NFinal answer:
To immunize interest rate risk for its debts, Apex Bank should allocate 42.9% in Zero Coupon Bond X and 57.1% in Zero Coupon Bond Y, matching the duration of the bonds with the duration of the liabilities. The correct answer is option c.
Step-by-step explanation:
To immunize the interest rate risk on the two debt obligations, Apex Bank is considering investing in zero coupon bonds. Immunization is a strategy used to manage interest rate risk by matching the duration of assets and liabilities, thereby ensuring that the investment returns are not affected by interest rate fluctuations.
The first step in immunizing is to calculate the weighted average time to receipt of the bank's obligations, also known as the duration of the liabilities. This is done using the present values and the time until payments are to be made for each debt.
In our case, for Debt 1 with a present value of $100 due in 5 years and Debt 2 with a present value of $100 due in 9 years, we calculate the weighted time to receipt as such:
(5 years * $100 + 9 years * $100) / ($100 + $100) = (500 + 900) / 200 = 1400 / 200 = 7 years.
Now, we need to invest in Bond X and Bond Y such that the combined duration of the bonds matches the 7-year duration of the debts. The formula to find the weights of the two zero coupon bonds in the bank's bond portfolio is:
(Duration of Debt - Duration of Bond Y) / (Duration of Bond X - Duration of Bond Y), and
(Duration of Bond X - Duration of Debt) / (Duration of Bond X - Duration of Bond Y).
Plugging in our values gives:
(7 - 11) / (4 - 11) = -4 / -7 = 0.571 or 57.1%, and
(7 - 5) / (4 - 11) = 2 / -7 = -0.286 or 28.6%. However, since we can't have a negative weight in a portfolio, we subtract from 1 to get the complementary weight for Bond X, which is 1 - 0.571 = 0.429 or 42.9%.
Thus, the correct weights for Bonds X and Y to immunize the interest rate risk are: 42.9% in Zero Coupon Bond X and 57.1% in Zero Coupon Bond Y. Hence, the correct option is C.