Hoover Index

From Open Risk Manual

Hover Index

For the purpose of measuring name, sector or geographic concentration, the Hoover Index is a simple index defined in terms of the absolute deviation from the mean (The L^1 norm). More precisely, if we have n exposures E_i summing up to a total exposure of


E_T = \sum^{n}_{i=1} E_{i}

an average exposure


E_m = \frac{E_T}{n}

and fractional exposures w_i are defined as


w_{i} = \frac{E_i}{E_T}

Then the Hoover index is defined as


H = \frac{1}{2}   \sum^{n}_{i=1} | w_i - \frac{E_m}{E_T} |  = \frac{1}{2}   \sum^{n}_{i=1} | w_i - \frac{1}{n} |

Implementations

Open Source implementations of the Hoover index are available in


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