Explanation

This question relates to the concept of duration gap or immunization in fixed income analysis. The key relationship is:

Duration Gap = Macaulay Duration - Investment Horizon

When interest rates change, there are two offsetting effects on a bond portfolio:

1. Price effect: Bond prices fall when interest rates rise (negative effect)
2. Reinvestment effect: Coupon payments can be reinvested at higher rates when interest rates rise (positive effect)

When the Macaulay duration equals the investment horizon, these two effects offset each other, providing immunization against interest rate changes.

Let's calculate the duration gap for each investor:

• Investor A: 5.5 years - 5 years = 0.5 years (positive gap)
• Investor B: 5.5 years - 2 years = 3.5 years (positive gap)
• Investor C: 5.5 years - 8 years = -2.5 years (negative gap)

Interpretation:

• Positive duration gap (duration > horizon): The portfolio is more sensitive to interest rate changes than the investment horizon. When rates rise, the price decline dominates over the reinvestment benefit.
• Negative duration gap (duration < horizon): The investment horizon is longer than duration. When rates rise, the reinvestment benefit over the longer horizon can offset or exceed the price decline.

Investor B has the largest positive duration gap (3.5 years), meaning their investment horizon is much shorter than the bond's duration. Therefore, they are most vulnerable to interest rate increases because:

1. They will suffer the full price decline when rates rise
2. They have only 2 years to benefit from reinvesting coupons at higher rates
3. The price effect will dominate significantly over the reinvestment effect

Investor C has a negative gap, so they actually benefit from rising rates over their 8-year horizon through higher reinvestment rates.

Investor A has a small positive gap, making them less vulnerable than Investor B but more vulnerable than Investor C.

Thus, Investor B (Option B) is the most vulnerable to an increase in interest rates.