Wall Street's main indexes closed higher Friday as investors honed in on the chance of a bigger interest rate cut by the Federal Reserve next week, with rate-sensitive small cap stocks outperforming.

Bets on the size of the Fed's cut have been volatile and were roughly even by late Friday.

Expectations for a 50 basis point cut jumped to 49% from 28% on Thursday,

CME's FedWatch Tool showed, compared with a 51% probability for a 25 basis point cut.

Former New York Fed President Bill Dudley said late Thursday there was a strong case for a 50-bps interest rate cut.

Reports in the Wall Street Journal and other media had said early Thursday the Fed faces a difficult decision on how much to ease on Sept. 18.

"There's just rumblings that have started to bubble up again that the discussion in the Fed is leaving 50 basis points on the table," Jim Baird, chief investment officer with Plante Moran Financial Advisors, Southfield, Michigan.

Prior to this, bets on the Fed sticking to a smaller 25-bps cut firmed on Thursday following news of slightly higher producer prices and August consumer prices data.

While the renewed hopes for a bigger cut were boosting large cap indexes on Friday they were most evident in the Russell 2000 small cap index. Smaller companies are more sensitive to interest rate changes as they depend more on borrowed money and floating rate loans.

Baird argued that stocks appeared to show investor optimism that a 50 basis point cut would not indicate a coming recession.

"If investors were looking at this and saying they have to move quicker because they're behind the curve you wouldn't see risk assets like small caps rally," said Baird. "You're seeing some of the riskier areas of the equity market advance pretty strongly today."

Jason Pride, chief of investment strategy and research at Glenmede in Philadelphia, said Friday's gains are probably related to Dudley's comment about a strong case for a 50 basis point cut.

According to preliminary data, the S&P 500 gained 30.05 points, or 0.52%, to end at 5,625.81 points, while the Nasdaq Composite gained 111.49 points, or 0.63%, to 17,681.17. The Dow Jones Industrial Average rose 297.03 points, or 0.72%, to 41,393.80.

A survey showed U.S. consumer sentiment improved in September as inflation subsided, though Americans remained cautious ahead of the November presidential election.

All three major U.S. benchmark indexes were trading near two-week highs, on track to log solid weekly gains.

Adobe sold off sharply after the Photoshop maker forecast fourth-quarter earnings below estimates.

And Boeing shares sank after its U.S. West Coast factory workers walked off the job early on Friday as they overwhelmingly rejected a contract deal.

Chinese e-commerce firm PDD Holdings fell after the Biden administration said it was moving to curb low-value shipments entering the U.S. duty-free under the $800 "de minimis" threshold.

Uber shares rallied after the ride-hailing platform said it would bring autonomous ride hailing to Austin, Texas, and Atlanta in partnership with Alphabet's Waymo.