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Index-tracking is a low-cost alternative to active portfolio management. The implementation of a quantitative approach, however, is a major challenge from an optimization perspective. The optimal selection of a group of assets that can replicate the index of a much larger portfolio requires both to find the optimal subset of assets and to fine-tune their weights. The former is a combinatorial, the latter a continuous numerical problem. Both problems need to be addressed simultaneously, because whether or not a selection of assets is promising depends on the allocation weights and vice versa. Moreover, the problem is usually of high dimension. Typically, an optimal subset of 30-150 positions out of 100-600 need to be selected and their weights determined. Search heuristics can be a valuable alternative to traditional methods, which often cannot deal with the problem. In this paper, we propose a new optimization method, which is partly based on Differential Evolution (DE) and on combinatorial search. The main advantage of our method is that it can tackle the index-tracking problem as complex as it is, generating accurate and robust results.

Although we can observe noticeable progress in gender diversity on corporate boards, these boards remain far from gender balanced. Our paper builds on social identity theory to examine the impact of corporate elites-men and women who sit on multiple corporate boards-on board diversity. We extend the main argument of social identity theory concerning favouritism based on homophily by suggesting that boards with men with multiple appointments are unwilling to include female board members to protect the monopoly value generated by their elite status. The empirical analysis, based on DAX 30 firms in the period of 2010-2015, shows that the presence of multi-board men is negatively associated with women's participation, while the presence of multi-board women and other women on management boards is positively related to gender diversity on boards. Furthermore, robustness tests support and confirm our conclusion that multi-board men have a significant association with board diversity, even with small size (i.e. 1 or 2). Additionally, we find a significant effect arising from pressure related to the introduction of gender quotas in Germany, effective in 2016, indicating the effectiveness of gender quota policies for board gender diversity.