Problem
I. You purchase a five-year, 13.76 % bond that is priced to yield 10 %. Your investment horizon is 4 years and the target amount is 16725.
i. Show that the duration of this annual payment bond is equal to 4 years.
ii. Show that, if interest rates rise to 11 % within the next year and that if your investment horizon is four years from today, you will still the target amount.
iii. Show that the same amount also will be earned if interest rates fall next year to 9 %.
II. A financial institution has an investment horizon of 2 years, 9.5 months. The institution has converted all assets into a portfolio of 8 percent, $1,000, 3-year bonds that are trading at a YTM of 10 percent. The bonds pay interest annually. The portfolio manager believes that the assets are immunized against interest rate changes.
i. Is the portfolio immunized at the time of bond purchase? What is the duration of the bonds?
ii. Will the portfolio be immunized one year later?
iii. Assume that one-year, 8 percent zero-coupon bonds are available in one year. What proportion of the original portfolio should be placed in zeros to rebalance the portfolio?