These funds are sponsored by an outside entity. The bank then advises the fund about what investments to make. It receives a fee from the fund for that service. Other banks offer private label funds. These funds are sponsored and managed by an outside entity but are sold exclusively through the bank.
Some mutual funds have names similar to a bank's name.
But just like other mutual funds or investment products, those funds are not backed by the bank or insured by the government. Some banks sell annuities. Annuities are investment products that can pay you a return annually or at regular intervals. When you buy an annuity, the insurance company invests your money and agrees to pay you back according to the terms of the annuity contract. Annuities can be part of a long-term retirement savings plan.