Portfolio A consists of a 1-year zero-coupon bond with a face value of $1,000 and a 10-year zero coupon bond with a face value of $1,000. Portfolio B consists of a single zero coupon bond with a face...

Portfolio A consists of a 1-year zero-coupon bond with a face value of $1,000 and a 10-year zero coupon bond with a face value of $1,000.

Portfolio B consists of a single zero coupon bond with a face value of $2,000 and 3.6 years remaining to maturity. The current yield on all bonds is 10% per annum.

1. Show that both portfolios have the same duration (start with B then do A).


2. Show that the percentage changes in the values of the two portfolios for a 0.1% per annum drop in yields are virtually the same.