# 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)?

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+
PVΔCurve
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

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Typo.

Simplify the complicated side; don't complify the simplicated side.

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