Market fundamentals still need to improve: Strategist

Closing Bell Exchange: Oil and S&P 500 correlation
Invest in eurozone & Japan: Pro
Will oil drive stocks higher?

On Monday, as the markets saw gains that brought the Dow and out of correction territory, investors were asking if we're in the clear yet.

Anastasia Amoroso, global market strategist at JPMorgan Asset Management, told CNBC's "Closing Bell" on Monday that she isn't so sure.

"I'm skeptical of this move because I think the fundamentals have to fundamentally improve here," she said.

"There's several obstacles that the market is running into and one of them, of course, is the big earnings obstacle. But that said, if this bottoming process that we're seeing in oil right now, if that is the real deal, that actually does help the fundamentals, too," Amoroso added.

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How to know markets are out of the woods
Trader on the floor of the New York Stock Exchange.
The S&P is closing in on a critical level

Anthony Chan, chief economist at Chase, told "Closing Bell" that he's a little more optimistic.

"I don't think that this rally is purely sustainable over the next week, two weeks. ... When you see bad news like euro zone PMIs and our own PMIs also a little bit weaker and the market rallying, it's telling you that the market is grasping for a bottom and its looking for things to improve moving forward," Chan said.

Despite the skittishness around European and Japanese equities, Riverfront Investment Group's director of international portfolio management, Chris Konstantinos, also told "Closing Bell" that his firm has been careful in snapping up buying opportunities in Japanese real estate.

"If you think about the impact of negative rates, we think that's a really, really good thing," Chan said.

"Mortgage rates in Japan are incredibly low now, cost of capital for the construction companies is really low. We think there's a secular growth story in Tokyo real estate," he said.

— CNBC's Christopher Hayes contributed to this report.