"The euro will become a favorite funding currency for carry trades as Greece’s crisis weighs on regional interest rates, according to Deutsche Bank AG."Huh??? I thought that interest rates go UP if the bond prices go DOWN, as is currently happening to Greece. The safest of Euro bonds (German Bunds) are still yielding slightly above comparable tenor US Treasuries and far above the level of Japanese bonds. Regardless of whether or not Greece defaults, this situation is unlikely to change in a direction that would enable a Euro carry-trade.
At a very elementary level, there are at least two reasons why a currency might experience a decline. One is a carry trade, where short-term borrowing in one currency is used to finance purchases of another, so that instututions and individuals sell the funding currency (driving down its price) and buy another.
The other is when weakness in the economy substantially decreases government revenue, necessitating increasing currency sales (or money printing) by the government itself.
If Euro continues to suffer it will not be because of reason #1.