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* Dollar index set to lose 0.2 pct on week
* Upbeat US data somewhat counters dovish Fed
* Sterling firm on more signs of UK economic strength (adds fresh quote)
By Anirban Nag
LONDON, June 20 (Reuters) - The dollar inched up on Friday, helped by gains against the safe-haven yen, but it was still headed for its worst week since early May against a basket of currencies after the Federal Reserve's surprisingly dovish policy outlook.
In contrast, the Bank of England's hawkish bias widened the yield gap between two-year British gilts and U.S. Treasuries, helping the pound to trade near 5 1/2- year highs against the dollar.
"Sterling is a favourite right now, and the BoE seems to be the only major central bank that is likely to deliver on higher rates," said Niels Christensen, an FX strategist at Nordea.
"The dollar hasn't had a great week after the Fed disappointed some who had positioned for a slightly more hawkish bias from (Fed chair) Janet Yellen. But as the data improves, the dollar will start to recover."
The dollar index was up 0.1 percent at 80.403, moving away from a one-month trough of 80.147. It was down 0.25 percent on the week, its biggest decline since early May.
Investors sold the dollar after the Fed on Wednesday sounded unconcerned by the outlook for inflation, despite signs price pressure is picking up. That dashed some expectations the Fed would start raising interest rates earlier than forecast, and it initially pushed U.S. Treasury yields down.
But U.S. data on Thursday showed new claims for jobless benefits fell last week and factory activity in the mid-Atlantic region accelerated in June. Treasury yields reversed course, and the dollar was trying to catch up with the latest pick-up in U.S. yields, traders said.
The dollar rose 0.2 percent against the yen, trading at 102.08 yen. Stock market gains also weighe on the safe-haven Japanese currency.
In a sign that risk appetite is likely to be supported, implied volatilities, a gauge of how sharp currency swings are likely to be, have fallen further after the Fed meeting.
The Fed and the Bank of Japan are still pumping billions into their economies and the European Central Bank will offer new four-year loans in September. With the global financial system awash with cash, volatility indices across asset classes have fallen, supporting riskier assets like stocks and higher-yielding currencies.
The one-month euro/dollar implied vol was at 4.50 percent, close to seven-year lows and mirroring similar moves in stock indices like the ViX and VSToxx.
The euro was down 0.2 percent on the day at $1.3586, well below the two-week high of $1.3644 it reached on Thursday.
Sterling hovered within striking distance of Thursday's 5 1/2-year high of $1.7064 after data showed UK factory orders grew at their fastest pace in six months in June. The report highlighted the probability that the BoE may raise rates well before the Fed.
"The economic news is still positive and there is no binding ceiling on rate expectations at current levels," said Adam Cole, head of G10 currency strategy at RBC Capital. "We favour using dips in the pound on key crosses to buy." (Additional reporting by Shinichi Saoshiro in TOKYO; Editing by Larry King)