An 8-year, 3.5% annual coupon bond is priced at 92.1492, with a yield to maturity of 4.7% and a Macaulay duration of 7.0705. If rates decrease by 75 bps, the percentage price change of the bond is closest to:
- A.β5.30%.
- B.5.07%.
- C.5.30%.
They give al the data needed to calculate the PV of the bond with the rate decrease:
N=8, PMT=3.5, I/Y= 4.7-0.75=3.95, FV=100
Therefore PV= 96.96
Change in price= 96.96/92.149 -1 = 5.2%
Why does the answer(below) calculate ModDur using MacDur and YTM ? ModDur= Mac/(1+Rf) , not YTM (???)
Help please!!!
- Correct because to determine the percentage price change of a bond for a given change in yield, first convert Macaulay duration (7.0705) to modified duration by dividing Macaulay duration by 1 plus yield per period.ModDur = 7.07051.047=6.75317.07051.047=6.7531Next, multiply annual modified duration by the change in yield.%ΞPVFullββ6.7531Γ(β0.0075)=0.0507%π₯PVπΉπ’ππββ6.7531Γ(β0.0075)=0.0507
- Incorrect because the price change is incorrectly calculated by using Macaulay duration, rather than modified duration. β7.0705 x (β0.0075) = β0.05303 β 5.3%.