Whether the stock market is soaring or plunging, it’s rare for the chairman of an exchange to do anything but extol the virtues of equities.

So it’s a bit refreshing to see NYSE Euronext Chief Executive Duncan Niederauer in action. For the second day in a row Friday, he questioned the strength of the U.S. market.

The Standard & Poor’s 500 Index has leapt an astounding 30 percent from its March 6 low, but Niederauer isn’t jumping on the bandwagon.

“It feels to me we're in a trader's market and not an investor's market,” he told CNBC.

In other words, the recent gains result from speculators looking to make a quick buck rather than investors’ enthusiasm about the long-term strength of U.S. companies — a classic bear-market rally.

Niederauer says the highs won’t last.

"The volume in March hasn't convinced me that it's the kind of volume you need to see to believe it was the real beginning of a turnaround," he says.

"Instincts tell me we're going to retrace one more time, and the rally I believe is the summer rally."

Niederauer made similar comments in an interview Thursday with the Financial Times.

Analysts are sharply divided as to whether the bear market is over. Pessimists like Nouriel Roubini say no, because the economy is still in the tank.

Others, like Marc Faber, say yes.

Some, like Faber, argue that the government’s massive fiscal and monetary stimulus will boost the economy and stock market alike.