duration question

[kgolf20]

Hi David, here is an excerpt from a much longer question:

"..... The current T-bond futures price is $90.80 per $100 par and the T-bond futures contract will be settled using a 20 year 8 percent coupon bond paying interest S/A. The contract is due to expire in a few days so the T Bond price and the T-bond futures price are virtually identical. Assume that the yield curve is flat and the that the corporate bond will continue to to yield 0.5 percent more than the T-bond per 6 month period (outside the excerpt, the corp bond is said to have a yield of 5% per 6 month period), even if the general level of market rates should change...."

The bigger questionis asking how many T-bond contracts should be used to hedge a corporate bond rate exposure. I understand the formula to calculate this hedge but the formula requires you to know the duration of the Treasury bond underlying the futures. I am having a tough time performing this calculation (the answer to the question says the t-bond duration should be 9.41)

Hope this isn't too confusing.. Thanks

Kyle

 

[David Harper CFA FRM]

Hi Kyle,

the corp bond throws me off, but I do get 9.41 t-bond duration if i assume the yield is 9% semi-annual (i.e., (5% - 0.5%) * 2 = 9%, i guess is was the question means).

If 9% is the yield, then duration is, say 10 bps shock: PV @ 9.1% = $89.95 [n=40, 4.55=I/Y, 4=PMT, 100=FV] and PV @ 8.9% = $91.66 [same except I/Y=4.45], so duration = (91.66 - $89.95)/($90.8*2*10 bps) = 9.41 so that looks like what it wants? David