I am comparing two vectors of values which indicate portfolio weights in monetary units at two different dates.
I wanted to quantify if the concentration in the portfolios changed. So I moved on with calculating the Gini index and the Herfindahl index for both vectors.
Now I got the result that the Gini index increased, but the Herfindahl index decreased. How can I understand this result?
I did it in R, so I provide you with the values and the code:
library(ineq) V0 <- c(6.162382e+01, 7.870565e+02, 2.922241e+03, 8.367593e-02, 3.306334e+01, 1.937308e+03, 2.114359e+01, 3.942730e+01, 2.682160e+00, 1.929470e+03, 2.052831e+03, 9.902533e+03, 9.603747e+03, 2.370503e+00, 3.841130e+01, 2.364905e+01, 3.627621e-01, 2.248296e+02, 2.330520e+03, 7.286694e+03, 5.218457e+00, 5.961622e-01, 0.000000e+00, 0.000000e+00, 5.048860e+03, 2.885924e+01, 3.051794e+02, 5.937953e+02, 6.668031e+00, 1.004851e+02, 3.319353e+02, 1.796081e+03, 1.407182e+03, 2.728721e+03, 3.892461e+04, 2.996096e+04) V1 <- c(1.07793e-03, 5.87720e-04, 1.95339e-04, 2.65183e+03, 8.58753e-04, 2.67605e-04, 4.86570e-05, 1.74857e-05, 1.00513e-04, 5.18214e+03, 9.09578e+03, 3.23243e+04, 4.41746e-03, 2.11019e-05, 2.87357e+04, 6.10592e+03, 2.25064e-03, 1.24105e-03, 1.63327e+04, 1.47689e-03, 1.60764e-04, 9.70041e-04, 2.64918e-06, 2.13185e-04, 1.95118e-03, 3.50591e+03, 2.97961e-03, 1.34459e-04, 1.10588e+03, 3.30131e-05, 2.41992e-04, 1.03209e-04, 2.25949e-03, 1.93734e-02, 1.50010e+04, 3.98032e+02) Gini(V0)  0.8202071 Gini(V1)  0.8503999 Herfindahl(V0)  0.187598 Herfindahl(V1)  0.1744127
Clearly, both vectors are rather unequal distributed. The high Gini index says exactly that. The Herfindahl index is rather low to my feelings, but I am not very experienced with inequality/concentration measures.