What would you call the company that 'owns' or oversees a mutual fund or index fund?
Solution 1:
It is called Mutual Fund Company:
A mutual fund is a company that brings together money from many people and invests it in stocks, bonds or other assets. The combined holdings of stocks, bonds or other assets the fund owns are known as its portfolio. Each investor in the fund owns shares, which represent a part of these holdings.
(www.sec.gov)