Today is 01/01/02. On 06/30/03 we will have to make a payment of $100. We can only invest in a risk-free pure discount bond (nominal $100) that matures on 12/31/02 and in a risk-free coupon bond, nominal $100, that pays an annual coupon (on 12/31) of 8% on the nominal value, and matures on 12/31/04. Assume a flat term structure of 7%.
a) How many units of each of the bonds should we buy in order to be immunized with respect to the duration?
b) In the context of the previous problem, suppose that right after the portfolio of bonds is formed, the interest rate goes up from 7% to 10%. Compute the new durations.