The other day, someone I regularly read on Twitter (@DividendMaster) noticed something interesting about interest rates, specifically ten-year government notes in OECD countries. (As always, my methods are transparent. Click here to download the Excel workbook (includes both monthly and annual data).
Take a look at this and see if you notice anything interesting:
That’s pretty hard to read. Here’s a closeup of the last three months:
Yes, you’re reading that right. The U.S. interest rate was the highest among these six countries in September. Spain and Italy? Really? (If it’s any relief, the interest rate on Greek sovereign debt was 5.89%, indicating that there is at least some sanity in the world.)
Also note that France and Germany are borrowing at interest rates considerably less than what the U.S. is paying.
The usual explanations for interest rate differentials among various countries are (1) differential inflation rates and (2) expected future exchange rate changes. Naturally the two are related. However, expected future exchange rate changes also incorporate a variety of other risks, including exchange rate risk and default risk.
Let’s assume the risk of U.S. default is less than either Italy or Spain. We need a theory of expected future exchange rates. The appropriate short-run model is uncovered interest parity (UIP).
Uncovered Interest Parity
Thus we see the expected rate of depreciation of the dollar is equal to the interest rate differential. We can use this to construct the following table:
The markets are saying the U.S. dollar is overvalued with respect to these currencies. The dollar is expected to depreciate vis-à-vis each of these countries.
But there’s still one problem. All these countries except the U.K. and the U.S. use the euro. How can the dollar be expected to depreciate by different amounts against a single currency? It can’t. There is only one spot U.S. dollar – euro exchange rate. The remaining differences must be due to default risk.
Let’s assume Germany’s sovereign debt has about the same risk as U.S. government securities. We need to modify our UIP equation to account for default risk. The easiest way is to simply define the default risk premium as follows:
where the subscript $/€G refers to the expected depreciation of the dollar vis-à-vis the euro in Germany and $/€O is the apparent expected depreciation of the dollar vis-a-vis another Eurozone country. Thus we have the following premiums for the risk of default:
What’s really interesting about this is that Italy is viewed as higher risk than Spain. Default risks for other Eurozone countries are in the Excel workbook.
 Material in this section is based on chapter 4 from Robert C. Feenstra and Alan M. Taylor, International Macroeconomics (2012). Worth Publishers, New York. Disclaimer: I wrote the instructor’s resource guide for this textbook.
 “interest rate” means “yield to maturity” here and throughout.
 Feenstra & Taylor, p. 113.