3.25%=5.5% (warning: very nerdy)

I have been away from the blog for the past week. After reading the discussion here early today, I think I have to explain why the interest rates in the Portuguese rescue package are not at all mysterious. Actually, there isn't even much genuine news around them.

This is hard and very nerdy, but here's my attempt at a short explanation:

1. The IMF interest rate follows a strict rule. There is no discretion involved. Anyone with a calculator could see it was going to be 3.25% for the first three years and 4.25% after, as soon as the size of the loan was announced.

2. The ESFS and the ESM have announced they follow the same rule as the IMF. They used to charge a bigger risk premium, but now the discussion is only whether they should charge an extra premium between 0 or 0.50%. That was the only thing under debate, and the only relevant news. So again anyone with a calculator could have figured out that the ESFS rate would be between 5.5% and 6%.

3. Why then 3.25% in the IMF loan and 5.5% in the EU loan? Because the first depends on the IMF's cost of funds (the SDR rate) whereas the second depends on the EU's cost of funds. The first is 0.52% right now, and the second is about 2,8% right now (it was 2,89% in January). So , here is (approximately) your 2,25% gap.

4. Why are the costs of funds so different? The main reason is that the IMF rate is variable, the ESFS rate is fixed. Or, to be more concrete: go to the bank to get a mortgage and they will offer you a rate if you want a variable loan (LIBOR + "Spread"), and a different rate if you want a fixed-rate loan. The difference between the two can be pretty high, but the bank is (roughly) offering you the same deal in expected value. I'd have to go super-nerdy to explain why. (A second reason for the gap is the exchange rate risk: the IMF lends in a different currency than euros, but I think the more important is the fixed-variable difference.)

5. What is the relevant interest rate for debt sustainability calculations over the next 7 years? That is tricky. If you believe the market prices for the swap contracts associated with the differences in point 4, then the answer is that 5.5% is the right number.

6. To sum up, the IMF rate and the ESFS rates are different things, apples and oranges. Converting the two loans into the same thing, you get that (approximately) 3,25%=5,5%.

Update: This is a hard and specialized topic, and my guess is that most economists would likely be confused about it. So there is no shame in getting it wrong. A tribute to Rui Peres Jorge, a journalist for Jornal de Negocios, and one of the best economics reporters in Portugal for explaining it well.

Update 2 (Sunday, 5/15): I have edited my previous update to remove references to some articles that were confusing about these calculations. Some people seem to have interpreted those links as some kind of criticism, which could not be farther from my intention. I was only trying to illustrate that this is a really technical and specific (nerdy) topic, so even good economists could get confused about it. My guess is that the majority of even my distinguished colleagues at Columbia wouldn't have known how these interest rates are set. Also, I completely agree that the interest rate charged is too high and that we may be able to negotiate it down. I know it is election campaign time in Portugal, and people are getting into smear campaigns, personal attacks and ego clashes but, please, don't drag me into it.

Finally, Diario Economico asked me to publish a longer article (simpler and in Portuguese) explaining these interest rates: it will come out in tomorrow's (Monday) edition.