The average house in Melbourne is around A$500,000, which is among the most expensive in the world. In a bid to help first home buyers, the Baillieu government plans cut stamp duty by 50 per cent (according to First Time Buyers Struggling to Keep Up). This is clearly a bad move as it will only increase the demand for houses which will in turn increase prices even more. Those buying houses at a time like this may think they are better off with a stamp duty discount, but with house prices and mortgage interest rates at record highs, it will likely put a lot of stress on home owners. Expect banks to make more money out of this.
My advice to first home buyers is to live with your parents for longer and to pay them rent. Usually parents are willing to charge lower rent to their children because they have been living with you for decades and know that you are trustworthy tenants. With the money you save from living with parents you could take advantage of the high Australian dollar and invest in overseas companies or you could buy shares in Australian banks.
If Australians continue to want to buy houses, this will only result in more bank profits as perpetual demand for housing will result in perpetually rising house prices, which will mean home buyers will need to go into more debt to fund their purchases. Greater demand for debt will mean that banks are able to charge higher prices for mortgages. They can increase interest rates or charge higher fees. This should lead to greater profits, all else equal, will lead to greater shareholder return.
If you want to invest in an Australian bank, I recommend one of the big four: Commonwealth Bank, Westpac, ANZ, or NAB.