Employees said Kelvin made “sexual innuendos at staff,” stroked people’s necks, took off his shirt and openly talked about his sex life. When the petition — which quickly drew thousands of signatures — first circulated, the company said Kelvin often greeted shareholders, investors, customers and colleagues with hugs. The company also said it had “clear and robust” HR policies in place, including a 24-hour help line for confidential and anonymous tips.

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David Bernstein, Ted Baker’s executive chairman, said that since Kelvin started the company, he has been the “driving force” behind the global brand. Kelvin opened the first Ted Baker store in Glasgow, Scotland, in 1988. Last year, the Tatler estimated Kelvin’s worth at more than $660 million.

“We are determined to learn lessons from what has happened and from what our employees have told us and to ensure that, while the many positive and unique aspects of Ted’s culture are maintained, appropriate changes are made,” Bernstein said in a statement.

Lindsay Page, who has served as the company’s acting chief executive, will continue to lead the company.

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In a statement, Kelvin said he had decided to step away from the company “so it can face 2019 with fresh energy and renewed spirit.” He wrote that the past few months have been “deeply distressing” and that he would be taking time privately with his family to consider what the future may include.

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Ted Baker responded with a two-pronged approach, said Timothy Coombs, a crisis communication expert at Texas A&M University. In addition to Kelvin stepping down, the company said it would specifically work to improve a company culture tainted by the allegations against him. That second step, Coombs said, is essential if Ted Baker wants to show investors that it is taking lessons away from Kelvin’s downfall.

Customers are less likely to shop elsewhere based on Kelvin’s alleged misconduct, Coombs said. But investors may be wary of whether a new leadership team could make for a bumpy transition or affect the brand’s worth. Midday Monday, Ted Baker’s stock was up nearly 3 percent.

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“That’s what investors are worried about: If there’s a big shake-up, is this going to be a problem?” Coombs said. “Is this going to cause a loss of stock value?”

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Over the past few years, several retail executives have been accused of sexual harassment or misconduct at work. Last year, model and actress Kate Upton accused Guess co-founder Paul Marciano of sexual harassment. An investigation looked into broader allegations, including inappropriate comments and texts, as well as unwanted kissing and groping. Marciano eventually resigned.

In 2017, Mark Light, the chief executive of Signet Jewelers, said he was retiring for health reasons. At the time, Light was the subject of a class-action arbitration in which 69,000 women who worked at Sterling Jewelers, a company subsidiary, said they received unequal pay and promotions.

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And in 2014, Dov Charney was ousted from the top of American Apparel over sexual misconduct allegations and misuse of company money. A decade earlier, a writer for Jane said Charney engaged in oral sex and masturbated in front of her. Charney was also reported to have worn only underwear in front of employees.

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Chief executives who were also founders often have an “outsize shadow” on the companies they run, said Kirthi Kalyanam, director of the Retail Management Institute at Santa Clara University in California. Those founders can dominate company culture, Kalyanam said, which can make overhauling that culture all the more complicated.

Any investigation into Kelvin’s conduct should also look into whether other executives knew about these allegations and hid them, Kalyanam said. He pointed to reports that casino managers around magnate Steve Wynn concealed allegations about him for decades.