Charles Murphy used to walk home through New York City’s Central Park to his 19-room townhouse for dinner with his family. Last year, he began voicing worries about money to his boss, hedge-fund billionaire John Paulson, who often joined him along the way.

At 56 years old, Mr. Murphy had a net worth in the tens of millions of dollars. He entered Columbia University at 16 and later earned law and business degrees at Harvard and Massachusetts Institute of Technology.

On Wall Street, he had a ringside seat to some of the biggest financial events of the past 20 years, from the 1990s merger boom to the dot-com bust to the Bernard Madoff scandal and the travails of American International Group Inc. He made millions of dollars at banks and investment firms in New York and London, despite his share of setbacks.

During those walks, though, Mr. Paulson found himself trying to reassure Mr. Murphy, according to a person who knew both men, offering reminders of all he had accomplished. “You don’t need to worry,” Mr. Paulson would say.

Mr. Murphy was blessed with a commanding presence and boundless ambition. Yet his concerns over maintaining the life he had created for himself, his wife, Annabella, and their three young sons consumed him. The very qualities that helped him build a fortune were no match for his fear of losing it.