By Sinead Carew

NEW YORK (Reuters) - The U.S. banking sector's dramatic rally post Election Day is likely just a taste of bigger gains to come, as investors expect banks to reap huge benefits from rising interest rates and lighter regulation under a Donald Trump presidency.

In recent years, bank stocks have been held back by heavy regulation and historically low interest rates which have sapped the earnings potential of their massive cash holdings.

But optimism about the sector's outlook is growing. Interest rates are rising and investors are betting that Trump will follow through on his campaign promise to review the increased number of regulations put on the banking system after it nearly keeled over in the 2008 financial crisis.

The S&P 500 bank subsector rose 10.2 percent in the three days following Trump's victory in the U.S. presidential election. This was the index's best three-day performance since August 2009.

In those three days, Wells Fargo Co shares rose 13.6 percent, JPMorgan Chase & Co climbed 9.5 percent and Bank of America gained 11.9 percent.

Some investors and analysts watching banks say the stocks are likely not near the end of their run.

"They are not close to being expensive yet," said Peter Kenny, senior market strategist at Global Markets Advisory Group in New York.

The S&P 500 banks are currently trading at about 11.2 times forward earnings estimates as a group, up from about nine times in February, when the index hit its lowest since May 2013.

Valuation is still well off peak levels of over 33 times earnings estimates in May of 2009, though it trades near levels seen between 2002 and 2008, before many current regulations were put in place.

If rates continue to rise and the Trump administration gives some clarity on how regulations will change, then bank valuations "certainly can move higher," Piper Jaffray analyst Kevin Baker said.

Baker stopped short of giving a specific P/E estimate but he pointed to the higher valuations of banks that are not designated as systemically important financial institutions, commonly referred to as "too big to fail".

Today, the minimum asset threshold for too-big-to-fail designated banks is $50 billion. If this threshold is lifted to $250 billion in a regulatory overhaul it would give a lot more flexibility that could likely boost valuations of banks operating in that range, Baker said.

Valuations for too-big-to-fail designated banks are at around 12.5 times forward earnings compared with multiples of 13 to 15 for banks outside of this category, according to Baker.

Ed Keon, managing director and portfolio manager of QMA, a multi-asset manager owned by Prudential Financial, said he has been buying into the Financial Select Sector SPDR Fund, the ETF that tracks the S&P financial sector, in the last couple of weeks.

He is betting on higher interest rates and a pick-up in economic growth. The potential for lighter regulation added to his enthusiasm for the sector.

"Of course, no one yet knows exactly what policy changes will occur and exactly how much they will help profits, but I think the benefit might be solid enough that I am maintaining my overweight holdings in the sector,” Keon said.

(Reporting by Caroline Valetkevitch, Chuck Mikolajczak and Sinead Carew; Writing by Sinead Carew; Editing by Daniel Bases and James Dalgleish)