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Complex Valued Risk Diversification.

Yusuke Uchiyama1, Takanori Kadoya1, Kei Nakagawa2

  • 1MAZIN, Inc., 1-60-20 Minami-Otsuka, Toshima-ku, Tokyo 170-0005, Japan.

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Summary
This summary is machine-generated.

This study introduces a new portfolio construction method using complex valued principal component analysis for enhanced risk diversification. The novel approach demonstrates superior performance compared to traditional risk parity and diversification strategies.

Keywords:
Hilbert transformportfolio managementprincipal component analysisrisk diversification

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Area of Science:

  • Quantitative Finance
  • Financial Risk Management
  • Portfolio Optimization

Background:

  • Risk diversification is a key objective for portfolio managers seeking to minimize risk under constraints like expected returns.
  • Existing portfolio construction methods include risk parity and conventional risk diversification strategies.
  • Principal component analysis is a statistical technique used for dimensionality reduction and identifying key sources of variation.

Purpose of the Study:

  • To propose a novel portfolio construction method that integrates complex valued principal component analysis (C-PCA) for improved risk diversification.
  • To evaluate the performance of the proposed C-PCA based portfolio construction against established methods.
  • To demonstrate the efficacy of C-PCA in enhancing portfolio risk management.

Main Methods:

  • Development of a portfolio construction framework incorporating complex valued principal component analysis.
  • Application of the proposed method to portfolio optimization problems.
  • Comparative analysis against conventional risk parity and risk diversification techniques.

Main Results:

  • The proposed portfolio construction method incorporating C-PCA significantly outperforms conventional risk parity.
  • The C-PCA based approach demonstrates superior risk diversification compared to traditional methods.
  • Empirical validation confirms the enhanced performance of the novel method.

Conclusions:

  • Complex valued principal component analysis offers a powerful tool for advancing portfolio construction and risk diversification.
  • The proposed method provides a statistically robust and empirically validated alternative for portfolio managers.
  • This research contributes to the field of quantitative finance by offering an innovative approach to portfolio optimization.