The Method For Missing Data In Portfolio

Harry.A.Markowitz founded the mordern portfolio theory in 1952,who was award Nobel Prize in economics inl990.He published the paper "Portfolio Selection"at this year.In this paper,he set out that return and risk were also the basic factor for the securities investor ,it would affect the investor's decision and action of investing.So he selected two basic parameter -the expected return and standard variance of portfolio -in his studying,the former denoted the degree of return,the latter denoted the risk degree.Optimizing portfolio is that the least risk in an unit return or the most return in an unit risk on the basic definition of Markowitz.The Markowitz portfolio theory promotes the development of mordern portfolio theory,it develops to three main ways:practicality, capital pricing, arbitrage pricing.But we find the histories differ in length in the ways of practicality. The securities markets do not appear at the same time so that the histories are different in length.We shoud analyse the histories when we construct the optimizing portfolio.The longer histories will offer us more information.This dissertation do some research in different histories.It falls into four chapters:chapter one briefly introduces some concepts of portfolio.Chapter two introduces Markowitz portfolio model and risk.Chapter three summarizes the means for missing data,introduces some meas in mathematics:Gibbs sampling, junction tree algorithm etc,these methods have themselves characteristics in different fields for missing data,it also introduce the EM algorithm.And chapter four is the kernel of this paper,it applies the method of missing data to economics.There are two versions of the missing data in finance:the one which has had the most attention involves relatively small breaks in the continuity of observations;the other is the different histories in length,we will think about the latter.For example, the histories are different in developing market and developed market.The histories in developing market are shorter than those in developed market,for the developed market appeared earlier than the developing market.If we discard information from the time series until all have the same length we will lose some available data.But the longer histories will tell us more information.To settle this problem,firstly given portfolio model -MV utility function,we can compute the weight in portfolio directly for the complete data.Because of the incomplete data we should complete the data before computing the weight,this dissertation offers two methods:EM algorithm and "combined-sample",and compares these method and "truncating" sample.At last we willgive an example.