# Quiz : bond hedging

Company X is holding \$55m par value of a 25 year semiannual pay corp. bond. The bond pays a 3.9% coupon and is currently priced at \$96.13, implying a YTM of 4.15% T-bond futures with one year to delivery are priced at \$96.5. The CTD for the T-bond futures is a 15 year, 4.1% coupon bond, currently yielding 3.9%. The CTD conversion factor is 1.082 Company X wish to hedge the corp bond using futures, with a hedge horizon 1 year from now. For the futures priced of \$96.5, the corresponding prices for the corp. bond and the CTD are \$99.337 and \$104.413. It can be estimated that the durations of the corp. bond and the CTD (for a 60 basis point change in yield) at the end of the hedge horizon will be 15.5 and 10.68. Calculate the number of futures needed to hedge the corp bond against a potential 60 basis point change in yields.

Man what a pain in the ass…here goes. (0-15.5)/(10.68/1.082)*(\$55MM*.9613)/96.5

BTW, I’m noticing that you didn’t give us a “multiplier” (or whatever you’d like to call it) for the Treasury futures contracts. Anyhow, the answer calculated from the equation above is \$795,160, but this would then need to be divided by the “multiplier”.

Incorrect, who want to try ?

multiplier is not specified in the question, but in the answer it say the multiplier is 1000.

BTW, 795 is not the answer

I’d like you to check the errata of whatever service provider you got this from before I waste any more energy on it. Yeah, I am that arrogant.

From the course material of schweser

BTW, I hate this question as well, but it helps me understand how much I learn from this topics.

Assuming the mult is 1000, which would be standard for a T-bond future, skill should be correct with the equation, but I got a different answer than his… ((0-15.5)/(10.68/1.082))*(52,871,500/96,500) = -861 contracts

what’s this for? the corresponding prices for the corp. bond and the CTD are \$99.337 and \$104.413. to calculate yield beta, which is not told in Q. I’d like to try # contract=15.5*55M*.9613*1.082*99.337/(10.68*96.5*104.413)

Answer is -822 contract. Who want to try??

I’m getting 735 contracts.

mib20 Wrote: ------------------------------------------------------- > Assuming the mult is 1000, which would be standard > for a T-bond future, skill should be correct with > the equation, but I got a different answer than > his… > > ((0-15.5)/(10.68/1.082))*(52,871,500/96,500) = > -861 contracts Yeah, I did it in Excel and forgot to divide by 1.082 when I first did it. I got 860 when I did it again.

860.36…damn conversion factors got me.

B_C Wrote: ------------------------------------------------------- > Answer is -822 contract. Who want to try?? it’s time to share the calculation. my result is -818. not far from yours.

annexguy Wrote: ------------------------------------------------------- > what’s this for? > the corresponding prices for the corp. bond and > the CTD are \$99.337 and \$104.413. > > to calculate yield beta, which is not told in Q. > > I’d like to try > # > contract=15.5*55M*.9613*1.082*99.337/(10.68*96.5*1 > 04.413) The way to calculate/derive yield beta is to regress returns of the two securities against each other; if they’re saying that you can just divide the 3.9 by the 4.15, that’s just wrong. You can’t calculate a yield beta from a static point in time - you need to run a regression and see their yields vary over time.

skill is 100% correct

skillionaire Wrote: > The way to calculate/derive yield beta is to > regress returns of the two securities against each > other; if they’re saying that you can just divide > the 3.9 by the 4.15, that’s just wrong. > > You can’t calculate a yield beta from a static > point in time - you need to run a regression and > see their yields vary over time. agree on the beta and regression. However, there is no other data to get beta. And the yield beta couldn’t be 1.Because using treasury future to hedge corp. bond is cross hedge. They react differently to yield change. Beta not equal to 1.

annexguy, bacdafucup please… your equation is 15.5*55M*.9613*1.082*99.337/(10.68*96.5*104.413) or (1) (Dollar Duration, bond-to-be-hedged) / (Dollar Duration, CTD) times (2) (CTD conversion factor / futures price) times (3) bond price, given a change to the CTD bond price? Is that how you set up? Ya lost me…