Before revision:  The  problem is studied , when there exists additional correlation constraint between the desired portfolio and another financial index , and the closed form solution for the optimal portfolio is obtained . We also mention to variance reduction and getting better diversified portfolio as the applications of correlation condition in this paper .
After revision:  The problem is studied , when there exists additional correlation constraint between the desired portfolio and another financial index , and the closed form solution for the optimal portfolio is obtained in closed form. The effects of the correlation constraint are explored; it turns out that this portfolio constraint leads to a more diversified portfolio .