If the minimum variance hedge ratio is calculated as 1.0, the hedge must be perfect.quot; Is this statement true?

If the minimum variance hedge ratio is calculated as 1.0, the hedge must be perfect." Is this statement true?

I know the statement is wrong. But i want to know under what condition it will be a perfect hedge and why it is incorrect when rho = 0.5 and standard deviation of spot is two times of standard deviation of future? Thanks a lot.