A firm has a liability, L, which requires a payment of $25,000 per year (paid annually at the end of the year), for 15 years, plus a final payment of $1,000,000 at the end of the 15th year. The following semi-annual coupon-bearing bonds, with a face-value of $1,000, are available for investment:
Bond 1 2 3
Maturity (Years) 22 15 5
Coupon 6% 7% 8%
(a) Construct an immunizing portfolio for L with 50% invested in Bond 1 and 50% invested in Bonds 2 and 3 combined. Report the portfolio weights and show your workings.
(b) Assess the effectiveness of your immunizing portfolio if the market YTM increases by 0.5%.
(c) What would the coupon rate need to be on Bond 1 for the immunization to be done by simply investing 100% in this (20 year) bond?
With more than an hour to spare, you finish the last calculation and hand the results to your new supervisor. He’s impressed. So much so that he offers to take you for lunch on expenses. As you tuck into your rib eye at Rockpool you start to realise that maybe all your hard work in 25503 Investment Analysis was worth it after all!
The optimum portfolio weights for the bonds 1,2 and 3 will be 50%, 0% and 50% respectively. The calculation are shown in the attached spreadsheet.
The increase in the YMT rate 0.5% will not create any impact on the portfolio as the portfolio due to the immunization of the portfolio structure.
The coupon rate of the Bond 1 will be 8.5% if the whole investment is made on Bond 1.