Question 1: Bank J&D has the following assets and liabilities: Assets 1: 200 shares of 2-year zero coupon bond with face value 1,000 (assuming risk free). Assets2: 300 shares of 4-year zero coupon bond with face value 1,000 (assuming risk free). Liabilities: The bank needs to pay 300,000 two years from now and 195,960 four years from now. Assuming that the spot rates are always 2% (flat term structure): a. Calculate the duration of the asset and liability portfolios b. Suppose that the bank is worried that all the spot rates will change from 2% to 3%. a. Show that the bank will not be able to pay his liabilities. b. How can you immunize the bank's portfolio?

Question 2: Suppose that bank of NYUSH has to pay 2,000 one year from now and 5,000 three years from now. The yearly yield is 10%. Assume that the bank hires your services in order to immunize the bank's obligations. The bank asked you to invest in two (or one) bonds: bond A with coupon rate of 7%, face value of 100 and two years to maturity; bond B with coupon rate 5%, face value of 100 and four years to maturity. A. Write down your strategy that will help the bank (provide all your strategy in details. For example, how many units of A and B you intend to purchase). B. The moment you purchase the bonds, the yield changes to 9%. Show that the bank can still pay his obligations using your strategy. C. Does the bank still immunize after one year? If not, what does it need to do in order to be immunized again?