Portfolio A consist of a one-year zero-coupon bond with a face value of $2000 and a 10-year zero-coupon with a face value of $6,000. Portfolio B consist of a 5.95-year zero-coupon bond with a face value of $5000. The current yield on all bonds is 10% per annum (continuously compounded).
a. Show that both portfolios have the same duration
b. Show that the percentage changes in the values of the two portfolios for a 0.1% per annum increase in yields are the same
c. What are the percentage changes in the values of the two portfolios for a 5% per annum increase in yields?
What are the convexities of the portfolios above? To what extent does (a) duration and (b) convexity explain the difference between the percentage changes calculated in part (c) of the above?