Explanation

To solve this duration-matching problem, we need to:

1. Calculate the current market value of the portfolio
   • Face value: USD 88 million
   • Maturity: 5 years
   • Yield: 4% with continuous compounding
   • Market value: $P = 88 \times e^{-0.04 \times 5} = \text{USD } 72.05 \text{ million}`$2`. Set up the duration equation
   • Let W = weight of 1.5-year bonds
   • Weight of 5-year bonds = (1 - W)
   • Desired portfolio duration = 3 years
   • Duration equation: $1.5 \times W + 5 \times (1 - W) = 3$3. Solve for W
   • $1.5W + 5 - 5W = 3$
   • $-3.5W = -2$
   • $W = 0.5714$
   • $(1 - W) = 0.4286`$4`. Calculate the market value of 1.5-year bonds
   • Value = $W \times \text{Total portfolio value}$
   • Value = $0.5714 \times 72.05 = \text{USD } 41.17 \text{ million}$

Why other options are incorrect:

• A (USD 30.88 million): This is the value of the 5-year maturity bond portion
• B (USD 37.72 million): This is $(1 - W) \times 88$ million (using face value instead of market value)
• D (USD 50.28 million): This is $W \times 88$ million (using face value instead of market value)