Shares of Cooper Cos. rose Friday after activist investor Jana Partners urged the medical-devices company to search for a new CEO and evaluate the sale of of a major business segment.

Cooper Cos. stock gained 0.2% to $53.90 in premarket trading on Friday after ending Thursday down 1.5%. Shares of the maker of contact lenses have fallen 34% and have declined 16% over the past 12 months.

That stock underperformance was a reason why Jana Partners demanded the company "immediately initiate" an external search for a new CEO while also evaluating the sale of its women's health and fertility business, CooperSurgical.

"The path to rehabilitation as a public equity starts with a new CEO," the activist hedge fund wrote in a letter Thursday. "Investor trust has been broken, and we believe confidence in Cooper's CEO is beyond repair."

"If the board has the misguided belief that a CEO change is unnecessary, we suggest it review the performance materials we are separately providing," Jana Partners added.

Barron's chose Cooper Cos. a stock pick on Aug. 7. Shares have declined 26% since then as of the closing bell on Thursday. The stock has fallen 29% since closing at $76.73 on Aug. 19, and has sharply dropped below key moving averages.