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Robust portfolio optimization with a hybrid heuristic algorithm

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  • Björn Fastrich

    ()

  • Peter Winker

    ()

Abstract

Estimation errors in both the expected returns and the covariance matrix hamper the constructing of reliable portfolios within the Markowitz framework. Robust techniques that incorporate the uncertainty about the unknown parameters are suggested in the literature. We propose a modification as well as an extension of such a technique and compare both with another robust approach. In order to eliminate oversimplifications of Markowitz’ portfolio theory, we generalize the optimization framework to better emulate a more realistic investment environment. Because the adjusted optimization problem is no longer solvable with standard algorithms, we employ a hybrid heuristic to tackle this problem. Our empirical analysis is conducted with a moving time window for returns of the German stock index DAX100. The results of all three robust approaches yield more stable portfolio compositions than those of the original Markowitz framework. Moreover, the out-of-sample risk of the robust approaches is lower and less volatile while their returns are not necessarily smaller.

(This abstract was borrowed from another version of this item.)

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File URL: http://hdl.handle.net/10.1007/s10287-010-0127-2
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Bibliographic Info

Article provided by Springer in its journal Computational Management Science.

Volume (Year): 9 (2012)
Issue (Month): 1 (February)
Pages: 63-88

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Handle: RePEc:spr:comgts:v:9:y:2012:i:1:p:63-88

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Web page: http://www.springerlink.com/link.asp?id=111894

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Related research

Keywords: Hybrid heuristic; Algorithm; Markowitz; Robust optimization; Uncertainty sets;

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References

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  1. Manfred Gilli & Enrico Schumann, 2009. "Optimal enough?," Working Papers 010, COMISEF.
  2. Ilir Roko & Manfred Gilli, . "Using Economic and Financial Information for Stock Selection," Swiss Finance Institute Research Paper Series 06-21, Swiss Finance Institute.
  3. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
  4. Gianfranco Guastaroba & Renata Mansini & M. Speranza, 2009. "Models and Simulations for Portfolio Rebalancing," Computational Economics, Society for Computational Economics, vol. 33(3), pages 237-262, April.
  5. Peter Winker & Marianna Lyra & Chris Sharpe, 2008. "Least Median of Squares Estimation by Optimization Heuristics with an Application to the CAPM and Multi Factor Models," Working Papers 006, COMISEF.
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Cited by:
  1. Bjöern Fastrich & Sandra Paterlini & Peter Winker, 2011. "Cardinality versus q-Norm Constraints for Index Tracking," Department of Economics 0642, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
  2. Akiko Takeda & Mahesan Niranjan & Jun-ya Gotoh & Yoshinobu Kawahara, 2013. "Simultaneous pursuit of out-of-sample performance and sparsity in index tracking portfolios," Computational Management Science, Springer, vol. 10(1), pages 21-49, February.
  3. Marianna Lyra, 2010. "Heuristic Strategies in Finance – An Overview," Working Papers 045, COMISEF.

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