See practice question below - in the solution why does PV0 change in the denominator (it appears they have just dropped a 9)?
Thanks in advance!
Consider the following information for a traditional (option-free) fixed-rate bond where PV0 is the bond’s original price, PV+ is the new price of the bond when the yield to maturity is increased, PV− is the new price of the bond when the yield to maturity is decreased, ∆Curve is the change in the benchmark yield curve, and ∆Yield is the change in the yield to maturity:
PV0** PV+ PV − ΔCurve ΔYield** 99.41172 99.32213 99.50132 3 bps 1 bp
Q. The bond’s approximate convexity is closest to:
C is correct. The bond’s approximate convexity (ApproxCon) is 10.05918, calculated as:
ApproxCon = (PV−) + (PV + )−[2 × (PV0)] / (∆Yield)2 × (PV0) = 99.50132 + 99.322123−(2 × 99.41172) / (0.0001)2 × 9.41172 = 10.05918