NEW YORK – Investors cast aside worries of another recession last week and bought stocks by the bucketful. This week brings hard evidence of whether they were right.

A new earnings reporting season kicks off Monday with Alcoa Inc., followed by dozens of other companies over the next few days. A question on everyone’s lips: Will these second-quarter reports show that companies are feeling better about the future, too?

“We’ll find out soon enough what the reality is,” says Howard Silverblatt, a senior analyst at Standard & Poor’s.

After dumping stocks since late April, investors last week drove the Dow Jones industrial average up 5.3 percent, its best weekly performance in a year. Some analysts say stocks had simply gotten too cheap for investors to resist. Others point to an International Monetary Fund report that the world economy could grow faster than projected. That took some of the fear out of the market.

“The economy is running on two cylinders but the risk of a double-dip recession” has fallen, says Peter Buchanan, senior economist at CIBC World Markets. “The market could go higher.”

Certainly, that is the view of professional stock pickers. When investors were selling stocks week after week, eventually driving shares down 13.6 percent from their April peak, Wall Street analysts never lost faith in the future.

They’re projecting that second-quarter operating earnings of S&P 500 companies rose 42 percent, according to S&P’s Silverblatt. They also think operating earnings in the current quarter, which ends Sept. 30, will jump 31 percent over a year ago. And in the following three months, they’ll jump again — 28 percent.

Then it’s up, up and away.

By the end of 2011, S&P 500 index companies should be earning more than they did at the peak of the credit bubble in 2006 — if you believe the professional prognosticators.

With hurdles so high, all eyes are on profit reports now. Analysts say they’ll be paying at least as much attention to what executives say about future earnings as to what’s been generated so far. Those forecasts will tell investors whether last week’s burst of optimism was justified.

Some big reports to watch besides Alcoa‘s: Intel Corp. on Tuesday, Google Inc. and JPMorgan Chase & Co. on Thursday and Bank of America Corp. on Friday.

Shannon Puls, who runs researcher EarningsWhispers.com in Jackson, Mo., says that even if earnings reports are upbeat, investors should think twice before jumping into the market. His reason: Wall Street analysts are saying to do it with both feet.

The problem, Puls says, is that analysts shy away from “gutsy calls” because if they’re wrong, clients could lose money and analysts will lose their jobs. So, Puls says, they predict in packs, often proving a “contrarian indicator.”

In other words, don’t do what they say. Do the opposite.

Puls says that analysts are now more optimistic than ever, and that means stocks could fall. He ranks analyst recommendations on more than 3,000 companies on a sliding scale, with 1 representing a strong “buy” and 5 a strong “sell.” The average call now: 2.07. That’s the lowest, or most bullish, in the nine years he’s been tallying the numbers.

Analyst ratings “have got to come down,” Puls says. “And that’s going to be bearish on stocks.”

Another reason for investors to exercise caution is all the corporate cash lying around in banks vaults, earning little. Companies worried about the future hoard money, just as people do. In March, cash at S&P 500 companies hit a record $837 billion. That’s equivalent to 1 1/2 years of their operating earnings.

The cash hoard of as June 30 won’t be known until mid-August, and it’s anyone’s guess what the level will be. But S&P’s Silverblatt is willing to predict this: It’ll hit a new record.