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Since the depths of the financial crisis, housing prices across the U.S. have been on an incredible rebound. But three states stand far above the rest when it comes to the risk that those prices may once again come tumbling down.

The fall and rise
As shown below, housing prices in the U.S. saw a meteoric rise and fall in the last decade. But after the calendar turned from 2011 to 2012, the average home price -- as measured by the Case-Shiller index -- has continued to rise:

Source: S&P Dow Jones Indices.

After the 30% dip in housing prices, many individuals remain weary and on guard about the prospect of the prices of their houses once again plummeting.

The riskiest states
Every three months, Arch Mortgage Insurance releases its Housing and Mortgage Market Review. It examines the odds that housing prices in specific states and cities will fall within two years, known as the Arch MI Risk Index.

It gauges things like unemployment, housing affordability, average income, and other economic data to try to gauge which cities and states present the biggest risk of housing prices falling.

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There are different levels of risk. Yuma, Arizona was the riskiest city, with a score of 65 -- meaning there is a 65% chances prices will be lower in two years' time -- whereas Iowa City was one of five cities with a score of just 1.

The odds home prices will fall across the U.S. stood at just 15%, an improvement of 4 percentage points relative to last year.

And while the three states shown in the slideshow below have also seen improvement over where they stood a year ago, currently they all have twice the risk of downside versus the nation as a whole. In fact, one state has more than half of the top 25 riskiest cities in the country.

Check out the slideshow below to see what states -- and cities within those states -- have the biggest risk of seeing their home prices fall over the next two years.

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The 3 Riskiest States to Buy a House from The Motley Fool

Patrick Morris owns shares of Apple and Bank of America. The Motley Fool recommends Apple and Bank of America. The Motley Fool owns shares of Apple and Bank of America. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.

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