SYDNEY—Hedge funds looking for the next housing bubble think they have found it—in Australia—and they are wagering more than $6 billion that the country’s banks will feel the pain.

Australia’s biggest banks are among the most profitable in the world. And investors have wrongly bet against Australia’s property market before. But the shorts think the housing market is closer to a downturn this time around, one that would add to the pain of rising bad debts and falling earnings.

...