Eli Lilly and Co. stock rose to a one-month high Tuesday after an analyst said the possible success of the company’s experimental Alzheimer’s drug could double the share price.

Lilly, based in Indianapolis, gained 3.9 percent, to close at $38.86 on Tuesday. They continued to rise Wednesday morning, climbing another 2 percent, to $39.63 each.

Expectations have been “extraordinarily low” for the success of Alzheimer’s drugs, so a Lilly success with solanezumab could boost the shares 50 percent to 100 percent, Tim Anderson, an analyst with Sanford C. Bernstein, said in a report.

“Eli Lilly and several of its competitors are willing to spend hundreds of millions of dollars on what is essentially a massive lottery ticket,” Anderson said. “If their drugs are successful in delaying the progression of Alzheimer’s disease, they could end up making Lipitor look like a mid-sized product,” he said in a note to clients sent Monday. Sales of solanezumab could reach $9 billion by 2020, he said.

Solanezumab is an antibody designed to clear protein fragments called beta amyloid that clutter the brains of patients with Alzheimer’s disease. Pfizer Inc., Johnson & Johnson and Elan are testing bapineuzumab, a similar drug.

Anderson cautioned that the drug’s chances of success are only 10 percent to 20 percent. Because of the large potential payoff, drugmakers have been willing to gamble on the medicines.

A leading theory of the disease is that amyloid causes the disease by harming brain cells. Debate over whether the theory is correct has increased as other drugs that target the protein have failed or shown murky results in trials. In August 2010, Lilly stopped development of a pill, semagacestat, that blocked amyloid by another mechanism, after trials found it didn’t slow disease progression.

As many as 5 million Americans have Alzheimer’s disease, according to the U.S. Centers for Disease Control and Prevention in Atlanta. Alzheimer’s is a degenerative neurological condition with no approved treatment to slow brain cell death.