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NEW YORK — Stocks broke a five-day losing streak Wed nesday as hope spread that China and the U.S. are taking convincing action to restart their economies.

Prices for key commodities such as oil and copper also soared, lifting shares of industrial companies that included Alcoa Inc. and Caterpillar Inc.

Speculation that China will unveil more government spending this week on major construction projects drove up worldwide prices for raw materials and the companies that produce them.

In Washington, the Obama administration announced details of a plan that could help struggling U.S. homeowners by lowering the cost of their monthly mortgage payments.

The rally was broad, lifting shares in every industry except financial services. Major indicators surged more than 3 percent during the day before ending with gains of more than 2 percent.

The advance followed five straight sessions of mostly unrelenting selling that left major indexes at levels not seen in more than a decade.

“Virtually everyone was expecting some sort of a bounce; we just didn’t know exactly when that would occur,” said Randy Frederick, director of trading and derivatives at Charles Schwab. “You can’t go down forever.”

The Dow Jones industrial average rose 149.82, or 2.2 percent, to 6,875.84.

Broader indexes also rose. The Standard & Poor’s 500 index added 16.54, or 2.4 percent, to 712.87. On Tuesday, the S&P 500 index fell to its first close below 700 since October 1996.

The Nasdaq composite index gained 32.73, or 2.5 percent, to 1,353.74. The Russell 2000 index of smaller companies rose 10.29, or 2.9 percent, to 371.30.

Four stocks rose for every one that fell on the New York Stock Exchange, where volume came to a moderate 1.8 billion shares.

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