An insurance company must make a series of payments equal to a fixed coupon bond with a Par value of $10,000 and an annual coupon of 10% over a period of 3 years. The current yield on such a fixed-coupon bond is 10%. The company wants to immunize this obligation. To do so, it can invest in a 2-year zero-coupon bond A (yielding 5%) and/or a perpetuity B that pays 10% coupon per year (yielding 25%).

a) Compute the immunizing portfolio using both Macaulay and Modified duration.

b) Immediately after the portfolio is set up, all yields change by 1%-point and remain constant thereafter. Compute the value of the immunization portfolios for both a change of +1%-points in all yields and for a change of -1%-points in all yields.

c) Comment on the findings under b)