You are working in the risk management unit of a pension fund. The fund provides workers with defined benefits payments after they retire. You estimate that you will need to pay a total $5 million per year over the next 30 years to meet your obligations. The first payment is due exactly a year from today and the interest rate is flat at 5%, annually compounded. The fund currently owns assets worth $60 million.

Compute the present value of your future liabilities. Is your pension fund underfunded and if so, by how much?

Compute the Macaulay and the modified duration of your liabilities.

Youre worried about future changes in yields. You can invest in two zero-coupon government bonds that have a maturity of 1-year and 30 year, respectively. How would you allocate your assets if you want to immunize your exposure to interest rate risk? Calculate the total amount invested in each of the two bonds.