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 yield decreases
• $P_+$ = Price when yield increases
• $P_0$ = Current price
• $\Delta y$ = Change in yield (in decimal form)

Given:

• $P_- = 132.41$ (price when yield decreases by 25 bps)
• $P_+ = 127.66$ (price when yield increases by 25 bps)
• $P_0 = 130.00$ (current price)
• $\Delta y = 0.0025$ (25 basis points = 0.25% = 0.0025)

Plugging in the values:

$\text{Effective Duration} = \frac{132.41 - 127.66}{2 \times 130.00 \times 0.0025}$ $= \frac{4.75}{2 \times 130.00 \times 0.0025}$ $= \frac{4.75}{0.65}$ $= 7.3077$

Rounded to one decimal place, the effective duration is approximately 7.3.

Why this is correct:

• The calculation follows the standard formula for effective duration
• 25 basis points = 0.25% = 0.0025 in decimal form
• The result matches option A (7.3)

Common mistakes to avoid:

• Forgetting to convert basis points to decimal (25 bps = 0.0025, not 0.25)
• Using the wrong denominator (should be $2 \times P_0 \times \Delta y$)
• Confusing effective duration with modified duration