Portfolio A consists of a one-year zero-coupon bond with a face value of $10,000 and a 5-year zero-coupon bond with a face value of $40,000. Portfolio B consists of a 4.121-year zero-coupon bond with a face value of $49940.5. The current yield on all bonds is 3% per annum (semi-annual compounded).

a.Calculate the price of both portfolios, and the durations both exactly and by approximation using a +/-0.001 (i.e., +/-0.1%) yield shift.

b.Show that the actual dollar and percentage changes in the values of the two portfolios is very close to that predicted by the duration approximation for a 0.25%=0.0025 increase in yields.

c.Show that the actual dollar and percentage changes in the values of the two portfolios is not very close to that predicted by the duration approximation for a 2.0%=0.02 increase in yields, and that the approximation is worse for portfolio A.

d.Calculate portfolio convexities (exact and approximate) and explain the results in part c.