At the son's West Side apartment, investigators found magazines, bullets and a shell that matched the gun found at the scene, police told the AP.
The law office representing Gilbert Jr. had no comment, AP reported.
The father's latest venture, Wainscott Capital Partners, was founded in 2011 to focus on investing in the stocks of biotechnology and health-care companies.
Wainscott—which shares the name of the area in the Hamptons where Gilbert had owned a home—is small by industry standards. The firm managed about $10 million as of September, according to marketing materials for a hedge fund conference. A person familiar with the fund confirmed that assets were likely about the same today, far less than the $200 million that has been widely reported.
Read MoreHedge fund founder, 70, slain in NYC apartment
Regardless of the hedge fund's size, Gilbert was excited about his new act.
"The long-term future for healthcare investing continues to be bright, and we are seeing more asset allocators approaching us to participate in an actively managed healthcare fund with risk minimization. We believe that Wainscott offers that vehicle," Gilbert wrote in a November email.
The fund produced strong returns in its first few years of existence, according to materials posted on the firm's website. It also was up more than 10 percent in 2014 through October, according to an email sent to clients and prospects.