The largest shareholder of Eli Lilly (LLY +1.57%) is selling 300,000 shares of the giant drugmaker, which would have a market value of $347 million (at the time of the announced sale).

The question for other Lilly shareholders, then, is, "Should you be selling too?"

And the answer is, "Absolutely not." For several reasons.

Not about the stock's growth potential

First, the shareholder in question is the Lilly Foundation, a tax-exempt private foundation established in 1968 and supported by donations from Eli Lilly. It owns about 9.6% of Lilly's outstanding shares, making it the largest shareholder.

And the sale is not being made because that foundation is suddenly bearish on Eli Lilly stock. Instead, it's a required annual charity payout. So, the sale, though rather large, has nothing to do with the stock's potential.

Second, Lilly is currently winning the race to dominate perhaps the biggest revolution in decades in pharmaceuticals. I'm talking about the rapid expansion of GLP-1 drugs. Late last year, Lilly's drug tirzepatide, which it markets as Mounjaro for diabetes and Zepbound for weight loss, became the world's best-selling drug, knocking Merck's cancer drug Keytruda out of the top spot.

Image source: Getty Images.

Morgan Stanley forecasts that the market for GLP-1 drugs will more than double to $190 billion between 2025 and 2035.

Finally, despite the 49% run-up in Lilly's share price over the past year, Wall Street sees additional upside. The average analyst price target for the stock is now $1,328, which is about 10% above the current price.

No, you shouldn't be selling Eli Lilly. You should be buying.