The errors‐in‐variable model in the optimal portfolio construction

A modification of Sharpe's method used in classical portfolio analysis for optimal portfolio building is considered in the paper. The conventional theory assumes there is a linear relationship between asset return and market portfolio return, while the influence of all the other factors is not included. We propose not to neglect them any more, but include them into a model. Since the factors in question are often hard to measure or even characterize, we treat them as disturbances over random variables used by classical Sharpe's method. The key idea of the paper is the modification of the classical approach by application of the errors–in–variable model. It is assumed that both independent (market portfolio return) as well as dependent (given asset return) variables are randomly distributed values related with each other by linear relationship and we build the model used for parameter estimation. To verify the model, an analysis was performed, based on archival data from Warsaw Stock Exchange. The results are also included.