Pension funds pay lifetime annuities to recipients. If a firm remains in business indefi- nitely, the...
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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. In this Table, bond maturities are expressed in years and the obligation is expressed in millions of EUR, paid yearly to beneficiaries. Table 3: Data to solve Question 4 for each data group Data group 1 Data group 2 Data group 3 Data group 4 Bond 1 Coupon 7% 1% 2% 2% Maturity 10 15 20 25 Bond 2 Coupon 3% 5% 7% 8% Maturity 25 20 15 10 Obligation 2 2.5 3 3.5 Report: The duration of your obligations, Bond 1, and Bond 2. The present value of your obligations (in million EUR). The weights and market values (in million EUR) 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 Excel's 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 Answers Question 4: Obligations Bond 1 Duration Present Value Bond 2 Portfolio Immunization: Weight Market Value Bond 1 Bond 2 Market Value Cash Flows: Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10 Year 11 Year 12 Year 13 Year 14 Year 15 Bond 1+ Bond 2 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. In this Table, bond maturities are expressed in years and the obligation is expressed in millions of EUR, paid yearly to beneficiaries. Table 3: Data to solve Question 4 for each data group Data group 1 Data group 2 Data group 3 Data group 4 Bond 1 Coupon 7% 1% 2% 2% Maturity 10 15 20 25 Bond 2 Coupon 3% 5% 7% 8% Maturity 25 20 15 10 Obligation 2 2.5 3 3.5 Report: The duration of your obligations, Bond 1, and Bond 2. The present value of your obligations (in million EUR). The weights and market values (in million EUR) 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 Excel's 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 Answers Question 4: Obligations Bond 1 Duration Present Value Bond 2 Portfolio Immunization: Weight Market Value Bond 1 Bond 2 Market Value Cash Flows: Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10 Year 11 Year 12 Year 13 Year 14 Year 15 Bond 1+ Bond 2
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