AP

Shares of Botox maker Allergan PLC  (AGN - Get Report)   slipped slightly after a major challenge by a billionaire hedge-fund mogul to the drug company's management.

Billionaire David Tepper, president of hedge fund Appaloosa LP, fired off a letter Tuesday demanding the Dublin-based pharmaceutical firm separate the roles of chairman and CEO.

Following the release of the letter, Allergan's stock fell 0.4% Tuesday to close at $138.01. The stock has sliding since Jan. 28, when it traded at $158.65.

Tepper said an "independent chairman with extensive pharmaceutical experience" is needed, citing "moribund corporate performance" and "ill-considered initiatives ... for several years now."

In a statement, Allergan said it had received Tepper's proposal and would continue to "engage" as it would with "any shareholder who has input and constructive ideas."

The statement argued Allergan has a "strong long-term growth outlook" and a "highly promising R&D pipeline."

"The Board of Directors is committed to strong governance practices and independent board leadership," Allergan said in its statement. "The company has been executing its strategy to drive growth and value for shareholders as it transforms into a global biopharmaceutical leader."

Still, a new challenge to Allergan's Botox, which generates $3.5 billion in sales for the company, has made investors nervous.

Allergan's stock price slumped nearly 4% on Monday after the U.S. Food and Drug Administration gave a green light to a rival to Botox, a new wrinkle treatment by Evolus Inc. (EOLS) called Jeuveau.

Evolus had said it will offer its new treatment for 20% to 25% less than Botox.

Allergan on Jan. 29 launched a new marketing campaign for Botox, "Own Your Look," aimed at expanding its core customer base of women between 34 and 45 years old.

The new campaign will "address millennial women and men who are increasingly curious about aesthetic treatments," the company said in a press release.