Subject to Section 53607, the board of supervisors may, by ordinance, delegate to the county treasurer the authority to invest or reinvest the funds of the county and the funds of other depositors in the county treasury, pursuant to Chapter 4 (commencing with Section 53600) of Part 1 of Division 2 of Title 5. The county treasurer shall thereafter assume full responsibility for those transactions until the board of supervisors either revokes its delegation of authority, by ordinance, or decides not to renew the annual delegation, as provided in Section 53607. Nothing in this section shall limit the county treasurer’s authority pursuant to Section 53635 or 53684.