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Chartered Financial Analyst Level 1

Chartered Financial Analyst Level 1

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An analyst gathers the following information about a bond:

  • Price: 96.00
  • Price with yield to maturity 10 basis points higher: 95.80
  • Price with yield to maturity 10 basis points lower: 96.30 The approximate convexity of this bond is closest to:

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Explanation:

Explanation:

The approximate convexity of a bond is calculated using the formula:

ApproxCon=(PV+)+(PV−)−2×(PV0)(ΔY)2×(PV0)\text{ApproxCon} = \frac{(PV_{+}) + (PV_{-}) - 2 \times (PV_0)}{(\Delta Y)^2 \times (PV_0)}ApproxCon=(ΔY)2×(PV0​)(PV+​)+(PV−​)−2×(PV0​)​

Where:

  • PV+PV_{+}PV+​ is the price when the yield decreases by 10 basis points (96.30).
  • PV−PV_{-}PV−​ is the price when the yield increases by 10 basis points (95.80).
  • PV0PV_0PV0​ is the original price (96.00).
  • ΔY\Delta YΔY is the change in yield (0.001 or 10 basis points).

Substituting the values:

ApproxCon=96.30+95.80−2×96.00(0.001)2×96.00=192.10−192.000.000001×96.00=0.100.000096≈1,042\text{ApproxCon} = \frac{96.30 + 95.80 - 2 \times 96.00}{(0.001)^2 \times 96.00} = \frac{192.10 - 192.00}{0.000001 \times 96.00} = \frac{0.10}{0.000096} \approx 1,042ApproxCon=(0.001)2×96.0096.30+95.80−2×96.00​=0.000001×96.00192.10−192.00​=0.0000960.10​≈1,042

Option A (521) is incorrect because the denominator is mistakenly multiplied by 2, as in the calculation of approximate duration.

Option C (2,604) is incorrect because the change in yield (0.001) is not squared, leading to an erroneous calculation.

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