Yep, it's another housing bubble

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Four months ago something troubling happened in the housing market. The home price affordability index tracked by the National Association of Realtors slipped below it's long-term trend line, marking a possible beginning of a housing bubble.

On Monday, we got the fourth month of home affordability data coming in below trend, which is a strong confirmation that the housing market is once again in a bubble. (The NAR index is published with a two-month delay, so the latest numbers are for July).

The affordability index measures the household income needed to qualify for a traditional mortgage on a median-priced single family home. So it's looking at a mortgage with a 20 percent down payment and a monthly payment below 25 percent of income at the currently effective rate on conventional mortgages.

When the index is at 100, that means that a household earning the median income has exactly the amount it needs to qualify for a conventional mortgage on a median-priced home. When it is above 100, it signals that the median income is higher than needed to qualify for a mortgage. An AI score of 130, for example, would indicate that households earning the median income would have 30 percent more income than needed to qualify.

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Rising interest rates and rising home prices put downward pressure on the affordability index, meaning homes are becoming less affordable. Rising incomes put upward pressure on the index, meaning homes are more affordable.

The index has been dropping rapidly since peaking in January at 210.7. We're now down to 157.8, according to the preliminary numbers released for July on Monday. Home prices have been rising and interest rates climbing, while wages haven't kept up. That's how we got to the lowest level of affordability seen since July of 2009.

According to the NAR, this shouldn't be dire news. A score of 157.8 officially indicates that a household earning the median income has 57.8 percent more income than needed to get a mortgage on a median priced home.

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Unfortunately, it's not clear that the index is very useful on its face. The index has never, in fact, dipped below 100 since the late 1990s. Even during the height of the last housing bubble, the indexes lowest score was 101—the affordability nadir hit in July 2006. This is what has led folks like Barry Ritholtz to declare the index "useless."

A recent paper by three economists from Robert Morris University in Pennsylvania, however, suggests that the index can be used to detect housing bubbles. Adora Holstein, Brian O'Roark, and Min Lu track the index against its long-term trend line. When the index falls below trend, it marks a possible start of a housing bubble. They suggest that when the monthly affordability index value falls below trend for at least three months, a housing bubble probably exists.

Using the monthly composite home affordability index from FRED, the database maintained by the St. Louis Federal Reserve bank, we can chart out every single monthly index report and construct a long-term trend line.

As the Robert Morris economists found, affordability fell below its long-term trend in the beginning of 2004—marking the beginning of the housing bubble. Homes remained below the long-term trend for affordability until December 2008.

This year affordability fell below the long-term trend in April. We remained below trend in the May, June and July reports.

If the Robert Morris economists are right about below trend affordability indicating a housing bubble, we're definitely there right now.

This does not mean that home prices are poised crash immediately. Keep in mind that home prices continued to climb for over two years after affordability fell below trend, peaking in April 2006. But it may mean that the Federal Reserve might need to start raising interest rates sooner than some expect in order to deflate our new housing bubble.

—By CNBC's John Carney. Follow me on Twitter @Carney