9.

a) You work for an insurance company, which needs to make a claim payment of $2 million in 8 years but is concerned about the interest rate risk. The company will choose to fund the obligation by investing in two securities, one is a 4-year zero-coupon bond, and the other is a perpetuity, both offering 10% return rates. What is the duration of the zero-coupon bond? What is the duration of the perpetuity? How would you allocate the fund between these two securities to immunize the interest rate risk? How much fund do you need as of now?

b) Suppose six-months already past after you finished the portfolio construction in part a. What are the durations for your liability and your two securities? What should you do to reallocate your portfolio for immunization purpose?