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. 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 cause for improving the solution any further, since any in-sample improvement will, out-of-sample, only lead to financially meaningless improvements and unpredictable changes (noise) in performance.

Keywords: Optimisation heuristics, Portfolio Optimisation, Threshold Accepting

JEL Classification: C61, G11