The modified duration of an 11-year, $1,000 Treasury bond paying a 10 percent semi-annual coupon and selling at par has been estimated at 6.8106 years. What will be the estimated price change on the bond if interest rates increase 0.10 percent (10 basis points) A. -$6.486 B. -$6.811 C. $6.811 D. $6.486
Question
The modified duration of an 11-year, 6.486 B. -6.811 D. $6.486
Solution
The price change of a bond due to a change in interest rates can be estimated using the formula:
ΔP = -D * Δy * P
where:
- ΔP is the change in price,
- D is the duration of the bond,
- Δy is the change in yield (in decimal form), and
- P is the initial price of the bond.
Given that the duration (D) is 6.8106 years, the change in yield (Δy) is 0.10 percent or 0.0010 in decimal form, and the initial price (P) is $1,000, we can substitute these values into the formula:
ΔP = -6.8106 * 0.0010 * 6.8106
Therefore, the estimated price change on the bond if interest rates increase by 0.10 percent is -6.811.
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