Question 5 (Total: 20 marks) (a) An insurer issues a portfolio of identical 20-year term insurance policies to independent lives aged 60. The sum assured for each policy is $50,000 payable at the end of the year of death. The mortality of the portfolio follows the Standard Ultimate Life Table and the effective interest rate is 5% per annum. Assume the same mortality applies to each life in the portfolio. (i) Briefly explain how to diversify mortality risk. Hence, write down the condition for the risk within the portfolio to be diversifiable. (3 marks) (ii) By using coefficient of variation, justify whether the mortality risk is diversifiable if 10,000 of the identical policies are issued. (5 marks) Question 5 (Total: 20 marks) (a) An insurer issues a portfolio of identical 20-year term insurance policies to independent lives aged 60. The sum assured for each policy is $50,000 payable at the end of the year of death. The mortality of the portfolio follows the Standard Ultimate Life Table and the effective interest rate is 5% per annum. Assume the same mortality applies to each life in the portfolio. (i) Briefly explain how to diversify mortality risk. Hence, write down the condition for the risk within the portfolio to be diversifiable. (3 marks) (ii) By using coefficient of variation, justify whether the mortality risk is diversifiable if 10,000 of the identical policies are issued