* Bank of America profit shrinks on $2.1 billion of charges

* UnitedHealth falls on higher-than-expected medical costs

* Tesla falls after flagging output hit from Red Sea disruption

* US producer prices unexpectedly fall in December

* Indexes: Dow down 0.26%, S&P up 0.12%, Nasdaq up 0.05%

Jan 12 (Reuters) -

U.S. stocks clung near the unchanged mark on Friday, oscillating between modest gains and losses, as a mixed bag of big bank earnings offset a cooler-than-expected inflation report that lifted hopes for interest-rate cuts from the Federal Reserve.

On Friday, data showed U.S. producer prices unexpectedly fell in December as the cost of goods such as food and diesel fuel declined, while prices for services were unchanged for a third consecutive month, in contrast to Thursday's hotter-than-expected consumer inflation print.

Expectations for a rate cut of at least 25 basis points by the Fed in March moved up to 79.5%, according to CME's FedWatch Tool, from 73.2% in the prior session. Friday's data also sent Treasury yields lower, although recent comments by some central bank officials have pushed back on any potential rate cuts.

"The PPI tells us something that is a little bit different than the CPI," said Michael Green, chief strategist at Simplify Asset Management in New York.

"It raises the probability that the Fed has the free and clear to decide to cut interest rates and the equity market really doesn't care all that much as long as rates are not pushing significantly higher."

The Dow Jones Industrial Average fell 99.33 points, or 0.26% , to 37,611.69, the S&P 500 gained 6.02 points, or 0.12 %, at 4,786.09 and the Nasdaq Composite gained 7.82 points, or 0.05 %, at 14,978.00.

Bank of America slipped 0.3% after its fourth-quarter profit shrank as the lender took $3.7 billion in one-off charges, while Wells Fargo's warning of a 7% to 9% drop in net interest income in 2024 sent the bank's shares down 2.9%.

But Citigroup rose 1.8% after reporting a $1.8 billion fourth-quarter loss and saying it expected further job cuts.

JPMorgan Chase edged 0.2% higher after reporting its best ever annual profit and forecasting higher-than-expected interest income for 2024.

The S&P 500 Banks index was down 0.5% after falling as much as 1.7%.

The Dow was pulled lower, largely due to a 3.6% decline in UnitedHealth after reporting higher-than-expected medical costs, accounting for nearly 130 points of downside pressure to the index.

Each of the three major indexes are on track for weekly gains, with the S&P 500 poised for its best week percentage gain since mid-December.

Delta Air Lines tumbled 8.4% after the carrier scaled down its annual profit outlook.

Tesla lost 4.4% after trimming prices of some new China models and plans to suspend most car production at its factory near Berlin.

Advancing issues outnumbered decliners by a 1.7-to-1 ratio on the NYSE and were roughly even on the Nasdaq.

The S&P index recorded 37 new 52-week highs and no new lows, while the Nasdaq recorded 127 new highs and 71 new lows.

(Reporting by Chuck Mikolajczak; Editing by Richard Chang)