Final answer:
To immunize a bond portfolio against interest rate changes, match the duration of the portfolio to the investment horizon using tools such as Treasury bond futures. Bond prices are based on the present value of future payments, and they fall if the market interest rate is higher than the bond's coupon rate.
Step-by-step explanation:
Immunizing a Bond Portfolio against Interest Rate Changes:
To immunize a bond portfolio worth $60 million against changes in interest rates over the next five months, a portfolio manager should match the duration of the portfolio with the duration of the liabilities or the time horizon over which the immunization is desired. In this case, the bond portfolio has a duration of 7.7 years in November. To immunize the portfolio, a possible strategy would involve using January Treasury bond futures. The cheapest-to-deliver bond on these futures has a duration of 8.2 years at maturity, which can be used to adjust the portfolio's overall duration.
Calculating Bond Prices:
- For a bond with an interest rate lower than the market interest rate, the price would not be more than the present value of its future payments. If the expected payment from the bond a year from now is $1,080 and the current market interest rate is 12%, you could invest $964 in an alternative investment to receive $1,080 after one year, given $964(1 + 0.12) = $1080. Hence, the bond price should not exceed $964.
- When considering a two-year bond with an 8% annual interest rate, the present value of its future payments must be calculated at the prevailing discount rate. If the discount rate is also 8%, the bond is worth its face value. However, if market interest rates rise and the discount rate becomes 11%, the present value of the bond's payments will decrease, and the bond's price will be lower than its face value.