I'd like to spread U.S. 10-year note futures vs. German 10-year bund futures?

Let's assume the following:

For the U.S. 10-year note future:
 - cheapest to deliver:  2.25%  15-Nov-2024
 - PV01 of CTD:  $620.10
 - conversion factor of CTD:  0.8006
 - price of CTD:  95.23

For the German 10-year bund future:
 - cheapest to deliver:  0.25% 15-Feb-2027
 - PV01 of CTD:  EUR 859.22
 - conversion factor of CTD:  0.611166
 - price of CTD:  96.85

Let's further assume that the spot EUR/USD foreign exchange rate is 1.23 and the forward f/x rate as of the delivery date of the future is 1.25 (purely hypothetical).

If I want to be both duration and foreign exchange neutral, how many German 10-year bund futures would I need to sell for every 100 contracts of U.S. 10-year that I bought?

Thanks!

When do you want to be duration neutral?  Today or at delivery?

I'd like to be duration neutral at all times from today up to delivery.  Though, in all likelihood, the spread position would be closed before we reach the delivery month (which in this case is March 2018).

Well, it's going to be mighty difficult, if not impossible, to be neutral at all times, obviously...

If I want to be both duration and foreign exchange neutral only today, how many German 10-year bund futures would I need to sell for every 100 contracts of U.S. 10-year that I bought?  What does that calculation look like?  Thanks.

It looks like about 68 contracts to have the same $ duration exposure to both curves (divide each CTD PV01 by the corresponding conversion factor, translate the EUR one into USD, and take the ratio of the two). Since the initial value of the Bund futures is zero, it does not generate an immediate currency exposure. However, the initial margin posting will generate a (small) currency exposure, but that would have to be hedged separately with a currency contract of sorts.

If I want to be both duration and foreign exchange neutral only today, how many German 10-year bund futures would I need to sell for every 100 contracts of U.S. 10-year that I bought?  What does that calculation look like?  Thanks.

It looks like about 68 contracts to have the same $ duration exposure to both curves (divide each CTD PV01 by the corresponding conversion factor, translate the EUR one into USD, and take the ratio of the two). Since the initial value of the Bund futures is zero, it does not generate an immediate currency exposure. However, the initial margin posting will generate a (small) currency exposure, but that would have to be hedged separately with a currency contract of sorts.

Thank you.  Here is how I see the math:

U.S. Treasury 10-year note future:
620.10 / 0.8006 = $774.54

German Bund future:
EUR 859.22 / 0.611166 = EUR 1,405.99
EUR 1,405.99 * 1.23 = $1,729.36

Hedge Ratio:
$774.54 / $1,729.36 = 0.4478

Buying 100 contracts of the U.S. Treasury note future would equate to a sale of 45 contracts of German bund futures, right?  (rather than the 68 contracts you mentioned... did you go the other way on the FX translation from EUR to USD?)

If I want to be both duration and foreign exchange neutral only today, how many German 10-year bund futures would I need to sell for every 100 contracts of U.S. 10-year that I bought?  What does that calculation look like?  Thanks.

It looks like about 68 contracts to have the same $ duration exposure to both curves (divide each CTD PV01 by the corresponding conversion factor, translate the EUR one into USD, and take the ratio of the two). Since the initial value of the Bund futures is zero, it does not generate an immediate currency exposure. However, the initial margin posting will generate a (small) currency exposure, but that would have to be hedged separately with a currency contract of sorts.

Thank you.  Here is how I see the math:

U.S. Treasury 10-year note future:
620.10 / 0.8006 = $774.54

German Bund future:
EUR 859.22 / 0.611166 = EUR 1,405.99
EUR 1,405.99 * 1.23 = $1,729.36

Hedge Ratio:
$774.54 / $1,729.36 = 0.4478

Buying 100 contracts of the U.S. Treasury note future would equate to a sale of 45 contracts of German bund futures, right?  (rather than the 68 contracts you mentioned... did you go the other way on the FX translation from EUR to USD?)

Yes, sorry, you are correct