An investment company has two bond portfolios. Portfolio A consists of a 5.95-year zero-coupon bond with a face value of $100,000. Portfolio B consists of a one-year zero-coupon bond with a face value of $40,000 and a 10-year zero-coupon bond with a face value of $120,000. The current yield on all bonds is 10% per annum. The current T-bond futures price is quoted as 93-02 with a face value of $10,000. The duration of the cheapest to deliver bond is 11 years Required:

1-What is the duration of Portfolio A, Portfolio B, and the Combined Portfolio consisting of Portfolio A and Portfolio B, respectively? (5 marks)

2-If the yield increases by 0.1%, what is the percentage change in the value of Portfolio A and Portfolio B respectively? (3 marks)

3- Suppose the company would like to hedge the value of the Combined Portfolios (i.e.: Portfolio A plus Portfolio B). How many bond futures are required, and should the company take a long or short position? (3 marks)

4- Suppose after half a year the interest rate increases by 0.2% and the futures price changes to 93-01. The company sells the bonds and closes the futures position. What is the gain or loss in the bond portfolios and in the futures contracts respectively? (3 marks)