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Managing Diversification
Attilio Meucci Bloomberg ALPHA, Portfolio Analytics and Risk March 12, 2009 Abstract: We propose a unified, fully general methodology to analyze and act on diversification in any environment, including long-short trades in highly correlated markets. First, we build the diversification distribution, i.e. the distribution of the uncorrelated bets in the portfolio that are consistent with the portfolio constraints. Next, we summarize the wealth of information provided by the diversification distribution into one single diversification index, the effective number of bets, based on the entropy of the diversification distribution. Then, we introduce the mean-diversification efficient frontier, a diversification approach to portfolio optimization. Finally, we describe how to perform mean-diversification optimization in practice in the presence of transaction and market impact costs, by only trading a few optimally chosen securities. Fully documented code illustrating our approach can be downloaded from MATLAB Central File Exchange
Keywords: entropy, mean-diversification frontier, transaction costs, market impact, selection heuristics, systematic risk, idiosyncratic risk, principal component analysis, principal portfolios, r-square, risk contributions, random matrix theory JEL Classifications: C1, G11 Working Paper SeriesDate posted: March 13, 2009 ; Last revised: March 17, 2009Suggested CitationContact Information
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