You are a risk manager for an insurance company. In 10 years from now, you know that you will have to pay out to your customers a total of $10 million.

a. What is the duration of your liability? Explain.

You have the possibility to invest in two bonds: a zero-coupon bond with maturity of 5 years and a face value of $1,000, and a perpetuity paying $100 per year. Both are currently yielding 7.5%.

b. What are the prices of the perpetuity and of the zero-coupon bond today?

c. What $ amount should you invest in the zero-coupon bond and in the perpetuity to fully fund and immunize the $10 million obligation over the 10 years?

d. If next year your target duration is 9 years, how much do you need to rebalance the two securities in your portfolio to remain completely hedged?