mo34 Wrote: ------------------------------------------------------- > > Question 18: and this is where the solution does > not make sense: > > Duration of CTD = 10.15 ( given). > > Price of future = 108500 > > Dollar duration of CTD = 108500 * 0.1015. > I don’t get it. Whose solution is this? So if the price of the futures contract is 108.5 and the conversion factor is 0.9 for the CTD, the invoice price for the bond is 108.5*0.9 = 97.65 + accrued interest (forget about that). So the futures contract is essentially a contract on something worth 97.65. So to get the value of the CTD you need to multiply by the conversion factor.
When you go long a bond future and hold to maturity, you are going to get a bond. There are lots of different bonds available to be delivered and each one has a conversion factor that is fixed and a function of the bond - not the market price, interest rates, etc. Hence if a 6.5% 2022 bond has a conversion factor of 1.05 (or something) that will never change. When the bond gets delivered, you get an invoice along with the bond for 1.05*futures price. It’s a bill you have to pay. Obviously, if someone delivers an 8.5% 2035 bond they deserve to get paid more than for the aforementioned bond so it has a higher conversion factor and you will have to pay more. Since these conversion factors are set in stone and have nothing to do with market prices, there is a bond that is CTD. In theory that’s the only one that should be delivered under the contract. Hence you can think about the futures contract as a contract for the CTD. That means at “expiration”: Futures*conversion factor = CTD Bond price So if the bond changes by 1%, the futures changes by 1%/conversion factor. That means that the “duration” of the futures contract is CTD duration/conversion factor.
ohhh nooo…the CTD issue rears its ugly head again. I had a tooth extracted this morning and don’t know what’s more painful – the right side of my jaw or the thought of getting back into this mess…
against my better judgment here… Joey, don’t you mean the DD of the futures = DD of CTD / conversion factor In the simplified CFA world, “duration” of the futures should = CTD duration, no?
JoeyDVivre, Regarding your statements: Futures*conversion factor = CTD Bond price So if the bond changes by 1%, the futures changes by 1%/conversion factor. I don’t think I understand you. A simple example: Futures price = 1 Conversion factor = 2 CTD Bond price = 2 1*2=2 Now if CTD Bond price goes up by 100% it will be 4. According to the formula futures price will also go up by exactly 100% (and not by 1%/conversion factor) to 2 2*2=4