PepsiCo shares popped Tuesday after Elliott Investment Management took a significant stake as the activist investor sees a "rare" and "historic" opportunity for a turnaround in the iconic soft drink giant.

Shares of PepsiCo climbed as much as 5% in morning trading before cutting gains to 2.4%. The stock was down about 2% this year before Tuesday's pop, significantly lagging the broader market as well as its rival Coca-Cola .

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The Paul Singer-founded Elliott's bet in Pepsi is worth $4 billion, becoming the consumer giant's top five active investors excluding index funds, according to FactSet. The activist investor sent a presentation and letter to Pepsi's board of directors Tuesday, detailing a clear agenda focused on restoring business momentum.

"While unfort

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