Analysis of a euro-dollar spread trade

The CBOT describes in the educational section of their web site several possible trades that can be made using the contracts available for trade. One that could be relevant to understand the apparent enslaving of the US stock market to the currency market is the German-US yield spread.

In essence, if you expect interest rates in the US to go up with respect to interest rates in Europe (Germany, in this case) you can profit from this buy lending to the europeans money borrowed from the americans.

How can you do that in a relatively straightforward way, without getting involved in the actual bond markets in both the US and Europe? By selling a US note futures contract and buying a German note futures contract at the same time. If you use the 10-year note in both cases you are dealing in the Bund - 10 year US note spread considered in the CBOT document.

However, when you deal with a spread you cannot just sell one contract of something and buy one contract of something else, because the price of different note contracts react differently to the same change in yield. Moreover, the two contracts involved are priced in different currencies, making the spread sensitive to currency rate risk.

The first correction that one has to make is due to the different reaction to yield changes and it needs to be doen even if both contracts are denominated in the same currency. If you want the spread to capture only the relative change in yield between the legs of the spread, you need to sell a different number of contracts of the first leg than the second leg. In bond parlance, the symbol DV01 denotes the dollar value of one point of yield, that is how much the price of the bond or note goes up (down) when the yield goes down (up) by one basis point. The following relationship must hold to make the spread capturing only relative yield changes:

DV01(1st leg) * (# of 1st leg contracts) =
DV01(2nd leg) * (# of 2nd leg contracts)

Moreover, both legs of the spread must be in the same currency, so if the 1st leg is a dollar denominated instrument and the 2nd one is euro denominated we have

(euro/US$) * DV01(1st leg) * (# of 1st leg contracts) =
DV01(2nd leg) * (# of 2nd leg contracts)

where (euro/US$) is the currency conversion rate and everything is expressed in euros.

Categories: bond market, interest rates, currencies