3. Portfolio A consists of a three-year zero-coupon bond with a face value of $5,000 and a 15-year zero-coupon bond with a face value of $12,000. Portfolio B consists of a 6-year zero-coupon bond with a face value of $7,000. The current yield on all bonds is 10% per annum (continuously compounded).

(a) Compute the durations of each portfolio.

(b) Compute the % changes in the values of the two portfolios for a 0.1% per annum increase in yields.

(c) What are the percentage changes in the values of the two portfolios for a 7% per annum increase in yields?

4. What are the convexities of the portfolios in Problem 3? To what extent does (a) duration and (b) convexity explain the difference between the percentage changes calculated in part (c) of Problem 3?