Only two of the 50 largest U.S. cities are affordable for first-time home buyers, according to a new analysis that weighs average list prices against local incomes. 

The report on first-time home buyer affordability, released this month by the personal finance site NerdWallet, invokes an old rule of thumb: First-time buyers should budget to purchase a home priced at no more than three times their household income. 

That rule may seem unrealistic. But two cities, Pittsburgh and Cleveland, have enough affordable housing that average list prices total less than three times the median household incomes for younger adults in those cities.  

In the fourth quarter of 2022, the average Pittsburgh home listed for $214,011, which is 2.6 times the area’s median household income for younger buyers, $82,170. The income figure covers adults ages 25 to 44, the typical age range for first-time home buyers. 

The average Cleveland home listed for $199,410, which is 2.9 times that city’s median household income for new buyers, $68,897. 

Home prices have been ticking down, and the inventory of homes for sale has been rising. That’s good news for buyers, who find themselves with much more leverage now than a year or two ago.  

The bad news? Mortgage rates are sky-high, at least by comparison to the low-interest bonanza of the last several years. The average rate for a fixed, 30-year mortgage hovers between 6 and 7 percent. At the start of 2022, rates stood near 3 percent. 

The median sale price for an American home rose by more than two-fifths between 2020 and 2022, peaking around $468,000. 

NerdWallet launched its affordability analysis in 2020. Up to now, none of the largest cities rated as “affordable,” when comparing sale prices to incomes.  

“In most locations, looking only at homes with prices three times your income right now is unrealistic,” wrote Elizabeth Renter, senior writer and data analyst at NerdWallet. “Your search results would be nearly empty.” 

The latest analysis finds Los Angeles the least affordable large city, with the average home priced at $919,230, more than 10 times the city’s median household income among younger buyers, $88,020. 

The average home in New York — the whole city, not Manhattan alone — cost $664,386, seven times the buyers’ income of $94,423.  

Chicago homes listed at an average $329,491, four times the buyers’ income, $83,408. 

If you use an affordability multiplier of four rather than three, budgeting for homes that cost up to four times a first-time buyer’s income, then several cities start to look marginally affordable. 

The average Philadelphia home cost $327,524, less than four times the buyers’ income of $85,443. Baltimore homes listed at an average $335,641, which is 3.6 times the buyers’ income, $92,514. 

Nationwide, homes were listed at 5.4 times the median income for younger adults in the fourth quarter of 2022. The least affordable cities include San Diego, Miami, San Francisco and Las Vegas. More affordable: Buffalo, N.Y., Detroit, St. Louis and Indianapolis. 

“Our national average shows us that it’s pretty realistic for potential first-time home buyers to be able to find a house for roughly five times their income,” Renter said in an e-mail interview. “But California buyers would balk at that number; after all, the state is home to some of the least affordable markets.” 

List prices fell 5 percent nationwide and 3 percent in large cities in the last quarter of 2022, after adjusting for inflation. Only eight large cities saw home prices increase, and the gains were small.  

When the report compares home prices in late 2022 to the market of a year earlier, the results range all over the map, illustrating how much one local real estate market can vary from another. Between the fourth quarter of 2021 and the same time in 2022, average home prices fell by 11 percent in New Orleans, by 9 percent in Austin, Texas, by 8 percent in Denver and by 6 percent in Houston. But prices rose sharply in Milwaukee, Memphis and Miami. 

During the same time period, the number of homes listed for sale nationwide rose by 44 percent. In large cities, listings rose by 63 percent in that span. Large inventories of unsold homes work to the favor of potential buyers.  

As home sales data trickles in for 2023, “we’ll likely see prices lower than they were in 2022,” Renter said. Mortgage rates, on the other hand, “are likely to stay high.”