Effective Convexity Question

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:

  1. 0.00101.
  2. 1.11769.
  3. 10.05918.
    Solution

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

Typo.