Instructions: The report for this final project should be written by all group members. You may have to answer all the following questions with explanation. Note that alpha_1 is the parameter related to the generalized Clayton copula and alpha_2 is for VAR related calculation. The report is due by 11:59pm on Jan. 6, 2021.

Company A is an insurance company, which has products such as group insurances, health insurances, auto insurances, etc. In addition, the company invests in a portfolio with six equities: Kodak($150,000), McDonald's($300,000), Intel($350,000), Merck($500,000), Wal-Mart($600,000) and Microsoft($560,000). Assume these six equities are uncorrelated and their volatilities are 3, 9, 8, 3, 12 and 6 percent, respectively. Company A has a total asset value of $100m, and company B has a total asset value of $200m. The expected rate of growth of A's asset value is 10% per annum with volatility 25% per annum. For B, the expected rate of growth is 5% per annum with volatility 10% per annum. The returns of them are linked by a generalized Clayton copula which is given by (10.174) in FERM (page 212) with alpha_1=1 and beta=2, if the total borrowing for company A and B consist of fixed borrowing of $50m and $100m, respectively, in each case repayable in exactly two years' time. Moreover, Company B is now rated as AA by Standard and Poor's.

1. How should company A build its risk management framework? (Hint: based on building blocks,30 points) 2. Determine the probability of default for these two companies and the joint probability that both of the companies will be insolvent in two years. (4 points each, 12 points) 3. Using the credit migration rates averaged over 1981 to 2009 (Table 14.9 in FERM, page 350), what are the probabilities that company B will have defaulted in one year, two years and three years by adopting the migration (12 points) and martingale approaches (6 points)? (18 points) 4. Using alpha_2=1.645, determine the corresponding VAR tools related values for the company (40 points) a. The portfolio variance in dollar units (2 points); b. The portfolio VAR (2 points); c. The individual VAR for each equity included in the portfolio (6 points); d. The diversification benefit (2 points); e. The marginal VAR for each equity included in the portfolio (6 points); f. The component VAR for each equity included in the portfolio (6 points); g. The percent contribution to VAR for each equity included in the portfolio (3 points); h. If the company updated the investments as Kodak($250,000), McDonald's($100,000), Intel($200,000), Merck($150,000), Wal-Mart($560,000) and Microsoft($560,000) in two years, determine the incremental VAR both by definition(the exact increment) and by approximation (4 points each, 8 points);i.

Can you provide any suggestion with explanation to reduce the portfolio VAR or enhance company A's risk tolerance? (5 points)