Research Of Robust Statistical Analysis Method For Stock Portfolio Investment

Obtaining higher income has been the most fundamental purpose of securities investment, but in investment activities, benefits always accompany with risks at the same time, That is to say, higher incomes, more risks, and vice versa. The main purpose of portfolio diversification, Which is building balance between risks and benefits, when risks are given in a certain case, investors could obtain maximum benefits. In this dissertation, the investment portfolio model is the object of the research, as we all know, the most traditional and classical theory is the mean variance model proposed by Markowitz in 1952. This model is of great significance in both theory and practice, in which the variance of stock historical returns is widely used by investors and researchers as a measure of risk. However, with the in-depth study, many researchers found that the using of variance to measure the risk might have some unavoidable defects. In order to overcome shortcomings of the existing theories and make a better use of the investment portfolio model to obtain higher returns, many experts and scholars have conducted extensive and in-depth discussions.In this dissertation, not only the portfolio investment model is investigated but also several models are improved with the perspective of robust. After improving, We would finally make a simulation and empirical analysis of them. Results of this paper can mainly be included as the following:Firstly: Construction of robust statistics. As one of traditional methods, methods of multivariate analysis are easily affected by outliers, We would finally to the distant from calculation results to actual situation. In this study, we would select suitable robust statistical methods to construct a robust factor analysis model and use the data of securities to make simulation study and empirical analysis with the robust traditional factor analysis and factor analysis. From both simulated and empirical results, we can know that robust method that we construct can more effectively resist outliers than the traditional method.Secondly: Improvement of mean variance model. For the mean- variance model, the properties of normal distribution are important hypothesis. In the tradeoff between income and risk, the variance and the mean of the securities return are best statistics if the stock return data is normally distributed. However, the traditional methods of investment combination construct the statistics are without considering the robustness of the statistics and the sensitiveness of outlier value. Therefore, in this study, with the idea of robust statistics, we would like to make the further improvement to the mean variance portfolio model for dealing with the financial data obtained our real lives and make the outliers have higher resistance. Furthermore, it could be seen from empirical results, by building the robust portfolio is better than the traditional method.Thirdly(Improvement of mean-absolute deviation model. Having compared with other investment portfolio model, mean-absolute deviation model is a robust model, but measurement of the rate of expected return is the mean value, while this mean value is not robust, therefore we replace the means by robust mean for improvement to obtain robust mean-absolute deviation model, and use the Chinese stock data for comparative analysis. From the analysis results, we can know that the robust mean absolute deviation model is better than the traditional method to resist the influence of outliers.Fourthly: Improvement of Sharpe ratio model. In the traditional regression method, each of the sample data is given equal weight, which enhances the impact of outlier values on the whole model. Therefore, in this paper, we have improved the Sharpe ratio model based on the idea of robust statistics, namely, we used robust regression in the regression analysis. The sample data are given different weights, with the rule that the greater residual, the smaller weight is, and the smaller residuals, the greater weight is, which can effectively reduce affect of the outliers on the calculation results of the model. Combined with Sharpe ratio model, we have construct the robust Sharp ratio model, the portfolio tend to have higher probability to approach the true investment value. By the empirical analysis, we can see that the improved Shapu index model has better robustness.Lastly: Development of robust portfolio investment systemIn this paper, with the combination of statistical methods and intelligent information system, on the basis of open source system R language, we have developed a "steady investment combination evaluation system" by achieving systematic algorithm and systematic evaluation and render the zoning maps for designing the portfolio investment system which finally has a certain practical value.