By Sinéad Carew and Shashwat Chauhan

(Reuters) -Wall Street's main indexes closed higher on 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, according to CME's FedWatch Tool, which showed 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 early Thursday said the Fed faced 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," said Jim Baird, chief investment officer with Plante Moran Financial Advisors, Southfield, Michigan.

In contrast, bets on Thursday that the Fed would opt for a smaller 25-bps cut firmed after news of slightly higher producer prices and Wednesday's consumer prices data.

While the renewed hopes for a bigger cut were boosting large cap indexes on Friday the optimism seemed most evident in the Russell 2000 small cap index <.RUT>, which rose 2.5% on the day and 4.4% for the week.

Smaller companies are more sensitive to 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 likely stemmed from Dudley's comment about the case for a 50 basis point cut.

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

The Dow Jones Industrial Average rose 297.01 points, or 0.72%, to 41,393.78, the S&P 500 gained 30.26 points, or 0.54%, to 5,626.02 and the Nasdaq Composite gained 114.30 points, or 0.65%, to 17,683.98.

All three major U.S. benchmark indexes ended close to roughly two-week highs and logged solid weekly gains.