A ten-year annual pay bond with a 5% coupon rate is trading with a market yield of 7.75%.What is the percentage change in price if the market yield decreases by 75 basis points immediately after the bond is issued?

Question

Quizplus · Accepted Answer

To calculate the percentage change in price, we need to use the formula:
Percentage change in price = -Modified duration x Yield change x 100
First, we need to calculate the modified duration, which is given by:
Modified duration = Macaulay duration / (1 + Yield-to-maturity)
The Macaulay duration of a 10-year bond with a 5% coupon rate is 7.72 years (you can use an online calculator or excel).
The Yield-to-maturity is 7.75%, which is given in the problem.
Therefore, the modified duration of the bond is:
Modified duration = 7.72 / (1 + 0.0775) = 7.17 years

Next, we need to calculate the yield change. The market yield decreased by 75 basis points, which is 0.75%. Therefore, the yield change is -0.0075.

Now, we can substitute the values in the formula to get the percentage change in price:
Percentage change in price = -7.17 x (-0.0075) x 100 = 5.67%

Therefore, the answer is C) 5.67%.

A Ten-Year Annual Pay Bond with a 5% Coupon Rate