By David Benoit And Suzanne Kapner 

Macy's Inc., in the eyes of some investors, should worry less about selling shoes and dresses and more about selling its real estate.

Activist investor Starboard Value LP on Wednesday said it had accumulated a stake in Macy's and is pushing the 157-year-old retailer to spin off its real-estate holdings. Starboard estimates that the move could boost Macy's share price by more than 70%.

Shares of Macy's rose 7.9% Wednesday, its biggest percentage gain since November 2013.

Other investors have been urging Macy's to find ways to extract value from its vast real-estate holdings, which comprise more than 800 stores it either owns or leases across the country, including its famous Herald Square location in New York City. Starboard Chief Executive Jeff Smith valued Macy's real estate at $21 billion. Before Starboard's disclosure, Macy's market value was $22.5 billion, meaning its retail operations weren't highly valued by investors.

Starboard, a fund managing roughly $4.8 billion, believes the company could separate its real-estate in strong-performing malls and enter into lucrative sale-leaseback transactions with its trophy properties, which in addition to Herald Square includes stores in Union Square in San Francisco and on State Street in Chicago.

Mr. Smith didn't disclose how big of a stake Starboard has taken, or when it was made. Speaking at a conference in New York Wednesday he said that while he was hopeful Macy's management was willing to work with him, Starboard was prepared for a fight.

Macy's said it is evaluating all options for its real-estate portfolio and the effect it would have across its operations. "We recognize the potential attractiveness of real-estate investment trusts and similar alternative real estate ownership structures in today's marketplace," Macy's said.

The company said it has worked to maximize shareholder value through share repurchases, increased dividends and continued investments in its business. Since 2009, Macy's shares have appreciated 504%, outpacing the 110% gain of the Dow Jones Industrial Average.

Still, slow sales growth has left Macy's exposed to demands for better returns. Sales at existing Macy's stores increased 1.4% in 2014, down from 2.8% in 2013 and 4% in 2012.

Macy's joins a slate of other big-name American companies, including chemical maker DuPont Co. and tech company Hewlett-Packard Co., that have fallen into the cross hairs of activists who typically push management to make radical changes, such as breaking apart into separate businesses or bringing in new leadership.

Activists have long had their eyes on the retail sector but with mixed results. William Ackman's Pershing Square Capital Management LP had high-profile runs at Target Corp. and J.C. Penney Inc. Both ended badly. Mr. Ackman lost more than $600 million in a failed turnaround for Penney and emerged the loser of a proxy fight at Target.

On the other hand, Jana Partners LLC made out well with its investment in PetSmart Inc., after it pressured the retailer to put itself up for sale. And Starboard successfully pushed Staples Inc. and rival Office Depot Inc. into a merger, a deal that is still awaiting regulatory approval.

With Macy's, Starboard is going back to an old theme: real estate. Recent moves by Hudson's Bay Co. and Sears Holdings Corp. to sell properties and lease them back have resurrected an old investment idea: that much of the value in retail lies in the bricks and mortar.

Splitting a retailer into an operating company and a property company makes it easier to see the value of the property and provides owners of the property company with a sort of insurance in case the retail business falters.

But Macy's would no longer have full control to react to a fast-changing market by closing, expanding or remodeling stores. It also would be saddled with lease payments, and executives would rather spend the money improving the underlying retail business, people familiar with the company have said.

"We like having control of our real estate," Karen Hoguet, Macy's chief financial officer, said in March.

Spurred by the recent Hudson's Bay and Sears deals and prodding from investors, Ms. Hoguet softened her stance in May when she told analysts that the company was working with its bankers to study all options. "If something would make sense, we obviously would do it," she said at the time.

Starboard Wednesday pushed back on concerns about control, saying leases and transactions can be done in a way to keep Macy's in control.

"In our conversations with them, we think they are receptive to looking into it," Mr. Smith said at CNBC's Delivering Alpha conference.

Starboard's effort has allies among other Macy's investors. HG Vora Capital Management LLC founder Parag Vora said his fund has held talks with Macy's management to consider options for its properties and that he was "pleased to see them moving in the right direction."

Veteran real-estate investor Eduardo Abush, whose Waterfront Capital Partners LLC counts Macy's as one of its top three positions, said the retailer is undervalued because its real-estate portfolio hasn't been recognized fully.

"This has been an evolution for the company, where they didn't give any credit to the notion of doing anything with real estate, to slowly mentioning it in a call, to referencing it again," said Mr. Abush. "It's become a drumbeat."

Macy's management is searching for ideas beyond its traditional department stores. The retailer plans to wade into the discount market this fall when it is scheduled to open six Macy's Backstage stores that will sell low-price goods. In February, it agreed to buy Bluemercury Inc., a chain of beauty stores, and it is looking to expand overseas.

Starboard is one of the most active of activists, launching new investments at a rapid clip. It has shown a willingness to target large companies ranging from Yahoo Inc. to Staples even with only small stakes.

It recently succeeded in pushing a similar move at restaurant operator Darden Restaurants Inc., a plan put in motion after Starboard threw out the entire board of Darden in a shareholder vote last year. Its victory over the Darden board, which resulted in Mr. Smith becoming chairman, garnered it widespread attention. Since that October shareholder vote, Darden shares are up nearly 50%.

Juliet Chung contributed to this article.

Write to David Benoit at david.benoit@wsj.com and Suzanne Kapner at Suzanne.Kapner@wsj.com

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