(Bloomberg Business) -- In the aftermath of the housing crisis, it seemed like millennials might give up on homeownership in favor of a lifetime spent renting squalid apartments in gentrifying urban centers. Fears of that grim scenario have mostly passed, and it’s not uncommon to hear of young faces at open houses, or to read surveys in which renters say they’re finally ready to fork over a down payment.

But wanting to buy a house and being able to afford one are different, according to new research conducted for Bloomberg by Zillow. Young homebuyers in some of the biggest U.S. cities may be out of luck, regardless of their solid credit and the cash they’ve socked away. In three of the 10 largest U.S. metro areas, fewer than half of the homes for sale on Zillow during the fourth quarter of 2014 were affordable to typical 23- to 34-year-olds. In Los Angeles, fewer than a third were within reach. To define affordability, Zillow used the median income of young adults in a given metro and assumed buyers would put 5% down and spend 30% of their monthly income on mortgage payments.

In Chicago, where builders are keeping pace with migration, young homebuyers are likely to find plenty of affordable units to choose from. In Los Angeles, not so much.