In less than one hour on Tuesday, the U.S. stock market surged by 4 percent -- for no apparent reason.

The last hour of trading was the most volatile final hour in two months -- and it occurred at a speed that frightens many, from experienced hedge-fund managers to mom-and-pop investors.

The late-day melt-up that pushed the S&P 500 index <.SPX> out of bear-market territory might be construed as good news. But it brings back echoes of the flash crash that saw markets dive by several hundred points in a matter of minutes, and it's a big reason many are staying away from the market.

Everyone is scared in both ways -- the shorts are scared, the longs are scared, everyone is scared. The high-net-worth investor is very, very scared, said Stephen Solaka, managing partner at Belmont Capital Group in Los Angeles, which manages money for independent wealth advisers and family offices.

Tuesday's move was the latest example of an erratic, high-octane stock market increasingly driven by levered exchange traded funds and complicated hedging and options strategies that unwind with dizzying speed.

It's a far cry from when the U.S. stock market was viewed as a place for capital-raising by businesses seeking to expand and a place for investors looking to put their savings to work.

It tends to result in some market participants feeling like the market is uninvestable. It's not good for mutual funds or hedge funds, said Michael Marrale, head of sales trading at RBC Capital Markets in New York.

The ostensible reason for Tuesday's move was an article published late in the day on the Financial Times website quoting the EU's commissioner for economic affairs, Olli Rehn, saying a plan was being worked out to recapitalize the region's troubled banking sector.

But Reuters reported similar comments earlier in the day, and Rehn's comments struck some people as covering old ground. Ken Polcari, a veteran of the NYSE floor at ICAP Equities, found the reasoning insufficient.

There is no clarity -- 'no formal decision' -- just more speculation, more rumors, and more innuendo, he said of the FT article.

WHAT WENT DOWN

Traders, analysts and investors interviewed by Reuters cited a number of factors, many of them technical, and linked to big positions around the 1100 level on the S&P 500.

That level was key for investors who had been betting heavily against stocks, which were pummeled in recent days on worries about the worsening European debt crisis.

With the index down more than 10 percent from its intraday high reached September 27 to its low on Tuesday, many investors riding that wave were caught leaning the wrong direction when stocks bounced sharply on the Europe reports.

The swift gains only really came after the market bounced back above 1100. That was in part due to investors covering heavy short bets against the S&P in key exchange-traded funds such as the SPDRS S&P 500 Index fund and in leveraged ETFs that are mainstays for traders in today's market.

Polcari says there was a rush by investors who were betting the market would fall to buy back stocks they had borrowed and sold. The buying fed on itself as more of the short-sellers rushed to cover bets, propelling the market higher.

It was the perfectly executed short squeeze - launched in the final 30 minutes of trading, revealing why being short in a bear market can suddenly cause you to bleed, he said.

Over the past two months, short interest on the SPDR S&P 500 exchange traded fund, a massive vehicle that tracks the S&P 500 and has over $78 billion in assets, increased to record levels, according to equity derivative analysts at JP Morgan.

For the SPY, there are 536.08 million shares shorted out of 724.13 million outstanding as of mid-September, or about 74 percent, according to Thomson Reuters data.

Short interest in this ETF is always going to be high as investors use it to hedge underlying long positions in stocks, but this still represents a sharp increase from the end of July when it was just 47 percent.

BLAST-OFF AT 1,100

The S&P climbed steadily between 3 p.m. and 3:30 p.m., but once it broke through 1,100, the gains accelerated, as the average rose 1 percent in the span between 3:39 p.m. and 3:45 p.m.

For Joe Donohue, money manager at Dimension Trading in Red Bank, New Jersey, the speed of the reversal was a classic sign of automated algorithmic trading.

I didn't know the move was for real until about 3:40 to 3:45, when my machine just lit up green like a Christmas tree, he said. That's when you know there's algo buying dictating the market. It certainly wasn't individual buyers.

Donohue's response was to close out short positions and buy a triple-leveraged long exchange traded fund that magnifies the performance of the Russell 2000 <.RUT> three times.

The Direxion Daily Small Cap Bull 3X Shares , which had its busiest day of trading in history on Tuesday, rocketed nearly 20 percent into the close. That ETF, along with the Proshares Ultrashort S&P 500 ETF , another leveraged ETF, are now often among the top 25 traded issues on U.S. exchanges.

Program trading and algorithmic trading was the cause, said Donohue. We're seeing moves in a half hour that used to take weeks. Obviously we were very oversold technically before, and essentially we had a 'melt-up' that was helped by the algo trading that just went off buying.

Adding to the fire was likely the activity of market makers and options dealers, who try to remain 'market neutral' by offsetting positions by hedging through the options market. When the market moves violently, they have to buy stocks to maintain a neutral exposure, as they aren't trying to bet on the direction of the market.

In a note to clients emailed Monday, JPMorgan derivatives strategist Marko Kolanovic noted the range between 1,075 and 1,125 could be subject to more volatility because those hedging the market would buy or sell heavily on violent moves in order to maintain neutral positions.

According to Trade Alert, December S&P 500 put options at the 1,100 strike was the third-largest in terms of existing positions, with more than 197,000 contracts outstanding. For investors who bought those puts as insurance for going long stocks, the late-day rally doesn't matter -- puts are insurance against their long position, which was doing well.

But market-makers who sold those puts find their hedges out of balance if the market rallies sharply, said Michael McCarty, managing director at Differential Research in Austin, Texas.

When you go through (1,100) that quickly it creates an incentive to balance your hedge when you're faced with so little time left in the day, he said. It can be akin to yelling 'fire' in a theater.

The extreme gyrations are unlikely to abate soon. Volatility futures suggest more wild swings in coming months, and the violent nature of Tuesday's rally is a characteristic associated with bear markets more than bull markets. It hasn't been lost on retail investors, who have pulled money from U.S. equity funds in six of the last seven months, according to the Investment Company Institute.

There's never been a more difficult time to navigate financial markets than where we are today, said Frank Porcelli, head of U.S. retail for BlackRock, one of the world's largest fund managers with $3.6 trillion in assets under management.

(Reporting by Ed Krudy and Doris Frankel; additional reporting by Jennifer Merritt, Jonathan Spicer, David Gaffen, Ryan Vlastelica, Chuck Mikolajczak and Mike Tarsala; Editing by Kenneth Barry)