Before revision:  A partial converse to the previous result is also established  , showing that the time of the overall minimum of the numeraire portfolio is in a certain sense unique in rendering undesirable the act of undertaking risky positions before it.
After revision:  A partial converse to the previous result is also established in the case of complete markets , showing that the time of the overall minimum of the numeraire portfolio is in a certain sense unique in rendering undesirable the act of undertaking risky positions before it.