# # of Contracts - Different Formulas - FI Duration

Anyone notice that there are 2 formulas one can use for # of Contracts when using futures to increase/lower duration? Schweser has: # of contracts = (DDt - DDp)/DDf where DDf = DDctd/CTD conv. factor Then on page 17 of CFAI in volume 4 I see: # of contracts = [((DDt - DDi) x Pi)/(Dctd x Pctd)] x Conv. Factor I haven’t yet reviewed this but it’s coming up later this evening for me… Is there a reason for the difference in formula’s used?

same formulas. in the top one the CTD conversation factor ends up being multiplied by the equestion. the bottom one: Dctd x Pctd = DDctd

Yeah, those formulas look the same to me. I was confused with the wording of one of the chapter-end questions though (Problem 2, CFAI Reading 29)- it said something along the lines: futures contract priced at \$X, with duration Y and conversion factor Z I was under the impression that since it refers to futures contract, I should just multiply XxY to get DDf. However, it ended up being a reference to CTD bond (thus, DDf = XxY/Z). It is not clear to me how to distinguish when we should use conversion factor and when we don’t need to (i.e the question does not talk about CTD bond, but instead just mentions futures).

tanyusha – I’ve been trying to get to the bottom of that same issue in another thread, but with no luck. The CFAI materials, as well as one of the questions on the free sample exam, seem completely screwed up in their use of “futures price” versus “ctd price”. Maybe this approach to getting some answers will work better: How many futures contracts will be needed to completely (duration) hedge a \$100MM fixed income portfolio with a duration of 8.0 and a yield beta of 1.0 under the following circumstances: A: Futures price = \$100k duration = 7.0 Conversion factor = 1.1 OR B: CTD price = \$100k duration = 7.0 Conversion factor = 1.1

I believe whenever future is mentioned it is CTD and DDctd = DD*CTD factor also remember that yield beta measures relationship between CTD bond and portfolio and not between futures and portfolio

I agree with compscikid… WHenever futures are mentioned, you need to use the CTD.

^ AGree

I’m confused. Isn’t the price of the futures contract different than the price of the CTD? Two different things, aren’t they?

I am still confused too. >I believe whenever future is mentioned it is CTD and DDctd = DD*CTD factor comp_sci_kid, future is always mentioned. Do you mean whenever convertion factor is mentioned it is CTD?