"If I am right, its share price will go to zero," says Bill Ackman, the founder of Pershing Square Capital, a hedge fund, who insists he has never felt so confident in shorting a company's stock.

On Dec. 20 he invited an audience of his peers to hear his declaration of war against Herbalife, a seller of dietary supplements and vitamins. His claim that the 32-year-old company is an "illegal pyramid scheme" had an immediate impact: Herbalife's share price fell from over $40 a couple of days before the presentation to $26 on Christmas Eve.

Herbalife is fighting back. Its managers deny Ackman's accusations and promise a detailed rebuttal soon. The company's shares have rallied, closing Friday at $37, a market capitalization of around $4 billion.

Herbalife is one of the world's best-known "multilevel marketing" companies, along with Avon and Amway. Hordes of independent individual sellers, many sporting badges with the slogan "Lose weight now. Ask me how," distribute its products. These sellers are recruited by people on a higher tier of the marketing structure, who receive a slice of the commission on sales made by those whom they recruit.

Multilevel marketing is a huge business. In 2011 direct selling (the vast majority of it through multilevel marketing) by about 16 million distributors generated sales of almost $30 billion in America, according to the Direct Selling Association, an industry group.

Multilevel marketers take pains to distinguish their businesses, which are legal, from pyramid schemes, which are not. In a pyramid, recruitment is everything. Multilevel marketing is not like this. Legitimate firms rely on sales of real products for their income, not on fees charged to new recruits. Ackman contends that Herbalife relies on recruitment, not sales of its products to genuine customers. Michael Johnson, Herbalife's chief executive, retorts that over 90 percent of product sales are outside its distribution network.

Ackman says Herbalife's marketing materials give a misleading impression of how easy it is to make money by selling its products.

Ackman is not always right, but he has made a pile of money by shorting overpriced firms such as MBIA, a bond insurer. His attack on Herbalife follows tough questioning of the company in May, shortly after its share price reached an all-time high of $73, by David Einhorn, another hedge funder who made a fortune by calling the housing bubble and financial crisis correctly.

Regulators so far have not reacted publicly to Ackman's accusations. Much may depend on Herbalife's detailed response at an event for analysts scheduled for Thursday. Analysts will want to see convincing evidence that most of its sales really are to people outside its network of distributors.