Question

12. You manage a pension fund, which provides retired workers with lifetime annuities. The fund must pay out $1 million per year to cover these annuities. Assume for simplicity that these payments continue for 20 years and then cease. The interest rate is 4% (flat term structure). You plan to cover this obligation by investing in 5- and 20-year maturity Treasury strips. (A) What is the duration of the funds 20-year pay-out obligation? (2 marks) (B) You decide to minimize the funds exposure to changes in interest rates. How much should you invest in the 5- and 20-year strips? What will be the par value of your holdings of each strip? (4 marks) Need to match the duration and also the market value of investment today should be equal to the total liabilities. So have the following two equations: (C) After three months, you re-examine the pension funds investment strategy. Interest rates have increased. You still want to minimize exposure to interest rate risk. Will you invest more in 20-year strips and less in 5-year strips? Explain briefly. (2 marks) (D) The yield to maturity of a 10-year zero-coupon bond is 4%. (i) If you buy the bond today and hold it for 10 years. What is your return? (Express this return as an annual rate.) (1 mark) (ii) Given only the information provided, can you compute the return on the bond if you hold the bond only for 5 years? If you answered yes, compute the return. If you answered no, explain why. (1 mark)

Answer 1

A) the duration of payout will be duration of annuities which is 20 years

B) To minimize exposure to interest rate risks better to opt for more of 5 year bonds and less of 20 year bonds. the par value should be such that 4% flat inteerst from each should add up to 1M in interest payment . So total of par values should be 25Million.

C) will prefer to invest more in 20 year bonds because the prices of these bonds would have fallen more than the 5 year bonds. Hence going forward chance are interest rate stabilizes ( flat or goes down) so the 20 years will give better returns. However if you foresee more interest rate hikes in the future one should switch to 5 year bonds  

D) i) For a YTM of 4% over 10 years the par value will have to discounted to 61.4 for a 100 par value bond. Translating this into annual rate of return is (100/62)^0.1 (Final value/Initial value)^1/time . This is equal to 5% annualized rate

ii) yes its possible . AS we know initial value at 61.4 and Return Rate 5% and time period is 5 years now . So 61.4 *(1.05)^5 = 78.38 ANSWER.