Greenlight Capital, the hedge fund firm led by David Einhorn, made a new investment in Macy’s Inc. in the fourth quarter, arguing the retailer could become a takeover target, according to a letter to investors that was obtained by Bloomberg.

A private equity firm and a real estate investment trust could team up to purchase the company and "unlock the value" of its land and buildings, Greenlight said in the letter, which was dated Tuesday. Shares of Macy’s jumped as much as 5.6 percent on the news.

In discussing a real estate deal, Einhorn echoes remarks from activist investor Starboard Value, which has been pushing for Macy’s to tap its properties since July. While Macy’s rejected that idea last year, the math may have changed after the shares lost more than half their value from a July high of $72.80, the New York-based hedge fund firm wrote.

“Even if this doesn’t happen, the shares are cheap,” wrote Greenlight, which established its position at an average price of $45.69.

Macy’s rose 3.4 percent to $39.15 at 12:07 p.m. in New York. The retailer’s real estate, including its flagship store in Manhattan, is worth $21 billion, according to Starboard’s analysis. That’s more than the company’s current enterprise value.

A leveraged buyout wouldn’t be a first for Macy’s. Edward Finkelstein, then CEO of the retailer, orchestrated a takeover in the ’80s with high-profile investors. That deal sputtered, and the chain filed for bankruptcy in 1992. It later merged with Federated Department Stores Inc., which itself had filed for bankruptcy after an acquisition by Canadian financier Robert Campeau in 1988.

E.ON, Mylan

Greenlight also said it established a new position in German power and gas producer E.ON SE, one of Europe’s largest utilities, saying investor confusion about its earnings and nuclear waste disposal will be alleviated in 2016. The hedge fund purchased a position in drugmaker Mylan NV on expectations that its pipeline of drugs and stock buybacks will boost shares.

Greenlight’s main fund lost 20.2 percent in 2015, its second-worst year since Einhorn started the fund in 1996. Even after that loss, Einhorn has made an average of 16.5 percent a year for the fund’s investors, the firm said in the letter.

"We have never had a year where so little went right," the firm wrote in the letter. "While we had a few shorts that did well, we couldn’t seem to find winning longs."

Greenlight sold its remaining position in chipmaker Micron Technology Inc., which was its biggest winner in 2014 and biggest loser in 2015. All told, the firm realized a gain after buying shares at an average of $19.93 and selling them at an average of $22.14.

It also exited wagers on semiconductor company Applied Materials Inc., Bank of New York Mellon Corp. and Cairn Energy Plc, an oil and gas exploration company. The hedge fund firm covered a short position in chip designer ARM Holdings Plc, the letter said.