The company bought 4,448 rental apartments in Texas and Florida. : (Bloomberg)—Starwood Capital Group, the investment firm led by billionaire Barry Sternlicht, is stepping up its investments in affordable apartments as demand for cheaper housing soars across the U.S. The company bought 4,448 rental units mainly in the Dallas-Fort Worth area, in Houston and across Florida, Starwood said in a statement Monday. Terms weren’t disclosed.