This paper implements an affine term structure model that accommodates "unspanned" macro risks for the Euro area, i.e. distinct from yield-curve risks. I use a Near-Cointegrated VAR-like approach to obtain a better estimation of the historical dynamics of the pricing factors, thus providing more accurate estimates of the term premium incorporated into the Eurozone's sovereign yield curve. I then look for notable episodes of the monetary cycle where long yields display a puzzling behavior vis-a-vis the short rate in contrast with the Expectation Hypothesis. The Euro-area bond market appears to have gone through its own "Greenspan conundrum" between January 1999 and August 2008. The term premium substantially contributed to these odd phenomena.