Elliott Investment Management has taken a $1 billion stake in Phillips 66 and is seeking as many as two board seats in a push to improve the company's performance, according to a Wednesday letter from the activist investor. Elliott's push for the board seats comes as Phillips has underperformed its competitors Marathon Petroleum and Valero . Elliott backed CEO Mark Lashier's plan to improve the company's performance. The CEO plans to do this through a more than $1 billion improvement in Phillips' refining segment, selling $3 billion in noncore assets and increasing the company's long-term capital return policy. Elliott said Phillips 66's stock has an upside of 75% from its last closing price of $118 if the company executes on these goals.

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Persons: Phillips, CNBC's David Faber, Elliott, John Pike, Mike Tomkins, Mark Lashier's Organizations: Elliott Investment Management, Phillips, Marathon Petroleum, Valero