Question 2 Consider a portfolio of two assets, labeled assets A and B with an initial investment of 1 million dollars. By estimation from historic data it is known that the annual volatilities of both assets are o A = 0.2 and ob = 0.5 respectively while the coefficient of linear correlation is PAB -0.3. a) Find the volatility of a portfolio when the initial investment is allo- cated by 1/3 to asset A and 2/3 to asset B. b) Assuming the log-returns follow a multivariate normal distribution estimate the Value at Risk and the Expected Shortfall at levels a = 0.95 and a = 0.99 of a portfolio with the initial investment split up as in part (a) using a parametric Gaussian approach and a linear approximation of the losses. c) Explain how to obtain the estimates of the volatilities and correla- tions from the historic data. Question 2 Consider a portfolio of two assets, labeled assets A and B with an initial investment of 1 million dollars. By estimation from historic data it is known that the annual volatilities of both assets are o A = 0.2 and ob = 0.5 respectively while the coefficient of linear correlation is PAB -0.3. a) Find the volatility of a portfolio when the initial investment is allo- cated by 1/3 to asset A and 2/3 to asset B. b) Assuming the log-returns follow a multivariate normal distribution estimate the Value at Risk and the Expected Shortfall at levels a = 0.95 and a = 0.99 of a portfolio with the initial investment split up as in part (a) using a parametric Gaussian approach and a linear approximation of the losses. c) Explain how to obtain the estimates of the volatilities and correla- tions from the historic data