Question 5. (4.5 marks)

You manage a pension fund that will provide retired workers with lifetime annuities. You determine that the payouts of the fund are essentially going to resemble level perpetuities of $2.24 million per year. The yield to maturity on all bonds is 14%.

(a). Assume the duration of six-year maturity bonds with coupon rates of 10% (paid annually) is 5 years, and the duration of 22-year maturity bonds with coupon rates of 7% (paid annually) is 11 years. Calculate how much of each of these two coupon bonds (in market value) you will want to hold in order to both fully fund and immunize your obligation.

(2.5 marks)

(b). Calculate the total par value of your holdings in the six-year maturity coupon bond.

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