Mean-Absolute Deviation And Mean Semi-Absolute Deviation Model Based On Nonparametric Estimation

With the economic globalization and the integration of financial markets,enterprise financing and especially overseas financing will depend on the stock markets more than the bank loans.It made that financial crisis transfer from Banks to diverse fields,such as stock markets,foreign currency market.It also intensified the volatility of financial markets and increased the risk of financial markets.So measuring risk effectively has become the core competitiveness of the financial world and major enterprise.Meanwhile,measuring risk effectively also has becomethe core research contents of the academic world and is a primary supervision of regulatory authorities.In order to achieve the purpose of risk diversification,portfolio optimization theory based on the established target income and risk tolerance and re-combined investment.That is how to minimize the risk of portfolio at an established return or how to maximize the return of portfolio at an established risk.Mean-absolute deviation portfolio selection model and mean semi-absolute deviation portfolio selection model are important portfolio optimization models.Just as the mean-variance portfolio selection model,mean-absolute deviation portfolio selection model and mean semi-absolute deviation portfolio selection model all rely on sample data.However,when a finite number of observations is available,small changes of the expected returns given by investors lead to great changes of the portfolio's optimal solution.Because observations that is available can only be finite in reality,therefore we need to use optimized and statistical methods to deal with observations.At present,the methods that were used for dealing with observations include robust optimization method and non-parametric estimation method,and this article uses non-parametric estimation method to deal with observations.Measuring risk by Absolute deviation and semi-absolute deviation,the article applies non-parametric estimation method in mean-absolute deviation portfolio selection model and mean semi-absolute deviation portfolio selection model to search for the optimal investment strategy.Firstly,the article gives kernel mean estimated formula of return and kernel median estimated formula of return.Therefore,it presents mean-absolute deviation portfolio selection model that based on nonparametric estimation and mean semi-absolute deviation portfolio selection model that based on nonparametric estimation.Then,the article selected observations from Chinese securities market and American securities market,used some software,such as MATLAB?R?EXCEL,to studied and analysed.Empirical analysis includes two parts.Part one,we calculated the optimal solution of the portfolio selection model and the portfolio selection models that based on nonparametric estimation,and built effective frontier.It turned out that the portfolio selection model that based on nonparametric estimation have less risk compared with the portfolio selection model.Part two,we predicted portfolio returns by using the optimal solution calculated from part one.The results shows that portfolio returns which were predicted by portfolio selection model that based on nonparametric estimation are bigger.Eventually,we get some conclusions.On the one hand,mean-absolute deviation portfolio selection model that based on nonparametric estimation outperforms mean-absolute deviation portfolio selection model,and mean-absolute deviation portfolio selection model that based on kernel median estimation outperforms mean-absolute deviation portfolio selection model that based on kernel mean estimation.On the other hand,mean semi-absolute deviation portfolio selection model that based on nonparametric estimation outperforms mean semi-absolute deviation portfolio selection model,and mean semi-absolute deviation portfolio selection model that based on kernel median estimation outperforms mean semi-absolute deviation portfolio selection model that based on kernel mean estimation.