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Of nearly 49 million mortgaged properties in the United States at the end of the third quarter, there are 6.4 million where the mortgage amount is greater than the value of the property. These underwater or negative equity properties represent 13% of all mortgaged properties in the U.S. It is an improvement from the 14.7% of underwater properties at the end of the second quarter and 19.8% at the end of the first quarter, however.

The data was released Tuesday by research firm CoreLogic Inc. (NASDAQ: CLGX).

The aggregate value of negative equity fell by $33.7 billion in the third quarter to a U.S. total of $397 billion, split almost evenly between first mortgages and first liens with home equity loans. According to CoreLogic, if home prices rise by 5%, another 1.2 million homes will no longer be underwater on their mortgages.

Nearly 10 million properties have positive equity below 20%, and 3.2% had less than 5% positive equity at the end of the third quarter.

CoreLogic’s CEO noted:

We should see a further rebound in consumer confidence and economic growth in 2014 as more homeowners escape the negative equity trap. Home price appreciation has helped more than 3 million property owners regain equity since the first quarter of 2013.

The five metropolitan areas with the highest percentage of properties with negative equity are Orlando-Kissimmee-Sanford, Fla., (32.3%); Tampa-St. Pete-Clearwater, Fla., (30.1%); Phoenix-Mesa-Glendale, Ariz., (23.2%); Riverside-San Bernardino-Ontario, Calif., (20.8%); and Chicago-Naperville-Arlington Heights, Ill. (20.5%).

The five with the highest percentage in positive equity are Houston (95.8%); Dallas (95.3%); Anaheim-Santa Ana-Irvine, Calif., (94.6%); Portland-Vancouver-Hillsboro, Ore., (93.4%); and Seattle (92.7%).

The five states with the highest percentages of homes with positive equity are Alaska (96.1%), Texas (96.1%), Montana (95.8%), North Dakota (95.7%) and Wyoming (95.4%). The five states with the highest percentage of homes with negative equity are Nevada (32.2%), Florida (28.8%), Arizona (22.5%), Ohio (18%) and Georgia (17.8%).