Shares of Hess (HES) surged 9% Tuesday to close at $68.11 after activist investor Elliott Management published a letter to shareholders saying that the oil and gas company's share price could surge to $126 per share if it were managed well.

Elliott, which took up a 4% stake in Hess this week, making it the company's largest independent investor, also said in its letter to shareholders that it "strongly advocates for Hess to conduct a full strategic and operational review to consider all pathways to maximize shareholder value."

Elliott, run by billionaire Paul Singer, argued that Hess lacks focus. It acts like a major oil and gas company, but since it's much smaller it cannot compete: "Hess is less than 1/11th the size of the majors it lists as its proxy peers. It is 1/23rd the size of Exxon (XOM) and 1/12th the size of Chevron (CVX). By definition, if Hess spreads itself as broad as a major with a fraction of the resources, it simply does not have the wherewithal to compete."

The hedge fund suggested Hess to spin off its Bakken shale assets and its downstream retail and marketing holdings, splitting the company into three parts as a consequence. The fund asserted that such a move would create additional value for shareholders.

Elliott is also seeking the nomination of five new independent directors to the Hess board. "New directors are needed for real change," the fund said in the letter. The candidates include Rodney Chase, former deputy chief executive of BP (BP); Harvey Golub, former chief executive of American Express (AXP); Karl Kurz, former chief operating officer of Anadarko Petroleum (APC); David McManus, a former executive at Pioneer Natural Resources (PXD); and Marshall Smith, the chief financial officer of Ultra Petroleum (UPL).

The hedge fund's letter comes just a day after Hess announced a set of restructuring and asset-shedding plans. Likely forced into action after hearing of Elliott's activist intentions last week, Hess announced that it would sell its network of oil-storage terminals and its refinery in Port Reading, New Jersey, by the end of February.

Hess would effectively leave the refinery business and become a predominantly exploration and production-based business, joining others such as ConocoPhillips (COP) and Marathon Oil (MRO), who have also exited the refining sector. Hess jumped 6.1% to close at $62.48 on Monday on the news.

"By closing the Port Reading refinery and selling our terminal network, Hess will complete its transformation from an integrated oil and gas company to one that is predominantly an exploration and production company and be able to redeploy substantial additional capital to fund its future growth opportunities," said John Hess, the company's chairman and CEO, in a statement Monday.

According to Barclays, Hess's fuel terminals could sell for between $1.5 billion and $2 billion, as they are situated along New York Harbor and other areas along the East Coast, where real estate prices are high, reports the Wall Street Journal.

As of late Monday afternoon, Hess seemed intent to hold on to its downstream assets, potentially setting up Hess management for a clash with Elliott. Hess spokesperson Jon Pepper told Bloomberg Monday that the company "plans to continue its long-term commitment to the retail and energy marketing business."

When reporting quarterly results Wednesday, Hess said that over 90% of its capital would be in its exploration and production business following its exit from refining, Reuters reported.

Hess posted a profit of $566 million, or $1.66 per share in the fourth quarter, compared with a loss of $131 million, or 39 cents per share, a year earlier. Revenue rose 10% to $9.69 billion. Also, oil and gas production rose 8% in the fourth quarter. Specifically, production from its Bakken shale assets soared 68%.

If investors' response to the recent flurry of news is any indication, however, Elliott, which succeeded in adding two new board members to BMC Software (BMC) last year, is more than likely to get its way.

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