As home prices continue to soar, millennials now believe affordability is the biggest hurdle standing between them and homeownership, according to CoreLogic’s latest Home Price Index and HPI Forecast, published Tuesday.

In June, the average cost of a home rose by 6.8 percent year-over-year while the price of a single-family property inched up 0.7 percent between May and June, according to the California-based property analytics firm.

The upward spike has persisted, stubbornly, since 2012, according to the data.

“One-third of millennial renters reported feeling they cannot afford a down payment to buy a home,” said Frank Martell, president and CEO of CoreLogic, in a statement issued Tuesday. “With home prices rising quickly over the past few years and supplies low, first-time homebuyers face ever-growing challenges to find and buy affordable entry-level homes.”

Even with the NAR pinning the median price of a home at $264,800, CoreLogic predicts prices will increase 5.1 percent by June 2019. Such prices, coupled with inventory shortages, are leading many millennials to view the idea of owning their own home as increasingly unattainable.

Renter under the age of 29 were more likely to want to buy a home than many older respondents, yet 63 percent of millennials reported the high price of a down payment or mortgage costs were holding them back, according to the new analysis. By contrast, the majority of Baby Boomers who said they don’t want to buy reported they have no interest in purchasing at their current age.