Portfolio A consists of a $20 million dollar position in a one-year zero-coupon bond (with a face value of $100) and a $60 million dollar position in a 10-year zero-coupon bond (with a face value of $100). Portfolio B consists of a $50 million dollar position in a 5.95-year zero-coupon bond (with a face value of $100). The current yield on all bonds is 10% per annum.

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

Explain part (a) in words (approximately one or two sentences max).