* U.S. repo rates fall for a second day * Front-month Eurodollar futures rise * Three-month dollar Libor unchanged By Richard Leong NEW YORK, June 6 The cost for banks and Wall Street to borrow dollars from investors fell on Wednesday prompted by speculation of further monetary easing by the U.S. Federal Reserve and the European Central Bank. Hopes of more stimulus measures from the two major central banks reduced the strain in the dollar funding market as investors last week hoarded cash and low-risk investments rather than lend money to garner higher returns. Still, money market funds and other investors remain anxious about Europe's fiscal problems spiraling into a global crisis, analysts and investors said. "Today there's liquidity but we know that liquidity could dry up quickly, but that's the risk investors have been preparing for the past four years," said Sean Simko, head of fixed income management at SEI Investments Co. in Oaks, Pennsylvania, which has $189 billion under management. Some dollars have been parked in the $1.6 trillion tri-party repurchase agreement market which banks and bond dealers depend on to fund their trades and operations. The overnight rate on repos secured by U.S. government debt was last quoted at 0.21 percent, compared with 0.24 percent late on Tuesday, according to Reuters data. This key short-term rate for dollar funding fell for a second day but remained about 12 basis points above the year's low seen back in mid-April. ECB President Mario Draghi said the ECB will continue to supply unlimited funding to euro zone banks at least until mid-January 2013. On the other hand, he downplayed the idea of another large three-year loan operation for now. The ECB injected more than 1 trillion euros into the banking system since December in a move to help banks to replenish their capital and to rid of soured sovereign investments. In the United States, Atlanta Federal Reserve chief Dennis Lockhart said on Wednesday the U.S. central bank might consider further monetary easing if the U.S. economy weakens due to high unemployment or Europe's debt trouble spills over to these shores. Bets on more Fed stimulus intensified in the wake of last Friday's poor domestic jobs report and the looming end of the Fed's $400 billion Operation Twist at the end of the month. Overnight, the repo rate has stayed higher than what some traders had thought. They had reckoned a seasonal decline in Treasury bill supply in the spring would drive up demand for repos and lower their interest rates. But the Fed's steady selling of its T-bill holdings due to Operation Twist resulted in a heavier supply of debt that Wall Street dealers have to finance, analysts said. Depleting the cash that would otherwise go into repos is the hefty redemption of money market funds since the beginning of the year. Money funds are major investors in repos. Money market fund assets fell $1.83 billion in the week ended June 5 to $2.545 trillion, according to Money Fund Report, a service of iMoneynet. Since end of 2011, money fund assets have fallen $126 billion or 5 percent. If Operation Twist ends as expected and not extended -- as some analysts are predicting, overnight repo rate should fall as banks and dealers will have less Treasury supply to finance. "A lot depends on Operation Twist," said Alex Roever, short-term fixed income strategist at JPMorgan Securities in New York. In the derivatives market, the rates on short-term dollar interest swaps fell, while Eurodollar futures rose, implying traders expect interbank costs for dollar will fall. The two-year swap rate, a gauge of short-term private credit costs in dollars, was down marginally to about 58.5 basis points, while its premium over comparable U.S. Treasuries fell for a third day to 33.25 basis points. Eurodollar futures for 2012 and 2013 deliveries rose 0.5 basis point to 3.5 basis points on the day, implying traders see further central bank actions lowering interbank borrowing costs. Offshore dollar trading picked up on Wednesday after its key hub - United Kingdom - was closed for two days due to market holidays. The benchmark London interbank offered rate on three-month dollars held at 0.46785 percent.