Firefly Value Partners said Jan. 17 that it wants Gulfport Energy Corp. (NASDAQ: GPOR) to buy back $500 million worth of shares, an action the hedge fund argues could help double the stock price of the natural gas and oil company.

The New York-based hedge fund, in a public letter, criticized how Oklahoma City-based Gulfport, which has a market capitalization of $1.5 billion, has allocated capital and complained that current board members may not be committed to pushing for improvements.

"The current board does not seem up to the task of fixing the company's capital allocation strategy and regaining investors' trust," wrote Firefly, which owns 8.1% of the company.

Its prescription for change begins with a call for share repurchases and a moratorium on issuing more shares, a practice that it says has diluted the company's value over the last years.

The hedge fund also wrote that it may be time to add a shareholder to the board who could energize the group to push for these changes.

"We propose an action plan that we believe allows Gulfport to create at least $9 per share of value for stockholders [over 100% of the current market capitalization] over the next 12 months," the letter said. Rising commodity prices would make the impact of the share buybacks even bigger.

The company's shares, which traded at $8.70 on the morning of Jan. 17, have tumbled 32% in the last year.

A Gulfport spokesman did not have an immediate comment.

This is the time of year investors who are pushing for change traditionally write public letters to companies that detail their complaints. Later they may run a proxy contest to seat newcomers on the board.

Firefly has been invested in Gulfport since 2013 and there have been private discussions, the hedge fund acknowledged.

A year ago the company authorized share repurchases of $200 million but stopped after having bought back $110 million worth of stock. Even if the program were revived, the buying would not "be nearly enough," the hedge fund said.

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Gulfport holds significant acreage positions in the Utica Shale of Eastern Ohio and the Scoop Woodford and Scoop Springer plays in Oklahoma.