A big short is going long on the U.S. housing market.

Donald Mullen Jr., the former Wall Street executive who a decade ago helped oversee Goldman Sachs Group Inc.’s lucrative bet against the U.S. housing market, co-founded real-estate investment firm Pretium Partners LLC, which is raising $1 billion to buy single-family homes to rent out to tenants, according to fundraising documents reviewed by The Wall Street Journal.

Mr....