Problem:
Portfolio A consists of a one-year zero-coupon bond with a face value of $2,000 and a 10-year zero-coupon bond with a face value of $6,000. Portfolio B consists of a 5.95-year zero-coupon bond with a face value of $5,000. The current yield on all bonds is 10% per annum (continuously compounded)
Required:
Question 1: Show that both portfolios have the same duration.
Question 2: Show that the percentage changes in the values of the two portfolios for a 0.1% per annum increase in yields are the same.
Question 3: What are the percentage changes in the values of the two portfolios for a 5% per annum increase in yields?
Note: Please provide equation and explain comprehensively and give step by step solution.