Explanation

When the risk-free yield curve moves up by 1 basis point (0.01%), both bond prices will decrease due to the inverse relationship between bond prices and yields.

Key factors:

• Both bonds have the same modified duration of 3 years
• Modified duration measures the percentage price change for a given change in yield
• The price change can be estimated using: ΔP/P ≈ -Modified Duration × Δy

Calculation:

• For both bonds: ΔP/P ≈ -3 × 0.0001 = -0.0003 or -0.03%

Price changes:

• Bond A (zero-coupon, price $900): ΔP ≈ $900 × (-0.03%) = -$0.27
• Bond B (priced at par, price $1000): ΔP ≈ $1000 × (-0.03%) = -$0.30

Analysis:

• Both bonds experience approximately the same percentage price decrease (-0.03%)
• The absolute dollar losses are slightly different due to different initial prices
• However, the question asks about what we "expect" to happen, and given the same modified duration, both bonds should move down by roughly equal amounts in percentage terms

Why not option D? Option D suggests bond B will lose more than bond A, but with identical modified durations, the percentage price changes should be approximately equal. The slight difference in dollar amounts is due to different initial prices, not different sensitivity to interest rate changes.