Ponder this one on your daily walk:
The key question asked by standard monetary models used for policy analysis is, How do changes in short-term interest rates affect the economy? All of the standard models imply that such changes in interest rates affect the economy by altering the conditional means of the macroeconomic aggregates and have no effect on the conditional variances of these aggregates. We argue that the data on exchange rates imply nearly the opposite: the observation that exchange rates are approximately random walks implies that fluctuations in interest rates are associated with nearly one-for-one changes in conditional variances and nearly no changes in conditional means. In this sense standard monetary models capture essentially none of what is going on in the data. We thus argue that almost everything we say about monetary policy using these models is wrong.
Or put it this way:
We have focused on exchange rates rather than the term structure of interest rates because the implications of exchange rates are so striking. Specifically, if exchange rates are random walks, then all of the fluctuations in interest differentials are accounted for by fluctuations in conditional variances and none by fluctuations in conditional means. The data are so opposite of what standard models assume that even the most die-hard defenders of them should take note: If these data are accurate, then almost everything we say about monetary policy is wrong.
That is from the May 2007 American Economic Review, here is an earlier version of the paper. I doubt if changes in interest rate differentials are driven by risk premia of the standard sort; I would sooner cite "noise plus news," but resist the pull toward calling that a "conditional mean." I’ll also note that calling exchange rates a "random walk" is in the "do not reject" rather than "accept" statistical category. Both asset price moves contain lots of junk information, so we shouldn’t be totally surprised if they don’t fit together in some simple manner. Those moves weaken the paradox presented, but don’t come close to offering a coherent account of what is going on.