* Fed's monetary policy meet starts Tuesday
* Sarepta soars after FDA approves muscle drug
* Real estate sector mints strong debut
* Dow down 0.2 pct, S&P flat, Nasdaq down 0.18 pct (Updates to close of U.S. market)
By Lewis Krauskopf
Sept 19 (Reuters) - A see-saw session on Wall Street on Monday ended little changed, with gains in big bank stocks offsetting a drag from Apple, as investors braced for the Federal Reserve meeting later this week.
The Fed is expected to leave interest rates unchanged at the two-day meeting, but investors will assess Chair Janet Yellen's speech on Wednesday to see if the central bank plans to hike as soon as December.
After trading solidly higher during the morning, the benchmark S&P 500 pulled back and slid briefly into negative territory. The index has tallied four daily moves of at least 1 percent in the past couple of weeks after two months of calm.
"The market has been all over the place. It's been driven by the threat of higher interest rates," said Jake Dollarhide, chief executive officer of Longbow Asset Management in Tulsa. "Most people feel the most unloved bull market in recent memory will be cut off at the knees by higher interest rates, and the Fed is certainly threatening that in the near term."
The Dow Jones industrial average fell 3.63 points, or 0.02 percent, to 18,120.17, the S&P 500 lost 0.04 points, to 2,139.12 and the Nasdaq Composite dropped 9.54 points, or 0.18 percent, to 5,235.03.
Traders are betting that there is only a 12-percent chance the Fed will raise interest rates this week, but see a 55-percent chance the central bank will do so in December, according to the CME's FedWatch website.
Investors also are eyeing the Bank of Japan's policy meeting on Tuesday and Wednesday, while the first debate of the U.S. presidential election is set for next Monday.
"You're in a cycle in the market where political uncertainty and economic uncertainty are just so high that investors are taking advantage of any move up to sell and any selloff to buy," said Rick Meckler, president of LibertyView Capital Management in Jersey City, New Jersey.
"As a result we're stuck in a trading range that we probably can't break out of until you get through the Fed meeting, and you get through probably the debate next Monday, and you get a lot closer to the next round of earnings releases," Meckler said.
JPMorgan, Bank of America and Wells Fargo all posted gains, and the KBW Bank index rose 0.5 percent.
Energy shares slipped 0.1 percent, pulling back as oil prices pared gains during the session.
"There seems to be still that strong correlation between what's going on in crude and what's going on in the broad market right now," said Chuck Carlson, chief executive officer at Horizon Investment Services in Hammond, Indiana.
The real estate sector gained 1 percent. The stocks debuted as the 11th major S&P 500 group.
Apple shares shed 1.2 percent after registering huge gains last week. The stock was the biggest drag on the three major U.S. indexes.
Sarepta Therapeutics' shares rocketed 73.9 percent to $48.94 after U.S. regulators approved its key muscle disorder drug.
About 6.1 billion shares changed hands on U.S. exchanges, below the 6.7 billion daily average for the past 20 trading days, according to Thomson Reuters data.
NYSE advancing issues outnumbered decliners 2.21-to-1 ratio; on Nasdaq, a 1.45-to-1 ratio favored advancers.
The S&P 500 posted 11 new 52-week highs and 3 new lows; the Nasdaq Composite recorded 95 new highs and 30 new lows. (Additional reporting by Yashaswini Swamynathan in Bengaluru; Editing by Saumyadeb Chakrabarty and Nick Zieminski)