Portfolio A consists of a one year zero coupon bond with a face value of $2000 and a 10 year zero coupon bond with a face value of $6000. Portfolio B consists of a 5.95 year zero coupon bond with a face value of $5000. The current yield on all bonds is 10% per annum continously compounded.

a) Show that both portfolio 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 portfolios for 5% per annum increase in yield?

d) What are the convexities of the 2 portfolios? To what extent does (a) duration and (b) convexity explain the difference between the percentage changes calculated in part c?