NEW YORK, Sept 13 (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.