Draghi's open mouth operations

Another Draghi shock on the order of 1% in the exchange rate between the Euro and the dollar:

The Euro had already drifted higher than it was before the last Draghi shock and this fall basically brings it back to the level of September 3rd. And of course Scott Sumner is again saying this is evidence that monetary policy is effective in a liquidity trap. Here's my post from the last time -- basically everything still applies. The variance in the exchange rate is so large that it swamps any impact of "open mouth operations".

Could Draghi perform an open mouth operation every day for the next few weeks and depreciate the Euro by 50%? Could he even say something again tomorrow and make the Euro fall a total of 4%?

In the information transfer model, the long run exchange rate depends on the relative NGDPs of the two countries in comparison, something that is largely out of the control of the central bank when those countries have low inflation (when the IT index is near 1).