On Genes, Insects, and Crystals: Determining Marginal Diversification Effects With Nature Based Algorithms

A popular argument states that most of the diversification in a portfolio can be obtained with a rather small number of securities. In this paper we present three algorithms to approach the underlying NP-hard problem of portfolio optimization with a cardinality constraint. All three of these algorithms are based on evolutionary processes found in nature: Genetic Algorithms, Ant Systems, and Simulated Annealing. We find that either of the algorithms is well suited to solve the problem. In addition, we show for the stocks in the FT-SE 100 that a small number of well selected stocks might well cause a better diversification than a large number of more or less arbitrarily picked stocks despite their respective weights in the portfolio being optimized.