Question

The Honorable East India Company must pay two liabilities, 100, 000 in exactly three years (t = 3) and 120,000 in exactly five years (t = 5). The current interest rate is 8% effective per year. The company wants to immunize itself from any potential change in interest rates, no matter how large, as the amount of silver and gold introduced to Europe by Spanish conquistadors is causing the rates to deviate frantically.

The company will attempt to achieve this by setting three zero-coupon bonds as assets associated with their liabilities, the bonds maturing at times 2, 4 and 6.

(a) (5 points) What form of immunization are they seeking to form: Redington Immunization or Full Immunization? Briefly explain.

(b) (5 points) Calculate the Macaulay duration and convexity for the liabilities, considered as a single portfolio of liabilities.

(c) (10 points) Is it possible for the company to achieve the form of immunization they would like to have? If it is, find the redemption amounts (A2 (at time 2),A4 (at time 4),A6 (at time 6)) for the three and zero-coupon bonds and justify that they immunize the liabilities. If it is not, explain it is not possible to fully immunize.

Answer 1