Saturday 14 May 2011

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.


  1. Thanks Ricardo.
    Actually, at this stage, we need "nerdy" information - economically sound, technically correct information.

    Knowing that difference in rates does not result from different risk assessments is an important point that you clarified!

  2. Ricardo, no link que indicaste aparece escrito "Tanto num caso, como noutro, a Europa aplicará sobre os respectivos custos de financiamento um "spread" de cerca 200 pontos base".
    Ou seja, há um spread sobre os custos de financiamento da parte europeia que não existe no caso do FMI, ou estou a ler mal?

  3. Ricardo, esquece o meu comentário anterior, estava a ler mal. Forte abraço.

  4. Luis,
    Podias estar a ler mal, mas estavas a pensar bem. Porque e' que a UE deve cobrar o mesmo premio de risco que o FMI? O problema 'e a diferente e, sobretudo, a stake da UE e' bem diferente.

  5. ja agora, uma pequena critica construtiva. o post parece-me ir no bom caminho mas nao me parece que esteja assim taaaaaoooo bem explicado.

    se for possivel (obviamente) seria interessante ter para cada uma das tranches fmi e UE o seguinte:

    - montante
    - prazo
    - indexante (e resp. valor 'a data de hoje)
    - spread (e estimat. de como foi atribuido)



  6. "grouchomarx",
    Exactamente, na mouche! O custo do hedge sao os tais 2,25%. Se Portugal tentar comprar o hedge para a parte do emprestimo que vem do FMI, descobre que a taxa total fica por 5,5%. Ou seja, quem acha que a taxa do FMI e' baixa/boa, gosta do risco, e tem espirito de especulador :-)
    Na critica tem toda a razao: nao esta' bem explicado. Mas precisava de muitas paginas e muito tempo para explicar, nao so' o que aponta, mas tambem o que e' uma swap, um hedge, a term structure, etc. O texto foi o melhor que consegui.

  7. Caro Ricardo, Portugal esta' entregue 'a bicharada, de cima a baixo.

    Acho que ha' muita gente em PT mesmo com cursos de gestao e economia e nao percebe ponta dum horn dos basicos.

    agora em yada, yadda, yadda, somos especialistas.

    e' triste.


  8. Presumo que façam swaps de taxa de juro para cobrir o risco. É muito dinheiro.

  9. Caro Ricardo

    o diferencial de taxas de juro das duas instituicoes tem a ver com gap entre swap/hedge e taxa variável, mas pensava que também teria a ver com os prazos a que IMF se financia (o seu funding é a 3 meses) vs. prazos a que se financia o novo mecanismo europeu (presumo que seja mais nao?).
    ou isto nao tem impacto?

  10. Useful blogging!

    I still think that the key question is what is the "actual" interest rate that Portugal will pay on the next three years. Given the deficit targets and the expected nominal growth, the (expected) actual interest rate decides the fiscal sustainability for Portugal.

    Are we are going to "actually" swap into a euro fixed rate of 7.5 years, the IMF funding? Is any nation swapping IMF funding (usually distressed nations)? Maybe there is, and that would be interesting.

    Making comparable the IMF and EU tranches by transforming them into 7.5 years euro debt is absolutely correct. It gives an exact interpretation for the premium that the EU charges on the loan. Hedging a 3 month floating interest rate basket of Euro, Sterling, US dollars and Yen.

  11. A decisão de fazer o hedge para taxa fixa ou manter em taxa variável não deve levar em conta as correlações que possam existir entre a taxa variável e a capacidade de pagar da economia portuguesa?

  12. Maybe this is displaced, but doesn't the EU scheme imply putting aside 20% of any loan, earning 0 interest rate, as a buffer?

  13. it is a difference between EFSF and EFSM. But yes as only 80% of the members are AAA. This is taken into account in the two calculations.

    but the point Pedro, (I think I was not explicit enough above):

    - the actual cost of IMF funding is 3.25 because we are not going to buy hedge on an emergency loan of the IMF. That would really be surprising.

    - the "alleged" spread from the EU (we do not know it yet) corresponds to what you will pay in the financial markets to hedge a 3 months flex rate basket if the 4 major World currencies. How generous...

  14. Joao,
    Essa e' uma pergunta dificil. Em teoria, o que interessa e' que e' uma taxa de juro anual que e' ajustada todas as semanas. Se a "expectations hypothesis of the term structure" for verdade, nao faz diferenca qual e' a maturidade das obrigacoes que estas a usar para extrair essa taxa. Mas, a tal hypothesis e' drasticamente rejeitada nos dados. Logo, sim tem impacto (nos "risk premium" e sobretudo nos "liquidity premium"), mas nao ha uma teoria universalmente aceite que torne facil ver qual e' o efeito em causa.

  15. Carlos Albuquerque,
    Sim, com certeza.

  16. Francesco,
    We corresponded on this by e-mail but I thought other readers might find it useful too: the swap or hedge has to be tailored because you are trying to swap an unusual bond (based on a basket not of currencies but of 3-month bonds; floating rate updated weekly; conditionality requirements on tranches of the loan; the IMF's repayment schedule
    ) and this is a big operation for the not-so liquid or deep market for swaps on 7 year bonds. So, while conceptually it is a simple hedge, I believe that you end having to get a price quote from an investment bank.

  17. @Ricardo

    I agree with you on the conceptual simplicity. I said currencies because the bonds are denominated in 4 different currencies (that compose the SDR) so you basically have both interest rate and currency (minor) risks.

    but my point is that the sense of causality is the other way around.

    first : the IMF tranche is short term and SDR, but Portugal cannot afford (neither Ireland nor Greece) to ask Goldman to swap it for a certain 7.5 years fixed euro interest rate. We will bear the risks and start to pay 3.25% on that tranche. There are many many other risks that we will not hedge...

    second the EU cannot justify her premium by saying (they are not, but apparently the numbers add up!) that is what Portugal must pay to swap the IMF loan and make it comparable to their loan.

    As someone said today, punishment is already embedded in conditionality. No need to add a second source of punishment through high interest rate that reduce the probability of success of the consolidation