On the basis of the portfolio theory, a multicriteria investment Boolean problem of minimizing lost profits is formulated. The problem considered is to find a set of all extreme portfolios. The quality of such portfolios is assessed by examining the stability of the set of extreme portfolios to perturbations of Savage’s minimax risk criterion parameters. The lower and upper bounds on the radius of the strong stability are obtained under the assumption that arbitrary H¨older’s norms are specified in the three spaces of the problem’s initial data. The case of the investment problem with linear criteria is considered separately. For this case, the attainability of the bounds is proven.