Managing diversification

Attilio Meucci introduces a diversification index that represents the effective number of bets in a portfolio. With this index, based on entropy and constrained principal component analysis, he performs mean-diversification management adjusted for transaction costs using a parsimonious set of optimal trades

The qualitative definition of diversification is very clear to portfolio managers: a portfolio is well diversified if it is not heavily exposed to individual shocks. However, oddly enough, there exists no broadly accepted, unique, satisfactory methodology to precisely quantify and manage diversification.

In the special case of systematic-plus-idiosyncratic factor models, diversification is measured as the percentage of risk explained by the systematic factors. However, 'idiosyncratic' shocks are

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