Randall Dillard blames his neighbors for inspiring his new career as a fund-of-hedge-funds manager. After a dozen years with Nomura International, the former head of the Japanese financial conglomerate’s London-based merchant bank retired in 2001 at the age of 44. Dillard, who grew up just south of Miami near Coconut Grove, rented a secluded villa on the Caribbean island of Mustique and traveled no farther than its white-sand beaches for several months.