Question

As a pension fund manager in 2020, you are given $67,556,416.88 to manage so that the fund will have at least $100,000,000 available in 2030, 10 years from now. The yield curve is flat, and the current interest rate for all maturities is 4%. The only bonds that you can buy are annual coupon Treasury bonds with 1-year maturities and bonds issued in 2020 that mature in 2040 (currently a maturity of 20 years). All bonds are issued at par. 1. How many of each Treasury bond should you buy today?

$_________________1-Year $_________________20-Year

Answer 1

Let us first calculate for 1-year maturity bonds. The idea is to have the value of the bond at least $100,000,000 in 2030 (ten years from now). Given the bonds are issued at par, the coupon rate is the same as the interest rate: 4%.

Coupon payment every year can be calculated as: -

Total cash at the end of 2021 is going to be $70,258,673.56 if investment in one 1-year maturity bond. I'll issue another bond in 2021 worth $70,258,673.56 and so on until total cash is $100,000,000. Let n bonds are issued. Henceforth,

We get n = 10 as the solution. Today we buy one bond, at roll it over nine times until 2029. We don't need to buy any 20-year maturity bond.