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Markowitz meets Talmud: A combination of sophisticated and naive diversification strategies

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  • Tu, Jun
  • Zhou, Guofu

Abstract

The modern portfolio theory pioneered by Markowitz (1952) is widely used in practice and extensively taught to MBAs. However, the estimated Markowitz portfolio rule and most of its extensions not only underperform the naive 1/N rule (that invests equally across N assets) in simulations, but also lose money on a risk-adjusted basis in many real data sets. In this paper, we propose an optimal combination of the naive 1/N rule with one of the four sophisticated strategies--the Markowitz rule, the Jorion (1986) rule, the MacKinlay and Pástor (2000) rule, and the Kan and Zhou (2007) rule--as a way to improve performance. We find that the combined rules not only have a significant impact in improving the sophisticated strategies, but also outperform the 1/N rule in most scenarios. Since the combinations are theory-based, our study may be interpreted as reaffirming the usefulness of the Markowitz theory in practice.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Financial Economics.

Volume (Year): 99 (2011)
Issue (Month): 1 (January)
Pages: 204-215

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Handle: RePEc:eee:jfinec:v:99:y:2011:i:1:p:204-215

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Web page: http://www.elsevier.com/locate/inca/505576

Related research

Keywords: Portfolio choice Mean-variance analysis Parameter uncertainty;

References

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  2. Lubos Pastor & Robert F. Stambaugh, . "Comparing Asset Pricing Models: An Investment Perspective," Rodney L. White Center for Financial Research Working Papers 16-99, Wharton School Rodney L. White Center for Financial Research.
  3. Jorion, Philippe, 1986. "Bayes-Stein Estimation for Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(03), pages 279-292, September.
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  5. Zhenyu Wang, 2005. "A Shrinkage Approach to Model Uncertainty and Asset Allocation," Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 673-705.
  6. MacKinlay, A Craig & Pastor, Lubos, 2000. "Asset Pricing Models: Implications for Expected Returns and Portfolio Selection," Review of Financial Studies, Society for Financial Studies, vol. 13(4), pages 883-916.
  7. Avramov, Doron, 2002. "Stock return predictability and model uncertainty," Journal of Financial Economics, Elsevier, vol. 64(3), pages 423-458, June.
  8. Kan, Raymond & Zhou, Guofu, 2007. "Optimal Portfolio Choice with Parameter Uncertainty," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(03), pages 621-656, September.
  9. 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(03), pages 293-305, September.
  10. Tu, Jun & Zhou, Guofu, 2004. "Data-generating process uncertainty: What difference does it make in portfolio decisions?," Journal of Financial Economics, Elsevier, vol. 72(2), pages 385-421, May.
  11. Michael W. Brandt & Pedro Santa-Clara & Rossen Valkanov, 2009. "Parametric Portfolio Policies: Exploiting Characteristics in the Cross-Section of Equity Returns," Review of Financial Studies, Society for Financial Studies, vol. 22(9), pages 3411-3447, September.
  12. Michaud, Richard O. & Michaud, Robert O., 2008. "Efficient Asset Management: A Practical Guide to Stock Portfolio Optimization and Asset Allocation," OUP Catalogue, Oxford University Press, edition 2, number 9780195331912.
  13. Doron Avramov, 2004. "Stock Return Predictability and Asset Pricing Models," Review of Financial Studies, Society for Financial Studies, vol. 17(3), pages 699-738.
  14. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
  15. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
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Citations

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Cited by:
  1. Allen, D. & Lizieri, C. & Satchell, S., 2012. "Mean-Variance versus 1/N: What if we can forecast? (Updated 22nd December 2013)," Cambridge Working Papers in Economics 1244, Faculty of Economics, University of Cambridge.
  2. 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.
  3. Yen, Yu-Min & Yen, Tso-Jung, 2014. "Solving norm constrained portfolio optimization via coordinate-wise descent algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 737-759.
  4. Erik Hjalmarsson & Peter Manchev, 2009. "Characteristic-based mean-variance portfolio choice," International Finance Discussion Papers 981, Board of Governors of the Federal Reserve System (U.S.).
  5. Behr, Patrick & Guettler, Andre & Truebenbach, Fabian, 2012. "Using industry momentum to improve portfolio performance," Journal of Banking & Finance, Elsevier, vol. 36(5), pages 1414-1423.
  6. Jonathan Fletcher, 2011. "An Examination of Dynamic Trading Stategies in UK and US Stock Returns," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 38(9-10), pages 1290-1310, November.
  7. Chiarawongse, Anant & Kiatsupaibul, Seksan & Tirapat, Sunti & Roy, Benjamin Van, 2012. "Portfolio selection with qualitative input," Journal of Banking & Finance, Elsevier, vol. 36(2), pages 489-496.
  8. Peter Christoffersen & Vihang Errunza & Kris Jacobs & Hugues Langlois, 2012. "Is the Potential for International Diversi?cation Disappearing? A Dynamic Copula Approach," CREATES Research Papers 2012-48, School of Economics and Management, University of Aarhus.
  9. Levy, Haim & Levy, Moshe, 2014. "The benefits of differential variance-based constraints in portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 372-381.
  10. Victor de Miguel & Alberto Martín Utrera & Francisco J. Nogales, 2013. "Parameter uncertainty in multiperiod portfolio optimization with transaction costs," Statistics and Econometrics Working Papers ws132119, Universidad Carlos III, Departamento de Estadística y Econometría.
  11. Pflug, Georg Ch. & Pichler, Alois & Wozabal, David, 2012. "The 1/N investment strategy is optimal under high model ambiguity," Journal of Banking & Finance, Elsevier, vol. 36(2), pages 410-417.
  12. Füss, Roland & Miebs, Felix & Trübenbach, Fabian, 2014. "A jackknife-type estimator for portfolio revision," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 14-28.
  13. DeMiguel, Victor & Martin-Utrera, Alberto & Nogales, Francisco J., 2013. "Size matters: Optimal calibration of shrinkage estimators for portfolio selection," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3018-3034.
  14. Bertrand Maillet & Sessi Tokpavi & Benoit Vaucher, 2013. "Minimum Variance Portfolio Optimisation under Parameter Uncertainty: A Robust Control Approach," EconomiX Working Papers 2013-28, University of Paris West - Nanterre la Défense, EconomiX.
  15. 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.
  16. Olivier Ledoit & Michael Wolf, 2014. "Nonlinear shrinkage of the covariance matrix for portfolio selection: Markowitz meets Goldilocks," ECON - Working Papers 137, Department of Economics - University of Zurich.

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