Explanation

Assuming parallel movements to the yield curve, the expected price change is calculated using the formula:

ΔP = -P × Δy × D

Where:

• P is the current price or net present value
• Δy is the yield change (1% or 0.01)
• D is duration (3 years for both bonds)

Calculations:

• Bond A (Zero-coupon bond, P = $900): ΔP = -900 × 0.01 × 3 = -$27

• Bond B (Priced at par, P = $1,000): ΔP = -1000 × 0.01 × 3 = -$30

Analysis:

• Both bonds have the same modified duration (3 years)
• Both experience price declines due to the upward yield shift
• Bond B loses more in dollar terms ($30) than Bond A ($27) because it has a higher current price ($1,000 vs $900)

Key Insight:

All else equal, the impact of a yield curve move is stronger in absolute dollar terms for bonds with higher current prices, even when they have the same duration. Upward parallel curve movements make bonds cheaper, and the bond priced at par (Bond B) experiences a larger dollar loss.

Therefore, both bond prices will move down, but bond B will lose more than bond A.