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Michael Hartnett, chief market strategist at BofAML, believes an improving macro environment coupled with high cash levels and diminishing geopolitical threats will lead to an "irrational exuberance" run that will catch fire during the summer.
The best trades, Hartnett said in a note, will be in emerging markets, utilities and telecoms, with the best contrarian bets to be on small-cap stocks and banks.
After that, though, the danger comes. Hartnett sees upward pressure on interest rates in the fall, with the market bracing for Federal Reserve action.
"When the end of zero rates is threatened, likely this autumn, both credit and stock markets should correct sharply," he said.
BofA has a full-year S&P 500 price target of 2,000.
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The team at Piper is somewhat more buoyant, though.
Should the forecast for the big 15 percent drop happen, it will be followed by the index hitting the firm's year-end target of 2,100—which in turn would be a 31 percent bull snapback and would soothe the nerves of investors after the harrowing drop.
"We believe this correction will help reset investors' expectations and create an attractive entry point for what we believe will be a strong finish to 2014," Piper said.
—By CNBC's Jeff Cox.