An insurance company has the liabilities with the following payment pattern, each at the end of the respective year: Year 3: $2.5 million. Year 7: $4.2 million. Year 20: $6.0 million. There are no other liabilities for the insurance company to consider. The discount rate for the liabilities is 3%. What is the duration of the liability? Use annual compounding. (Do not compute the modified duration!) QUESTION 11 The insurance firm has two objectives. It wants to earn at least 11% per year, and it wishes to immunize its liabilities. It has the following investment opportunities available: Common Stocks Stock A, Dividend 5.0%, Duration 3 years. Stock B, Dividend 14.3%, Duration 7 years. Coupon Bonds 30-YR, Yield 11.0%, Duration 20 years. Zero-Coupon Bonds 3-YR, Yield 1.5%. 5-YR, Yield 2.0%. 7-YR, Yield 2.0%. 10-YR, Yield 2.0%. 20-YR, Yield 3.0%. To match the duration of its liabilities with its investments, the insurance company decides to purchase the 30-year coupon bond and stock B. What are the weights of the portfolio that satisfy the insurance company's requirements? Weight in the 30-year coupon bond: % Weight in stock B: % Expected return: % QUESTION 12 With duration matching, the portfolio is immunized against small changes in interest rates. Describe what the insurance company has to do to be perfectly immunized against all changes