Remember that philosophy-class question -- the one that goes, "If a tree falls in the forest and no one hears it, did it make a sound?"

In the corporate world, the question is: If a CEO abruptly resigns and the stock barely budges, does it really matter?

That's the issue at Alkermes (NASDAQ:ALKS), where David Broecker abruptly resigned as CEO, president, and director on Sept. 11. That day, the stock rose a mere $0.07 per share (or 0.7%).

Richard Pops, who held the CEO job for 16 years before becoming chairman in April 2007 when Broecker took over, resumed his previous position.

Partners depart
Besides the traditional "thank you for your service" comments, Pops said in the press release announcing the change, "Alkermes is an exciting company and David [Broecker] leaves it in a strong position." Um, maybe.

First, in March 2008, Eli Lilly (NYSE:LLY) told Alkermes that it was cancelling research and development of an inhaled form of insulin.

Second, last December, Cephalon (NASDAQ:CEPH) and Alkermes terminated their agreement for Cephalon to market Vivitrol, a once-a-month treatment for alcoholism. Vivitrol began sales in mid-2006, but had apparently been a big disappointment. As of the first quarter of fiscal 2010, which ended June 30, sales hadn't improved much under Alkermes' control.

Third, last month, Johnson & Johnson (NYSE:JNJ) told Alkermes it was dropping their project to create a once-a-month injectable version of the antipsychotic Risperdal Consta. J&J continues to sell Risperdal Consta, which also uses Alkermes' technology, and which is injected every two weeks.

Although Alkermes is working on other products, the triumvirate of setbacks leaves no margin for error. Manufacturing and royalty revenue from J&J for Risperdal Consta accounted for 77% of Alkermes' $47.5 million in revenue for the most recently completed quarter.

That's three big disappointments under Broecker's watch. However, it's hard to gauge the blame, because these projects were initiated when Pops was CEO.

Waiting for the FDA
Broecker also left with one big question unanswered -- a question that holds the key to Alkermes future.

In July, the Food and Drug Administration began reviewing a once-a-week version of the diabetes drug exenatide. Alkermes' contender seeks to improve on the convenience of Byetta exenatide, from Lilly and Amylin Pharmaceuticals (NASDAQ:AMLN), which is now injected twice daily.

If the FDA says "yes," Alkermes could enjoy a big payday, because clinical trials indicate the drug performs better than Januvia and Actos, from Merck (NYSE:MRK) and Takeda, respectively.

If the FDA says "no," or if it asks for more information or tests, Alkermes will have a hard time elevating its stock, which is down by one-third since before its setbacks began.

Alkermes needs a more diversified portfolio, and investors need a favorable FDA verdict on exenatide.

Is Alkermes a good investment now? Head on over to CAPS and give it a thumbs-up or -down. While you're there, add a comment as to why you think that way. It won't cost you a dime.

Fool contributor Robert Steyer doesn't own shares of any companies cited in this story. Johnson & Johnson is a Motley Fool Income Investor selection. The Fool has a disclosure policy.