Explanation

Effective convexity measures the sensitivity of the duration measure to changes in interest rates. It is given by the formula:

$$C = \frac{1}{P} \left[ \frac{P^+ + P^- - 2P}{(\Delta r)^2} \right]$$

Where:

• $P^+$ is the value of the bond when all rates increase by $\Delta r$
• $P^-$ is the value of the bond when all rates decrease by $\Delta r$
• $P$ is the current bond price
• $\Delta r$ is the change in interest rates

From the table:

• Current interest rate: 4.00%
• Current bond price $P = 97.8910$
• When rates decrease to 3.95% ($\Delta r = -0.05\%$): $P^- = 97.9430$
• When rates increase to 4.05% ($\Delta r = +0.05\%$): $P^+ = 97.8566$
• $\Delta r = 0.0005$ (0.05% in decimal form)

Calculating:

$$C = \frac{1}{97.8910} \cdot \left[ \frac{97.8566 + 97.9430 - 2 \cdot 97.8910}{(0.0005)^2} \right]$$ $$C = \frac{1}{97.8910} \cdot \left[ \frac{195.7996 - 195.7820}{0.00000025} \right]$$ $$C = \frac{1}{97.8910} \cdot \left[ \frac{0.0176}{0.00000025} \right]$$ $$C = \frac{1}{97.8910} \cdot 70,400$$ $$C = 719.1672$$

Therefore, the estimated effective convexity is approximately 719.2, which corresponds to option D.