# When calculating CIP between EU and US, which interest rates data to use?

I am wondering which data to use to test the Covered Interest Rate Parity between Europe and the United States. Recap that for the CIP to hold, it should mean that

F/S = (1+r)/(1+r*) where

• F = the 1-period ahead forward rate on the EUR/USD exchange rate
• S = the spot rate of the EUR/USD exchange
• r = domestic interest rate
• r* = foreign interest rate

For the forward rate I use the 1-month rates available on many resource sites, this holds true for the spot rate. However, which interest rate should I use for the domestic and foreign one?

My guess was to use the Euribor (1-Month) for the European and the Daily Treasury Yield (1-Month) or the USD Libor (1-Month).

However, then there is a huge gap between F/S and (1+r)/(1+r*); i.e. F/S yields values around 0.9-0.95 whereas (1+r)/(1+r*) yields values around 0.5 (when using USD Libor), meaning that the CIP definitely does not hold.

Recap that the lastest rate on the T-bill (1-Month) equals 0.03 and USD libor 0.1992 whereas the Euribor (1-Month) equals 0.112. Also recap that the forward rate (1-month) on EUR/USD is about 1.25 and the spot rate about 1.31.

An explanation could be of course the absence of transaction costs, but does this explain such a large gap? And secondly, if I wanted to calculate the CIP with transaction costs, does anybody know where to get the BID and ASK quotes on the Euribor and Treasury Bill?

In summary: - Which interest rate should I use for Europe and US? - Why is there such a large gap? - Where to get the BID and ASK quotes on the Euribor and T-bill?

Thank you.

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Your 1 month forward rate is wildly wrong (based on Bloomberg FRD command). I suspect that if you got 0.04 for that ratio, then you're also doing something wrong in that calculation as well (you're right to use 1 month rates). At a minimum, you need to account for the fact that you are only investing over a one month period (instead of a year). – John May 9 '13 at 13:46
@John Thanks for the quick response. The forward rate was indeed wrong (1.2 bid and 1.3 ask). For the calculation I still haven't figured out what the issue is. However, when using the USD libor instead of the Treasury bill, I do get a ratio around 0.5 (the ratio F/S is arround 0.9). I found an article (still working paper though, see: Coffrey, Hrung and Sarker (2009)) that finds evidence of CIP deviations after the financial crisis. – JohnAndrews May 9 '13 at 14:31
You F/S is still off, but not as off. The ratio is also way off. You have to use interest rates as a percent, so 6bps is $0.06/100$ and you also have take into account that you are only investing over a limited period. I got significantly closer numbers. – John May 9 '13 at 14:43
Can you clarify the latest - to take into account that you invest over a limited period - ? Do you get closer numbers with USD Libor or the T-Bill? – JohnAndrews May 9 '13 at 14:46
As in en.wikipedia.org/wiki/Compound_interest. If you set up the math properly, you will get a difference between the two, but it will be nowhere near as large as the differences you are reporting. – John May 9 '13 at 16:31

## 1 Answer

stay away from using rates that are based on unsecured funding -- there is differential risk premia embedded if you do, e.g., the health of the US banking system versus that of Europe's when using libor usd versus euribor. also, those rates are liable to manipulation. what you want to use are the rates charged for borrowing in one country versus the rates conferred to lend in another on a collateralized basis. barring the availability of such data, as a proxy using mid quotes on US tbills and mid quotes on german tbills -- both are relatively risk free -- should do the trick (too bad both are near 0, if not negative, as Germany's was until a few months ago.) Also note in this case, because the euro is the currency of so many different countries, each with their own government securities, the Euro/US pair has several associated CIP calculations possible. Though indeed, for many of the countries, the gov securities are not rated anywhere near 'risk free' and therefore cannot be used.

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Agree with the German bills, considering they largely control policy on the Euro. – jeff m May 9 '13 at 21:43