# 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 *PV*_{0} 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:

**PV _{0}**

**PV**

_{+}**PV**

_{−}

**ΔCurve**

**ΔYield**

99.41172

99.32213

99.50132

3 bps

1 bp

**Q.** The bond’s approximate convexity is *closest *to:

- 0.00101.
- 1.11769.
- 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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