  We consider a Bayesian financial market with one bond and one stock where the
aim is to maximize the expected power utility from terminal wealth. The
solution of this problem is known, however there are some conjectures in the
literature about the long-term behavior of the optimal strategy. In this paper
we prove now that for positive coefficient in the power utility the long-term
investor is very optimistic and behaves as if the best drift has been realized.
In case the coefficient in the power utility is negative the long-term investor
is very pessimistic and behaves as if the worst drift has been realized.
