The Mean-Variance Theory Based On Nonparametric Kernel Estimation Method

In1952, H.M.Markowitz put forward "Portfolio Selection Theory",it is surely a sign that the modern portfolio theory has been born.It is known as the" Wall Street First Revolution", and won the Nobel Economics Prize in1990. Markowitz portfolio theory now is also the core part of the modern financial portfolio theory,The core problem of the portfolio is that in an uncertain environment combining assets effectively and realizing the balance of the revenue maximization and the risk minimization.Estimating mean is very important in Markowitz portfolio theory, but estimation of the mean use the simple arithmetic average, the returns in the past time consider equal weight,the result of the simple arithmetic average can meet the theoretical requirements when the sample size is sufficiently large (or tend to infinity). Obviously, it is inconvenient for practical application.In this paper,Based on nonparametric kernel estimation method study the mean.The kernel density method has the advantage that we can through a given sample to estimate the overall probability density distribution. With the help of the Matlab software, select the appropriate kernel function and adjust the window width to fit the outer contour of the histogram to get the discrete values of the overall sample probability density function,With the help of the Eviews.using a known distribution to fit the probability density function, and find the ideal distribution After a series of researchm,we have found that the best fitting distribution in choosed stocks is the linear combination normal distribution and logistic distribution[1].Three strategies from choosed A-share market investment examine this approach the excellent properties. Firstly, considering the daily return rate as short-term investments,we select six stocks from Shanghai and Shenzhen stock markets during listing date to February28,2014as a portfolio. Secondly, considering monthly return rate as the medium-term investment, we select six stocks from Shanghai and Shenzhen stock markets during listing date to March1,2014and a no-risk stock as a portfolio. Finally,considering season return rate as long-term investment,we select six stocks from Shanghai and Shenzhen stock markets during listing date to March1,2014as a portfolio.Stocks are selected in different industries, and is the representative enterprises, industries are not related as much as possible. Through the programming calculation comparison,there are obvious differernce between the rate of the new method and the rate of Markowitz approach.