  In this paper, we use replica analysis to investigate the influence of
correlation among the return rates of assets on the solution of the portfolio
optimization problem. We consider the behavior of the optimal solution for the
case where the return rate is described with a single-factor model and compare
the findings obtained from our proposed methods with correlated return rates
with those obtained with independent return rates. We then analytically assess
the increase in the investment risk when correlation is included. Furthermore,
we also compare our approach with analytical procedures for minimizing the
investment risk from operations research.
