# Reading 29, Example 11 (v4, p17)

Can somebody PLEASE explain example 11 in reading 29?? In the example, we have: Portfolio value = 50MM Portfolio duration = 9.52 Target duration = 7.5 Futures contract “priced at” 100,000 Futures contract duration = 8.47 Conversion factor = 1.1 I understand the rationale behind the basic formula on p17 that: # Contracts = [(Dt - Di) x Pi]/(Dctd x Pctd) x Conversion Factor This is basically the same as saying: # Contracts = (DD Adjustment / DDctd) x Conversion Factor Or that: # Contracts = (Exposure of Portfolio / Exposure of CTD) x (Exposure of CTD / Exposure of Futures) What I can’t for the life of me figure out is how they apply this in Example 11, where they calculate: # Contracts = [(7.5 - 9.52) x 50,000,000]/(8.47x100,000) x 1.1 = -131.17 The example specifically states that the FUTURES CONTRACT is “priced at” 100,000. That would make the price of the CTD = Futures Price x Conversion Factor = 100,000 x 1.1 = 110,000. The calculation would be: # Contracts = [(7.5 - 9.52) x 50,000,000]/(8.47 x 110,000) x 1.1 = -119.24 This same issue of when and how to incorporate the conversion factor pops up in a number of places both on AF and, most notably, in Question 15 of CFA’s free practice exam. If anybody can help resolve my confusion over this, it’d be much appreciated…

isn’t it always multiply by Conversion factor?

You are multiplying the Conversion Factor twice in your last equation… That’s why its wrong.

My point is that depending on what information you’re given in the problem, it seems that you WOULD use the CF twice (once in the denominator to figure out the DD of the CTD, and once to adjust for the ratio of DDctd to DDf; and yes, they would cancel each other out). It really depends on what you’re given in the question. If you’re given the price of the CTD, then no, you don’t need to use the conversion factor in the denominator. But if you’re given the price of the Futures, as in the example, why wouldn’t you have to use the conversion factor to get the relevant dollar duration for the denominator?

Can somebody please take a look at the original post and think through the issue I’m getting at. If you’re given the FUTURES price and the FUTURES duration, the number of contracts required has to equal Dollar Duration of Portfolio / Dollar Duration of Futures. It’s only if you’re given the Duration of the CTD and the Price of the CTD that you need to use: (DD of Portfolio / DD of CTD) x Conversion Factor. I’m assuming here that yield beta = 1 for simplicity. Yet this isn’t the approach CFAI is taking either in the free sample exam q 15 or in example 11 of reading 29. Just seems plain wrong to me…

7.5-9.52 50 mil ----------- x ----------- x 1.1 8.47 100,000 Dont need to price the 100,000 again, it’s like your pricing it twice.