The paper deals with the problem of finding an optimal one-time rebalancing strategy for the Bachelier model, and makes some remarks for the similar problem within Black-Scholes model. The problem is studied on finite time interval under mean-square criterion of optimality. The methods of the paper are based on the results for optimal stopping problem and standard mean-square criterion.

The solution of the problem, considered in the paper, let us interpret how and - that is more important for us -when investor should rebalance the portfolio, if he wants to hedge it in the best way.