Optimal enough?

Abstract

An alleged weakness of heuristic optimisation methods is the stochastic character of their solutions: instead of finding the 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 that the randomness of the ‘optimal’ solution obtained from the algorithm can be made so small that for all practical purposes it can be neglected. More importantly, we look at the relevance of the remaining uncertainty in the out-of-sample period. 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 there is no more cause for improving the solution any further: any in-sample improvement leads out-of-sample only to financially meaningless improvements and unpredictable changes (noise) in performance.

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Correspondence to Enrico Schumann.

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Both authors gratefully acknowledge financial support from the eu Commission through mrtn-ct-2006-034270 comisef; the data set was provided by DynaGest S.A., Geneva.

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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Gilli, M., Schumann, E. Optimal enough?. J Heuristics 17, 373–387 (2011). https://doi.org/10.1007/s10732-010-9138-y

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Keywords

  • Optimisation heuristics
  • Portfolio optimisation
  • Threshold accepting