4. (19 Points) You are the manager of a fund that will need to make the following liability cash flows at the end of each of the next two years: End of Year 1 2 1 YTM | Liability CFS 500 1,200 4.82% The only assets available to invest in to back these liabilities are the following bonds: Face Zero coupon Coupon Bond Coupon Term Coupon rate value yield r(0,t) Price Bond YTM 3.00% 1,000 4.00% 990.38 4.00% 5.00% 1,000 5.00% 1,000.46 4.98% 1 (a) Explain the difference between a portfolio that is cash flow matched and a portfolio that is immunized. [4 points] (b) Calculated the modified duration of the liabilities. [7 points] (c) Construct a portfolio using the above bonds such that the portfolio is cash flow matched [8 points]