NEW YORK (Reuters) - The Federal Reserve is in focus next week, as uncertainty swirls over how much the U.S. central bank will cut interest rates at its monetary policy meeting and the pace at which it will reduce borrowing costs in coming months.

The S&P 500 index is just 1% shy of its July record high despite weeks of market swings sparked by worries over the economy and seesawing bets on the size of the cut at the Fed's Sept. 17-18 meeting.

After fluctuating sharply throughout the week, Fed funds futures on Friday showed traders pricing an almost equal chance of a 25 basis point cut and a 50 basis point reduction, according to CME Fedwatch. The shifting bets reflect one of the key questions facing markets today: whether the Fed will head off weakening in the labor market with aggressive cuts, rather than take a slower wait-and-see approach.

"The market wants to see the Fed portray a level of confidence that growth is slowing but not falling off a cliff," said Anthony Saglimbene, chief market strategist at Ameriprise Financial. "They want to see ... that there's still this ability to gradually normalize monetary policy."

Investors will focus on the Fed's fresh economic projections and interest rate outlook. Markets are pricing in 115 basis points of cuts by the end of 2024, according to LSEG data late on Friday. The Fed's June forecast, by comparison, penciled in one 25-basis point cut for the year.

Walter Todd, chief investment officer at Greenwood Capital, said the central bank should opt for 50 basis points on Wednesday. He pointed to the gap between the 2-year Treasury yield, last around 3.6%, and the Fed funds rate of 5.25%-5.5%.

That gap is "a signal that the Fed is really tight relative to where the market is," Todd said. "They are late in starting this cutting cycle and they need to catch up."

Aggressive rate cut bets have helped fuel a Treasury rally, with the 10-year yield down some 80 basis points since the start of July to around 3.65%, near its lowest level since June 2023.

But if the Fed continues to project significantly less easing than the market does for this year, bonds will have to reprice, pushing yields higher, said Mike Mullaney, director of global markets research at Boston Partners.

Rising yields could pressure stock valuations, Mullaney said, which are already high relative to history. The S&P 500 was last trading at a forward price-to-earnings ratio of 21 times expected 12-month earnings, compared to its long-term average of 15.7, according to LSEG Datastream.

"I find it implausible that you're going to get P/E multiple expansion between now and year-end in a rising (yield) environment," Mullaney said. With the S&P 500 up about 18% so far this year, it may not take much to disappoint investors with next week's Fed meeting. Focus has turned to the employment market as inflation has moderated, with job growth coming in less robust than expected in the past two monthly reports. The unemployment rate jumped to 4.2% in August, one month after the Fed projected it reaching that level only in 2025, said Oscar Munoz, chief US macro strategist at TD Securities. That indicates the central bank may need to show it will move aggressively to bring down rates to their "neutral" level, he added."If the (forecast) disappoints, meaning they turn more conservative and they don't ease as much ... I think the market might not take it well," Munoz said.