April 1, 2010
Risk, pp. 74-79, May 2009
Bloomberg Education & Quantitative Research and Education Paper
We propose a unified, fully general methodology to analyze and act on diversification in any environment, including long-short trades in highly correlated markets with complex derivatives.
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.
Number of Pages in PDF File: 23
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 Classification: C1, G11
Date posted: March 13, 2009 ; Last revised: October 11, 2010
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