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):

1. Calculate the duration of the asset and liability portfolios
2. Suppose that the bank is worried that all the spot rates will change from 2% to 3%.
3. Show that the bank will not be able to pay his liabilities.
4. How can you immunize the bank's portfolio (before the change happens)?