## Friday, November 5, 2010

### Wonkistan: "QE2, News, and Differential Impacts in Asset Markets"

Good as the piece is, the comments might be better. Some sharp folks hanging out at Menzie and James' place. See also Wednesday's "QE2: Been there, done that".
From Econbrowser:
Typically, economists assume that news, defined as information that induces revisions to expectations of the future value of relevant variables, should affect asset prices simultaneously, and in a consistent manner. That's why today's announcement of QE2 has somewhat surprising effects, if one is to believe that QE2 had already been priced in [0].
QE2's Impact on the Exchange Rate
First, consider the impact on the USD/EUR exchange rate.

Figure 1: USD/EUR exchange rate. Source: finance.yahoo.com.
Note the fairly large impact on the exchange rate; the dollar depreciated by about 0.43% (log terms) by about 6pm Eastern time. If QE2 had been fully priced in, then (in a risk-neutral investor world) there should have been no impact on the exchange rate. It's hard to argue that the amount of quantitative easing -- \$600 billion worth of purchases of long term treasuries -- announced was much larger in magnitude than what the market expected; hence the puzzle. (Note, however, the USD/JPY did not move appreciably, while USD/GBP appreciated; but USD/EUR is the dominant currency pair so I’m putting greater weight on this rate.)
To see this, let the exchange rate equal current fundamentals and the interest differential and uncovered interest parity holds:
st = Mt + λ(Etst+1-st)
st = [1/(1+λ)]Mt + [λ/(1+λ)]Etst+1
Where s is the log exchange rate, expressed in terms of home currency required to buy a unit of foreign currency; and Et(.) is the mathematical expectations operator, conditioned on the information set available at time t.
Then note that:
st+1-st = (st+1-Etst+1) + {Etst+1-st}
Substituting in the expression for the exchange rate, one obtains:
st+1-st =[1/(1+λ)](Mt+1-EtMt+1) + [1/(1+λ)](Et+1st+2-Etst+2) + {Etst+1-st}
Note that "news" shows up in two places: first, as "surprises" in the fundamentals, namely realizations of the fundamentals that differ from what was expected; second, as information that forces revisions in the expectation of the exchange rate in period t+2, possibly due to expected changes in M in periods t+3 and t+4 and so forth. On 11/3, no actual purchases of long term Treasurys were implemented, so the first term drops out. However, the second term possibly remains -- but news accounts suggest that there was no surprises in the magnitude of the planned purchases. [Note: there is a tension between using something that looks like a flex-price monetary model with UIP for motivation, and modeling quantitative easing -- but I think it's not an essential problem.]
My conclusion is that QE2 was mostly, but not entirely, priced into exchange rates. This is buttressed by a time series plot encompassing the period when QE2 was becoming increasingly discussed as a reality.

Figure 2: Log nominal value of USD, Bank of England index (blue), and Fed broad index (red), rescaled to September 1, 2010 = 0. Sources: Bank of England and Federal Reserve Board via FREDII.

A Different Response in the Bond Market
However, the puzzle reappears to the extent that the bond market seemed to take the announcement in stride, and indeed CR argued that the monthly purchases were in line with expectations (if not under-expectations, see here [1]). Thirty year yields actually rose; this was attributed to the fact that the purchases were expected to be in the 2.5 to 10 year maturities....MORE