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The Macaulay duration of an 11-year, $1,000 Treasury bond paying a 10 percent semi-annual coupon and selling at par has been estimated at 6.9106 years. What will be the estimated price change on the bond if interest rates increase 0.10 percent (10 basis points)? A. -$6.582 B. $6.582 C. -$6.911 D. $6.911

Question

The Macaulay duration of an 11-year, 1,000Treasurybondpayinga10percentsemi−annualcouponandsellingatparhasbeenestimatedat6.9106years.Whatwillbetheestimatedpricechangeonthebondifinterestratesincrease0.10percent(10basispoints)?A.−1,000 Treasury bond paying a 10 percent semi-annual coupon and selling at par has been estimated at 6.9106 years. What will be the estimated price change on the bond if interest rates increase 0.10 percent (10 basis points)? A. -6.582 B. 6.582C.−6.582 C. -6.911 D. $6.911

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Solution

The Macaulay duration is a measure of a bond's sensitivity to changes in interest rates. The estimated price change of a bond due to a change in interest rates can be calculated using the formula:

Change in Price = - Duration * Change in Yield * Price

Here's how we can calculate the estimated price change for the bond:

  1. Determine the Duration: The Macaulay duration of the bond has been estimated at 6.9106 years.

  2. Determine the Change in Yield: The change in interest rates is 0.10 percent, or 0.0010 in decimal form.

  3. Determine the Price: The bond is selling at par, so its price is equal to its face value of $1,000.

  4. Calculate the Change in Price: Substituting these values into the formula gives us:

Change in Price = - 6.9106 * 0.0010 * 1,000=−1,000 = -6.9106

Therefore, the estimated price change on the bond if interest rates increase by 0.10 percent is -6.9106,whichroundsto−6.9106, which rounds to -6.911.

So, the correct answer is:

C. -$6.911

This problem has been solved

Similar Questions

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