Ackman, who runs Pershing Square Capital Management, an activist hedge fund, has bet heavily against Herbalife by using "short" trades that will be profitable if the price of the company's stock falls. Ackman has been trying to convince other investors to take similar positions, most memorably in a shouting match he got into with Carl Icahn, a rival investor, on live television in January 2013. Icahn has taken the opposite position and has defended Herbalife.
Herbalife has vigorously denied Ackman's arguments, and says it operates like a multi-level marketing company similar to Avon, Amway and Mary Kay.
The company has not been accused of any crime and insists that its operations are legal. The Securities and Exchange Commission, the Federal Trade Commission and the Attorneys General of New York and Illinois are investigating Herbalife, but no charges have been brought against the company since Ackman announced his short position in 2012.
Investors appeared to dismiss Ackman's latest allegations Tuesday and bid up the company's stock. Herbalife shot up $13.75 to $67.77. Trading volume was more than 15 times the daily average. The stock is still down 14 percent this year.
Nutrition clubs have become an increasingly lucrative business model for Herbalife in the last 10 years, with more than 4,000 operating in the U.S. alone, according to the company.
Ackman alleged that nutrition club attendees were not actually consumers of the products. Instead attendees were often recruits to become nutrition club operators of their own. These recruits should not be thought of as customers, but rather the next layer in the pyramid.
Pyramid schemes are illegal because they eventually collapse once there are no more people to recruit.
Ackman bet $1 billion against Herbalife in 2012. Ackman said he spent $50 million of investors' money and two years investigating Herbalife.
"Once again, Bill Ackman has over-promised and under-delivered on his $1 billion bet against our company," Herbalife said in a statement Tuesday.
Ackman argues he is in it for "the long haul." He has also repeatedly said that any personal profits he would make from the collapse of Herbalife would be donated to charity.
At the end of his presentation in midtown Manhattan, Ackman appeared to tear up when discussing his campaign against the company. Ackman alleged that Herbalife's business model takes advantage of often poor people with minimal educations who are trying to find a way to start a business.