Quaternion Valued Risk Diversification

Risk diversification is an important topic for portfolio managers. Various portfolio optimization algorithms have been developed to minimize portfolio risk under certain constraints. As an extension of the complex risk diversification portfolio proposed by Uchiyama, Kadoya, and Nakagawa in January 2019 (Yusuke et al. Entropy. 2019, 21, 119.), we propose a risk diversification portfolio construction method which incorporates quaternion risk. We show that the proposed method outperforms the conventional complex risk diversification portfolio method.