Pension funds pay lifetime annuities to recipients. If a firm remains in business indefi- nitely,...
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Pension funds pay lifetime annuities to recipients. If a firm remains in business indefi- nitely, the pension obligation will resemble a perpetuity. Suppose, therefore, that you are managing a pension fund with obligations to make perpetual payments. Your task is to immunize the value of your portfolio, using two bonds. The yield curve is flat at 9% and data on the coupons and maturities of the two bonds as well as the size of the obligation are given in Table 3.
Table 3: Data for solving Question 5. Bond maturities are expressed in years and the obligation is expressed in millions of e, paid yearly to beneficiaries
Bond 1: Coupon 2% Maturity 25
Bond 2: Coupon 8% Maturity 10
Obligations: 3.5
Face Value: 1000
The duration of your obligations, Bond 1, and Bond 2.
The present value of your obligations (in mill e).
The weights and market values (in mill e) of the two bonds that fully immunize your portfolio. Note: The solution to this problem involves solving a linear equation with one unknown. Do not use excels solver to find the solution, because the solver does not do well with solving linear problems.
The market value of the portfolio cash flows in the subsequent 15 years, stemming jointly from the two bonds.
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