New Delhi, Oct. 17 -- Novo Nordisk has already conquered the world of weight loss. Millions use its powerful drug to shed pounds. Diabetes patients swear by it. Investors have made fortunes. But now, the Danish pharmaceutical giant is making a bet that could be even bigger-using the same blockbuster drug to treat Alzheimer's disease.

It's a gamble that could have astronomical upside and enormous risk. And we'll find out by the end of 2025 whether it pays off.

Last month, a senior executive at the company casually dropped what appears to be a bombshell during a conference in Vienna. Ludovic Helfgott, the executive vice-president for product and portfolio strategy, called the company's Alzheimer's trial a "lottery ticket"-uncertain, risky...