New Evidence on the Puzzles. Results from Agnostic Identification on Monetary Policy and Exchange Rates.

There are a couple of things to note at this point. First, the Dornbusch
overshooting hypothesis requires a number of auxiliary assumptions beyond
conditional UIP. Second, even if there is overshooting, conditional UIP might
be violated if the quantitative magnitudes do not satisfy 1.

Second, the hedging strategies described above are conditional on a single
monetary policy shock only. To literally execute such a strategy in practice,
where one wishes to only exploit possible gains from a single monetary policy
shock, one would need to ”insure” away all other influences such as other
contemporaneous and all future shocks until maturity k .

Third and perhaps most importantly: while many papers in the literature
- including Faust and Rogers (2003) - have documented (explicitely or im-
plicitely) significant violations of conditional UIP, this may not suffice for an
investor contemplating exploiting this deviation at some date t. The hedging
position executed for a single dollar at stake is a random variable with payoff
in terms of US goods given by

Xt+k = (1 - e^ρk)e⁽ⁱ0→k^+p0-pk⁾                         (2)

if executed in the “hypothetical” manner of insuring against all other shocks.
Think of X_t+k as a component of a portfolio bearing exchange rate risk due
to a monetary policy shock. Our aim is to study the price for the risk of this
component in isolation.

Let e^mt,t+k be the stochastic discount factor of this investor between t and
t + k. Standard asset pricing theory implies that

0=Et[e^mt,t+kXt+k]

Compare this with the general problem of short-selling any Dollar-denominated
asset upon the occurrence of a monetary policy shock at date t, and invest-
ing the proceeds at the short rate i_0→k . Let the random return of that asset
between period t and t + k be given by RR_t+_k, and let ρ_t+_k = i₀→_k — log RR_t+_k

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