PORTLAND, Ore. — Herbalife Ltd.’s shares fell sharply for a second day on hedge fund manager William Ackman’s allegations that the nutritional supplements company is a pyramid scheme.

The chief executive of Pershing Square Capital Management said Wednesday that he has been shorting the company’s stock for months. (Short sellers earn money when a stock declines.) Ackman detailed his allegations Thursday at the Sohn Conference Foundation meeting in New York.