Pension funds pay lifetime annuities to recipients. If a firm will remain in business indefinitely, the pension obligation will resemble a perpetuity. Suppose, therefore, that you are managing a pension fund with obligations to make perpetual payments of $3.5 million per year to beneficiaries. The yield to maturity on all bonds is 17.5%.
a. If the duration of 5-year maturity bonds with coupon rates of 14.8% (paid annually) is 4 years and the duration of 20-year maturity bonds with coupon rates of 8% (paid annually) is 11 years, how much of each of these coupon bonds (in market value) will you want to hold to both fully fund and immunize your obligation?
b. What will be the par value of your holdings in the 20-year coupon bond?
| Pension funds pay lifetime annuities to recipients. If a firm will remain in business indefinitely, the pension obligation will resemble a perpetuity. Suppose, therefore, that you are managing a pension fund with obligations to make perpetual payments of $3.5 million per year to beneficiaries. The yield to maturity on all bonds is 17.5%. |
| a. | If the duration of 5-year maturity bonds with coupon rates of 14.8% (paid annually) is 4 years and the duration of 20-year maturity bonds with coupon rates of 8% (paid annually) is 11 years, how much of each of these coupon bonds (in market value) will you want to hold to both fully fund and immunize your obligation?
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Related questions
| Pension funds pay lifetime annuities to recipients. If a firm will remain in business indefinitely, the pension obligation will resemble a perpetuity. Suppose, therefore, that you are managing a pension fund with obligations to make perpetual payments of $1.2 million per year to beneficiaries. The yield to maturity on all bonds is 15.0%. |
| a. | If the duration of 5-year maturity bonds with coupon rates of 11.0% (paid annually) is 4 years and the duration of 20-year maturity bonds with coupon rates of 4% (paid annually) is 11 years, how much of each of these coupon bonds (in market value) will you want to hold to both fully fund and immunize your obligation? (Do not round intermediate calculations. Enter your answers in millions rounded to 1 decimal place. Omit the "$" sign in your response.) | |
| 5 year bond | $ million | ||
| 20 year bond | $ million | ||
| b. | What will be the par value of your holdings in the 20-year coupon bond? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places. Omit the "$" sign in your response.) | |
| Par value | $ million |
2a) The following prices and maturities of zero coupon bonds are given below:
| Maturity (Years) | Price ($) |
| 1 | 925.38 |
| 2 | 890.00 |
| 3 | 816.30 |
| 4 | 735.03 |
i) A 10% coupon bond with a maturity of 3 years is currently selling at $1,080.07 in the market. The coupons are paid annually.
Strip the bond and determine whether there is an arbitrage opportunity. Clearly explain how you would profit from the arbitrage.
ii) Use the given zero coupon bonds to design a synthetic forward loan that starts 2 years from now (at the end of year 2), and is paid back 2 years later (at the end of year 4). Assume you are the lender in this transaction. How is the interest that you charge over the two years of this loan related to the implied forward rates?
2b) A pension plan will pay me $12,000 per year for a 6-year period, starting next year. My pension fund wants to immunize its position.
i) What is the duration of its obligation to me if the yield curve is flat at 5%?
ii) If the pension fund uses a 4-year zero coupon bonds and a perpetuity with yield to maturity of 5% p.a. to construct the immunized position, calculate the fraction of wealth that needs to be placed in each bond.
