  In general, underestimation of risk is something which should be avoided as
far as possible. Especially in financial asset management, equity risk is
typically characterized by the measure of portfolio variance, or indirectly by
quantities which are derived from it. Since there is a linear dependency of the
variance and the empirical correlation between asset classes, one is compelled
to control or to avoid the possibility of underestimating correlation
coefficients. In the present approach, we formalize common practice and
classify these approaches by computing their probability of underestimation. In
addition, we introduce a new estimator which is characterized by having the
advantage of a constant and controllable probability of underestimation. We
prove that the new estimator is statistically consistent.
