Some billionaire hedge-fund managers buy sports teams. Richard Perry snapped up one of New York’s most influential luxury department-store chains. Perry’s passion project — Barneys New York Inc. — filed for chapter 11 protection yesterday with plans to close 15 of its 22 stores and with new financing that gives it time to find a buyer, the Wall Street Journal reported. Barneys’ troubles reflect the litany of woes hurting retailers across the U.S.: The company faced a sky-high rent increase and ran into difficulty navigating the rise of e-commerce. The unraveling of Barneys is a blow for Perry, who developed a personal interest in the fortunes of the nearly century-old company known for taking chances on little-known designers. Perry’s hedge fund gained control in 2012 by swapping its debt for equity. All in, Perry Capital invested less than $300 million, a fraction of what it once managed. Perry shuttered his fund in 2016, though it continues to hold several less liquid assets, including the Barneys stake.