There is a sharp bifurcation in views about the euro, and it seems useful to review what time series analysis can tell us about EUR valuation.
If we use the usual suspects to explain the EUR exchange rate during the past 11 years, we obtain quite different results by allowing the computer to cut up the regression into the segments it prefers. A breakpoint regression (dividing 11 years of daily data into five distinct periods) gets a nearly perfect fit. The regressors are the US-German 5-year yield spread, the respective yield slopes, and US 5-year b/e five years forward,
Ordinary Least Squares gives us an 83% fit and a huge residual (about 10 cents) at the end:
The breakpoint regression isolates the past two years. With the same regressors, we get a good fit for the euro:
Either the euro is 10 cents rich and likely to crash, or it is well predicted by present and expected future interest rate differentials (the forward US breakeven rate functions here as a proxy for prospective changes in Federal Reserve policy). A countervailing factor might be trouble in Italy, which is always bad for the euro.
In the second case, we reasonably may expect that the end of QE in Europe will lead to higher yields and a higher euro. In the first case, the euro already has run in front of expectations about ECB policy changes and is quite vulnerable.
Intuitively, it seems likely a regime shift occurred in the past two years, after a long period of extreme risk to the eurozone. It makes sense to treat the past two years of data separately.