Value-At-Risk and Expected Short Fall (14 marks) a) Consider stocks A and B whose annualised rate of return having the following characteristics: Stock Standard Deviation A 12% B 15% Coefficient of correlation (p) between the two stocks is 0.7. i) What is the daily 99% VaR of a portfolio consist of $5 million of Stock A and $10 million of Stock B? Given the 99% normal percentile is 2.33. Assume there are 252 trading days in a year. (3 marks) ii) What assumptions on the statistic model have you made in the calculation of (i)? (2 marks) b) The following shows the historical return series of Stock C. Day Daily Return of Stock C Day Daily Return of Stock Cl 1 12.0% 16 9.0% 2 12.0% 17 16.0% 3 -8.0% 18 -1.0% 4 -2.0% 19 7.0% 5 2.0% 20 19.0% 6 4.0% 21 4.0% 7 -2.0% 22 14.0% 8 5.0% 23 11.0% 9 9.0% 24 6.0% 10 28.0% 25 11.0% 11 -50.0% 26 -1.0% 12 10.0% 27 -2.0% 13 6.0% 28 2.0% 14 4.5% 29 6.5% 15 1.0% 30 3.2% i) What are the procedures required to find the 90% daily Value-at-Risk (VaR) of stock C using historical simulation? (3 marks) ii) What is the 90% daily Value-at-Risk of an $1million investment in stock C? (1 mark) iii) What is the 90% daily Expected Shortfall of an $1million investment in stock C? (1 mark) iv) Using the results in part ii) and iii), explain why expected shortfall is more desirable than value-at-risk when used in regulatory requirement. (4 marks)