* Canadian dollar rises 0.3% against the greenback * Canada sheds one million jobs in March * Price of U.S. oil increases 4.7% * Canadian bond yields fall across much of the curve TORONTO, April 9 (Reuters) - The Canadian dollar strengthened against its U.S. counterpart on Thursday along with gains for stocks and higher oil prices, with the currency fluctuating after domestic data showed a record level of job losses. At 9:36 a.m. (1336 GMT), the Canadian dollar was trading 0.3% higher at 1.3968 to the greenback, or 71.59 U.S. cents. The currency, which on Tuesday touched an 11-day high at 1.3941, traded in a range of 1.3955 to 1.4076. Canada shed one million jobs in March while the unemployment rate soared to 7.8%, official data showed, as the coronavirus outbreak forced the closure of non-essential businesses. Ottawa is rolling out more than C$200 billion in measures to support the economy, while the Bank of Canada has slashed interest rates to 0.25% and has begun quantitative easing, a program of buying government bonds in large-scale. The U.S. Federal Reserve has also been active. On Thursday, it announced a massive $2.3 trillion program to bolster local governments and businesses impacted by the coronavirus pandemic, which boosted U.S. equity markets . Canada runs a current account deficit and is a major producer of commodities, including oil, so the loonie tends to be sensitive to the global flow of trade and capital. U.S. crude prices were up 4.7% at $26.26 a barrel on expectations the world's leading crude producers will at a meeting later in the day overcome obstacles that have so far prevented a deal to cut output. Canadian government bond yields were lower across much of the curve, with the 10-year down 1.8 basis points at 0.795%. (Reporting by Fergal Smith)
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