Fixed Income -- Derivatives overylay

CFA Level III Fixed Income
#1

I’m looking at page 75 with regards to derivative overlays. Seems like the interest rate futures from last year and the equation

number of contracts = (durationtarget - durationinitial)/PCTD*DurationCTD * Conversion factor.

Aside from that, they use the equation

Number of contracts = (Liability BPV - Asset BPV) / Futures BPV

where Futures BPV = BPV of cheapest to deliver / Conversion factor cheapest to deliver

On page 74, it states in the second last paragraph. THe key point is that although eligible T-notes are roughly equivalent on will be identified as the cheapest to deliver. Importantly, the duration of the 10-year futures contract is assumed to be the duration fo the CTD t-note.

Im confused. Do we always use the 10 year future as the CTD? On the next page they go over a 6.5 year t-note and a 10 year t-note and conclude that the number of contracts is 1,432 if the 6.5 year T-note is used as the CTD and number of contracts is 1,032 if the 10 year is used as CTD.

It has a concluding statement in the text that says – Clearly, the asset manager must know the CTD T-note to use in the derivatives overlay stragegy. The difference between 1,432 and 1,032 of 400 is significant.

From the initial text statement I would use the 10-year note but then this example says the manager must know the CTD T-note to use. How does he chose and which one do we use for the calculation?

#2

Now completely confused.

On page 77 contingent immunization is discussed and there’s a statement in the first paragraph and it says "The derivatives overlay example is to hold a portfolio of short-term bonds having a market value of USD 225,750,000 and 1,432 10-year futures contracts (assuming that the CTD eligible security is the 6.5 year T-note).

Does this mean if the 10-year futures contract is held if the 6.5 year is the CTD. Would it be that the 6.5 year contract is held if the 10-years futures contract is the CTD.

And then from my first post, how do you know which is the CTD?

So confused. Any help is MUCH appreciated. Thanks