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Optimal enough?

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Author Info

  • 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.

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Bibliographic Info

Paper provided by COMISEF in its series Working Papers with number 010.

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Length: 15 pages
Date of creation: 14 Jun 2009
Date of revision:
Handle: RePEc:com:wpaper:010

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Web page: http://www.comisef.eu

Related research

Keywords: Optimisation heuristics; Portfolio Optimisation; Threshold Accepting;

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References

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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. M. Gilli & E. Kellezi & H. Hysi, 2006. "A Data-Driven Optimization Heuristic for Downside Risk Minimization," Computing in Economics and Finance 2006 355, Society for Computational Economics.
  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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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. Björn Fastrich & Peter Winker, 2012. "Robust portfolio optimization with a hybrid heuristic algorithm," Computational Management Science, Springer, vol. 9(1), pages 63-88, February.
  3. Manfred Gilli & Enrico Schumann, 2010. "Calibrating Option Pricing Models with Heuristics," Working Papers 030, COMISEF.

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