But the fund manager had an even more distinctive credential to showcase in his marketing material in June 2013: He was a “U.S. congressman,” Representative Alan Grayson, Democrat of Florida, a member of the House Foreign Affairs Committee. Now he is also among the leading Democratic candidates for one of Florida’s United States Senate seats.

This highly unusual dual role — a sitting House lawmaker running a hedge fund, which until recently had operations in the Cayman Islands — has led to an investigation of Mr. Grayson by the House Committee on Ethics.

The inquiry has become public, but emails and marketing documents obtained by The New York Times show the extent to which Mr. Grayson’s roles as a hedge fund manager and a member of Congress were intertwined, and how he promoted his international travels, some with congressional delegations, to solicit business.

Interviews and the documents show that Mr. Grayson told potential investors in his hedge fund that they should contribute money to the fund to capitalize on the unrest he observed around the world, and to take particular advantage when there was “blood in the streets.”