A silly/scary thought experiment on the Swiss Franc

The ECB is generally expected to launch a QE program sometime next week (late Jan 2015), last week the SNB dropped its price ceiling relative to the Euro.  What would happen if the SNB had retained the peg and the ECB started a large QE program?

1.  QE should devalue the Euro
2.  The Franc then rises vs the Euro
3.  The SNB steps in and prints Francs to buy Euros and maintain the peg.

Simple, right?  But we totally skipped WHAT the ECB is buying.  What if they decided to pursue QE by purchasing Francs?  What kind of mad world do we live in if that happens?

1.  ECB prints Euros to buy Francs
2.  Francs rise double fast (purchases increase the number of Euros AND decrease the number of Francs availible)
3.  SNB steps in, prints 2X (more than 1X as many, not necessarily 2X) as many Francs to maintain peg.
4.  SNB purchases pull Euros out of the market sterilizing their QE.
5.  ECB prints Euros and buys Francs
Repeat steps 2-5

If both banks honor their commitments and react reasonably quickly to price changes we would (expect) to see the Franc hit 1.20 and stick like glue.  With both sides having infinite ammunition in this fight there is no logical end in sight.  What should happen to those currencies compared to other currencies?  Other than some froth early on I think you can make a case for nothing (I think you could also make a case for nothing followed by complete collapse).  No new Euros will functionally hit the market before being snapped up by the Swiss and no new Francs will enter flows, they will be stocked up by the ECB. 

Is the effect really neutral though?  I think perhaps not.  In the end the banks will lose some control over their own currency and gain some control over the other parties currency.  If these two entities were of equal size then the effects would be a wash, but because the ECB represents a much more massive economic conglomerate than Switzerland the relative number of Francs it would have to put on the market to alter the value of the Swiss currency is much smaller.  In this game of chicken the Swiss would be giving up sovereignty (conservatively) ten times as quickly as the ECB would be. 

Don't believe me?  Imagine the ECB initiates QE equal to 100% of Swiss GDP (lets pretend everything ends up 1:1 nicely for simplicity) by buying Francs- the SNB expands its balance sheet by 100% of GDP by purchasing Euros to sterilize this action.  Now the ECB turns around and uses those Francs to buy US dollars.  What happens to the value of the Franc with around 800 billion newly minted ones hitting the market and 800 billion dollars getting soaked up?  Unless the Swiss want massive inflation (not 2-5% inflation but double and maybe triple digit inflation) they have to dump some of their holdings- which are overwhelmingly Euro denominated- to soak up those Francs and the Euro should depreciate vs the Franc (and also vs the Dollar). 

There is a lie floating around the ether that a CB can control its own currency with enough gumption.  That may be true (its probably not) but it immediately becomes false when a country pegs to another currency, and becomes false and really dangerous when it comes to pegging vs a much larger currency. 

If we combine this post with one from earlier today we have a rational explanation for the Swiss abandoning the peg.  That little (ie 20-30 billion francs) increase in late 2014 in SNB holdings indicate that the Swiss had not convinced the market of its commitment to maintain the peg.  To match a big QE program from the ECB the Swiss would be giving up substantial autonomy for future moves.  Even if the ECB wasn't specifically buying up Francs it would still be the major buyer of paper when Francs were flooding the market.  Either directly or indirectly the ECB would be major players in the Franc's future.