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Judging by its track record, May isn’t a promising month for stocks. Since World War II, the S&P 500 has gained an average of 0.31 percent in May. For all months, the average gain is 0.67 percent.

“It’s a very undistinguished month,” Stovall said.

Among stocks making big moves:

• Sears Holdings Corp. soared 15 percent, the biggest gain in the S&P 500. The operator of Kmart and Sears stores expects to post a first-quarter profit thanks to a gain from the sale of some U.S. and Canadian stores. The company’s stock has jumped 99 percent so far this year.

• Archer Daniels Midland Co. gained 7 percent after the food conglomerate reported profits that beat analysts’ expectations. Profits dropped by nearly a third over the past year, pulled down by one-time charges and lower weaker results from its ethanol and oilseeds businesses.

• Avon Products Inc. fell 8 percent, the largest drop in the S&P. The company said earnings plunged 82 percent, hurt by a bigger restructuring charge, commodity costs and rising labor costs. The results were worse than analysts had expected.