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.-$6.811B.$6.486C.-$6.486D.$6.811
Question
The modified duration of an 11-year, 6.811B.6.486D.$6.811
Solution
The modified duration of a bond is a measure of the bond's price sensitivity to changes in interest rates. The formula to calculate the estimated price change of a bond given a change in interest rates is:
Price Change = - Modified Duration * Change in Interest Rates * Initial Bond Price
In this case, the modified duration is 6.8106 years, the change in interest rates is 0.10 percent (or 0.0010 in decimal form), and the initial bond price is $1,000.
Price Change = - 6.8106 * 0.0010 * 6.8106
Therefore, the estimated price change on the bond if interest rates increase 0.10 percent (10 basis points) is:
A. -$6.811
Note: The negative sign indicates that the bond's price will decrease if interest rates increase.
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