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
Please contact us if you know diversification measures which are not on the above list.

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