Heuristics for cardinality constrained portfolio optimisation

In this paper we consider the problem of finding the efficient frontier ass ociated with the standard mean-variance portfolio optimisation model. We ex tend the standard model to include cardinality constraints that limit a por tfolio to have a specified number of assets, and to impose limits on the pr oportion of the portfolio held in a given asset (if any of the asset is hel d). We illustrate the differences that arise in the shape of this efficient frontier when such constraints are present. We present three heuristic alg orithms based upon genetic algorithms, tabu search and simulated annealing for finding the cardinality constrained efficient frontier. Computational r esults are presented for five data sets involving up to 225 assets.