Early in Tuesday's morning session, the S&P 500 Index dipped to a low of 1,074, dropping more than 20 percent from the May 2 high of 1,370 and taking the index into bear market territory.

Then, at the last hour of Tuesday's regular session, stocks roared back on news that Eurozone leaders are discussing plans to recapitalized Europe's vulnerable banks. Doing so eases the market's fear that losses from Eurozone peripheral sovereign debt would trigger a banking crisis.

On Wednesday, U.S. stocks extended the gains on mixed economic data (better-than-expected ADP jobs report, worse-than-expected Challenger jobs report, and benign ISM non-manufacturing PMI report).

The S&P 500 rallied 1.79 percent to close at 1,144.04, the Dow Jones Industrial Average climbed 1.21 percent to close at 10,939.95, and the Nasdaq Composite surged 2.32 percent.

Wednesday's strong performance prompted some to ponder if Tuesday's morning session low was a bottom for U.S. stocks, which has been declining for several months.

A counter-trend equity rally has emerged [and] investors are now asking if they should buy or sell into this rally, said Sam Stovall, Chief Equity Strategist at Standard and Poor's, in a research note.

Stovall said the market priced in low expectations for corporate earnings and Friday's jobs report, which possibly sets the stage for a rally.  The excess of pessimism from investors in the past week only adds more fuel to the fire from a contrarian perspective.    

Moreover, history shows that stocks often rally in quarters preceded by vicious declines in the prior quarter (as was the case for the third quarter), noted Stovall.

However, he believes the rally will only be a counter-trend rally that will eventually hit resistance around 1,250, which is about 10 percent above current levels.

Then, he expects the S&P 500 to drop into bear market territory either later this year or during the first part of 2012. His June 2012 target for the index is 1,150.