-sample analysis.The portfolio yield is estimated from the optimal solution obtained above.The result of the forecast is compared with that of the Shanghai composite 180 index.The results show that the forecast rate of the return based on nonparametric investment portfolio model is higher than minimax portfolio model.Whether it is permitted to sell short or not,the methods used in the Chinese stock market and the American stock market.In the end,we can get a smooth portfolio frontier.Under the same expectation rate of the return,the minimax portfolio model based on nonparametric estimation is better than the minimax portfolio model.The minimax portfolio model with nonparametric kernel median estimation is superior to the minimax portfolio model with nonparametric kernel mean estimation.