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Robust Portfolio Optimization with a Hybrid Heuristic Algorithm


  • Björn Fastrich
  • Peter Winker


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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    References listed on IDEAS

    1. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    2. Winker, Peter & Fang, Kai-Tai, 1995. "Application of threshold accepting to the evaluation of the discrepancy of a set of points," Discussion Papers, Series II 248, University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy".
    3. R.H. Tütüncü & M. Koenig, 2004. "Robust Asset Allocation," Annals of Operations Research, Springer, vol. 132(1), pages 157-187, November.
    4. I. Roko & M. Gilli, 2008. "Using economic and financial information for stock selection," Computational Management Science, Springer, vol. 5(4), pages 317-335, October.
    5. Manfred Gilli & Enrico Schumann, 2009. "Optimal enough?," Working Papers 010, COMISEF.
    6. Gianfranco Guastaroba & Renata Mansini & M. Speranza, 2009. "Models and Simulations for Portfolio Rebalancing," Computational Economics, Springer;Society for Computational Economics, vol. 33(3), pages 237-262, April.
    7. 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. 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.
    2. Marianna Lyra, 2010. "Heuristic Strategies in Finance – An Overview," Working Papers 045, COMISEF.
    3. Björn 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.

    More about this item


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

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