Design a portfolio of the two bonds that will protect the pension from fluctuations in interest

Question:

You have been hired by a local bank to help them design a bond portfolio to fund a $10 million pension obligation that will come due in 4 years. The managers of the bank would like to use a 2-year zero coupon bond along with an 8-year zero coupon bond to fund this obligation. Suppose that the yield curve is flat so that the yields to maturity on all zero coupon bonds are 5%.

1 - Design a portfolio of the two bonds that will protect the pension from fluctuations in interest rates. Provide boththe current percentage and monetary positions in this portfolio.

2 - Suppose, that right after you create this portfolio, the yield curve shifts to 6% at all maturities. Calculate what you expect the future value of the investment in the two bonds to be in year 4. Do you meet the obligation of the bank? Explain any difference.