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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.

Suggested Citation

  • Björn Fastrich & Peter Winker, 2010. "Robust Portfolio Optimization with a Hybrid Heuristic Algorithm," Working Papers 041, COMISEF.
  • Handle: RePEc:com:wpaper:041
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    9. Peter Winker & Marianna Lyra & Chris Sharpe, 2011. "Least median of squares estimation by optimization heuristics with an application to the CAPM and a multi-factor model," Computational Management Science, Springer, vol. 8(1), pages 103-123, April.
    10. Marc G. Genton & Elvezio Ronchetti, 2008. "Robust Prediction of Beta," Springer Books, in: Erricos J. Kontoghiorghes & Berç Rustem & Peter Winker (ed.), Computational Methods in Financial Engineering, pages 147-161, Springer.
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    Cited by:

    1. Khodamoradi, T. & Salahi, M. & Najafi, A.R., 2020. "Robust CCMV model with short selling and risk-neutral interest rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    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.
    4. Bj�rn Fastrich & Sandra Paterlini & Peter Winker, 2014. "Cardinality versus q -norm constraints for index tracking," Quantitative Finance, Taylor & Francis Journals, vol. 14(11), pages 2019-2032, November.
    5. Jang Ho Kim & Woo Chang Kim & Frank J. Fabozzi, 2018. "Recent advancements in robust optimization for investment management," Annals of Operations Research, Springer, vol. 266(1), pages 183-198, July.
    6. David Quintana & Roman Denysiuk & Sandra García-Rodríguez & Antonio Gaspar-Cunha, 2017. "Portfolio implementation risk management using evolutionary multiobjective optimization," Post-Print hal-01881379, HAL.

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    Keywords

    Hybrid heuristic algorithm; Markowitz; Robust optimization; Uncertainty sets.;
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