Value-At-Risk and Expected Shortfall (15 marks) Consider stocks A and B with the rates of returns having the following characteristics: Coefficient of correlation () between the two stocks is 0.5. Suppose you are going to invest $10 millions in the minimum variance portfolio consists of stock A and B only. How much (in dollar amount) do you have to invest in Stock A and Stock B respectively? [2] What is the daily 99% VaR of the above portfolio? Given the 99% normal percentile is 2.33. Assume there are 252 trading days in a year. [2] ii) What assumptions on the statistical model have you made in the calculation of (ii)? [2] b) The following shows the historical return series of Stock C. i) What are the procedures required to find the 90% daily Value-at-Risk (VaR) of stock C using historical simulation? [3]