A new report from real estate data and analytics firm CoreLogic says that the number of U.S. homeowners in negative equity declined by 4 million homes in 2013, with 13.3 percent of homeowners, or 6.5 million homes, still underwater.  

Massachusetts fared better than the U.S. as a whole, with 10.9 percent of Bay State homeowners underwater. It ranked 26th among all states.

Most of the drop came in the first three-quarters of the year, with the number of homes in negative equity status staying almost flat between the third and fourth quarters. The national aggregate value of negative equity was $398.4 billion for fourth quarter 2013, compared with $401.3 billion for third quarter 2013, a decrease of $2.9 billion.

Of the 42.7 million residential properties with positive equity, 10 million have less than 20 percent equity. Borrowers with less than 20 percent equity, referred to as "under-equitied," may have a more difficult time obtaining new financing for their homes due to underwriting constraints. Under-equitied mortgages accounted for 21.1 percent of all residential properties with a mortgage nationwide in 2013.

More than 1.6 million residential properties, or 3.3 percent of mortgaged homes, have less than 5 percent equity, referred to as near-negative equity. Properties that are near-negative equity are considered at risk if home prices fall, the report said. In the Bay State, 2.5 percent of homes are at near-negative equity.

"The plight of the underwater borrower has improved dramatically since negative equity peaked in December 2009 when more than 12 million mortgaged homeowners were underwater," Mark Fleming, chief economist for CoreLogic, said in a statement. "Over the past four years, more than 5.5 million homeowners have regained equity, reducing their risk of foreclosure and unlocking pent-up supply in the housing market."

Nevada had the highest percentage of mortgaged properties in negative equity at 30.4 percent, followed by Florida (28.1 percent), Arizona (21.5 percent), Ohio (19.0 percent) and Illinois (18.7 percent). These top five states combined account for 36.9 percent of negative equity in the United States.

The bulk of home equity for mortgaged properties is concentrated at the high end of the housing market. For example, 92 percent of homes valued at greater than $200,000 have equity compared with 81 percent of homes valued at less than $200,000.