Most fund managers typically prefer small portfolios of assets instead of very large diversified portfolios. This could be translated into a constraint on the maximum and minimum number of assets to be included in the portfolio (cardinality constraint). With such extra but realistic constraint, common optimization algorithm, such as quadratic programming will not be able to solve the portfolio optimization problem.
In this paper, Ant Colony Optimization has been used to solve portfolio optimization problem with cardinality constraint on the maximum number of assets. The results show that in accordance with some well-known financial researchers' viewpoints, a small portfolio of assets could be found having has a comparable performance with much diversified portfolios. In addition, the results confirm that marginal contribution of additional assets in portfolio diversification decreasing which means after reaching certain number of included assets, adding extra stock to the portfolio does not have significant impact on the portfolio diversification and could not increase its risk adjusted performance.