NEW YORK — Stocks started 2011 with a big lift on Monday, and that could be a promising sign for the rest of the year. Investors call it the “January barometer.” According to the Stock Trader’s Almanac, a gain in the Standard and Poor’s 500 stock index over the first five days of January has led to annual gains nearly 90 percent of the time. “All of the forecasts come out of Wall Street, and those expectations for the year give January a nice indicative effect of what the year will look like,” said Jeffery Hirsch, the editor of the Stock Trader’s Almanac.