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Answer: Both bond prices will move down, but bond B will lose more than bond A.
## 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.**
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A trading portfolio consists of two bonds, A and B. Both have modified duration of 3 years and face value of USD 1,000. Bond A is a zero-coupon bond, and its current price is USD 900. Bond B pays annual coupons and is priced at par. What is expected to happen to the market prices of bond A and bond B, in dollar terms, if there is a parallel upward shift in the yield curve of 1%?
A
Both bond prices will move up by roughly the same amount.
B
Both bond prices will move up, but bond B will gain more than bond A.
C
Both bond prices will move down by roughly equal amounts.
D
Both bond prices will move down, but bond B will lose more than bond A.
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