A very good post by Menzie Chin at Ecnobrowser explores the meaning of an expression often used by regulators, traders, and the media, the strength (or weakness) of a currency.
Chin tells us (and I hope I am not oversimplifying a lucid explanation) that it really signifies two things. The first meaning is the value of the currency in trade terms:
The first is the level of the dollar, adjusted for price levels. This is sometimes referred to as price competitiveness, and can be measured by the trade weighted value of the dollar after adjustment by the CPI (as in the the Fed’s index) or unit labor costs (as in the IMF’s series reu).
Purchasing power measures, including the Economist’s famed Big Mac index, fall in this category.
The second “value of a currency” is not simply its value relative to other currencies, but the prevailing rate of return available on assets in the host country from the perspective of someone in another currency (or to make better generalizations about the currency’s value, against a basket of currencies). This is a more complicated exercise, since one’s view will depend on the holding period of the asset, the expectations for appreciation or depreciation of the currency, and the expected cash flows in foreign currency terms of the investment:
But….[there is] a second (and in my mind confusing) use of the “strong dollar” term…. the returns on dollar assets denominated in a common currency.So consider the expected return on dollar assets:
i US – i EU – E[d(s)]
Where i US is the interest rate on dollar asset, i EU is the interest rate on euro asset, and E[d(s)] is the expected rate of dollar depreciation against the euro over the horizon consistent with the maturity of the debt instruments. The greater the anticipated depreciation, the lower the expected return in dollar terms on dollar assets, holding all else constant. To the extent that uncovered interest parity does not hold (see  [pdf] for definitions,  and  for discussion), one might think that the as this term declines, capital inflows decline (admittedly, this is an old fashioned view, but as far as I can tell, this is how economists in the financial sector and practitioners talk, to a first approximation).
So, since a weaker dollar at a given instant is a plus to the extent that it encourages expenditure switching, we don’t want a strong dollar. But to the extent that expectations regarding further weakening over time of the dollar tend to diminish capital inflows, we prefer a “strong dollar” (at least if we want to finance the ongoing incipient current account imbalance).
Let me stick my neck out by adding a couple of observations as someone who has evaluated investments in foreign currencies (and both from the US and non-US perspective). At least when I have ever done the math (and these have been for private equity investments or corporate acquisitions, which have more uncertainty than bonds as to the annual cash flows and the appropriate time horizon for analyzing the investment), I have always taken the view that merely looking at differential returns isn’t sufficient.
The investors I have worked with require an additional return for taking currency risk at all. Attitudes about currency risk vary considerably over time, and in a bubble (Japan in the late 1980s) investors sometimes will be of the view that their currency is so highly valued that they’ll pretty much ignore currency risk (and you recall where that got the Japanese). But most of the time, investors expect a reward for going outside their home currency (and I see it as justified, given that they are operating at an information disadvantage).
In addition, most of us have come to think like carry traders: investing in a currency whose assets offer high yields is attractive. But generally speaking, currencies whose assets offer high yields suffer from inflation, which means in the long haul the currency will fall more than currencies that offer lower yields. And in the stone ages of my youth, most investors were loath to invest in a currency that offered high yields precisely because they were sensitive to the risk of currency depreciation.
The very operation of the carry trade (as well as the dollar pegs set by some countries) has distorted this pattern. Speculation (the carry trade assumes you can get through the exit when you need to ) is playing a large role in the currency markets. If credit becomes more costly, or Japanese retail traders get badly burned, we may see the older historical patterns become more common.