An Optimization Study of Diversification Return Portfolios

The concept of Diversification Return (DR) was introduced by Booth and Fama in 1990s and it has been well studied in the finance literature mainly focusing on the various sources it may be generated. However, unlike the classical Mean-Variance (MV) model of Markowitz, DR portfolios lack optimization theory for justifying their often outstanding empirical performance. In this paper, we first explain what the DR criterion tries to achieve in terms of portfolio centrality. A consequence of this explanation is that practically imposed norm constraints in fact implicitly enforce constraints on DR. We then derive the maximum DR portfolio under given risk and obtain the efficient DR frontier. We further develop a separation theorem for this frontier and establish a relationship between the DR frontier and Markowitz MV efficient frontier. In the particular case where the variance vector is proportional to the expected return vector of the underlining assets, the two frontiers yield same efficient portfolios. The proof techniques heavily depend on recently developed geometric interpretation of the maximum DR portfolio. Finally, we use DAX30 stock data to illustrate the obtained results and demonstrate an interesting link to the maximum diversification ratio portfolio studied by Choueifaty and Coignard.