* Euro, sterling fall on worries over banks, econ
* Euro down 0.3 percent at $1.3261
* Stocks buoyed by UK bail bailout plan, Obama optimism
* Trade subdued as U.S. markets closed on Monday
(Adds quotes, updates prices)
By Tamawa Desai
LONDON, Jan 19 (Reuters) - The euro and sterling were lower on Monday as investors remained cautious about the ailing banking sector and faltering economy, overriding a new UK bank bailout plan and optimism for more U.S. stimulus steps.
Britain threw its troubled banks another multi-billion pound lifeline on Monday by allowing them to insure against steep losses and guaranteeing their debt to stop the credit crunch pushing the economy into a deep slump.
European shares rose around one percent as recently hammered banks such as Barclays bounced back, buoyed by news of the UK rescue plan
But ongoing bank troubles were highlighted as shares in Royal Bank of Scotland fell sharply after it said it had made a loss of more than 20 billion pounds ($30 billion) last year, the biggest loss in British corporate history, including a huge goodwill hit on its purchase of parts of ABN AMRO in 2007.
"There are still heavy losses being announced by the banking sector and the market fears the government taking major stakes in banks," said Ian Stannard, senior currency strategist at BNP Paribas.
As of 1004 GMT, the euro was down 0.3 percent at $1.3261, after hitting a session low of $1.3252. It had earlier risen to $1.3387 on trading platform EBS, the highest in a week.
The euro fell 0.3 percent to 120.21 yen, slightly below a one-week high of 122.20 yen struck earlier in the day on EBS.
Sterling reversed early gains after the UK Treasury said the BoE would set up a facility to buy private sector assets with an initial fund of 50 billion pounds as part of a multi-pronged plan to save the UK banking sector.
UK gross domestic product data due out on Friday is also expected to confirm Britain in recession.
"The UK bailout plan had limited impact on the currency market as it was largely flagged over the weekend. Equity markets opened higher, and there was a modest improvement in risk appetite," said Daragh Maher, currency strategist at Calyon.
"But investors may say, hold on, there was a need for a bailout, so there are questions whether the equities rally will be sustainable," he added.
The euro was also weighed down as investors took a dim view that euro zone policymakers were dragging their feet to support the economy.
Traders will keep an eye on a speech by European Central Bank President Jean-Claude Trichet, after he indicated last week that the ECB may not be ready to cut rates again until March.
Trade was somewhat subdued as financial markets in the United States were closed on Monday for Martin Luther King Day.
President-elect Barack Obama is set to take office on Tuesday, and many investors have been hoping he will act aggressively to help pull the economy out of recession.
The dollar was roughly flat at 90.60 yen, after hitting a one-week high of 91.31 yen on EBS touched earlier in Asian trade.
Higher-yielding currencies such as the Australian and New Zealand dollars gained, rising 0.7 percent and 0.4 percent, respectively.