J.C. Penney’s board approved a “poison pill” designed to fend off potential takeover threats after hedge fund manager William Ackman acquired one-sixth of the retailer. The company’s shares fell 3 percent on the news.

The plan would go into effect if any Penney shareholder buys 10 percent or more of the stock, or if shareholders such as Ackman’s Pershing Square Capital Management LP that own at least that much buy more.

The threshold is just above the 9.9 percent stake that Vornado Realty Trust has disclosed that it holds in the retailer. According to a regulatory filing, Ackman has been building an alliance with Vornado at J.C. Penney.

“It does kind of stop them in the tracks from acquiring any more of the company,” Wall Street Strategies analyst Brian Sozzi said. The news also could be a negative for shareholders who bought J.C. Penney stock after Ackman’s stake was disclosed, Sozzi said.

“If I’m a shareholder, if you bought in right at the very top when all this Ackman news hit, he might not be buying any more and he might decide this is not worth his time and he might dump his shares.”

Wall Street Strategies has a stake in J.C. Penney and sold it last week, Sozzi said.

Should the poison pill be activated, each holder of common stock could exercise a right to buy a fraction of a preferred share, which would carry voting rights that would dilute Ackman’s stake, and prevent him from being able to control the company.

Ackman would be unable to participate in the rights plan if he acquired more common shares, according to a filing with the U.S. Securities and Exchange Commission.

Since companies began in the early 1980s to implement such plans, known as “poison pills,” no one has successfully challenged one, said Espen Eckbo, a professor at Dartmouth College’s Tuck School of Business.

“Most will think it’s too costly to break through the plan and get diluted,” he said.

Pershing Square earlier this month said it had acquired a 16.5 percent stake in Penney. On the same day, Vornado Realty LP disclosed a 9.9 percent stake in the company.

The rights plan expires on Oct. 14, 2011.

Ackman, Vornado and J.C. Penney could not immediately be reached for comment.

J.C. Penney is based in Plano, Texas, and operates more than 1,100 department stores.

Shares of J.C. Penney were down $1.05 at $32.82 in morning trading on the New York Stock Exchange.