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## Friday, 13 December 2013

### Diversification Measures

Below a (growing) list of diversification measures...
• N - number of positions in a portfolio
• $1 / \sum_{} w^2_i$ - number of "effective positions"
• Herfindahl Index = $\sum_{} w^2_i$ - concentration in exposures
• Gini Index - another way to express concentration in exposures
• Standard deviation of portfolio constituent weights - dispersion of exposures
• Shannon entropy of portfolio constituent weights - since weights have the properties of a probability, Shannon entropy can be used as a dispersion measure
• Shannon entropy of Diversification index - see A. Meucci
• Diversification Ratio - portfolio volatility calculated with a correlation matrix of ones divided by actual portfolio volatility
• Diversification Index - inverse of the diversification ratio, Tasche(2008).
• Degree of Diversification - portfolio volatility of the global minimum variance portfolio divided by actual portfolio volatility
• % of idiosyncratic risk - residual risk measured in the context of a single- or multiple-factor model
• % of total variability explained by first principal component - dependence on a single-most important factor