Prob. 1. Immunization In this problem, we try to solve the example in the lecture slides (Example 11.2 in the textbook). You can refer to the textbook for more information. The question is as follows: An insurance company must make a payment of $19,487 in seven years. The market interest rate is 10%, so the present value of the obligation is $10,000. The company wants to fund the obligation using three-year zero-coupon bonds and perpetuities paying annual coupons. How to construct the immunization portfolio? There are the four steps we need to take to solve this problem: a) Find the duration of the liability. b) Find the durations of the two bond instruments. c) Find the asset mix that sets the duration of assets equal the duration of liabilities. d) Find the dollar amount into each asset in order to fund the obligation. Now we try to check if the bond portfolio we find can actually achieve the goal of immunization. e) Show that the portfolio exactly meets the obligation if market interest rate remains at 10%. f) What happens when market interest rate drops to 9%? g) What happens when market interest rate goes up to 11%? h) Based on Part (f) and (g), does your bond portfolio achieve the goal of immunization? Prob. 1. Immunization In this problem, we try to solve the example in the lecture slides (Example 11.2 in the textbook). You can refer to the textbook for more information. The question is as follows: An insurance company must make a payment of $19,487 in seven years. The market interest rate is 10%, so the present value of the obligation is $10,000. The company wants to fund the obligation using three-year zero-coupon bonds and perpetuities paying annual coupons. How to construct the immunization portfolio? There are the four steps we need to take to solve this problem: a) Find the duration of the liability. b) Find the durations of the two bond instruments. c) Find the asset mix that sets the duration of assets equal the duration of liabilities. d) Find the dollar amount into each asset in order to fund the obligation. Now we try to check if the bond portfolio we find can actually achieve the goal of immunization. e) Show that the portfolio exactly meets the obligation if market interest rate remains at 10%. f) What happens when market interest rate drops to 9%? g) What happens when market interest rate goes up to 11%? h) Based on Part (f) and (g), does your bond portfolio achieve the goal of immunization