In spite of falling housing prices, it still is as unaffordable to buy a house as it was during the height of the housing boom, according to a new study.

Even though housing prices and mortgage interest rates have hit record lows, buying a house still is as expensive as it was in 2007 -- when housing prices were astronomical -- because banks are requiring heftier down payments and have stopped letting borrowers make low initial payments, according to a recent study by Andrew Davidson and Alexander Levin of Andrew Davidson & Co., a financial research firm. (H/t the Wall Street Journal.)

Among non-agency loans, the total cost of buying a house (as a percentage of property value) has barely fallen since peaking in 2008 because the "equity cost" -- that is, the down payment -- has spiked since 2006 and stayed elevated, according to the study. Among non-agency loans, the "equity cost" of buying a house (as a percentage of property value) cost more between 2009 and 2011 than at any other time since the new millennium. The "equity cost" for all borrowers has more than doubled since 2006, according to the study.

So much for housing affordability.

This study demonstrates that the reality of the housing market is more complicated than it seems. Previous studies have found that homeownership now is cheaper than renting -- if you can afford it. Renting cost 15 percent more than homeownership at the end of last year, according to recent research by Deutsche Bank cited by the Wall Street Journal. Buying a house is also cheaper than renting in 98 of the 100 largest metropolitan areas, according to research by Trulia, a real estate website.

The 30-year mortgage interest rate hit record lows in May, according to Freddie Mac. That is largely thanks to efforts by the Federal Reserve to bring down interest rates to boost the economy. Housing prices also have continued to fall across the country, according to the S&P/Case-Shiller Home Price Indices. But homeownership still is a distant dream for many.