Mean-Variance Models with Missing Data

A common challenge in the theory of portfolio selection is that certain assets have shorter return histories than others. Consequently, historical data of the returns have missing data. This paper deals with portfolio selection models of mean-variance type in which missing data exist. Two simple methods for constructing a vector and a matrix starting from a matrix of rate of returns are presented. One considers a standard minimum variance model in which the vector and the matrix built replace the vector of means and the matrix of covariance. Several numerical experiments are made and the effect of missing data on the efficient frontiers associated to the minimum variance models is investigated.