Shares of Arlington-based Graham Holdings jumped Friday after the company announced plans to spin off Cable One, which provides television, telephone and Internet service in 19 states.

The company has been mum on its intentions for Cable One should regulators approve plans to make the business unit a separate publicly traded company, but speculation about the prospects prompted investors to pounce.

Graham Holdings, which trades as GHC on the New York Stock Exchange, closed Friday at $878.87, up 10.8 percent.

“The separation will position Graham Holdings to pursue continued growth opportunities, while enabling Cable One to focus entirely on its video, Internet and voice services and to attract a more natural stockholder base,” Donald E. Graham, chairman and chief executive, said in a statement.

The decision to spin off Cable One, one of Graham Holdings’ largest and most secure business units, marks a departure from executives’ previous remarks that they intended to hold on to well-performing businesses, said Liang Feng, an equity analyst at Morningstar.

Turning Cable One into an independent company opens the door for a potential sale or for raising money and growing its subscriber base, speculation that Feng said is probably contributing to the company’s elevated stock price.

“If Graham Holdings were to spin off Cable One and make no changes in the capital structure or no changes on their willingness to sell, I think investors who have pushed this [stock price] up might be a bit disappointed,” Feng said.

A spokeswoman for Graham Holdings declined to comment.

Revenue from the cable division was $600.4 million for the first three quarters, down 1 percent compared with $607.1 million during the corresponding period last year. The company counted 694,236 customers as of Sept. 30, a 2.6 percent decline from its 712,424 customers a year ago.

Nevertheless, operating income for the cable division ticked up 6 percent to $128 million for the first nine months of the year.

Graham Holdings is pressing forward after selling The Washington Post and its affiliated publications last year to founder Jeffrey P. Bezos for $250 million. The newspaper had been its flagship business for decades and a passion of Graham’s.

In addition to Cable One, Graham Holdings is best known for its ownership of for-profit education company Kaplan, the online site Slate and a collection of television stations. In recent years, the company acquired two home-health-care companies, a manufacturer of construction jacks and a provider of combustion equipment.

Graham named his son-in-law and former LivingSocial chief executive Timothy O’Shaughnessy president of Graham Holdings in October. He started this month.

“It’s time for a new story,” Graham told employees in October. “This has always been the company that owned The Washington Post; that’s no longer us. But we’ve got something amazing and special for the future.”