An investor, with mean-variance utility EU(X) (X)-1 Var(X), is interested in an asset A that generates return in one year according to a Normal distribution with mean 5 and variance 8, as well as an asset B that generates return in one year according to a Normal distribution with mean 7 and variance 12. The returns of the two assets are independently distributed. [25%] (a) (b) (c) Find the optimal portfolio choice between the two assets for the investor. Find the Value-at-Risk of the portfolio you found in part (a) in one year with confidence level 95% Find the expected shortfall of the portfolio you found in part (a) in one year with confidence level 95% (d) Discuss why your answers to part (b) and part (c) are the same or different. An investor, with mean-variance utility EU(X) (X)-1 Var(X), is interested in an asset A that generates return in one year according to a Normal distribution with mean 5 and variance 8, as well as an asset B that generates return in one year according to a Normal distribution with mean 7 and variance 12. The returns of the two assets are independently distributed. [25%] (a) (b) (c) Find the optimal portfolio choice between the two assets for the investor. Find the Value-at-Risk of the portfolio you found in part (a) in one year with confidence level 95% Find the expected shortfall of the portfolio you found in part (a) in one year with confidence level 95% (d) Discuss why your answers to part (b) and part (c) are the same or different