Question

1) Suppose we have a 6-year bond with a 9.5% annual coupon, and a $1000 par value. The current yield on comparable securities is 8%.
  What is the price of this bond? What is the duration?
If interest rates were to rise to 10.11%, what is the convexity? What does this mean?

2) Given an YTM on comparable bonds of 7.5%, calculate the duration for the following bonds. Explain the differences.
5-year maturity, 5% coupon paid annually.
5-year maturity, 11% coupon paid annually.
8-year maturity, 5% coupon paid annually.
8-year maturity, 11% coupon paid annually.

Please use excel to answer these questions, as well as show the formula's for both of these questions. Thank you.

Answer 1

Duration can be a good measure of how bond prices may be affected due to small and sudden fluctuations in interest rates. However, the relationship between bond prices and yields is typically more sloped, or convex. Therefore, convexity is a better measure for assessing the impact on bond prices when there are large fluctuations in interest rates. If a bond's duration rises and yields fall, the bond is said to have positive convexity. In other words, as yields fall, bond prices rise by a greater rate—or duration—than if yields rose. Positive convexity leads to greater increases in bond prices. If a bond has positive convexity, it would typically experience larger price increases as yields fall, compared to price decreases when yields increase.