Complex Valued Risk Diversification

Abstract

Risk diversification is one of the dominant concerns for portfolio managers. Various portfolio constructions have been proposed to minimize the risk of the portfolio under some constrains including expected returns. We propose a portfolio construction method that incorporates the complex valued principal component analysis into the risk diversification portfolio construction. The proposed method is verified to outperform the conventional risk parity and risk diversification portfolio constructions.

Quaternion Valued Risk Diversification

“…The complex risk diversification portfolio method, proposed by Uchiyama, Kadoya, and Nakagawa in January 2019 [7], was the first to include dynamic asset information in portfolio optimization. We tried to include more complex dynamic information in portfolio optimization by naturally extending complex risk to quaternion risk.…”

“…In this section, we review the CVRD method, according to Uchiyama, Kadoya, and Nakagawa [7], which is the conventional method used for comparison in this paper.…”

“…However, this covariance matrix cannot incorporate dynamic information of the time-series, in terms of the return of the assets. Therefore, Uchiyama, Kadoya, and Nakagawa proposed a method called complex valued risk diversification (CVRD) [7]. The traditional risk diversification portfolio was inspired by empirical orthogonal function methods developed in the field of meteorological physics.…”

Fluctuations of water quality time series in rivers follow superstatistics

“…A given time series is then said to follow c 2 , inverse c 2 , or log-normal superstatistics, depending on what the actual distribution of b is. As superstatistics was originally derived for temperature fluctuations, b is often interpreted as an inverse temperature (Uchiyama and Kadoya, 2019), related to the local kinetic energy in the system. But in general, it is just a fluctuating inverse variance parameter of a given time series.…”

“…Originating in turbulence modeling (Beck, 2007), superstatistics has been applied to many physical systems, such as plasma physics (Livadiotis, 2017;Davis et al, 2019), Ising systems (Cheraghalizadeh et al, 2021), cosmic ray physics (Yalcin and Beck, 2018;Smolla et al, 2020), self-gravitating systems (Ourabah, 2020), solar wind (Livadiotis et al, 2018), high energy scattering processes (Beck, 2009;Sevilla et al, 2019;Ayala et al, 2020), ultracold gases (Rouse and Willitsch, 2017), and non-Gaussian diffusion processes in small complex systems (Chechkin et al, 2017;Itto and Beck, 2021). Furthermore, the framework has successfully been applied to completely different areas, such as modeling the power grid frequency (Schä fer et al, 2018), wind statistics (Weber et al, 2019), air pollution (Williams et al, 2020), bacterial DNA (Bogachev et al, 2017), financial time series (Gidea and Katz, 2018;Uchiyama and Kadoya, 2019), rainfall statistics (De Michele and Avanzi, 2018), or train delays (Briggs and Beck, 2007). The overview article (Metzler, 2020) provides a recent introduction to superstatistics and non-Gaussian diffusion.…”