Explanation

Effective duration measures the sensitivity of a bond's price to changes in interest rates. The formula for effective duration is:

$\text{Effective Duration} = \frac{P_- - P_+}{2 \times P_0 \times \Delta y}$

Where:

• $P_-$ = Price when yields decrease
• $P_+$ = Price when yields increase
• $P_0$ = Current price
• $\Delta y$ = Change in yield (in decimal form)

Given:

• Current price $P_0 = 102.31$
• Price when yields increase by 20 bps: $P_+ = 101.12$
• Price when yields decrease by 20 bps: $P_- = 103.74$
• $\Delta y = 0.0020$ (20 bps = 0.20% = 0.0020)

Calculation:

$\text{Effective Duration} = \frac{103.74 - 101.12}{2 \times 102.31 \times 0.0020}$

$= \frac{2.62}{2 \times 102.31 \times 0.0020}$

$= \frac{2.62}{0.40924}$

$= 6.40$

Verification:

• $2.62 / 0.40924 = 6.40$

Therefore, the effective duration is closest to 6.40, which corresponds to option B.