CTD price vs. Futures Price

[NR2004]

When calculating number of contracts to hedge with interest rate futures, I’m having a hard time understanding when to use CTD price and when to use CTD conversion factor.
The “Kingsbridge” assessment on CFAI’s website uses CTD price in the denominator, then multiplies by the conversion factor in the numerator. However, the “Kapoor” assessment #4 uses the Futures price in the denominator and uses the conversion factor in the numerator.
I thought CTD price = futures price * conversion factor (although in Kingsbridge, this is not the case, as Futures price is 100,500, CTD price is 97,500 and conversion factor is 1.12), so in theory, if you use the futures price in the denominator, you wouldn’t then multiply by the conversion factor. I am beyond confused!!

 

[der Pate]

sorry for the late answer, this one bothered me for a long time as well but now i think i got it. In the example you are given the CTD Duration which is 8.35. Thus in order to get to the Futures Duration you have to divide the CTD duration by the conversion factor 1.15, which gives you 7.2609.
If you then plug that into the formula the result is correct solution (-2.25*255.000.000)/(7.2609*97.500), which gives you 811 contracts.
Remember if you use the futures price and the future duration, no conversion factor is needed, whereas with CTD you need to multiply by the Conversion factor to have the number of futures you need in the result.
actually quite easy, spent long time with this thing.

 

[der Pate]

this was for the Kapoor example

 

[cebrach]

If you are given CTD, use it. If you are given a conversion factor, use it.