Wilson HTM has been in a trading halt since Monday pending the release of an announcement, purportedly about an independent investigation into Mr Coppin's conduct.
A statement released this evening on the Australian Securities Exchange announced that allegations of inappropriate conduct by Mr Coppin by two former employees had not been substantiated.
But in a separate matter to the internal investigation, the statement revealed that Mr Coppin has expressed interest in proposing a buyout of Wilson HTM's securities business.
"However, the Board and Mr Coppin have agreed it is not appropriate for him to pursue any potential buyout while remaining managing director," said the statement.
"Accordingly, Mr Coppin has resigned to avoid a potential conflict of interest, with his resignation effective immediately," it said.
No proposal for the securities business has been received, according to the statement.
Alexander Grant has been appointed as the acting chief executive of WIlson HTM.