Abstract
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.
Highlights
A combination of multiple financial assets generated as a result of deciding which and how much to invest in multiple financial assets is called a portfolio
The most famous portfolio optimization algorithm is the mean variance (MV) approach proposed by Markowitz [1]
Maximum risk diversification (MRD) portfolios have been proposed, which use principal component analysis to construct a principal component portfolio which is uncorrelated from the original assets and equalizes the risk contribution of each principal component portfolio to the portfolio risk
Summary
A combination of multiple financial assets generated as a result of deciding which and how much to invest in multiple financial assets is called a portfolio. Maximum risk diversification (MRD) portfolios have been proposed, which use principal component analysis to construct a principal component portfolio which is uncorrelated from the original assets and equalizes the risk contribution of each principal component portfolio to the portfolio risk. Entropy 2020, 22, 390 empirical orthogonal function method, the complex orthogonal function is determined by performing principal component analysis on the Hermitian matrix of the analytic signal, as an evolution of the method that uses principal component analysis of the Hermitian matrix of the time-series data (corresponding to the covariance matrix of the returns in the risk diversification portfolio). After forming the complex variable time-series from Hilbert-transformed return series of each asset, calculating the complex valued matrix, and constructing the risk diversification portfolio, the authors realized risk diversification including dynamic risk information while outperforming the traditional portfolio construction methods. We use a quaternion signal, which has a four-dimensional information of amplitude and three phases, in order to try to more precisely find signal movements which cannot be observed in a complex signal
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