Mr. Kim is managing a pension fund with annual payments of $5 million to beneficiaries that are expected to be made for the next 5 years. Mr. Kim would like to immunize his liability by investing in two different bonds: a 2-year annual coupon-paying bond with 10% coupon rate and a 6-year zero-coupon bond. Each bond has a face value of $1,000 and the YTM on all bonds is 8%.

1. (10 points) Find the Macaulay's duration for (i) the liability, (ii) the 2-year bond, and (iii) the zero coupon bond. Show calculations.

2. (4 points) Calculate the convexity for the 2-year bond.

3. (6 points) If yields change from 8% to 10%, what will be the percentage change in price for the 2-year bond (including the convexity effect). Compare this to the actual percentage change in price. Are the two percentage changes in prices identical?

4. (6 points) How much of each of the two bonds (in market value) will Mr. Kim want to hold to fully immunize his obligation?

5. (14 points) Now suppose that interest rates immediately rise from 8% to 10%. What happens to the net position, that is, to the difference between the value of asset and liability?