There are no openly gay CEOs across the 1000 biggest US companies, according to the New York Times.

The newspaper reports that despite an upsurge in the percentage of the companies that have anti-discrimination policies, not a single chief executive has openly declared their sexuality.

Human Rights Campaign’s corporate equality index found this year that 91% of the 1000 biggest companies have non-discrimination policies in place, up from 61% in 2002.

Nancy Vitale, the chief human resources officer at Genentech, who is a lesbian, said: “It’s beyond anti-discrimination policy.

“It absolutely goes to — do people feel comfortable being themselves?”

Apple CEO Tim Cook topped Out Magazine’s power list three years in a row between 2011 and 2013, despite not having come out publicly.

He came second on this year’s list, edged out by TV host Ellen DeGeneres.

Deena Fidas, the director of Human Rights Campaign’s workplace equality program, said: “If we learned anything from the equal rights movements, it’s that legislation and policies are not enough.

“When a straight woman says, ‘My husband is out of town, I’m stretched this week’, it’s just a professional talking about her life.

“When a lesbian says, ‘My partner’s out of town’, it’s deemed unprofessional.”

“There has to be an actual culture of inclusion.”

The Human Rights Campaign’s research found that among all levels of LGBT employee, 53% had not disclosed their sexuality at work.