Securities and Exchange Commission Chairman Mary Jo White announced a sweeping set of initiatives Thursday to address potential risks posed by the $60-plus trillion asset-management industry, including steps to tighten restrictions on mutual funds and other firms.

Among the most significant ideas is a plan that would likely cause funds to curb their use of risky derivatives to boost returns. The idea could target some of the hottest and most-controversial investments offered to the public, including so-called alternative mutual funds.