IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v10y2010i1p107-119.html
   My bibliography  Save this article

Power mapping with dynamical adjustment for improved portfolio optimization

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/14697680902748498
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/14697680902748498?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1683, August.
    2. Vijay K. Chopra & Chris R. Hensel & Andrew L. Turner, 1993. "Massaging Mean-Variance Inputs: Returns from Alternative Global Investment Strategies in the 1980s," Management Science, INFORMS, vol. 39(7), pages 845-855, July.
    3. Pafka, Szilárd & Kondor, Imre, 2003. "Noisy covariance matrices and portfolio optimization II," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 487-494.
    4. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    5. Frost, Peter A. & Savarino, James E., 1986. "An Empirical Bayes Approach to Efficient Portfolio Selection," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(3), pages 293-305, September.
    6. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
    7. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1684, August.
    8. Pafka, Szilárd & Kondor, Imre, 2004. "Estimated correlation matrices and portfolio optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 623-634.
    9. Jorion, Philippe, 1986. "Bayes-Stein Estimation for Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(3), pages 279-292, September.
    10. Giada, Lorenzo & Marsili, Matteo, 2002. "Algorithms of maximum likelihood data clustering with applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 315(3), pages 650-664.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Istvan Varga-Haszonits & Fabio Caccioli & Imre Kondor, 2016. "Replica approach to mean-variance portfolio optimization," Papers 1606.08679, arXiv.org.
    2. Varga-Haszonits, Istvan & Caccioli, Fabio & Kondor, Imre, 2016. "Replica approach to mean-variance portfolio optimization," LSE Research Online Documents on Economics 68955, London School of Economics and Political Science, LSE Library.
    3. Plachel, Lukas, 2019. "A unified model for regularized and robust portfolio optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 109(C).
    4. Candelon, B. & Hurlin, C. & Tokpavi, S., 2012. "Sampling error and double shrinkage estimation of minimum variance portfolios," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 511-527.
    5. Wang, Christina Dan & Chen, Zhao & Lian, Yimin & Chen, Min, 2022. "Asset selection based on high frequency Sharpe ratio," Journal of Econometrics, Elsevier, vol. 227(1), pages 168-188.
    6. Thomas J. Brennan & Andrew W. Lo, 2010. "Impossible Frontiers," Management Science, INFORMS, vol. 56(6), pages 905-923, June.
    7. Fabio Caccioli & Imre Kondor & Matteo Marsili & Susanne Still, 2014. "$L_p$ regularized portfolio optimization," Papers 1404.4040, arXiv.org.
    8. Frahm, Gabriel & Memmel, Christoph, 2008. "Dominating estimators for the global minimum variance portfolio," Discussion Papers in Econometrics and Statistics 2/08, University of Cologne, Institute of Econometrics and Statistics.
    9. Kolm, Petter N. & Tütüncü, Reha & Fabozzi, Frank J., 2014. "60 Years of portfolio optimization: Practical challenges and current trends," European Journal of Operational Research, Elsevier, vol. 234(2), pages 356-371.
    10. Penaranda, Francisco, 2007. "Portfolio choice beyond the traditional approach," LSE Research Online Documents on Economics 24481, London School of Economics and Political Science, LSE Library.
    11. Frahm, Gabriel & Wiechers, Christof, 2011. "On the diversification of portfolios of risky assets," Discussion Papers in Econometrics and Statistics 2/11, University of Cologne, Institute of Econometrics and Statistics.
    12. Dangl, Thomas & Randl, Otto & Zechner, Josef, 2016. "Risk control in asset management: Motives and concepts," CFS Working Paper Series 546, Center for Financial Studies (CFS).
    13. Moorman, Theodore, 2014. "An empirical investigation of methods to reduce transaction costs," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 230-246.
    14. Long Zhao & Deepayan Chakrabarti & Kumar Muthuraman, 2019. "Portfolio Construction by Mitigating Error Amplification: The Bounded-Noise Portfolio," Operations Research, INFORMS, vol. 67(4), pages 965-983, July.
    15. Joo, Young C. & Park, Sung Y., 2021. "Optimal portfolio selection using a simple double-shrinkage selection rule," Finance Research Letters, Elsevier, vol. 43(C).
    16. Kourtis, Apostolos & Dotsis, George & Markellos, Raphael N., 2012. "Parameter uncertainty in portfolio selection: Shrinking the inverse covariance matrix," Journal of Banking & Finance, Elsevier, vol. 36(9), pages 2522-2531.
    17. Behr, Patrick & Guettler, Andre & Miebs, Felix, 2013. "On portfolio optimization: Imposing the right constraints," Journal of Banking & Finance, Elsevier, vol. 37(4), pages 1232-1242.
    18. Meade, N. & Beasley, J.E. & Adcock, C.J., 2021. "Quantitative portfolio selection: Using density forecasting to find consistent portfolios," European Journal of Operational Research, Elsevier, vol. 288(3), pages 1053-1067.
    19. Fabio Caccioli & Imre Kondor & Matteo Marsili & Susanne Still, 2016. "Liquidity Risk And Instabilities In Portfolio Optimization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-28, August.
    20. Frahm, Gabriel, 2010. "An analytical investigation of estimators for expected asset returns from the perspective of optimal asset allocation," Discussion Papers in Econometrics and Statistics 1/10, University of Cologne, Institute of Econometrics and Statistics.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:quantf:v:10:y:2010:i:1:p:107-119. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.