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Optimal enough?

Author

Listed:
  • Manfred Gilli
  • Enrico Schumann

Abstract

An alleged weakness of heuristic optimisation methods is the stochastic character of their solutions. That is, instead of finding a truly optimal solution, they only provide a stochastic approximation of this optimum. In this paper we look into a particular application, portfolio optimisation. We demonstrate two points: firstly, the randomness of the ‘optimal’ solution obtained from the algorithm can be made so small that for all practical purposes it can be neglected. Secondly, and more importantly, we show that the remaining randomness is swamped by the uncertainty coming from the data. In particular, we show that as a result of the bad conditioning of the problem, minor changes in the solution lead to economically meaningful changes in the solution’s out-of-sample performance. The relationship between in-sample fit and out-of-sample performance is not monotonous, but still, we observe that up to a point better solutions in-sample lead to better solutions out-of-sample. Beyond this point, however, there is practically no more cause for improving the solution any further, since any improvement will only lead to unpredictable changes (noise) out-of-sample.

Suggested Citation

  • Manfred Gilli & Enrico Schumann, 2009. "Optimal enough?," Working Papers 010, COMISEF.
  • Handle: RePEc:com:wpaper:010
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    File URL: http://comisef.eu/files/wps010.pdf
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    References listed on IDEAS

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    1. Bertsimas, Dimitris & Lauprete, Geoffrey J. & Samarov, Alexander, 2004. "Shortfall as a risk measure: properties, optimization and applications," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1353-1381, April.
    2. Moshe Leshno & Haim Levy, 2002. "Preferred by "All" and Preferred by "Most" Decision Makers: Almost Stochastic Dominance," Management Science, INFORMS, vol. 48(8), pages 1074-1085, August.
    3. Manfred Gilli & Evis Këllezi & Hilda Hysi, "undated". "A Data-Driven Optimization Heuristic for Downside Risk Minimization," Swiss Finance Institute Research Paper Series 06-02, Swiss Finance Institute.
    4. Manfred GILLI & Enrico SCHUMANN, 2009. "An Empirical Analysis of Alternative Portfolio Selection Criteria," Swiss Finance Institute Research Paper Series 09-06, Swiss Finance Institute.
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    Citations

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    Cited by:

    1. 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.
    2. Joseph Andria & Giacomo Tollo & Raffaele Pesenti, 2015. "Detection of local tourism systems by threshold accepting," Computational Management Science, Springer, vol. 12(4), pages 559-575, October.
    3. Manfred Gilli & Enrico Schumann, 2010. "Calibrating Option Pricing Models with Heuristics," Working Papers 030, COMISEF.
    4. Tae-Seok Jang, 2015. "Identification of Social Interaction Effects in Financial Data," Computational Economics, Springer;Society for Computational Economics, vol. 45(2), pages 207-238, February.
    5. Björn Fastrich & Peter Winker, 2012. "Robust portfolio optimization with a hybrid heuristic algorithm," Computational Management Science, Springer, vol. 9(1), pages 63-88, February.

    More about this item

    Keywords

    Optimisation heuristics; Portfolio Optimisation; Threshold Accepting;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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