Heuristics for cardinality constrained portfolio optimisation

In this paper we consider the problem of finding the efficient 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 specified 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 differences that arise in the shape of this efficient frontier when such constraints are present. We present three heuristic algorithms based upon genetic algorithms, tabu search and simulated annealing for finding the cardinality constrained efficient frontier. Computational results are presented for five data sets involving up to 225 assets.