It's been a tumultuous few days for global markets. Investors have grown anxious about what the end of Federal Reserve bond buying means for the economy while worrying about a possibly emerging credit crunch in China.
Although markets appeared to regain their poise on Friday, the turmoil has investors asking where stocks will head next.
The bulls are pointing to stronger economic growth as reason for optimism that stocks will resume their climb. The bears, meanwhile, worry the U.S. economy may not be quite ready to stand on its own without continued central bank support.
Here's what the bulls say:
"Don't worry" about the stock market gyrations touched off by Ben Bernanke's taper comments, Ron Baron, CEO of Baron Capital, wrote in an email to CNBC's Becky Quick.
The buy-and-hold billionaire doesn't "think turbulence will last" and blamed computer trading and persistent fear among traders who "remember [the U.S.] almost had [a] Depression five years ago."
"Over the long term, I think the stock market is going to grow 7 percent a year," about the same rate as the overall economy, not adjusting for inflation, Baron said, adding this has been the norm for generations and he doesn't see that changing.
(Read More: Is the Drop in Financial Markets an Overreaction?)
David Tepper, head of widely watched hedge fund Appaloosa Management, also said Fed tapering may be good news.
"All the concern in the markets is because the Fed sees the economy stronger in the future," he said in a statement.
"The bond (market) is concerned about the strength," he wrote. "A 10 (year) bond at 2.4 or even at 3 (percent) if it's because of strength is ultimately healthy. I obviously thought they should start to taper. Bottom line when the dust settles only one place to be STOCKS. "
Morgan Stanley CEO James Gorman also said the recent selloff in equities was an overreaction.
"I suspect that over the next few days we see a little more stability in equities," he told CNBC.
"This is not a time when fear should take over," he continued."This is the last in a series of hurdles that the markets have had to go through as they work their way back to a more normal environment."
On to the bears:
Doug Kass of Seabreeze Partners told CNBC that QE has made the markets "a heroin addict." "Now," he added, "with this tapering ahead of the market, it's soon to become a methadone addict. The problem is, too frequently, methadone addicts fall back into addiction."
Kass said that QE was the "wrong antidote" to what ails the economy.
"I don't believe that the economy is strong enough to sustain itself unless we have this heroin, or easy money, for some time to come," he said. "And what concerns me about the market fundamentally is that if the stock market continues to drop, it's almost self-fulfilling, trickle-down, no longer works."
And from a technical standpoint, there's a case for stocks to head 3 percent to 5 percent lower, Oppenheimer's Carter Worth said Thursday.
"Once you're down more than 5 percent, history shows you don't stop there," he said. "You typically go down quite a bit more."
Marc Faber, editor of "The Gloom Boom & Doom Report," also told CNBC there's plenty of room for further declines. But while the Fed news may play a part, China could also roil markets.
(Read More: What's Really Behind China's Cash Crunch)
"The Chinese economy is much weaker than the official statistics suggest," Faber said.
"My view would be that at the present time, the Chinese economy is growing at something like 4 percent per annum, and without huge credit expansion there would probably be no growth at all."