A 6% coupon bond paying interest annually has a modified duration of 10 years, sells for $800, and is priced at a yield to maturity of 8%. If the YTM increases to 9%, what is the predicted dollar change in price based on the bond’s duration?

(Round to 2 decimal places.)

Question

A 6% coupon bond paying interest annually has a modified duration of 10 years, sells for $800, and is priced at a yield to maturity of 8%. If the YTM increases to 9%, what is the predicted dollar change in price based on the bond’s duration?

(Round to 2 decimal places.)

BlackTom AI · Accepted Answer

Modified duration measures the approximate percentage price change for a 1.00 (i.e., 100 basis point) change in yield, so it is the direct tool to estimate dollar price change here.

1. Relevant knowledge points and concepts
- Modified duration (Dmod) ≈ percentage change in bond price per unit change in yield: ΔP/P ≈ −Dmod × Δy.
- Δy must be expressed in decimal form (e.g., 1% = 0.01).
- The dollar change in price is ΔP = (ΔP/P) × P0.
- This is a linear approximation; convexity is ignored for small yield changes.

2. Complete reasoning process step by step
- Given: Dmod = 10 years, initial price P0 = $800, initial YTM = 8%, new YTM = 9%.
- Compute the change in yield: Δy = 9% − 8% = 1% = 0.01.
- Apply the duration formula to get the percentage price change: ΔP/P ≈ −Dmod × Δy.

3. Calculations with intermediate steps
- ΔP/P ≈ −10 × 0.01 = −0.10 (i.e., −10.0%).
- ΔP = (−0.10) × $800 = −$80.00.

4. Why the correct answer is correct
- Modified duration directly gives the sensitivity of the bond price to yield changes. Multiplying the negative percentage change (−10%) by the current price ($800) yields the predicted dollar decrease of $80. The negative sign indicates a price decline when yields rise.

5. Why other common approaches are incorrect
- Using Δy = 0.1 (treating 1% as 10%) would yield −$800, which misinterprets basis points and is off by a factor of 10.
- Using Macaulay duration without converting to modified duration would be wrong unless an adjustment for yield is applied. The coupon rate is irrelevant to this calculation once modified duration and price are known.
- Ignoring the negative sign would incorrectly predict a price increase rather than a decrease.

6. Conclusion
- The predicted dollar change in price based on the bond’s modified duration when YTM increases from 8% to 9% is −$80.00, which matches the provided answer (−80).

A 6% coupon bond paying interest annually has a modified duration of 10 years, sells for $800, and is priced at a yield to maturity of 8%. If the YTM increases to 9%, what is the predicted dollar change in price based on the bond’s duration? (Round to 2 decimal places.)数值题

类似问题

A zero-coupon bond has three years until maturity. The bond’s face value is $100 and the price today is $80. The bond’s duration is:

Consider the following statements. Choose the correct statement.

Question at position 18 Which bond is most sensitive to interest rate changes?All equal5-year, 8% coupon3-year, 10% coupon10-year, 3% coupon

Which of the following two semiannual Treasury bonds is more price sensitive to changes in interest rates? 1) A par value bond X, with 5-year-to-maturity and 10% coupon rate. 2) A zero-coupon bond Y, with 5-year-to-maturity and 10% yield to maturity.

An investor buys a 6% annual payment bond with three years to maturity. The bond has a yield-to-maturity of 8% and is currently priced at 94.845806 per 100 of par. The bond’s Macaulay duration is closest to:

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单