Notes: A Reformulation of a Mean-Absolute Deviation Portfolio Optimization Model

The purpose of this note is to present a reformulation of the model presented by Konno and Yamazaki (1991). In their paper, it was claimed that (under the assumption that there is no upper limit on the investment in an asset) the number of nonzero assets in the optimal portfolio is at most 2T + 2, where T is the number of time periods in the data base used to approximate the parameters of the return distributions of the assets. The formulation we present, which is shown to be equivalent to that of Konno and Yamazaki, has a bound of T + 2 on the number of nonzero assets in the optimal portfolio.