Explanation

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

$\text{Effective Duration} = \frac{V_- - V_+}{2 \times V_0 \times \Delta y}$

Where:

• $V_-$ = portfolio value when rates decrease (USD 127.723 million)
• $V_+$ = portfolio value when rates increase (USD 122.164 million)
• $V_0$ = initial portfolio value
• $\Delta y$ = change in yield (30 basis points = 0.0030)

First, we need to find the initial portfolio value $V_0$. Since the portfolio changes symmetrically with rate changes, we can estimate:

$V_0 \approx \frac{V_- + V_+}{2} = \frac{127.723 + 122.164}{2} = \frac{249.887}{2} = 124.9435 \text{ million}$

Now calculate effective duration:

$\text{Effective Duration} = \frac{127.723 - 122.164}{2 \times 124.9435 \times 0.0030}$ $= \frac{5.559}{2 \times 124.9435 \times 0.0030}$ $= \frac{5.559}{0.749661}$ $= 7.414$

The effective duration is approximately 7.414, which is closest to 7.38 (Option A).