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Schr\"{o}dinger Risk Diversification Portfolio

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  • Yusuke Uchiyama
  • Kei Nakagawa

Abstract

The mean-variance portfolio that considers the trade-off between expected return and risk has been widely used in the problem of asset allocation for multi-asset portfolios. However, since it is difficult to estimate the expected return and the out-of-sample performance of the mean-variance portfolio is poor, risk-based portfolio construction methods focusing only on risk have been proposed, and are attracting attention mainly in practice. In terms of risk, asset fluctuations that make up the portfolio are thought to have common factors behind them, and principal component analysis, which is a dimension reduction method, is applied to extract the factors. In this study, we propose the Schr\"{o}dinger risk diversification portfolio as a factor risk diversifying portfolio using Schr\"{o}dinger principal component analysis that applies the Schr\"{o}dinger equation in quantum mechanics. The Schr\"{o}dinger principal component analysis can accurately estimate the factors even if the sample points are unequally spaced or in a small number, thus we can make efficient risk diversification. The proposed method was verified to outperform the conventional risk parity and other risk diversification portfolio constructions.

Suggested Citation

  • Yusuke Uchiyama & Kei Nakagawa, 2022. "Schr\"{o}dinger Risk Diversification Portfolio," Papers 2202.09939, arXiv.org.
  • Handle: RePEc:arx:papers:2202.09939
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    References listed on IDEAS

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    1. Victor DeMiguel & Lorenzo Garlappi & Raman Uppal, 2009. "Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy?," The Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1915-1953, May.
    2. Yusuke Uchiyama & Kei Nakagawa, 2020. "TPLVM: Portfolio Construction by Student’s t -Process Latent Variable Model," Mathematics, MDPI, vol. 8(3), pages 1-10, March.
    3. Yusuke Uchiyama & Kei Nakagawa, 2020. "TPLVM: Portfolio Construction by Student's $t$-process Latent Variable Model," Papers 2002.06243, arXiv.org.
    4. Kei Nakagawa & Yusuke Uchiyama, 2020. "GO-GJRSK Model with Application to Higher Order Risk-Based Portfolio," Mathematics, MDPI, vol. 8(11), pages 1-12, November.
    5. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
    6. Kei Nakagawa & Mitsuyoshi Imamura & Kenichi Yoshida, 2018. "Risk-Based Portfolios with Large Dynamic Covariance Matrices," IJFS, MDPI, vol. 6(2), pages 1-14, May.
    7. Thorsten Poddig & Albina Unger, 2012. "On the robustness of risk-based asset allocations," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 26(3), pages 369-401, September.
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