The Dow Jones industrial average was up 134 points, or 0.9 percent, at 14,733 as of noon eastern Tuesday, making up half of the 265 points it lost a day earlier.
Home construction topped 1 million last month, the highest level since June 2008.
Strong earnings from companies including Coca-Cola also propelled the market higher. Coke jumped 6 percent to $42.27.
The Standard & Poor's 500 climbed 16 points to 1,569, a gain of 1 percent.
The Nasdaq composite rose 37 points to 3,253, a rise of 1.1 percent.
Small company stocks rose even more than the broader market as investors moved money into riskier investments.
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