A pension fund must pay $100M in 15 years. Suppose the fund has $65M in cash rig

Question

A pension fund must pay $100M in 15 years. Suppose the fund has $65M in cash right now. Assume that the term structure is currently flat at 3.3%.
a) What is the PV of fund's liabilities? What is the PV of fund's liabilities if the interest rate falls to 2.7%?
b) The fund's manager considers duration-based hedging of interest rate risk. He can use 10-year bond with annual coupon rate of 2% and 20-year zero-coupon bond for that, both with par values of $1,000. Construct the hedging porfolio of the two bonds that has the same market value and the same interest rate sensitivity (measured using the duration model) as the pension fund liability.
c) Suppose that the government introduces a new "Early Retirement Program", which allows individuals to retire earlier but with a smaller pension. The pension fund expects 25% of its clients to take advantage of this program to retire in 10 years instead of 15 years and with a pension of 80% of the standard level. What is the new hedging porfolio?

Explanation / Answer

I 10-year bond with annual coupon rate of 2% and 20-year zero-coupon bond for that, both with par values of $1,00n this problem we are given the desired amount A = $50,000, and we wish to know the amount of principal required to attain that amount. The annual interest rate is r = 8%, the number of compoundings per year is n = 2, and the number of years is t = 18. The periodic interest rate is

R = r/n = 8%/2 = 4% =.04  ,

and over the life of the loan the number of compoundings is

N = n

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