Updated from 12 p.m. EDT

The euro climbed to an all-time high against the greenback Tuesday after the Federal Reserve chopped its fed funds target rate by a bigger-than-expected 50 basis points.

The euro was recently buying $1.3970, up from $1.3867 late Monday in New York. The yen was little changed at around 115.72 to the dollar.

Elsewhere in the currency markets, the British pound was stronger against the dollar, rising to $2.0124 from $1.9964 earlier in the session. Along with the rate cut, there was increasing confidence in the U.K. that the Bank of England may be able to avert a banking crisis.

Action in sterling has been dominated for the last two sessions by news that depositors were scrambling to withdraw funds from ailing lender Northern Rock. Relative tranquility seems to have returned to the market after the government promised to guarantee savers' money at the troubled bank, and shares of Northern Rock rallied in London trading.

The exchange-traded funds that track the foreign exchange market were mixed. The CurrencyShares Euro Trust ( FXE) was up 0.7%, and the CurrencyShares Yen Trust ( FXY) was down 0.4%.

The ETF that tracks the value of the pound, CurrencyShares British Pound Sterling Trust ( FXB), was up 0.9% recently.

The PowerShares DB G10 Currency Harvest ( DBV), which follows multiple currencies, was rising 1.5%.

Earlier, earnings news out of Lehman Brothers ( LEH), a bank more exposed to the ailing mortgage business than most, had a buoying effect on the U.S. currency.

However, the euro gained the upper hand after the Fed reduced rates. Most traders were expecting a 25-point cut. When rates come down, the dollar tends to head lower.