investment company; investment firm
General business term for a company that manages investment funds.
He works for a major investment company.
hedge fund firm
Colloquial abbreviation; often refers specifically to a hedge fund management firm.
That hedge fund firm is known for its high-risk management.
Compound of ファンド (fund) and 会社 (company). The colloquial sense is an abbreviation of ヘッジファンド会社.