The euro has dramatically fallen against the greenback this month, since the surprising U.S. employment report (which was actually not really good behind the appearances, although there has indeed been some moderately positive developments in the job market).
I don't think the euro has much more to fall. From a fundamental perspective, nothing has changed: the Fed is and will remain more dovish than the ECB. Two year bunds yield a lot more than two year notes. And the structural current account deficits of the U.S. are not being addressed.
From a valuation perspective, although the euro is a bit expensive, in my opinion the current price is about halfway from fair value (~1.20) to the all time highs of 2008 (~1.60). As the euro is not at all undervalued by any measure (quite the contrary), I believe there are better ways to play dollar weakness. However I do think the risks are tiltled towards a higher euro in the near term: from a technical perspective, it's already oversold, with 12 down days in the past 15 trading days:
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