Heuristics for cardinality constrained portfolio optimisation

In this paper we consider the problem of "nding the e$cient frontier associated with the standard mean}variance portfolio optimisation model. We extend the standard model to include cardinality constraints that limit a portfolio to have a speci"ed number of assets, and to impose limits on the proportion of the portfolio held in a given asset (if any of the asset is held). We illustrate the di!erences that arise in the shape of this e$cient frontier when such constraints are present. We present three heuristic algorithms based upon genetic algorithms, tabu search and simulated annealing for "nding the cardinality constrained e$cient frontier. Computational results are presented for "ve data sets involving up to 225 assets.