NEW YORK ( TheStreet) -- U.S. stocks surged Tuesday as investors focused on the possibility of more monetary stimulus from the Federal Reserve, looking past ongoing questions about the stability of the eurozone.

Hopes that the central bank could come across with another round of quantitative easing were stoked by comments from Charles Evans, the president of the Federal Reserve Bank of Chicago, who was quoted as saying he's in favor of "pretty much any accommodative policy."

The major U.S. equity indices all managed to finish just below their session highs despite anxiety about Greece's general elections, which will take place this coming weekend. In addition, Spanish 10-year bond yields reportedly reached 6.85%, the highest level on record, earlier in the day as global investors remain unimpressed with the $125 billion bailout plan for the country's banking system.

The Dow Jones Industrial Average jumped 163 points, or 1.31%, at 12,574. The blue-chip index wiped out Monday's losses, which snapped a four-day winning streak.

The S&P 500 gained more than 15 points, or 1.17%, to finish at 1324, and the Nasdaq leapt 33 points, or 1.19%, to settle at 2843.

Within the Dow, 29 of 30 components finished higher, led by American Express ( AXP), Bank of America ( BAC), Boeing ( BA) and DuPont ( DD).

Boeing rose more than 3.5% after Bernstein Research lifted its rating on the plane maker to outperform with a $92 target price (up from $85), saying concerns about 787 deliveries are "overdone" and that the valuation is attractive at current levels.

"An important caveat to our upgrade is that we remain well below consensus in our EPS estimates for 2012 and 2013, which suggests future negative revisions," the firm noted. "But, there is no historical correlation between Boeing's share price and earnings revisions. We believe that the value in Boeing's stock comes from the long term outlook, not from short term earnings."

The only blue chip on the downside was United Technologies ( UTX), which lost 0.36%.

The strongest sectors were energy, basic materials, capital goods and conglomerates.

The market will be mulling over the Greek elections throughout the week, a scenario that constitutes a recipe for volatility, given how difficult it is to assess popular opinion in the country right now.

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