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

But wanting to buy a house and being able to afford one aredifferent, according to new research conducted for Bloombergby Zillow. Young homebuyers in some of the biggest U.S. cities maybe out of luck, regardless of their solid credit and the cashthey’ve socked away. In three of the 10 largest U.S. metro areas,fewer than half of the homes for sale on Zillow during thefourth quarter of 2014 were affordable to typical 23- to34-year-olds. In Los Angeles, fewer than a third were withinreach. To define affordability, Zillow used the median incomeof young adults in a given metro and assumed buyers would put5% down and spend 30% of their monthly income on mortgagepayments.

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

In fact, most of California is looking out of reach. Eightout of the 10 cities with the lowest share of affordable listingsin the fourth quarter of 2014 were in the Golden State. It’s notjust metros with reputations for being expensive, such as SanDiego (27%), San Francisco (36%), and San Jose (38%). More than 60%of the listings in Sacramento, Modesto, and Fresno wereunaffordable for most millennials. That’s likely a function ofshrinking supply—in all three cities there were fewer thanhalf as many listings at the end of 2014 as at the end of 2010—butit hammers home a key point about millennial homebuyers: They maybe ready to buy—financially, psychologically, biologically—butunable to afford the cities in which they hope to live.

So where can the typical local millennial afford the largestshare of for-sale homes?

Income, of course, isn’t the only factor that determinesaffordability. The Zillow data don’t factor in the cost of living,which may tilt the affordability equation in some cities. Studentdebt can make buying a home challenging for high earners.Meanwhile, working wages aren’t the only way first-time buyers getmoney for a home. Twenty-seven percent got cash gifts from friendsand relatives in 2013, according to the National Association ofRealtors. That leads to a distressing thought: New York and SanFrancisco may be in play if you have help from your parents. Ifnot, well, Akron is probably nice in the springtime.

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