solution

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.

You’re 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.