  The portfolio optimization problem in which the variances of the return rates
of assets are not identical is analyzed in this paper using the methodology of
statistical mechanical informatics, specifically, replica analysis. We define
two characteristic quantities of an optimal portfolio, namely, minimal
investment risk and concentrated investment level, in order to solve the
portfolio optimization problem and analytically determine their asymptotical
behaviors using replica analysis. Moreover, numerical experiments were
performed, and a comparison between the results of our simulation and those
obtained via replica analysis validated our proposed method.
