But Mr. Grayson’s activities have long concerned his campaign aides. In private emails in June, Mr. Grayson’s aides pleaded with him to close the hedge fund, convinced that its focus on investing in nations hit by political or economic strife, and its ties to the Cayman Islands, a notorious tax haven, sharply conflicted with his image as a scold of Wall Street — even if he had not done anything wrong.

“This is going to be the drip, drip, drip story that never goes away,” Doug Dodson, Mr. Grayson’s Senate campaign manager until the end of 2015, wrote in a June email to Mr. Grayson, saying his political opponents would “try to make you look like a hypocrite and a fraud and not the populist you claim to be.”

Mr. Grayson rejected the advice, the emails show. “I still think that it would be taken, wrongly, as an admission of guilt,” he wrote back.

Sometimes, Mr. Grayson deployed his aides to work for the fund and his political activity at the same time. Todd Jurkowski, a former spokesman in Mr. Grayson’s House office, was the vice president for investor relations when the fund was started while also serving as treasurer for Mr. Grayson’s campaign in 2012.

More recently, David Keith, finance director for Mr. Grayson’s Senate campaign, was being paid about $1,000 a month, in part to help Mr. Grayson in a search for new investors in his hedge fund, Mr. Keith said in an interview. He worked for Mr. Grayson from early 2014 to late 2015, he said.

Mr. Grayson first won a seat in Congress representing the Orlando area in 2008 but failed to win re-election in 2010. In 2011, he started the Grayson Fund, which he said would specialize in investments in developing countries in Asia and Latin America. Mr. Grayson was elected again to the House in 2012, but he kept the fund open.