WASHINGTON — As home prices rise, so do concerns that a new housing-market bubble may be appearing, particularly in cities with double-digit annual growth rates.

Are there red flags in recent data?

“I wouldn’t say that we have bubbles today. But if prices keep rising at these rates, pretty soon you will be in bubble territory,” said Dean Baker, co-director of the Center for Economic and Policy Research, a Washington think tank. “Generally, you don’t see situations with rapidly rising prices and they just stop.”

Before the bubble burst, year-over-year price growth was about 17 percent. The current rebound has yet to reach such a frenzied pace, though home prices recently posted year-over-year growth of 12 percent, the fastest rate since 2006, according to the Case-Shiller index that tracks 20 cities.

Many of the cities with the largest price gains are where housing crashed hardest when the bubble burst. For example, Las Vegas home prices recently posted year-over-year growth of 22 percent, but remain more than 50 percent below a 2006 peak, according to the most recent S&P/Case-Shiller report. Prices in both Phoenix and Miami are also more than 40 percent below local peak levels in those cities, despite recent price jumps.

“What’s important to keep in context is that those double-digit gains are off of very low prices. Even with those gains, prices are still relatively low,” said Frank Nothaft, chief economist at federally controlled mortgage buyer Freddie Mac.

Tight inventory, pent-up demand and investors have supported price gains. Despite those gains, prices are 26 percent below peak levels, according to Case-Shiller’s 20-city composite index. Take San Francisco, for example, where inventory is lean and competition is fierce between would-be buyers. Among the 20 cities tracked by the Case-Shiller index, San Francisco recently posted the fastest year-over-year growth, hitting just under 24 percent. Yet even there, prices are 26 percent below peak.

Looking forward, such large price gains are unsustainable, especially as rising mortgage rates cut affordability and income growth plods along. At a certain point, rapidly rising prices mean investors looking for high rates of return will be less interested. With fewer investors, first-time buyers and others may have a better shot at participating in some of the hottest markets. Rising prices also encourage greater home construction, which expands inventory levels and eases some pressure on prices, though builders have complained about a deteriorated infrastructure making it tough to ramp up work.

Jed Kolko, chief economist at real estate site Trulia, compared current prices with historical prices, incomes and rents, and found that home prices were 7 percent undervalued in the second quarter, compared with being overvalued by a peak of 39 percent in the first quarter of 2006.

“Even with the recent price increases, home prices nationally remain undervalued relative to fundamentals and much lower than in the last bubble. That’s why today’s price gains are actually still a rebound, not a bubble,” Kolko said in a blog post.

But is housing affordable?

In a healthy market, owning a home should be within reach for a typical family, economists say.

A gauge from the National Association of Realtors, a trade group, indicates that affordability has declined 18 percent since January, hitting 172.7 in May, but is 17 percent above its average in the past decade. A reading of 100 means that a household with median income would have exactly enough income to qualify for buying a median-priced existing single-family home.

Separate analysis from CoreLogic recently found that Hawaii and the District of Columbia were unaffordable, while other pricey areas were near peak affordability.

In an alternative view of affordability, Trulia’s Kolko calculates the gap between the cost to buy versus rent, including items such as maintenance, insurance and mortgage payments. For June, he found that it was about 40 percent cheaper to buy a home than rent, compared with 46 percent cheaper in March 2012. Back in September 2006, it was 15 percent more expensive to buy than to rent.

“Because mortgage rates are still near long-term lows, and because prices fell so much after the housing bubble burst and remain low relative to rents even after recent price increases, buying is still much cheaper than renting,” Kolko said in a blog post. “Mortgage rates would have to rise a huge amount — to 10.5 percent — to tip the math in favor of renting.”

The presence of large numbers of troubled properties also differentiates the current housing market from those in the past. While shadow inventory — which includes properties with seriously delinquent mortgages, in foreclosure or held by mortgage servicers — has been declining, it remains relatively high.

Shadow inventory dropped to about 2 million homes in April from a peak of 3 million in early 2010, but far higher than 650,000 in early 2006, according to CoreLogic. Fewer distressed homes, which are sold at a discount to other properties, means that year-over-year price comparisons are skewed up. As distressed homes work their way out of the system, this effect will decline.

For those who are dubious about the housing market’s health, here’s one potential red flag: House flipping is back.

So far this year about 250,000 single-family homes have been sold that were also sold within the prior 12 months, according to RealtyTrac, an online foreclosure marketplace. If that pace is maintained, there could be about half-a-million flipped homes by the end of the year, up 4 percent from last year and almost double the total in 2005.

“Yes, there is a red flag. High levels of flipping are indicative of a market that is speculative and at risk of becoming overheated,” said Daren Blomquist, vice president at RealtyTrac.

But Blomquist said the high level of flipping is likely a short-term trend given recent flipping dropoffs in areas such as Southern California, Phoenix and Las Vegas.

“If that pattern is repeated in other parts of the country in the next six to 12 months, then it will be a sign the market is not getting overheated,” Blomquist said. “However, if flipping continues at a high level, then it could indicate another housing bubble forming in some markets.”