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Power mapping with dynamical adjustment for improved portfolio optimization

Author

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  • Rudi Schafer
  • Nils Fredrik Nilsson
  • Thomas Guhr

Abstract

For financial risk management it is of vital interest to have good estimates for the correlations between the stocks. It has been found that the correlations obtained from historical data are covered by a considerable amount of noise, which leads to a substantial error in the estimation of the portfolio risk. A method to suppress this noise is power mapping. It raises the absolute value of each matrix element to a power q while preserving the sign. In this paper we use the Markowitz portfolio optimization as a criterion for the optimal value of q and find a K/T dependence, where K is the portfolio size and T the length of the time series. Both in numerical simulations and for real market data we find that power mapping leads to portfolios with considerably reduced risk. It compares well with another noise reduction method based on spectral filtering. A combination of both methods yields the best results.

Suggested Citation

  • Rudi Schafer & Nils Fredrik Nilsson & Thomas Guhr, 2010. "Power mapping with dynamical adjustment for improved portfolio optimization," Quantitative Finance, Taylor & Francis Journals, vol. 10(1), pages 107-119.
    • Handle: RePEc:taf:quantf:v:10:y:2010:i:1:p:107-119
    DOI: 10.1080/14697680902748498
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    References listed on IDEAS

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    Cited by:

    1. Pharasi, Hirdesh K. & Seligman, Eduard & Sadhukhan, Suchetana & Majari, Parisa & Seligman, Thomas H., 2024. "Dynamics of market states and risk assessment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    2. Li, Yan & Jiang, Xiong-Fei & Tian, Yue & Li, Sai-Ping & Zheng, Bo, 2019. "Portfolio optimization based on network topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 671-681.
    3. Hirdesh K. Pharasi & Eduard Seligman & Suchetana Sadhukhan & Parisa Majari & Thomas H. Seligman, 2020. "Dynamics of market states and risk assessment," Papers 2011.05984, arXiv.org, revised Sep 2023.
    4. Zhao, Longfeng & Wang, Gang-Jin & Wang, Mingang & Bao, Weiqi & Li, Wei & Stanley, H. Eugene, 2018. "Stock market as temporal network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 1104-1112.
    5. Schäfer, Rudi & Guhr, Thomas, 2010. "Local normalization: Uncovering correlations in non-stationary financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3856-3865.
    6. Hirdesh K. Pharasi & Suchetana Sadhukhan & Parisa Majari & Anirban Chakraborti & Thomas H. Seligman, 2021. "Dynamics of the market states in the space of correlation matrices with applications to financial markets," Papers 2107.05663, arXiv.org.
    7. M.C. M�nnix & R. Sch�fer & O. Grothe, 2014. "Estimating correlation and covariance matrices by weighting of market similarity," Quantitative Finance, Taylor & Francis Journals, vol. 14(5), pages 931-939, May.
    8. Justo Puerto & Federica Ricca & Mois'es Rodr'iguez-Madrena & Andrea Scozzari, 2021. "A combinatorial optimization approach to scenario filtering in portfolio selection," Papers 2103.01123, arXiv.org.
    9. Thilo A. Schmitt & Rudi Schäfer & Dominik Wied & Thomas Guhr, 2016. "Spatial dependence in stock returns: local normalization and VaR forecasts," Empirical Economics, Springer, vol. 50(3), pages 1091-1109, May.
    10. Hirdesh K. Pharasi & Kiran Sharma & Anirban Chakraborti & Thomas H. Seligman, 2018. "Complex market dynamics in the light of random matrix theory," Papers 1809.07100, arXiv.org, revised Sep 2018.

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